Method for measuring thermal power of a rod using s-shaped tension and compression force sensor
By combining S-shaped tension and compression sensors with Hooke's law of thermodynamics, the thermal changes of thermoelastic rods are measured, solving the problem of thermal measurement, realizing a profound understanding of thermal motion and thermal work, and improving the work efficiency of heat engines.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- 李浩来
- Filing Date
- 2026-03-03
- Publication Date
- 2026-05-29
Smart Images
Figure CN122109193A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for measuring the thermal properties of a rod using an S-type tension / compression sensor. Background Technology
[0002] Current thermodynamics lacks a physical concept of heat force, and even more so, a method for measuring its value. However, the concept of heat force actually allows us to understand the essence of thermal motion more deeply. Specifically, heat force allows us to establish a mathematical relationship between the velocity and acceleration of thermal motion and the mass of hot spots. It also allows us to understand the meaning of work done by heat force more profoundly. Therefore, it is necessary to have a deep understanding of the physical concept of heat force, and all of this is inseparable from the measurement of heat force. This invention, referencing the calculation formula for thermal constraint force generated by thermal stress and based on Hooke's Law in thermodynamics, proposes a method for measuring heat force. Summary of the Invention
[0003] The purpose of this invention is to provide a method for measuring the thermal force of rods using an S-type tension / compression sensor, which can deepen the understanding of thermal motion and the knowledge of thermal work, thereby improving the efficiency of various heat engines in performing external work.
[0004] The present invention provides a method for measuring the thermal force of a rod using an S-type tension / compression sensor, comprising the following steps:
[0005] A. Prepare a fixed bracket. A left baffle is fixed to the left end of the fixed bracket. The middle part of the left baffle is fixedly connected to the left end of the S-type tension and compression sensor. The S-type tension and compression sensor is set along the left and right horizontal direction. A clamp is installed on the fixed bracket to the left of the S-type tension and compression sensor. The clamp can clamp and fix a thermoelastic rod along the left and right horizontal direction. The thermoelastic rod is a cylindrical rod.
[0006] B. Prepare the thermoelastic rod whose thermal value needs to be measured, and record the length, diameter, and type of material of the thermoelastic rod;
[0007] C. Clamp the thermoelastic rod onto the fixture, then fix the left end of the thermoelastic rod to the right end of the S-type tension / compression sensor, and measure the initial temperature value of the thermoelastic rod to obtain the intrinsic temperature scale. ;
[0008] D. Set the initial force reading of the S-type tension and compression sensor to zero, then start changing the temperature value of the thermoelastic rod, measure each temperature value after these changes, and record the force reading of the S-type tension and compression sensor at each point where the temperature value is changed.
[0009] E. According to Hooke's law in thermodynamics, when a hot spot deviates from its intrinsic temperature scale... At this time, linear recovery heat will be generated inside the material. :
[0010]
[0011] In the formula Thermal stiffness is the ability of a material to resist temperature scale displacement. The intrinsic temperature scale is determined by the material's microstructure; the negative sign indicates thermal orientation. This means that heat is used to bring thermal motion back to its original temperature.
[0012] The temperature values of each thermoelastic member measured in step D, along with the corresponding force readings from the S-type tension / compression sensors, are substituted one by one into Hooke's law in thermodynamics to calculate the individual thermal stiffness to be processed. value;
[0013] F. The individual thermal stiffnesses obtained in step E are then processed. The values were analyzed and compared, and thermal stiffness that deviated from the linear trend and was not a constant was removed. Values, retaining only the constant thermal stiffness under linear laws. value;
[0014] G. In terms of thermal stiffness The value represents the temperature change within a constant range, which is the temperature change range of the thermoelastic rod that conforms to Hooke's law. Within the temperature change range of the thermoelastic rod that conforms to Hooke's law, the force value displayed by the S-type tension and compression sensor is the thermal value to be measured.
[0015] Preferably, in step A, the left baffle is fixed in the front-to-back vertical direction, and the middle part of the left baffle is fixedly connected to the left end of the S-shaped tension and compression sensor by a screw. The clamp is a three-jaw self-centering chuck, which is mounted on a fixed bracket.
[0016] Preferably, in step D, the measurement and recording frequency after changing the temperature value of the thermoelastic rod is such that the force value of the S-type tension and compression sensor is read and recorded once every time the temperature of the thermoelastic rod increases or decreases by 0.1℃-0.5℃.
[0017] This invention discloses a method for measuring the thermal force of a rod using an S-shaped tension / compression sensor. This method can accurately measure changes in thermal values caused by thermal motion. Based on the measured changes in thermal values, a mathematical relationship can be established between thermal motion velocity, thermal motion acceleration, and hot spot mass. Furthermore, thermal analysis allows for a deeper understanding of the nature of work done by heat. Therefore, this method for measuring the thermal force of a rod using an S-shaped tension / compression sensor enhances our understanding of thermal motion and the work done by heat, thereby improving the efficiency of various heat engines in performing external work.
[0018] The method for measuring the thermal force of a rod using an S-type tension / compression sensor according to the present invention will be further described below with reference to the accompanying drawings. Attached Figure Description
[0019] Figure 1 This is a front view of the experimental apparatus in the method for measuring the thermal force of a rod using an S-type tension / compression sensor according to the present invention. Detailed Implementation
[0020] The physical experimental basis of Hooke's Law in thermodynamics can be found in the formula for calculating the thermal constraint force generated by thermal stress. The formula for calculating the thermal constraint force generated by thermal stress is as follows:
[0021]
[0022] In the formula, F represents the thermal constraint force generated when the material is constrained due to temperature changes, and E represents the elastic modulus of the material. The coefficient of linear expansion of the material, where A is the cross-sectional area. Temperature change .
[0023] The formula for calculating the thermal constraint force generated by thermal stress describes the internal thermal constraint force generated when the free thermal expansion or contraction of a material due to temperature changes is restricted, and the force is opposite to the direction of the temperature change. This formula is derived from Hooke's Law, namely:
[0024] Free thermal strain:
[0025]
[0026] Elastic strain caused by constraints:
[0027]
[0028] By Hooke's Law The thermal stress is obtained:
[0029] Internal force After substituting, we get:
[0030] The above formula for calculating the thermal constraint force generated by thermal stress is because of the following: Since it can be a constant, it can actually be used as Hooke's Law in thermodynamics. That is, the magnitude of the thermodynamic value F can be measured using the formula for calculating the thermal constraint force generated by thermal stress, thus making heat a measurable physical quantity. In other words, we can write the formula for calculating the thermal constraint force generated by thermal stress as Hooke's Law in thermodynamics:
[0031]
[0032] Furthermore, based on the mathematical expression of Hooke's Law in thermodynamics, we can also design an instrument for measuring thermodynamic force F using the ideal gas law, namely:
[0033]
[0034] Then, after organizing, we get:
[0035]
[0036] Let K be:
[0037]
[0038] From this, we can derive Hooke's Law in thermodynamics:
[0039]
[0040] When a material cannot expand freely due to external constraints, the restoring force F generated inside it is proportional to the temperature difference ΔT. This is a fundamental conclusion in classical thermoelasticity, which has a solid theoretical foundation and wide applications in engineering physics and materials science.
[0041] Thermal constraint force is essentially a static internal force (constant at steady-state temperature) that acts on the constraint structure. According to Newton's third law, when a material exerts a force on a constraint, the constraint exerts a reaction force of equal magnitude and opposite direction on the material.
[0042] Therefore, by simply inserting a force sensor into the constraint path, the thermal value can be directly measured. The key point is that the force does not exist in a vacuum; it must be transmitted through contact. By installing an S-shaped tension / compression sensor on the force transmission path, the thermal value can be obtained by reading the sensor.
[0043] S-type tension and compression sensors can convert force into electrical signals using strain gauges / piezoelectric effect, and can be used for material thermal stress testing and high-temperature fastener monitoring.
[0044] Typical experimental method (taking a metal rod as an example)
[0045] Specimen preparation: Machin a standard cylindrical specimen. Both ends are machined flat to ensure good contact.
[0046] Installation: Place the sample in a rigid fixture, fix one end, and connect the other end to an S-type tensile / compression sensor. Place the entire device in a temperature-controlled furnace or environmental chamber.
[0047] Test process: Initial temperature Zero-force signal. Temperature rise to... Maintain a constant temperature. Record the force value F output by the S-type tension / compression sensor.
[0048] Result verification: Measured F vs. theoretical value In comparison, the error is typically less than 5% within the elastic range.
[0049] The experimental curve will show that the force increases linearly with temperature, perfectly verifying... .
[0050] Nuclear power plant pipeline monitoring: The main cooling pipeline generates a huge ΔT due to start-up and shutdown. Engineers installed high-temperature S-shaped tensile and compressive sensors on the support frame to monitor the thermal constraint force in real time and prevent fatigue fracture.
[0051] Sensor temperature resistance: Ordinary strain gauges are typically ≤ 200°C; higher temperatures require quartz piezoelectric sensors, which can reach 600°C; or optical force measurement, such as fiber optic gratings.
[0052] Thermal drift compensation: The sensor itself will experience zero drift when heated. A blank control experiment is required. When there is no sample, the drift is measured and subtracted.
[0053] Achieving complete constraint: It is difficult to achieve 100% rigid constraint in practice, but as long as the constraint stiffness is much greater than the material stiffness, the error can be ignored.
[0054] Thermal constraint is a real, engineerable form of thermal force and should not be reduced to a mere byproduct of stress.
[0055] In a closed thermodynamic system, the sum of the absolute values of the momentum of all particles involved in thermal motion can only increase or remain unchanged, and cannot decrease.
[0056] The sum of the absolute values of the momentum of all particles is a physical quantity that can characterize the degree of motion of particles. It has a unidirectional tendency to change, which cannot be reduced but can only be increased or remain unchanged.
[0057] The sum of the absolute values of the momentum of all particles in a thermodynamic system, M:
[0058]
[0059] The physical meaning of the sum of the absolute values of the momentum of all particles is to measure the intensity of the motion of all particles in the system. If this value increases, it means that the particles are moving faster overall. That is to say, in a closed system, when particles collide with each other, although the total momentum cancels out and is conserved, the absolute value of their momentum will spontaneously increase.
[0060] The sum of the absolute values of the momentum of all particles will spontaneously increase or remain unchanged. This is due to the constraints of the conservation of energy and the conservation of momentum.
[0061] The total kinetic energy must remain constant, and the total momentum must remain constant (usually 0). To satisfy both conditions simultaneously, the system spontaneously tends towards a state where momentum is distributed as evenly and dispersedly as possible among the particles. The absolute value of the momentum of all particles measures not the "motion" itself, but the "irreversible, recorded history" of the "motion." It may be a history-dependent, non-local physical quantity, related to all collisions of the system from the past to the present, not just the state of the system at a particular instant. It is the accumulation of the absolute value of momentum exchanged in every collision that has occurred in the past. Even if the total kinetic energy of the particles remains constant at the current moment (satisfying the law of conservation of energy), once a collision occurs, the "trace" of momentum exchange is permanently recorded and accumulated. This "trace" is the increasing part of the "absolute value of momentum." It describes the sum of the "historical cost" or "irreversibility" of the system's motion, and therefore it only increases and never decreases.
[0062] The sum of the absolute values of the momentum of all particles no longer describes the "state" of the system, but rather the "path dependence" and "history" of the system's evolution. This is completely different from the starting point of entropy, which describes the "possibilities of a state." The law that the absolute value of momentum "only increases and never decreases" in a closed system is a new law independent of the conservation of energy and momentum.
[0063] The sum of the absolute values of the momentum of all particles is not momentum itself. Momentum, after being treated as an absolute value, is treated as a scalar. It measures the sum of the "intensity of motion" of all particles in the system, caring only about the magnitude of velocity and not about direction. It is not conserved. Because it is a scalar addition with no directional cancellation, it describes the total amount of "impact" within the system.
[0064] The sum of the absolute values of the momentum of all particles can be understood as follows: In a closed system, although the total momentum (vector) is conserved, the sum of the absolute values of momentum (scalars) spontaneously increases (or remains unchanged). This means that while collisions between particles maintain the overall "directional balance," they make each particle "run faster."
[0065] The sum of the absolute values of the momentum of all particles is indeed a completely new physical idea independent of existing conservation laws (energy, momentum), because it describes an increase in the "dispersion" of motion within the system.
[0066] The sum of the absolute values of the momentum of all particles only concerns how fast the object is moving (the magnitude of its velocity), not which direction it is moving in. The sum of the absolute values of momentum is simply the sum of the magnitudes of the momentum of all particles in the system. This "sum of the absolute values of the momentum of all particles" is a scalar sum, always greater than or equal to zero, and only increases. This law of "only increasing and never decreasing" in a closed system is a new law independent of the conservation of energy and the conservation of momentum.
[0067] In physics, any monotonically changing physical quantity can be used to define the direction of time. Therefore, we can define the direction of time's passage by the increase of the sum of the absolute momentum of all particles. This means that in a closed particle system, time can be understood using the sum of the absolute momentum of all particles. The larger the sum of the absolute momentum, the "older" the system; the smaller the sum of the absolute momentum, the "younger" the system. This is a definition of time based purely on dynamics (the intensity of particle motion) rather than statistics (disorder).
[0068] Suppose we discover a microscopic system whose entropy appears unchanged, but the sum of the absolute values of the momentum of all its particles is increasing. This can be explained by:
[0069] In a specially designed closed container, the particles appear to have reached thermal equilibrium (maximum entropy), but the temperature of the container's inner wall is slowly and continuously rising.
[0070] The old theory: This violates the second law of thermodynamics (entropy no longer increases, but energy flows from low temperature to high temperature).
[0071] New theory: This is easy to explain: the sum of the absolute values of the momentum of all the particles in the system is still increasing! This means that the intensity of the collisions between the particles is accumulating, and this accumulated, irreversible momentum is eventually converted into heat energy through collisions with the container walls, leading to an increase in temperature.
[0072] The sum of the absolute momentum of all particles is not a useless quantity, but a potential, entirely new measure of time. It provides us with another purely dynamic perspective for understanding irreversibility. This is precisely the cutting edge of theoretical physics—the search for the deep origins of time and complexity.
[0073] The sum of the absolute momentum of all particles is a physical concept that is parallel to, complementary to, but independent of entropy. It starts from the fundamental kinetic momentum of particles and also captures the unidirectional nature of system evolution. This is a very profound insight. For it to become an accepted theory, the next step is to find a physical state in which entropy remains almost constant, but the sum of the absolute momentum of all particles increases significantly, thus experimentally distinguishing it from entropy. A thermally balanced closed system can indeed exhibit an increasing sum of absolute momentum while entropy remains constant.
[0074] Entropy (disorder) is a statistical average concept. When a system reaches thermal equilibrium, its macroscopic state (temperature, pressure) has stabilized, so the entropy remains constant.
[0075] The sum of the absolute values of the momentum of all particles, M, is a concept of instantaneous dynamics, which describes the total "force" of the motion of all particles at this moment.
[0076] In thermal equilibrium, although the particles appear stationary on a macroscopic scale, they are actually undergoing chaotic and random thermal motion (Brownian motion) on a microscopic scale. The direction of these particles' velocities is random, but the magnitude of their velocities (i.e., the absolute value of their momentum) is constantly changing.
[0077] Conclusion: In thermal equilibrium, the sum of the absolute momentum values M of all particles is not a fixed constant, but a random variable that fluctuates wildly over time. It may be high one second and low the next, but its average value is stable.
[0078] The sum of the absolute values of the momentum of all particles, M, defines the "direction of time." The fact that "the absolute value of momentum is increasing" actually suggests a very bold physical idea: perhaps the direction of the passage of time is not determined by entropy, but by the sum of the absolute values of the momentum of all particles (M).
[0079] The old theory (entropy): Time flows from low entropy to high entropy.
[0080] New idea (M): Time flows from the sum of the absolute values of low momentum M to high momentum M.
[0081] In thermal equilibrium, although entropy is saturated, the random fluctuations of the sum of the absolute momentum values M of all particles still "mark" the passage of time. The sum of the absolute momentum values M is unique every second, recording the evolutionary trajectory of the system's microscopic state.
[0082] The physical idea that the sum of the absolute momentum of all particles is essentially an attempt to redefine the direction of time using a dynamic quantity (momentum). This is a highly original and profound perspective, transcending the framework of traditional thermodynamics and directly questioning the essence of physical quantities. Thermal equilibrium can have an inherent difference in thermal velocity, and the absolute value of momentum can characterize the inherent velocity difference within this thermodynamic system. The absolute value of momentum characterizing the system's inherent velocity difference is indeed the core value of this physical idea. It reveals a "hidden dimension" overlooked by traditional physics.
[0083] The sum of the absolute momentum of all particles is more sensitive than entropy. It not only describes the disorder of a system like entropy, but also captures the velocity gradient within the system, thus predicting its future evolution. This is a profound insight that transcends existing frameworks. In essence, this new physical idea targets all thermally moving particles within a thermally moving system—a comprehensive statistical analysis.
[0084] The sum of the absolute values of the momentum of all particles does something that traditional physics rarely does: it doesn't let any particle go unpunished, but adds up all their "force".
[0085] Traditional statistics (entropy) is a macroscopic average, concerned with probability distribution. For example, it only cares about what percentage of particles have velocities within a certain range, without caring about which specific particle it is.
[0086] The sum of the absolute momentum values of all particles (M) is a microscopic accumulation. It focuses on each specific particle. It records the absolute momentum value of each particle and then adds them directly together.
[0087] Entropy: Once a system reaches thermal equilibrium, entropy "forgets" itself. It can no longer distinguish whether the system has just evolved from a non-equilibrium state or has been in equilibrium for a long time.
[0088] The sum of the absolute momentum of all particles, M: Even if the system is in macroscopic thermal equilibrium, the absolute momentum of each particle still fluctuates wildly at the microscopic level. The instantaneous value of M records the system's "fingerprint" on the timeline. It knows what is happening in the system at this very moment.
[0089] The sum of the absolute values of the momentum of all particles is actually redefining the direction of time using the fully aimed kinetic quantity (M).
[0090] The principle of entropy increase: Time flows from low entropy to high entropy.
[0091] The new idea of the sum of the absolute values of the momentum of all particles is that time flows from low M to high M, or from a certain distribution of M to another distribution.
[0092] The sum of the absolute momentum of all particles is a completely new physical observation. It is not satisfied with macroscopic averages, but delves into each microscopic particle, attempting to find the code of the universe's evolution from the most fundamental motion.
[0093] Analyzing microscopic particles requires the use of quantum mechanics, specifically the wave function. Having complex nature, wave function It must be defined in the complex field, where its imaginary part carries phase information and determines quantum interference and entanglement behavior. Experiments have shown that without imaginary numbers, quantum mechanics cannot fully describe the microscopic world (e.g., Bell's inequality is violated).
[0094] Example: Electron spin state | In the equation >=α∣↑>+β∣↓>, the complex phase difference between α and β directly controls the measurement probability.
[0095] Probability wave refers to the wave function in quantum mechanics. Its physical unit is determined by the definition of probability density. It is the probability density.
[0096] wave function Its unit is the square root of the probability density unit. The wave function itself has no directly observable physical meaning; only the square of its modulus corresponds to the observable probability density.
[0097] However, in physical experiments, we have never observed particles exhibiting the wave-like phenomenon of spreading and expanding over time. Therefore, it is necessary to reinterpret probability waves based on this physical phenomenon. For this purpose, we can reasonably assume that a quantum density field exists in the space surrounding a particle, and we can then interpret the wave function in the Schrödinger equation... Defined as a wave field describing "quantum density," only the physical meaning is changed, not the mathematical form, that is:
[0098]
[0099] Here, ρ is the spatial density of the quantum itself, not the "probability of finding the particle".
[0100] The amplitude of the wave in the quantum density field It is a real, diffuse, superimposed interference spatial field function that describes the distribution density of quantum objects in space.
[0101] For single-particle systems The quantum is equal to the spatial extension density quantum itself. It is not a point particle, but rather diffuses in space in the form of a density field.
[0102] For multi-particle systems: ρ is the quantum number density / quantum matter density.
[0103] The Schrödinger equation is not an evolution equation of probability, but a wave propagation equation of the amplitude of the quantum density field. Superposition, interference, and diffraction are all wave behaviors of the density field itself.
[0104] A particle is singular, a point-like entity, and is not diffuse; a quantum is a group, a diffuse field / matter unit, constituting the wave background; wave function This only describes the spatial density distribution of this group of quanta, and is unrelated to probability. Particles move within the quantum group; they will appear where the quantum density is higher, and the higher the quantum density, the more likely the particle is to be located. The total number of quanta in the group remains constant; it cannot be created or destroyed. It obeys the law of conservation of quantum quantity, and is unrelated to probability. In other words, the wave function determines the quantum, and particles follow the quantum density.
[0105] In our new interpretation of quantum waves, the mathematical form is exactly the same as that of existing quantum mechanics. The way the Schrödinger equation is written, the form of the solution, and all the calculated numerical results (energy levels, diffraction fringes, spectra, dynamic processes) are no different from standard quantum mechanics. We have not modified the equation, but only the understanding of what the Schrödinger equation is describing.
[0106] The Schrödinger equation describes the quantum wave density field of a particle. The meaning is the spatial density of the quantum group. The relationship between waves and particles is that waves are waves and particles are particles. They are separated in terms of spatial coordinates. Particle behavior is a definite entity and will stay in places with high quantum density. The normalization meaning is that the distribution of quantum waves determines the position of particles, and there is no collapse.
[0107] In summary, the Schrödinger equation remains the same, but we have presented a new physical picture: quantum waves fluctuate, and particles follow the quantum density.
[0108] In our new interpretation of quantum waves, the mathematical steps, calculation results, and experimental matching degree of the actual solution to the Schrödinger equation are exactly the same as those of standard quantum mechanics; the only difference is that the physical meaning of each step is replaced by a split image of quantum wave + particle.
[0109] General application steps: Write the standard Schrödinger equation directly.
[0110]
[0111] Physical significance: The Schrödinger equation is the propagation / evolution equation of quantum waves, not probability waves.
[0112] Solve The wave function is obtained using standard methods (separation of variables, numerical solutions, perturbation theory, etc.). Physical meaning: It is the spatial amplitude of quantum waves.
[0113] Calculate Physical meaning: The density distribution of a quantum group in space, not the probability density.
[0114] Analyzing particle behavior: Particles are isolated point objects, naturally inclined to appear in regions of high quantum density.
[0115] Larger particles are more likely to appear here. Smaller particles are less likely to appear here;
[0116] Conservation significance
[0117] This refers to the conservation of the total number of quantum particles, not the total probability equaling 1.
[0118] 1. One-dimensional infinite potential well (the simplest bound state problem)
[0119] The standard procedure is to solve the equation to obtain the standing wave solution, energy level, and position distribution.
[0120] Our new interpretation is applied: the solution The amplitude of the standing wave of a quantum wave in a potential well. This is equivalent to the density distribution of quanta within the well; particles can only move within the well and most frequently appear at the peaks of the quantum density. Energy levels are equal to the intrinsic vibrational energy of the quantum wave, not the probability energy levels of the particles.
[0121] 2. Hydrogen atom
[0122] Solving the spherically symmetric Schrödinger equation yields the energy levels, angular momentum quantum number, and electron cloud.
[0123] Our new interpretation applies: = The amplitude of the quantum wave field surrounding the proton. The electron cloud we usually talk about is now equal to the quantum density distribution cloud, no longer a probability cloud. Electrons (particles) are most stable and most frequently found in the shell with the highest quantum density (near the Bohr radius). Spectral lines = the energy difference when a quantum wave jumps from one density distribution to another.
[0124] 3. Double-slit interference (core experiment of quantum phenomena)
[0125] Standard procedure: Solve the wave equation to obtain interference fringes.
[0126] New interpretation and application: Quantum waves pass through two slits simultaneously, causing interference, and on the screen... The quantum density fringes after interference are equivalent to particles (electrons / photons) hitting the screen one by one, preferentially landing on the bright quantum density fringes. It is not necessary for particles to pass through two slits at the same time, nor is it necessary for probability wave interference.
[0127] 4. Quantum tunneling effect (real devices such as tunneling diodes and scanning tunneling microscopes (STM))
[0128] Standard procedure: Solving the equation reveals that the wave function can penetrate the potential barrier.
[0129] Our new interpretation applies:
[0130] Quantum waves can extend and penetrate potential barriers. There is still quantum density outside the barrier, so particles may appear outside the barrier. The magnitude of the penetration current is determined by the magnitude of the quantum density outside the barrier. Our new interpretation does not change the Schrödinger equation itself, nor does it change any actual calculation process. All existing physical applications (atoms, molecules, semiconductors, quantum devices, spectroscopy) can be used directly. It simply changes the picture from particles appearing randomly with probability to quantum waves evolving, with particles tending to areas with high quantum density.
[0131] In our new interpretation of quantum waves (particles ≠ quantum, wave function = quantum density field, particles tend to move into the high-density region of quantum), all the mathematical formulas, algorithms, hardware principles, and Schrödinger equations of quantum computing remain completely unchanged. Only the underlying physical picture is changed from probability evolution to quantum density field evolution + particle orientation and localization. The applications are still all valid and are more intuitive.
[0132] The core application of the Schrödinger equation in quantum computing under a new interpretation
[0133] 1. Quantum bits: no longer "probability superposition", but quantum density superposition.
[0134] Existing answers: , , It is the probability of obtaining 0 / 1.
[0135] New interpretation: Describing quantum density fields, , It refers to the density ratio of quantum particles in the 0 / 1 states; the carrier particles of qubits tend to appear in the state with higher quantum density.
[0136] The Schrödinger equation still applies: it describes how the quantum density field evolves with time / gate operations.
[0137] 2. Quantum gates: Instead of changing probability amplitudes, they manipulate quantum density fields.
[0138] All quantum gates (Hadamard, CNOT, phase gates, etc.) are still unitary transformations in mathematics, and in physics they become: using external fields to manipulate the amplitude, phase, and distribution shape of the quantum density field.
[0139] The role of the Schrödinger equation: to accurately give the evolution trajectory of the quantum density field under the action of a gate.
[0140] 3. Quantum superposition: It is not that probabilities exist simultaneously, but that quantum density polymorphism coexists. Quantum parallelism is not probabilistic parallelism, but that quantum density fields are simultaneously distributed in multiple computational states, and particles are simultaneously guided by the quantum density of the entire space.
[0141] The calculation process is as follows: the Schrödinger equation drives the quantum density field to flow, superimpose, and interfere in the computational space.
[0142] 4. Quantum interference: It is not a probability cancellation / conversion, but quantum density interference.
[0143] The core of quantum acceleration, such as Grover search and Shor's decomposition, is interference:
[0144] The current solution is to cancel out the probability of incorrect answers and amplify the probability of correct answers.
[0145] Our new explanation is that the quantum density of the incorrect state cancels out and weakens, while the quantum density of the correct solution state strengthens and grows together; the particle eventually naturally tends toward the correct solution with the highest density.
[0146] The essence of quantum acceleration: using the Schrödinger equation to control the quantum density field and focus the density onto the answer.
[0147] 5. Quantum entanglement: It is not a probabilistic correlation, but a global binding of many-body quantum density fields.
[0148] Multi-qubit entangled state: Instead of measuring the probability of one instant determining another, multiple particles share the same overall quantum density field; a change in density in one place will cause a synchronous response in the quantum density of the entire system, and the tendency behavior of the particles will naturally remain correlated.
[0149] 6. Quantum measurement: No wave function collapse, only localization of the quantum density field.
[0150] Measurement is not a probability collapse, but rather a redistribution and high localization of the quantum density field after coupling with the detector; the particle eventually falls at the position of maximum density, and the output result is uniquely determined by the quantum density distribution.
[0151] In quantum computing, we still use the exact same Schrödinger equation, the same algorithm, and the same hardware; only the physical meaning changes from "probability is evolving" to "quantum density field is evolving," with particles following higher density. All quantum computing applications—quantum algorithms, quantum simulations, quantum sensing, and quantum error correction—can be directly applied. All calculations, formulas, solutions, and results remain unchanged; only the new physical interpretation replaces the standard probability wave interpretation. The mathematics and computation remain completely unchanged. The Schrödinger equation, wave function solutions, and... The calculations, normalized integrals, quantum algorithms, experimental predictions… all the computational steps and results are exactly the same as in standard quantum mechanics, without changing a single notation. Only the physical meaning is replaced, namely, that the wave function is a probability wave. = The probability density of particle occurrence, replaced by a wave function, is the quantum density wave. = Quantum spatial density, particles tend to appear at the point of maximum quantum density. Only the interpretation changes, the calculations remain the same throughout; the only change is the understanding in your mind that this is the evolution of a quantum density field, with particles following the density, regardless of probability.
[0152] The light wave function is not the probability amplitude of photons, but the density field of light quanta.
[0153] Laser is equivalent to a highly coherent and highly concentrated quantum density field;
[0154] Photons naturally tend to appear in the modes and directions with the strongest quantum density, which is why lasers have good directionality and high brightness.
[0155] For single-photon interference / double-slit interference, the calculation remains completely unchanged:
[0156] The wave functions are superimposed, the interference is constructive and destructive, the fringe distribution and intensity curve are exactly the same.
[0157] We simply offer a new explanation: it's not the probability waves of photons interfering with each other, but rather the quantum density field of light undergoing wave-like interference; photon particles simply tend to fall onto the bright fringes with higher density.
[0158] Individual photons are emitted one after another, eventually accumulating into stripes, which is simply a gradual "sampling" of the quantum density field.
[0159] For photon detection and photon counting, the calculation remains completely unchanged:
[0160] Detection probability ∝ light intensity ∝ The response formulas for all detectors remain unchanged.
[0161] Our new interpretation: It's not the "probability density of detecting photons," but rather the density of photons at that location; the higher the quantum density, the easier it is for photons to appear there, and the easier it is for the detector to respond.
[0162] IV. Spontaneous Emission / Stimulated Emission
[0163] The calculations remain completely unchanged: Fermi's golden rule, transition rates, radiation spectra... all remain unchanged.
[0164] The new explanation suggests that atomic transitions are not "randomly emitting photons according to probability," but rather that the quantum density field around the atom is excited and redistributed; the emitted photon particles fly out along the direction and pattern of the quantum density field.
[0165] Entangled photon pairs (a core experiment in quantum optics) have completely unchanged computational results:
[0166] The calculations of the two-photon wavefunction, correlation function, polarization correlation, and Bell's inequality remain unchanged.
[0167] The new explanation is not that "there is a mysterious correlation between the probabilities of two photons," but rather that the two photons share the same overall quantum density field; the orientation / polarization of a photon particle is determined by the overall density field, and therefore they are naturally correlated.
[0168] Nonlinear optics (frequency doubling, sum-frequency conversion, parametric down-conversion) calculations remain completely unchanged:
[0169] Nonlinear polarization, phase matching, coupled wave equations, and invariant output spectrum.
[0170] New explanation: It is not that photons are converted into photons of a new frequency according to probability, but rather that nonlinear coupling and energy exchange occur between quantum density fields of different frequencies; the newly generated photon particles appear in the places where the new density field is strongest.
[0171] The cavity quantum electrodynamics calculations remain completely unchanged: the cavity mode wavefunction, Rabi oscillation, and photon localization formulas remain unchanged.
[0172] New interpretation: The cavity highly localizes and enhances the quantum density field of light; atomic / photon particles are "captured" by the high-density field, and their behavior is determined by the quantum density distribution of the cavity.
[0173] In a quantum density field, photons tend to move towards locations with higher quantum density. This is the complete application of the new interpretation in quantum optics.
[0174] New quantum density field model:
[0175] An electron is a single point particle (unique, solid, and non-diffuse); the wave or electron cloud of the wave function is a quantum density field (a group of quanta) independent of the electron; electrons tend to go to the place with the highest quantum density; the relationship between wave and particle is that wave is wave and particle is particle, completely separate and completely independent of probability.
[0176] The new model posits that particles are not equivalent to quanta, and that an electron is equivalent to a point particle. A quantum is equivalent to an independent wave field, a distinction that neither Bohr's nor standard quantum mechanics can achieve. The new model does not use probability / chance to explain the hydrogen atom.
[0177] The new model posits that electron cloud equals quantum density, and electrons simply tend to gravitate towards areas of high quantum density.
[0178] The new model retains the electron as a real point particle while also accommodating waves. Rutherford and Bohr argued that only particles can explain waves. Standard quantum mechanics turns particles into probability waves, losing their realism.
[0179] The new model retains both point particles and real-world quantum fields, without altering the Schrödinger equation. It only changes the worldview, keeping the solutions, energy levels, spectra, and radii unchanged. The only difference is that the word "probability" is replaced with "quantum density."
[0180] In the new model, particles are particles, quanta are quanta, wave functions describe quantum density, and electrons tend to follow positions with high density. This is the only hydrogen atom model in which real particles and real wave fields coexist.
[0181] In all experiments, we have never truly observed a particle "growing larger, spreading out, or dispersing"—electrons, photons, protons… what we detect is always a single point. A complete particle, never a half-particle, a dispersed, cloud-like particle.
[0182] The so-called electron cloud is just a statistical distribution of observational results; it does not mean that the particles actually turned into a cloud and dispersed.
[0183] Particles must be point particles; they can never expand or diffuse like waves. This is not a conjecture, but a direct adherence to experimental observation. However, the current quantum mechanics' probabilistic wave / wave-particle duality is precisely counterintuitive and logically contradictory in this respect, forcibly making a particle both a particle and a wave, existing both here and there.
[0184] From the perspective of physical intuition and experimental facts, the new model's starting point is more simple, practical, and reliable than the orthodox interpretation. Its scheme is extremely clean, self-consistent, and does not disrupt existing physics. It does not change any formulas, overturn the Schrödinger equation, or negate experiments. It only does one thing: replaces the probability that the diffused state is a particle with the diffused state being an independent quantum density field. Particles are always points and tend to be located at areas of high quantum density. This is the idea of minimal modification and maximum benefit at the interpretation level. It preserves the fact that particles are always points, do not disperse, do not split, and do not diffuse. It also preserves: all waves, interference, diffraction, energy levels, spectra, etc. It discards the most mysterious and confusing probability waves, wave function collapse, and the non-real nature of particles, thus solving the century-old puzzle of "why particles do not disperse like waves."
[0185] The orthodox explanation cannot answer: If it is a wave, why does the particle never disperse? If it is a particle, why does it exhibit wave-like behavior?
[0186] The new idea can be explained in a single sentence: what disperses is not particles, but quantum fields; particles simply follow the density of the quantum field and remain forever as points. This is the most straightforward and least counterintuitive picture of the coexistence of "particle reality and wave nature" among all current interpretations.
[0187] The physical essence of a quantum density field is a field diffused in the space outside the particle. This field of the particle comes from the particle itself. The particle is the source of the quantum field, and the place where the quantum density is high is the place where the particle likes to stay.
[0188] The new model is faithful to experiments, logically consistent, mathematically fully compatible with existing quantum mechanics, and perfectly preserves the physical fact that particles are always points and never diffuse or disperse. It is a new interpretation of quantum mechanics.
[0189] The primary criterion for judging whether a new interpretation is good or not is whether it can reduce paradoxes and clarify the physical picture.
[0190] The new model directly eliminates the particle dispersion paradox in the classical paradox of quantum mechanics.
[0191] Standard version: Particles are both points and waves that spread and form clouds, which is contradictory.
[0192] The new model states that particles are always points and never disperse; what diffuses is the quantum density field, thus eliminating the paradox.
[0193] Wave function collapse paradox
[0194] Current explanation: The probability wave collapses suddenly upon measurement, without any physical process, faster than light, and is illogical.
[0195] The new model: there is no collapse, only particles in a quantum density field, and measurement only shows the result, thus eliminating the paradox.
[0196] Wave-particle duality paradox
[0197] Current explanation: A particle is both a particle and a wave, forcibly combining two contradictory properties.
[0198] The new model: waves are waves, particles are particles, each in its proper place, eliminating the need for "both are and are not," thus removing the paradox.
[0199] The new model does not overturn existing physics; it merely clarifies the chaotic logic. It can significantly reduce paradoxes and restore the physical picture to clarity and consistency. The new model only replaces the physical interpretation of the wave function; all the mathematics, formulas, calculation steps, and final numerical results are exactly the same as standard quantum mechanics.
[0200] The new model does only one thing: it replaces the statement that the wave function equals a probability wave with the statement that the wave function equals a quantum density field, with particles tending towards higher quantum densities. Apart from this, all the calculations in quantum mechanics are completely preserved and unchanged. At least logically, the new conjecture resolves the paradox under the probability wave interpretation that particles cannot expand and disperse, yet still need to expand and disperse.
[0201] The standard probability wave interpretation inherently contains a logical inconsistency: experimentally, particles are always points, neither expanding nor dispersing. Theoretically, however, particles must become waves, diffuse, expand, and disperse. The same object must both always be a point and be able to become a diffuse wave—this is a blatant logical contradiction.
[0202] The new interpretation does only one thing: it breaks down the same thing into two: particles are always points, never expanding or dispersing; and the wave function describes the diffusion, fluctuation, and distribution of the quantum field. The premise of the paradox is directly dismantled, resulting in instantaneous logical consistency, without any conflict or forced interpretation. From the perspective of logical consistency alone, the new interpretation is superior to the probability wave interpretation. Then, all other existing interpretations from quantum mechanics can be consistently replaced and transformed into this new one.
[0203] Under this new interpretation, entanglement becomes simple, natural, and without paradox.
[0204] Entanglement is equivalent to two particles sharing the same overall quantum density field. This field is diffuse, global, and unified, but it is not a probability wave. Both particles are point particles, guided by this unified quantum field. Measuring one particle is equivalent to measuring its position / state in the shared field. The state of the other particle is not "instantly changed," but is determined by the correlation distribution of the same overall field.
[0205] In its simplest terms, entanglement isn't about particles transmitting signals across a distance, but rather two particles sharing a common map of quantum field relationships. Seeing the position of one point naturally tells you the corresponding position of the other on the map. There's no action at a distance, no wave function collapse, no ghost phenomena, and no logical fallacies. Quantum entanglement transforms from the most bizarre quantum puzzle into the most natural phenomenon of quantum density field relationships.
[0206] For quantum communication, all the technologies, protocols, algorithms, security, experimental results, and engineering implementations remain completely unchanged.
[0207] The only change: the most mysterious and difficult-to-understand parts of quantum communication have all become logically sound and no longer bizarre.
[0208] The new interpretation enhances our understanding of the three core elements of quantum communication:
[0209] 1. Quantum key distribution (QKD / BB84, etc.)
[0210] Standard explanation: Photons are probability waves; measurement causes the wave function to collapse; eavesdropping disturbs the probability distribution and is thus detected.
[0211] New interpretation: Photons are point particles that never disperse;
[0212] What is being transmitted is the state of the quantum density field;
[0213] Eavesdropping inevitably disturbs the quantum density field distribution, causing the particle's orientation to change immediately, which the communicating party can directly detect.
[0214] The principles, formulas, and experiments of security remain unchanged; the only difference is that the probability perturbation is replaced with quantum density field perturbation, making the concept more physical and concrete.
[0215] Quantum entanglement distribution (the core resource of quantum communication)
[0216] Standard explanation: Entangled particles, no matter how far apart they are, collapse instantly upon measurement, like a ghost effect at a distance.
[0217] A new interpretation: The two particles share the same overall quantum density field; their correlation is a correlation of the field, not an influence between the particles in space; measuring one particle simply reads the state of this unified field, while the state of the other particle is inherently determined by the same field. Without the faster-than-light paradox or any mysterious mechanisms, quantum entanglement transforms from a "mystical black box" into a clear field physics concept.
[0218] Quantum teleportation
[0219] Standard explanation: Quantum states are "instantaneously transported" through probability wave collapse.
[0220] New interpretation: What is being transmitted is neither particles nor faster-than-light signals, but rather the correlation information of quantum density fields; the state of particles is guided by the field, and state transfer is completed through the correlation of classical channels and entangled fields. This is entirely consistent with relativity, has no logical flaws, and the process is clear and causally sound.
[0221] The new interpretation makes no technological changes to quantum communication; it only does one thing: replaces all the counterintuitive, paradoxical, and metaphysical explanations of quantum communication with the understanding that particles are points that do not disperse; that fluctuations occur in quantum density fields; and that particles tend towards higher densities. This is a self-consistent, intuitive, and paradox-free physical picture.
[0222] Simply put, quantum communication will still be used the same way, but it's finally easier to explain and understand.
[0223] The new interpretation of quantum density field plus real particles is not just a repair of the physical interpretation, but also a clean and self-consistent rectification of the underlying philosophy and worldview of quantum mechanics.
[0224] The new interpretation has reclaimed the objective reality of the quantum world.
[0225] The philosophical dilemma of the standard probability wave interpretation: particles do not have a definite objective state, and only observation "collapses" into reality, giving the world a strong observer-dependent and unreal character.
[0226] A new interpretation: Particles are real, tangible point objects, and quantum density fields are objectively existing fields; neither depends on observation, humans, or consciousness. The quantum world is inherently real; observation is merely seeing, not creating. This returns to materialistic realism, completely eliminating idealistic speculation from quantum mechanics. It smooths out the divide between the microscopic and macroscopic worldviews.
[0227] The worldview split brought about by standard quantum mechanics:
[0228] Microscopic: probabilistic, unreal, without trajectory, counterintuitive. Macroscopic: deterministic, real, causal, intuitive. The rules of these two worlds are contradictory and cannot be reconciled philosophically.
[0229] The new interpretation: Particles are always points, never scattered; fields are responsible for fluctuations and guidance; the difference between the microscopic and macroscopic is merely the presence or absence of quantum field guidance and the difference in the intensity of guidance, not two sets of worldviews or two sets of logic. The world is unified, self-consistent, and continuous, no longer separated into microscopic and macroscopic worlds. This restores the fundamental dignity of causality.
[0230] Standard probability wave: The appearance of particles is truly random, without cause or causation, and is essentially unpredictable.
[0231] A new interpretation: Where particles appear is determined by the causal distribution of the quantum density field; it's not a causeless effect. It's just that we can't directly see the quantum density field, which makes it seem random. The quantum world still obeys causality; there are no metaphysical events that escape the law of causality. This ends the philosophical paradox of logic arising from wave-particle duality.
[0232] The standard interpretation is forced to accept that something is both a particle and a wave, violating the law of contradiction in formal logic.
[0233] The new interpretation: waves are waves, particles are particles, each fulfilling its function without contradiction. The world adheres to a clear logical law of identity, eliminating the need to accept the anti-logical philosophy of "both A and not A." This new interpretation pulls quantum mechanics out of the philosophical trap of being anti-realistic, anti-causal, anti-logical, and anti-common sense, establishing a completely new quantum worldview that is objectively real, logically consistent, causally unified, microscopically and macroscopically consistent, and entirely materialistic. This is not merely a reinterpretation of the wave function, but rather a complete and logical philosophical foundation for quantum mechanics, one that aligns with human reason.
[0234] For the energy levels of a hydrogen atom, the potential energy term obtained based on Coulomb's law, i.e., the Coulomb potential, is smooth and continuous, gradually changing with r. Therefore, it can be considered to correspond to the smooth and gradually changing topographical framework of mountains and valleys. Low energy levels (small n, such as n=1): deep potential energy wells, corresponding to smooth bowl-shaped deep valleys (flat bottom, smoothly rising outwards); high energy levels (large n, such as n=2, 3): shallow potential energy wells, corresponding to smooth ring-shaped high-altitude peaks (flat rings, further smoothly rising outwards); n→∞: potential energy approaches 0, corresponding to flat outer plains, without peaks or valleys, and the electric field strength approaches 0.
[0235] wave function With quantum density (Continuously differentiable, smooth distribution), corresponding to the stable probability distribution of electrons in smooth terrain.
[0236] ψ(r) density peak → The location where electrons are most likely to appear in the potential energy topography (the gentle area of the mountain peak / valley).
[0237] At quantum density nodes (approaching 0) → locations where electrons are almost nonexistent (smooth transition slopes between peaks and valleys, without abrupt deep valleys).
[0238] Quantum number subdivision → smooth subdivision structure of terrain (no abrupt steps, only smooth differences in height and shape).
[0239] l Differences: The smoothness of the shape of the peaks / valleys varies (s track: dome-shaped and smooth; p track: three-lobed and smooth; d track: five-lobed and smooth).
[0240] m differs: differences in the smooth spatial orientation of the shape (without abrupt turning).
[0241] Spin-orbit coupling / external magnetic field: smooth energy level differences, corresponding to smooth, small height differences in the terrain (no abrupt serrations, only gentle steps).
[0242] The corrected geometry of the n=2 and n=3 energy levels (quantum mechanics)
[0243] n=2 (2s, 2p)
[0244] Undisturbed: 2s (a dome-shaped, gentle small peak) and 2p (a three-lobed, gentle small peak) smoothly overlap on the same large ring-shaped mountain peak, without any abrupt boundary changes.
[0245] Spin-orbit coupling: 2p splits into 2p1 / 2 and 2p3 / 2, corresponding to two adjacent, highly smooth, gradually changing small peak groups, with a smooth transition slope in between.
[0246] Zeeman effect: It further splits into micro-peaks with minimal height difference and smooth distribution, without abrupt tooth-like structures.
[0247] n=3 (3s, 3p, 3d)
[0248] The 3s orbit has nested peaks and valleys. (Small peak near the core + middle valley + outer main peak): This corresponds to a smooth small bulge and small depression that appears during the smooth outward rise from the bottom of the valley. It perfectly matches the smooth distribution of probability density and no longer violates the geometric logic.
[0249] The splitting of 3p and 3d: both are smooth, gradual differences in shape and height.
[0250] III. Geometric Mapping of Transitions and Selection Rules
[0251] Transition: An electron instantaneously jumps from one smooth peak / valley to another smooth peak / valley along a smooth transition slope. The instantaneity is a quantum property, and the path is smooth.
[0252] Selection rule (Δl=±1, etc.): Only smoothly matched transition slopes can be crossed; between mismatched shapes are smooth slopes that are too gentle / steep for electrons to jump, and there are no abrupt valleys.
[0253] All energy level structures are without any abrupt changes, and the energy level peaks, valleys, and transition slopes are all continuous and smooth curved surfaces;
[0254] Quantum number subdivision (l / m / s / j / m) j The corresponding differences are that the energy levels are all smooth gradual changes in shape and height, rather than step-like abrupt changes;
[0255] Transition process: Electrons jump instantaneously along a smooth transition slope of energy level, and can cross a smooth slope that matches the shape of the corresponding energy level according to the selection rule.
[0256] By allowing the energy levels to adopt a smooth, gradually changing electric field topography, the continuity between the Coulomb potential and the quantum mechanical wave function can be perfectly matched.
[0257] Geometric picture: n=1 is a smooth, bowl-shaped deep valley, n=2 is a smooth, ring-shaped high mountain peak, with a continuous smooth transition slope in between; the nested peaks and valleys of the s orbital are smooth convexities and concaves, no longer violating geometric logic. This is completely consistent with all mathematical results of quantum mechanics and experimentally measured continuous electric field / probability distributions.
[0258] The energy level diagram above provides us with a completely new anchor point for spatial visualization:
[0259] For beginners, it can transform abstract concepts like "energy levels, quantum numbers, and transitions" into mental images like "valleys, peaks, and slopes," making it a hundred times easier to understand than concepts like wave functions and quantum density.
[0260] For those doing theory or engineering, this geometric picture can be used directly as a mental scaffold. For example, when designing semiconductor energy level structures, instead of calculating the Schrödinger equation, one can first "carve" the required energy level peak height and spacing in one's mind, and then verify it with formulas.
[0261] More importantly, it does not exclude any subsequent expansions. Whether it is terrain distortion with the addition of multi-electron shielding or terrain stretching under external fields, it can be intuitively reflected in this energy level picture, which is more visual than pure mathematical derivation.
[0262] We will now use this energy level geometry model to explain the covalent bonds in hydrogen molecules.
[0263] We use a geometric model of smooth, gradually changing energy level peaks and valleys to provide a very simple qualitative explanation of the covalent bonds in hydrogen molecules, without introducing any complex formulas, and only retaining the core spatial picture.
[0264] The core premise is that a single hydrogen atom in its ground state consists of 1 proton and 1 electron, corresponding to a smooth, bowl-shaped valley (n=1 energy level), with the electron stable at the bottom of the valley.
[0265] Two isolated hydrogen atoms: each has its own independent valley, and between the valleys is a flat, field-free "plain" where electrons do not affect each other.
[0266] Covalent bond formation: When two hydrogen atoms come close together, their respective electric field topography (valley) merges smoothly, forming a new molecular-level topography.
[0267] The geometricization process of the covalent bond in a hydrogen molecule: Initially, the two isolated hydrogen atoms are far apart, each with its own independent bowl-shaped valley, and electrons are "sunk" in their respective valleys. The total energy of the molecule is equal to the sum of the energies of the two isolated atoms. The approach process (terrain merging): When the distance between the two atomic nuclei shrinks to the length of the covalent bond, the two bowl-shaped valleys smoothly merge into a double-bottomed saddle-shaped valley.
[0268] The middle saddle: the region between the two cores, where the potential energy is slightly higher than the two valleys, but it is still a smooth and continuous transition;
[0269] Valley bottom: The location near the two atomic nuclei, where the potential energy is lowest. This new terrain is a smooth potential energy distribution resulting from the superposition of the electric fields of the two nuclei, which perfectly conforms to the molecular orbital theory of quantum mechanics.
[0270] The behavior of electrons (covalent core): The two electrons (with opposite spins) are no longer confined to their respective valleys, but tend to remain in a stable position within the entire double-bottomed saddle-shaped valley:
[0271] Electrons tend to appear in the saddle region between the two nuclei (corresponding to bonding molecular orbitals), which is equivalent to an electron bridge pulling the two atomic nuclei together;
[0272] This distribution results in the total energy of the molecule being lower than the sum of the energies of two isolated atoms (the decrease in energy is the root cause of the stability of covalent bonds); geometrically, it means that the electron distribution changes from a single valley to a "double valley + saddle distribution", without abrupt changes and with a smooth transition throughout.
[0273] The essence of covalent bonds (geometric conclusion): The covalent bonds of hydrogen molecules correspond to the double-bottomed saddle-shaped energy valley formed by the smooth fusion of the electric field topography (valley) of two hydrogen atoms. Electrons are stably distributed in this shared valley, thus binding the two atomic nuclei together.
[0274] Antibonding orbitals: If electron spins are the same, a double-peak topography will be formed, with potential energy higher than that of isolated atoms. The molecule is unstable and cannot form covalent bonds.
[0275] Bond length: The optimal width of a double-bottomed saddle-shaped valley, corresponding to the equilibrium spacing between the two cores; there are no sudden changes in field strength throughout the entire process, and all terrain changes are smooth and gradual.
[0276] It's important to note that the combined valley has lower potential energy and can release energy, which is precisely the source of covalent bond energy. Using our smooth, gradually changing mountain peaks, the valley model can be explained as follows:
[0277] In the initial isolated state, there are two independent hydrogen atoms, each with a bowl-shaped valley (ground state energy level, potential energy E0), with electrons at the bottom of their respective valleys.
[0278] As the distance between the two atomic nuclei shrinks to the covalent bond equilibrium distance, the two bowl-shaped valleys smoothly merge into a lower and wider double-bottomed saddle-shaped common valley. The lowest potential energy value of this new valley, Emolecule, is lower than the valley bottom potential energy E0 of a single hydrogen atom (in quantum mechanics, this is the energy reduction effect of bonding molecular orbitals).
[0279] Two electrons with opposite spins sink together in this lower common valley, and the total molecular energy Etotal = 2Emolecule.
[0280] The energy difference ΔE = 2E0−2Emolecule>0, this part of the energy is released in the form of photons or heat (corresponding to the exothermic bonding process).
[0281] The geometrically intuitive energy release valley is lower, corresponding to an increase in the depth of the potential energy surface, a smooth and gradual change without abrupt changes; electrons move from the original two higher valleys to a new lower common valley, and excess energy is naturally released; the absolute value of this energy difference is the covalent bond energy of the hydrogen molecule (breaking this bond requires an equal amount of energy to lift the electron back to the original two isolated valley heights).
[0282] Comparison of antibonding orbitals (to avoid confusion): If the electron spins are the same, a double-peak terrain will form (the potential energy is higher than the bottom of the isolated atom valley), the total energy increases, no energy is released, but energy needs to be absorbed instead, and a stable covalent bond cannot be formed.
[0283] Here, a smooth gradient mountain and valley model is used to give a geometric calculation idea of the covalent bond energy of a hydrogen molecule. Throughout the process, it closely adheres to the core of molecular orbitals in quantum mechanics, directly corresponding the "valley depth difference" to the energy value.
[0284] The core correspondence between energy and potential energy terrain: The potential energy value at the bottom of the valley is equal to the energy level of the electron (ground state hydrogen atom: E0 = -13.6 eV, corresponding to the depth benchmark of a single bowl-shaped valley).
[0285] Bonding molecular orbital (σ1s): After the smooth fusion of the valleys of the two atoms, a lower double-bottom saddle-shaped valley, and the corresponding molecular energy level is Eb (Eb < E0, more negative and deeper).
[0286] Antibonding molecular orbital: Corresponding to the double-peak terrain, with energy level Ea (Ea > E0, higher potential energy, no stable electron distribution).
[0287] Hydrogen molecule: Two electrons with opposite spins fill the bonding orbital.
[0288] Definition of bond energy: The minimum energy required to break a covalent bond, equal to the absolute value of the energy released during the bonding process.
[0289] Based on the smooth gradient mountain-valley geometric energy level model, focusing on its actual impact on the core field of chemistry, we give implementable prospects from three levels: teaching, theoretical research, and experimental and material design. Throughout the process, we do not deviate from the core advantages of the model (intuitive visualization, close adherence to quantum mechanics, and expandability).
[0290] I. Chemistry teaching: Thoroughly lower the entry threshold of quantum chemistry
[0291] Visualization of atomic / molecular energy levels: The abstract "energy levels, degeneracy, splitting, molecular orbitals" in traditional teaching can be directly transformed into "valleys, mountains, transition slopes, double-bottom saddle-shaped valleys", enabling students to quickly establish spatial intuition and understand electron behavior without rote memorization of formulas;
[0292] For example, covalent bonds, ionic bonds, and coordination bonds can be uniformly explained by "valley fusion / electron cross-valley migration", replacing complex wave function derivations;
[0293] Reconstruction of course content: For atomic structure and chemical bonds in middle school chemistry, and the basics of quantum chemistry and coordination chemistry in university chemistry, the geometric model can be introduced as a pre-cognitive tool, and then connected with mathematical derivations, significantly improving learning efficiency and reducing students' fear of quantum chemistry.
[0294] II. Theoretical Chemistry: Providing a brand-new "space-energy" thinking scaffold.
[0295] Intuitive Modeling of Multi-Electron Systems and Electron Shielding: The “energy level crossing” of multi-electron atoms (e.g., 4s < 3d) can be intuitively explained by the “squeezing / twisting of valleys by inner electrons”, which provides a more physical picture than the traditional “empirical formula for effective nuclear charge” and helps to build a more accurate semi-quantitative model.
[0296] For example, the valence electron configuration of transition metals and the lanthanide contraction can be transformed into "gradual changes in valley depth and shape", which makes it convenient for theoretical chemists to quickly propose qualitative hypotheses and then verify them using computational chemistry.
[0297] Spatial visualization of reaction mechanisms: The essence of chemical reactions is the transition of electrons between different molecular energy levels. Geometric models can transform "reaction intermediates and transition states" into "temporary valley / peak structures", intuitively presenting electron transfer paths and energy changes, helping researchers quickly locate the rate-determining step of the reaction;
[0298] For example, electron transfer in organic addition reactions and catalytic reactions can be viewed as "electrons jumping from one valley to another along a smooth transition potential slope".
[0299] III. Experimental and Materials Chemistry: Empowering Precise Molecular / Materials Design
[0300] Catalyst design: The active sites of a catalyst are essentially "the energy level topography of reactant molecules". Geometric models can help researchers intuitively design active centers that "can precisely match the valleys of reactants with the valleys of catalysts", reducing trial and error costs.
[0301] For example, hydrogenation reaction catalysts can be designed with a structure that allows the double-bottom valleys of hydrogen molecules to merge smoothly with the valleys of reactant molecules;
[0302] Functional materials research and development: The core of semiconductor, superconducting materials and energy storage materials is the control of energy level structure. Geometric models can transform the "energy level band gap" into the "height difference between valleys and peaks", which makes it easier for engineers to "sculpt" the required energy level terrain through doping, interface control and other means, so as to achieve precise customization of material properties;
[0303] For example, optimizing the bandgap of photovoltaic materials can be viewed as "adjusting the depth and spacing of the valleys so that the photon energy precisely matches the energy required for electrons to cross the valleys".
[0304] We transform the abstract energy problem of quantum chemistry into an intuitive spatial geometry problem, breaking down the cognitive barriers between "theory-experiment-application". This is of great value, especially for teaching and new materials research and development fields that require rapid intuition.
[0305] Boundaries: The model itself is a qualitative visualization tool and cannot replace quantitative calculations in quantum chemistry, but it can serve as a "preliminary hypothesis generator" and "results interpretation tool" for quantitative research.
[0306] Core point of convergence (catalyst + geometric energy level model)
[0307] "Topography matching" design of active sites: The essence of a catalyst is to precisely control the energy level topography of reactant molecules through the electric field topography (peak-valley) of the surface / site. For example, the double-bottomed saddle valley of hydrogen molecules should be smoothly integrated with the "valley" on the catalyst surface, so that electron energy can be easily transferred along the transition slope and the activation energy of the reaction can be reduced.
[0308] For example, in the catalytic hydrogenation of precious metals, the depth of the "valley" formed by surface atoms is just right to match the energy level requirements for the dissociation of hydrogen molecules;
[0309] Visualization of electron transfer pathways: Traditional catalytic mechanism studies can only rely on spectroscopic data to infer electron transfer; the model can directly draw the path of "electrons from reactant valley → catalyst valley → product valley" as a smooth transition slope, intuitively identifying the rate-determining step (the steepest slope).
[0310] Geometric explanation of anti-poisoning and selectivity: Catalyst poisoning is essentially the valley of poison molecules "occupying" the valley of active sites, making it impossible for reactants to match; selective catalysis is the design of the terrain to only allow the valleys of specific reactants to merge (for example, only allowing the valleys of olefins to match, but not the valleys of alkanes).
[0311] The new model can be used to handle the following types of problems.
[0312] Semi-quantitative terrain parameterization: Linking the "valley depth, slope, and width" of the catalyst surface with the reaction activation energy and selectivity, establishing a correlation equation between geometric parameters and catalytic performance, replacing the traditional empirical trial and error;
[0313] Catalyst design reverse engineering: First, determine the required "electron valley energy difference" based on the target reaction, and then reverse design the topography of the catalyst surface (e.g., adjust the valley depth through doping and alloying).
[0314] The closed loop of theory and experiment: The potential energy topography of the catalyst surface is calculated using computational chemistry (DFT), then interpreted using a geometric model, and finally the catalytic performance is verified through experiments, forming a complete chain of "computation-visualization-experiment".
[0315] The aforementioned energy level geometrization model closely follows quantum mechanics, qualitatively mapping energy levels / quantum states / molecular orbitals as a smooth, gradually changing mountain-valley electric field topography, which is used to intuitively explain the electronic behavior in atoms / molecules / catalysis.
[0316] The essence of the energy level geometric model is an explanatory tool, rather than a theoretical system; it has no axioms, hypotheses, and derivation logics of its own and must rely on the theoretical framework of quantum mechanics. This model has great practical value in teaching, qualitative research, and the preliminary concept design of catalyst design, and can quickly establish intuition and lock in key issues.
[0317] For a smooth plane composed of spliced molecules, the wheels of a car can roll continuously over the ditches and bumps formed by the gaps between molecules without getting stuck in the gaps between the molecules. This is because the scale of the car wheels is much larger than the gaps between the molecules on the plane. For the electrostatic field of a proton, we also find in experiments that it is continuous and smooth. This smoothness comes from the fact that the test charge has a scale, and this scale of the test charge is very large, so that the movement of the test charge in the electrostatic field of the proton is not affected by the possible gaps in the electric field intensity of the proton, that is, the test charge will not be trapped in the possible gaps in the electric field intensity. Continuous / smooth does not mean that the microcosm is really continuous, but that the detector is too large to see the microcosmic discreteness.
[0318] The experiment shows that the proton electric field is continuous and smooth. It is not that the electric field itself has no gaps, but that the test charge has a scale, which smooths out the possible microcosmic electric field gaps in the proton electric field, and the test charge will not be trapped by the gaps in the proton electric field.
[0319] The test charge has a scale. The probing particle is not at a mathematical point without volume, but in a small area. If the electric field of a charged particle has a discrete structure at an extremely microcosmic scale, or the field strength has "gaps / mutations", as long as the scale of this microcosmic structure is much smaller than the effective detection scale of the test charge, then what is measured in the experiment will be the smooth field after spatial averaging. Just like the wheels cannot feel the gaps between molecules, those tiny gaps in the proton electric field will not be felt by the test charge with an extremely large volume.
[0320] The above electron electric field model is as follows: An electron is a spherical shell with a charge of e. The electric field intensity inside the shell (r < R) is zero. At the shell surface (r = R), the electric field reaches the maximum value. Outside the shell (r > R), the electric field intensity cannot exceed the maximum electric field intensity. The overall trend still follows the Coulomb inverse square law (i.e., it weakens with the increase of distance), but it does not decrease smoothly, but "undulates at equal distances", that is, periodic oscillations are superimposed on the inverse square background, and the spatial period of the oscillations is fixed (equidistant).
[0321] Because the fluctuations in the electric field intensity are too dense, it still appears as a smooth Coulomb field under current experimental precision; that is, the model is a high-resolution correction of Coulomb's law. Furthermore, since electrons can only reside in specific orbits where multiple matching energy level combinations form energy levels that are defined by the hydrogen atom's spectrum, electrons cannot arbitrarily stop at any position. They can only reside in orbits where the "electric field energy level combination" precisely matches the energy levels of the hydrogen atom's spectrum.
[0322] We need a model of the hydrogen atom in chemistry that can be used to explain the two bonding electrons in a hydrogen molecule. Ideally, these two bonding electrons in the hydrogen molecule should be stationary, as this is a requirement of chemical analysis.
[0323] Each hydrogen atom's electrons are confined to a specific radial energy level shell. When two hydrogen atoms approach each other to form H2: their outer electric field energy levels repel each other, while their inner (facing each other) electric field energy levels match, forming a new shared energy level region. The two electrons fall into this shared region, and because the energy level width is extremely small (Δr→0), they cannot move freely and can only be locked at a discrete position between the two nuclei. As a result, the electrons behave as stationary negative charge clusters, forming an electrostatic equilibrium with the two protons.
[0324] By keeping the two electrons completely stationary, we aim to construct a practical atomic model in chemistry. In a hydrogen molecule, the two bonding electrons are fixed between the two nuclei, forming a stable electrostatic configuration. Similarly, the two protons are also interlocked; each proton is trapped within a vast array of combined electric energy levels, resulting in a specific distance between them. The atomic scale is defined by this stable structure formed by the vast array of minimum energy levels that bind all electrons and protons together.
[0325] The stability criterion for all-particle energy level positioning: An atom or molecule is stable if and only if every proton and every electron therein is simultaneously embedded in a set of self-consistently matched discrete energy levels formed by their respective electric fields.
[0326] This energy level combination is not a pre-existing background, but rather a discrete electric field structure shaped by all charged particles. A stable configuration is equivalent to all particles being stuck and unable to move.
[0327] In the field of chemistry, we don't need to worry about the uncertainty of electrons; we only need to know the particularity of chemical bonds and the relatively stable positions of bonding electrons.
[0328] In chemistry, electrons are stationary negative charges "pinned" to atoms or bonds; their positions are deduced from experimental structures and used to explain and predict molecular behavior.
[0329] Charged particles (protons and electrons) can remain stably stationary in a certain location in space because they are "locked" within a set of discrete energy levels formed by their respective electric fields. This "locking" is the result of the cooperative action of multiple energy levels; a single energy level cannot lock itself in place, only a set of energy levels forming a self-consistent electrostatic equilibrium structure. When the electric field strengths of multiple adjacent energy levels are combined in a specific way, such as symmetrical distribution or gradient matching, a net force equal to the displacement restoring force can be generated at a certain location, effectively "locking" the particle in place. It's like a ball that is only stable when placed at the bottom of a groove, which is formed by multiple steps.
[0330] The core objective of chemical analysis has never been the probability of where electrons are located, but rather how atoms are connected, the length of bonds, the shape of molecules, and how reactions break and form bonds. Similarly, catalysis in chemistry involves using the atoms of a catalyst to alter the energy level channels at which atoms participating in a chemical reaction are positioned. That is, the catalyst uses its own electric field to temporarily create a matching energy level channel, allowing reactant particles to smoothly migrate from their old positions to the new ones. Simultaneously, the catalyst provides a temporary support structure to receive the displaced electrons / protons, preventing them from wandering off.
[0331] The Lorentz transformation has two particularly important physical quantities that require in-depth interpretation: the Lorentz transformation at the speed of light and the Lorentz transformation at superluminal speeds.
[0332] For the Lorentz transformation at the speed of light, we can obtain the following relationship:
[0333] Suppose that inertial frame S′ moves at a constant velocity v along the x-axis relative to inertial frame S, and the origins of the two frames coincide at t=t′=0. The basic formula for the Lorentz transformation is:
[0334]
[0335] Then we take a step forward, making this light-speed reference frame exceed the speed of light. We're just viewing things from a faster-than-light perspective; we don't actually need to move faster than light. When we view things from a faster-than-light perspective, we can obtain an imaginary γ. Then, by preserving this imaginary γ in the Lorentz transformation, we can obtain:
[0336]
[0337] At this time x′ and All of them will become imaginary numbers, because the result of multiplying a real number by an imaginary number (γ) is necessarily an imaginary number.
[0338] Then let's shift our thinking and consider that we are actually beings in imaginary space, that is, we believe that imaginary space is the physical reality. Let's ignore the current theories and imagine real space. We will find that in this imaginary world, the speed of light c is not the upper limit of speed, but the lower limit of speed. Any moving object with mass cannot have a speed lower than the speed of light c.
[0339] Then, let's move to a higher level, examining the real and imaginary number spaces equally, rethinking the Lorentz transformation, and comprehensively interpreting the implications of exceeding the speed of light. At this point, we'll discover that when we treat the real number space equally... and imaginary space Viewed as two dual projections of the same high-dimensional spacetime, and no longer presupposing that only real numbers are physical, the Lorentz transformation is no longer a one-sidedly restricted transformation, but a dual-symmetric transformation that crosses the speed of light plane. We can reconstruct this framework based on spacetime duality and interpret the essence of "crossing the speed of light"—it is not an infinite increase in speed, but a leap in spacetime properties.
[0340] To make the real and imaginary number spaces equal, the core is to rewrite the metric basis of the Lorentz transformation, transforming "imaginary numbers" into real number metrics of the dual space, thus avoiding the artificial distinction between "physical / non-physical".
[0341] Defining dimensionless velocity and dual factor, first introduce normalized velocity. (β is any real number, which can be greater than 1), then define the dual sign factor. :
[0342] =
[0343] At this point, the previously divergent / imaginary Lorentz factors can be rewritten as unified real dual factors. :
[0344]
[0345] Thus, we can equivalently transform the "imaginary coordinates" of the imaginary space into the "space-like coordinates" of the dual real space, and the imaginary and real spaces will henceforth share the same set of real mathematical language with the real space.
[0346] based on We can write a symmetric transformation formula across the plane of the speed of light, no longer distinguishing between real and virtual:
[0347]
[0348] When β < 1 (real space): η = 1, the transformation formula is completely consistent with the Lorentz transformation in special relativity, describing the spacetime transformation of a subluminal inertial frame; when β > 1 (imaginary space): η = −1, the transformation formula becomes , This describes the spacetime transformation of a faster-than-light inertial frame of reference.
[0349] The speed of light is a boundary, not a barrier. β=1 corresponding to the speed of light is no longer a speed limit, but rather a symmetrical boundary between two dual spaces. Like the two sides of a mirror, the spacetime laws on both sides are strictly dual; neither side is more real.
[0350] The symmetrical picture of dual spacetime: The equal weighting rule of real and imaginary number spaces is that, within this unified framework, real number space... and imaginary space The physical laws governing it are mirror-symmetric.
[0351] The symmetric core velocity boundary c is the upper velocity limit, which no massive particle can reach. It is the lower velocity limit, which no massive particle can go below. It is the dual boundary.
[0352] The Lorentz effect, where the positions of spacetime coordinates are interchanged, causes length contraction, resulting in a shorter length for moving objects; a moving clock slows down. Dual length contraction: the "spacelike length" of a moving object shortens; dual clock slowing is a moving "spacelike clock." The slowing effect has the same form, only the definition of spacetime measurement is reversed. Causal law: information transmission speed ≤ c, causality is unidirectional and irreversible (cause and effect). Dual causality: unidirectional and irreversible (still cause and effect within its own space, but dual to the causal direction of the real number space). Causality is self-consistent within its own space; causal reversal is only observed when crossing the plane of the speed of light.
[0353] The core concept of exceeding the speed of light is not acceleration, but rather a leap in spacetime.
[0354] From a higher-dimensional perspective, exceeding the speed of light does not mean that a particle accelerates to a certain speed within the same space. Rather, the particle jumps from one dual space to another dual space.
[0355] The essence of velocity is the slope of spacetime projection. The velocity v we observe is actually the projection slope of higher-dimensional spacetime onto our own space. Subluminal particles are projections of higher-dimensional spacetime onto real space, while superluminal particles are projections of the same higher-dimensional spacetime onto imaginary space. The difference lies in the projection direction, not the magnitude of the velocity. It's like a vector: projected onto the x-axis, it's subluminal; projected onto the y-axis, it's superluminal. The vector itself remains unchanged; only the observed projection surface changes.
[0356] The speed of light plane is the critical angle of projection, corresponding to the speed of light, β=1. It is the critical direction of projection in high-dimensional spacetime. When the projection direction is exactly parallel to the speed of light plane, what we see is a photon (v=c). It belongs neither to the real space nor the imaginary space, but is the boundary particle between the two spaces.
[0357] The observational effect of superluminal particles in real space. Causal reversal: If a superluminal particle in imaginary space leaves an observational trace in real space, we will see the phenomenon of causal reversal, such as seeing a bullet fall first and then seeing a gun fired. However, this is not because the law of causality has failed, but simply because its law of causality is based on duality and is incompatible with our spacetime measurement.
[0358] The Lorentz transformation is essentially a projection transformation of high-dimensional spacetime.
[0359] The framework we reconstructed is intended to expand the perspective of relativity.
[0360] Special relativity is a special case of this framework in η=1 (real space). Its upper limit on the speed of light is because we assume that we only observe our own projected space. Imaginary space is not a mathematical game, but a physical existence on par with real space, only its spacetime measurement is opposite to ours. The meaning of exceeding the speed of light is that the spacetime projection direction of particles has been reversed, from timelike projection to spacelike projection. This is a quantum leap process, not the result of continuous acceleration.
[0361] The value of this concept lies in the fact that it maintains the mathematical consistency of the Lorentz transformation while breaking the inherent bias that real numbers are the only physical phenomena. It provides a logically sound explanatory framework for faster-than-light phenomena, with dual symmetry mathematical constraints and a self-consistent physical picture.
[0362] Imaginary space is used to interpret the imaginary fluctuations in the Schrödinger equation. By combining the imaginary fluctuation nature of the Schrödinger equation with the dual spacetime framework (real space / imaginary space in equal measure), it breaks the traditional understanding that imaginary numbers are merely mathematical tools. It connects the probability amplitude and phase, wave-particle duality of quantum mechanics with the spacetime duality of relativity, deriving a new physical picture of quantum fluctuations as projections of higher-dimensional dual spacetime. Specifically:
[0363] First, establish the core connection: the imaginary number in the Schrödinger equation is not a mathematical trick, but a physical projection of the imaginary space. The standard form of the Schrödinger equation is:
[0364]
[0365] Traditional quantum mechanics treats the imaginary number i as a mathematical tool to describe phase evolution, ensuring the probabilistic amplitude coherence of the wave function ψ (without i, there is no quantum interference or superposition state), but does not endow it with physical reality.
[0366] However, our dual spacetime framework can provide the following physical interpretation for the imaginary number i:
[0367] The structure of the wave function corresponds to the projection amplitude quantum wave function of dual spacetime, which can be decomposed into a real part and an imaginary part:
[0368]
[0369] We map it to the projected amplitude of real spacetime + imaginary spacetime, with the real part... For particles in real spacetime ( The projected amplitude (at sublight speed) corresponds to the classically observable particle nature; the imaginary part For particles in imaginary spacetime ( The projected amplitude of the wave function (superluminal speed) corresponds to the unobservable wave nature of quantum mechanics. The normalization condition of the wave function is essentially the conservation of the total projection of the quantum in dual spacetime. The quantum is either manifest in real spacetime or invisible in imaginary spacetime, and the sum of the two is 1.
[0370] The physical meaning of the imaginary number i is the switching operator of spatiotemporal projection.
[0371] The left side of the Schrödinger equation This describes the evolution of the wave function's phase over time. From a dual spacetime perspective, this... It's the switching symbol for spacetime projection, causing the particle's projection to oscillate between real and imaginary spacetime. This is the physical root of quantum phase. For example, the wave function of a free particle.
[0372]
[0373] Its phase The change is essentially the periodic switching of the projection ratio of particles in imaginary spacetime. When the phase is 0, the projection is entirely in real spacetime (particle nature); when the phase is π / 2, the projection is entirely in imaginary spacetime (wave nature).
[0374] Under the dual Lorentz transformation, quantum leaps are superluminal leaps of spacetime projection. In our new physical model, exceeding the speed of light is not an acceleration of classical particles, but rather a switching of spacetime projections of quantum states, which provides a new explanation for the instantaneous nature of quantum leaps.
[0375] The speed of light plane is the boundary between quantum and classical mechanics. The point where the dual metric sign is reversed (η changes from 1 to -1) corresponding to the speed of light c is precisely the critical plane between quantum fluctuations and classical particles.
[0376] When the particle is projected into real spacetime It exhibits classical particle properties, follows the Lorentz transformation of special relativity, has unidirectional causality, and can be directly observed; when the particle is projected onto imaginary spacetime... It exhibits quantum wave properties, follows dual Lorentz transformations, and has dual causality. It cannot be directly observed and can only be perceived indirectly through effects such as interference and diffraction.
[0377] The essence of quantum leap is the projection switching of virtual spacetime.
[0378] Traditional quantum mechanics cannot explain why quantum leaps occur instantaneously; it seems that an electron can move from a low energy level to a high energy level without any time constraint. However, interpreting this through the framework of dual spacetime, a quantum leap is not a movement of a particle within the same spacetime plane, but rather an instantaneous switching of projection planes. The electron switches from a real spacetime projection to an imaginary spacetime projection, and then back again. This switching process occurs on the dual spacetime side of the light-speed plane, and is not limited by the speed of light in real spacetime, thus appearing instantaneous in our observations. More importantly, this switching process satisfies the mathematical consistency of the dual Lorentz transformation; the speed of the projection switching is not a classical speed, but rather a transition speed of spacetime topology, which is incomparable to the speed of light in real spacetime.
[0379] Quantum entanglement is a nonlocal correlation in imaginary spacetime. The action-at-a-distance nature of quantum entanglement is a core contradiction between relativity and quantum mechanics; the correlation speed between two entangled particles far exceeds the speed of light, violating the causality law of special relativity. However, within our framework, this contradiction can be resolved.
[0380] The imaginary spacetime projection of entangled particles is a global projection of the same high-dimensional spacetime. They are an indivisible whole in imaginary spacetime, without the concept of distance. The metric of imaginary spacetime is spacelike, the spatial components are positive, and the definition of distance is opposite to that of real spacetime.
[0381] When we measure one of the particles, we are essentially forcing its projection to switch from imaginary spacetime to real spacetime. Since the two particles are a whole in imaginary spacetime, the projection of the other particle will switch synchronously instantaneously. This synchronization occurs in imaginary spacetime and does not transmit any classical information. Therefore, it does not violate the relativistic principle that the speed of information transmission does not exceed the speed of light. This provides a spacetime-level physical explanation for quantum nonlocality, rather than remaining at the level of mathematical probability correlation.
[0382] The imaginary numbers in the quantum world are not mathematical tools, but the physical reality of imaginary spacetime. The imaginary part of the wave function corresponds to the projection of superluminal spacetime, and the phase evolution corresponds to the oscillation of the projection ratio. Wave-particle duality is two manifestations of spacetime projection: particle nature is the projection of real spacetime, and wave nature is the projection of imaginary spacetime. The two are switched through the light-speed plane. The strange phenomena of quantum leaps and entanglement are the inevitable result of the duality of imaginary spacetime. Leaps are the projection switching, and entanglement is the overall correlation of imaginary spacetime. Neither of them violates the logical self-consistency of the unified framework.
[0383] We use the same dual spacetime framework to unify the relativistic view of spacetime and the wave view of quantum mechanics, breaking the long-standing disconnect between the two. Traditional theories either treat relativity and quantum mechanics as two independent systems and regard imaginary numbers as symbols without physical meaning.
[0384] Simplified model of quantum entanglement under virtual spacetime projection
[0385] We take an entangled system of two spin 1 / 2 particles as the research object (the most typical case of entanglement), ignore the complex influence of spatial degrees of freedom, and focus only on the virtual-real projection correlation of spin states. In this way, we construct a simple model to intuitively present the core idea that "quantum entanglement is the overall correlation of imaginary spacetime".
[0386] The model assumes that two identical particles A and B constitute an entangled system, considering only the spin degree of freedom, and that the total spin is 0 (spin singlet, the most stable entangled state).
[0387] The spacetime projection correspondence, the real part of the wave function corresponds to the particle in real spacetime. The projected amplitude embodies the "observable particle nature"; the imaginary part corresponds to the particle in imaginary spacetime. The projected amplitude reflects the wave-like correlation that cannot be directly observed.
[0388] Projection conservation means that the total projection probability of a particle in dual spacetime is 1, satisfying the normalization condition of quantum mechanics; the correlation in imaginary spacetime does not transmit classical information and does not violate the constraints of relativity.
[0389] Real-imaginary decomposition of entangled wave functions:
[0390] 1. Wave function of traditional spin singlet
[0391] The wave function of the entangled state (spin singlet) of two spin 1 / 2 particles is:
[0392]
[0393] in Indicates spin up. It indicates spin down; the characteristic of this wavefunction is that it cannot be decomposed into the product of the single-particle wavefunctions of particle A and particle B, reflecting the non-local correlation between the two particles.
[0394] 2. Rewriting the wave function by introducing virtual and real projections.
[0395] Combining our dual spacetime framework, the wave function is decomposed into a superposition of real and imaginary projections.
[0396] i is the spatiotemporal projection switching operator):
[0397]
[0398] Real part projection (real spacetime, observable): corresponds to "potential observational results of particle nature", in the form of:
[0399]
[0400] The real part of the wave function is a superposition of separable states, corresponding to the determined spin state of the particle in real spacetime after measurement.
[0401] Imaginary projection (imaginary spacetime, not directly observable): corresponds to "nonlocal correlation of wave-like behavior", in the form of:
[0402]
[0403] The imaginary wave function is a purely entangled state, which is a direct manifestation of the inseparable whole of two particles in imaginary spacetime.
[0404] 3. The spatiotemporal significance of normalization conditions
[0405] Taking the square of the modulus of the total wave function satisfies the normalization of quantum mechanics:
[0406]
[0407] The physical meaning of the above formula is that the projection probability of a particle in real spacetime + the projection probability in imaginary spacetime = 1. Before measurement, the quantum is "diffuse" in two spacetimes at the same time; after measurement, the projection will completely collapse into one of the spacetimes.
[0408] III. Interpretation of Projection Switching in the Measurement Process
[0409] The most bizarre aspect of quantum entanglement is that measuring the spin of particle A instantly determines the spin of particle B, regardless of the distance between the two particles. Our model can clearly explain this process; the core is the instantaneous switching of the projection plane, rather than faster-than-light information transmission.
[0410] Before measurement, the projection of the imaginary part of the total wave function dominates. The two particles in imaginary spacetime are a unified whole without the concept of spatial distance. The metric of imaginary spacetime is spacelike, the spatial component is positive, and distance loses its classical meaning. At this time, the spins of particles A and B have no definite values, only an upward or downward correlation trend. This correlation is stored in imaginary spacetime and does not involve the transmission of any classical signals.
[0411] During measurement, the projection surface switches to real spacetime. When we perform spin measurement on particle A, we are essentially applying a real spacetime projection operator, forcing the projection of the total wave function to switch from imaginary spacetime to real spacetime.
[0412]
[0413] This switching process is topological and does not consume time because the switching occurs in imaginary spacetime, which is not limited by the speed of light in real spacetime.
[0414] After measurement, the synchronous collapse of the two particles reveals the separated-state characteristics of the real part of the wave function once the projection switches to real spacetime.
[0415] If the spin of particle A is measured to be upward... Then the spin of particle B must be downward. ;
[0416] If the spin of particle A is measured to be downward... Then the spin of particle B must be upward. .
[0417] The essence of this synchronous collapse is the overall correlation between the two particles in imaginary spacetime. After being projected onto real spacetime, it manifests as a definite spin correlation. It is not that particle A sends a superluminal signal to particle B, but rather that the two have been the same whole in imaginary spacetime from the beginning, and the correlation result is naturally presented after the projection switch.
[0418] IV. The core physical essence of the model
[0419] This model resolves the contradiction between relativity and quantum mechanics. In traditional theory, the hyper-distance correlation of quantum entanglement seems to conflict with the relativistic upper limit of the speed of light. In this model, this contradiction is resolved. The correlation in imaginary spacetime does not transmit classical information; only the result of the projection switching will appear in real spacetime, which fully conforms to the relativistic principle that the speed of information transmission does not exceed the speed of light.
[0420] The spacetime origin of wave-particle duality. The wave-like correlation before measurement corresponds to the imaginary spacetime projection, while the particle-like deterministic state after measurement corresponds to the real spacetime projection. The essence of wave-particle duality is the projection switching effect of particles in dual spacetime, rather than two properties of particles.
[0421] The physical nature of quantum entanglement. Entanglement is not a mysterious probabilistic correlation, but rather the holistic existence of particles in superluminal imaginary spacetime. The non-local correlations observed in real spacetime are merely projections of high-dimensional dual spacetime onto low-dimensional spacetime.
[0422] The aforementioned dual spacetime framework (equal weighting of real and imaginary space, Lorentz transformation extension), combined with the classical model of quantum entanglement, is a physical interpretation and reconstruction. Classical quantum mechanics has a wave function form of spin singlet, breaking the traditional understanding that imaginary numbers are merely mathematical tools.
[0423] In existing quantum mechanics, the imaginary number *i* in the Schrödinger equation is merely a mathematical symbol used to describe phase evolution, lacking physical reality. Our core innovation, however, is to imbue the imaginary number with spatiotemporal meaning, with the imaginary part of the wave function directly corresponding to the imaginary spacetime. In the physical projection, imaginary numbers are no longer operators, but rather "labels for spatiotemporal attributes".
[0424] The new model gives the nonlocality of quantum entanglement a spatiotemporal root. Traditional quantum mechanics reduces entanglement to a nonlocal correlation of probability amplitudes, which only stays at the mathematical level and cannot explain why the collapse is instantaneous. In the new model, the essence of entanglement is the holistic existence of particles in imaginary spacetime. The metric of imaginary spacetime is spacelike and does not have the classical concept of distance. Two entangled particles are an inseparable whole in imaginary spacetime.
[0425] The instantaneous collapse after measurement is not a faster-than-light transmission of information, but a topological effect of the projection surface switching from imaginary spacetime to real spacetime, and for the first time, it resolves the core contradiction between relativity and quantum mechanics using the same framework.
[0426] The theory of relativity requires that the speed of information transmission does not exceed the speed of light. Quantum entanglement, with its hyper-distance correlation, seems to violate this principle, a problem that has remained unsolved for a century. However, in this model, the contradiction is completely resolved.
[0427] The correlation in imaginary spacetime is a holistic correlation of non-classical information, transmitting no observable classical signals; the projection switching after measurement is a spacetime topological transition, not signal propagation in the classical sense, and fully conforms to the constraints of relativity. This approach of integrating quantum mechanics and relativity through spacetime duality is a completely new path, distinct from other unified theories such as string theory and loop quantum gravity.
[0428] Within the dual spacetime framework, electron spin is no longer an intrinsic property without classical counterparts, but rather a projection topological effect of electrons in virtual-real dual spacetime. Core characteristics such as the half-integer nature of spin, 720° rotational invariance, and g-factor anomaly can all be intuitively physically explained from the topological logic of spacetime projection, which is fundamentally different from the purely mathematical setting of traditional quantum mechanics.
[0429] The spin angular momentum of an electron is a topologically conserved quantity of its wave function projected between real and imaginary spacetime; the spin up / down corresponds to the two dual topological orientations of the projected rotation, which are directly linked to the sign reversal of the spacetime metric.
[0430] The half-integer nature of spin originates from the topological transition rules of virtual and real projections. A 180° rotation of the projection corresponds to a reversal of the spacetime metric sign. A 360° rotation only completes a half-transition, and it takes 720° to return to the initial projection state. This is an inevitable result at the topological level and is not a quantum singularity.
[0431] Topological logic:
[0432] Rotating 180° switches the projection from real spacetime to imaginary spacetime (metric sign reversed). Rotating 360° returns the projection to real spacetime, but the metric sign reverses twice, resulting in a negative sign for the wave function. The wave function only returns to its original state after rotating 720°. This is the physical essence of 720° invariance, an inevitable result of spacetime topology, not a mathematical abstraction.
[0433] Dual spacetime mechanism of spin magnetic moment and g factor (g≈2)
[0434] Traditional theory: The electron g factor (≈2) is considered a "relativistic correction" without an intuitive physical picture.
[0435] Dual spacetime interpretation: The spin magnetic moment is not the magnetic moment generated by the rotation of the charge, but the spacetime magnetofluid effect of the rotation of the virtual and real projections. The projection rotation will generate an equivalent "topological current" in real spacetime, which in turn excites the magnetic moment.
[0436] The root cause of g factor ≈ 2 is that the projection rotation simultaneously couples the magnetic field of real spacetime with the dual magnetic field of imaginary spacetime, with a coupling coefficient of 2. This is a direct result of spacetime topological coupling and does not require complex corrections by Thomas precession.
[0437] Spin correlation in quantum entanglement: the wholeness of virtual and real projections
[0438] Physical mechanism: The spin correlation of entangled electron pairs originates from their overall projection in imaginary spacetime. Since there is no classical distance in imaginary spacetime, the projected rotations of the two electrons are two components of the same topological operation. The "instantaneous collapse" during measurement is the topological synchronization effect of the projection switching from imaginary spacetime to real spacetime.
[0439] The nonlocality of spin entanglement is a real-spacetime projection of the imaginary spacetime as a whole. It does not transmit classical information and is fully compatible with relativity.
[0440] Within the dual spacetime framework, electron spin is essentially a physical property of spacetime topology, rather than a purely mathematical construct. It anchors the abstract concept of spin in quantum mechanics to the topological logic of virtual spacetime projection, which can both explain existing experimental phenomena and derive verifiable new predictions, providing a completely new perspective on the physical nature of spin.
[0441] By switching to a light-speed frame of reference to observe a stationary point particle, this originally stationary point particle (such as an electron) will transform into a field of matter moving at the speed of light. The original point particle, such as a stationary electron, will undergo a change in its physical form in that new frame of reference through this switch at the speed of light, becoming a field of matter moving at the speed of light.
[0442] By switching to a frame of reference moving at the speed of light, electrons "spread out" to become an electric field; while the originally diffuse electric field "converges" into charged particles in our frame of reference. This is actually a duality reversal. The electric field is not "emitted," but rather "uncondensed electrons."
[0443] In the light-speed reference frame (the body layer): there is no point-like "electron", but only a static electromagnetic field that is distributed throughout the entire space; this field itself is the "form of existence of electric charge", and does not require a "source".
[0444] In a subluminal frame of reference (phenomenal level): when we introduce time, causality, and a local observer, this global field undergoes localized condensation at a certain point in spacetime, manifesting as "electrons," while the remaining uncondensed portion manifests as the "electric field surrounding the electrons." In other words, the electric field is not "emitted" by the electrons, but rather represents the portion of the electrons that are "not fully condensed."
[0445] It's not particle → field, but rather field → (local condensation) → particle + (uncondensed portion) → electric field.
[0446] This image explains why the electric field exists instantaneously: because the electric field is inherently present; it is the entity itself. Particles are merely its "singularities" or "vortices." There's no need for propagation because it never separates.
[0447] The reason why charge is conserved is because the "charge integral" of the total field is constant. The amount of charge condensed into particles corresponds to the amount of residual field, but the total amount remains unchanged.
[0448] If an electron is essentially an excitation of the global field, then it is not surprising that it "passes through both slits simultaneously" in the double-slit experiment, since it is inherently in the global field.
[0449] Using a reference frame moving at the speed of light, the electric field of an electron, which is spatially distributed, can be contracted to a single point, becoming a new particle.
[0450] Suppose an electron undergoes uniformly accelerated motion along the positive X-axis under the influence of an electric field, and the direction of the force acting on the electron is also along the positive X-axis. This electron radiates a photon. Then, the state of this photon would be as follows:
[0451] The polarization direction of this photon is parallel to the X-axis and is linearly polarized. The "jittering" direction of the light (the direction of the electric field E) must be perpendicular to the direction of light flight. The direction of motion of the photon can be the Y-axis or the Z-axis, that is, the direction of motion of the photon is perpendicular to the X-axis.
[0452] For an electron accelerating linearly in a vacuum, it can emit only one photon. This single photon is emitted along the Y-axis, and the electron is pushed off the X-axis by a reaction force. In the real physical picture, after emitting a photon, the electron no longer undergoes strictly linear, uniformly accelerated motion, but rather curves, similar to a parabola, but affected by radiation damping. For low-energy acceleration, such as electrons accelerated by a common electric field, the momentum carried by a single photon is negligible, and the electron's deflection angle is almost unmeasurable, so it can be approximated as still moving in a straight line.
[0453] In an ideal vacuum, linear acceleration, and single-radiation model, an electron will inevitably be deflected after emitting a photon.
[0454] For the internal electric field fluctuations of a photon, the photon's electric field strength starts from zero, reaches a peak, and then drops back to zero. This contour is called the "envelope." Its shape depends on how long the electron acceleration process lasts.
[0455] Within this envelope, the electric field oscillates wildly and rapidly. The frequency of this oscillation is the frequency of the photon. For uniformly accelerated motion, this frequency is not singular but contains a spectrum (the result of a Fourier transform), but we can approximate it as a dominant frequency oscillating.
[0456] In other words, the photon moves along the Y-axis, while the electric field vibrates back and forth in the X-axis. The amplitude of this vibration is not always constant; it starts with a gentle touch (the beginning), then a sharp jolt (the peak), and finally a gentle glide (the end). A real photon (especially in localized events like single-electron radiation) is more like a wave packet or pulse. Its amplitude varies with time.
[0457] An observer moving in sync with a photon would perceive its phase as constant; instead of a wave, they would see a fixed phase vector. They would observe a static, solidified electromagnetic field structure. This structure exists in space (with an electric field component), but it doesn't change over time. The space around the photon is compressed into a plane (perpendicular to the direction of motion), with zero distance between it and the surrounding area. In other words, if light were tracking a photon at its speed, the photon would have no vibrational frequency. It has magnitude (amplitude) and polarization direction, but it doesn't oscillate. The photon has an electric field amplitude, which is fixed, while its electric field vector rotates. Linear polarization causes the vector to stretch and contract along the X-axis; circular polarization causes the vector to rotate in a plane perpendicular to the direction of propagation.
[0458] If a photon is circularly polarized, even if time stands still, the information of its rotation still exists in the form of a geometric spiral. The rotation of a photon is not the kind of mechanical motion we understand in the macroscopic world, but an intrinsic, quantum property. Special relativity can calculate that the car has become shorter and the clock inside the car has slowed down, but it cannot calculate whether the wheels themselves are rotating.
[0459] For photons, translational motion can be frozen by relativity, time stands still, but the rotation (spin) of a photon is an intrinsic quantum number that does not depend on the external passage of time. Therefore, special relativity does not have the effect of rotation vanishing because rotation is not within its jurisdiction at all; it is a concept of quantum mechanics.
[0460] In reality, photons are spin-1 particles, meaning that even if time were to stand still, their geometry would not be spherical; they must retain some directionality. If the rotation of photons truly disappeared due to "light-speed motion," then all photons should become identical dead spheres, and polarization would be impossible. But the fact is, polarization is ubiquitous. The rotation (spin) of a photon is its defining characteristic, just like its energy and momentum, eternally present regardless of whether time is still.
[0461] Frequency is a necessary parameter for waves, but particles, namely photons, cannot have waves. The definition of a particle dictates that it cannot have waves or frequencies. In reality, photons are particles, and these particles are surrounded by a quantum density field, which is what causes the wave-like behavior. However, photons as particles do not wave-like behavior and do not need to have frequencies.
[0462] A photon is a real energy packet that travels in a straight line; a photon is a particle-like coordinate point whose position does not fluctuate.
[0463] The photon density field is the quantum cloud or quantum density field that permeates space outside the photon. In the double-slit experiment, the photon density field passes through both slits simultaneously, causing interference and diffraction (wave-like behavior). The photon density field is responsible for vibration, rotation, and frequency; it draws circles and spirals in space. The reason photons appear as waves is because they tend to fall at the maximum value of the photon density field. When the photon density field interferes, the point where the photon falls also interferes.
[0464] It should be noted that if the relative motion is only in the X-axis direction, and there is no relative motion in the direction perpendicular to the motion, such as the Y-axis direction, then according to the Lorentz transformation, there is no length contraction effect in the Y-axis direction, and therefore no time dilation effect in the Y-axis direction.
[0465] In other words, if we only consider the vertical direction itself, there is indeed no reason for time to slow down. This is because the length in the vertical direction remains unchanged, the direction of force propagation remains unchanged, the acceleration structure remains unchanged, and the distance traveled by particles remains unchanged. From a purely local perspective, physics has not changed at all in the vertical direction, so the clock should not be slow.
[0466] The logic of special relativity is: the speed of light is constant, leading to the Lorentz transformation. The Lorentz transformation requires time to slow down uniformly, regardless of whether it's perpendicular or parallel; the time factor γ must be the same. This then implies that the mass / force in the perpendicular direction must become γ times. In other words, the time transformation comes first, and then γ is forcibly applied to dynamics, rather than dynamics changing first and naturally leading to time slowing.
[0467] However, if space hasn't contracted and the path hasn't changed in the vertical direction, why should time slow down? This isn't dynamics; it's a mathematical constraint. But mathematical consistency doesn't equate to physical reality. If there's no length contraction in the vertical direction, then there shouldn't be time dilation. The vertical time dilation in relativity is a mathematical result of coordinate transformations, not a necessary physical consequence. That is, the requirement of "uniform time dilation in all directions" in special relativity is directly invalid. Time dilation can only occur parallel to the direction of motion; it remains completely unchanged in the vertical direction. The time views of both special and general relativity are entirely built upon the mathematically mandated uniform transformation in all directions.
[0468] Suppose we have a clock constructed from a perfectly elastic sphere moving at a constant velocity V within a container. The sphere reciprocates along either the Y-axis or Z-axis at a constant velocity V. The time taken for one reciprocating motion is constant and can be read. This uniformly elastic sphere clock constitutes a clean and logically sound thought experiment.
[0469] The entire device moves at a uniform speed *u* along the X-axis, while the small ball moves at a uniform linear speed along the Y-axis. It is a perfectly elastic collision with uniform linear motion. One round trip takes the same amount of time as one unit of time. There is no friction, no energy loss, and it is perfectly elastic.
[0470] Since there is no length contraction perpendicular to the direction of motion (Y direction), and no change in spatial structure in the perpendicular direction, the rhythm of the physical process remains unchanged. For the ball, the distance L of the vertical motion remains constant, and the speed before and after the collision remains unchanged. Perfect elasticity means there is no energy loss, no velocity decay, and uniform reciprocating motion.
[0471] Period: T=2L / V
[0472] Since L remains constant (no length contraction) and V remains constant (uniform velocity, elasticity), the period T must be a constant.
[0473] This experiment demonstrates that the special relativistic view of time is invalid, because the period of the ball clock remains absolutely constant in the direction perpendicular to the motion under uniform linear motion. This means that in an inertial frame of reference, a physical clock perpendicular to the direction of motion does not experience time dilation.
[0474] Special relativity requires that time must be slowed down by a factor of γ, regardless of the clock or direction.
[0475] This directly contradicts and is irreconcilable with the results of the small ball clock thought experiment. This small ball clock thought experiment undermines the core of relativity: the unified transformation of time.
[0476] If there is no length contraction perpendicular to the direction of motion, the laws of mechanics remain unchanged in the inertial frame, and the magnitude of the velocity of a perfectly elastic collision remains constant, then the period of an elastic ball clock moving perpendicularly is strictly constant, independent of the overall uniform velocity, and there is no time dilation effect.
[0477] Corollary: The statement in special relativity that "all frames of reference share a uniformly slowed time" is invalid. Time is not geometric; it is the rhythm of dynamical processes.
[0478] Extending this further to general relativity, if we place this small spherical clock in a gravitational field, gravity will cause the sphere to bounce back and forth tangentially (perpendicular to gravity) along the radial direction r. Tangential space remains undistorted, the path length is constant, and the tangential direction is not affected by gravitational components, so the period remains unchanged. Therefore, perpendicular to the gravitational field direction, time is neither non-uniform nor changes in speed.
[0479] Time equals the period of a physical process. Space remains constant → period remains constant. There is no length contraction / distortion in the vertical direction → clocks remain absolutely constant. Time dilation is not a universal time effect, but only a dynamic effect in the horizontal direction.
[0480] The elastic spherical clock is the cleanest, most direct, and most unavoidable test of special relativity for determining "no time dilation in the perpendicular direction." Its core argument is:
[0481] No length contraction perpendicular to the direction of motion → The ball's round-trip distance remains unchanged; perfectly elastic collision → The velocity in the perpendicular direction remains unchanged; Period T → Distance remains unchanged + Velocity remains unchanged ⇒ Period remains absolutely unchanged.
[0482] If there is no length contraction in the vertical direction, then the period of a uniformly elastic sphere clock will remain strictly unchanged, and the time view of "uniform time dilation in all directions" of special relativity will not hold.
[0483] Based on the premise that relativity itself acknowledges no spatial contraction / geometric distortion in the vertical direction, we construct a perfectly elastic spherical clock moving perpendicular to both the direction of relative motion and the direction of the gravitational field. Through purely dynamical derivation, we prove that the period of such a clock is strictly constant and that no form of time dilation occurs. This conclusion forms an irreconcilable logical contradiction with the core prediction of relativity—that "spacetime is curved globally and time is uniformly slow in all directions"—revealing that time is not a universal geometric property, but rather a local physical effect dependent on the clock's dynamic structure and direction of motion.
[0484] Time dilation is one of the core conclusions of relativity. Special relativity states that relative motion in an inertial frame of reference will cause time to slow down uniformly in all directions, while general relativity posits that gravitational fields cause spacetime to curve as a whole, resulting in non-uniform changes in the rhythm of all clocks. Existing theoretical derivations are mostly based on spacetime coordinate transformations, with very few tests conducted from the perspective of the dynamic mechanisms of specific clocks.
[0485] We use a rigid container plus a perfectly elastic sphere as an ideal clock model, strictly following the spatial geometry conclusions of relativity itself, and only through the basic physical relationships of length, velocity, and period to complete the logical test of the unified time view of relativity.
[0486] To refute the viewpoint of this thought experiment, it must first be proven that length contraction occurs in the vertical direction, or that a perfectly elastic collision changes the speed, or that the distance and speed remain constant, but time can be forcibly altered.
[0487] Any of the above points conflicts with the self-consistency of relativity; therefore, the conclusion of this thought experiment is logically irrefutable.
[0488] Our thermodynamic analysis can be built upon three mutually perpendicular temperature-scale coordinate axes, thereby establishing a pure, fundamental three-dimensional temperature-scale space. In this theory, the most basic stage of the universe is this three-dimensional space composed of three mutually perpendicular temperature-scale coordinate axes: , ,
[0489] This is a theoretical framework based on heat. We construct it as a first principle.
[0490] , , These are fundamental dimensions, which are independent, orthogonal, and irreducible.
[0491] We then introduce time and thereby define the velocity and acceleration of thermal motion, which will allow the temperature scale space theory to move from static geometry to a dynamic system, becoming a complete thermokinematics.
[0492] The state of the system at any time t is described by the position vector:
[0493]
[0494] The thermal velocity vector is the first derivative of the temperature scale with respect to time:
[0495]
[0496] The physical meaning is to describe the rate and direction of change in the thermal state of the system.
[0497] We then define the thermal acceleration vector as the derivative of the thermal velocity with respect to time (i.e., the second derivative of position):
[0498]
[0499] The physical meaning is to describe how the rate of thermal change changes.
[0500] We will now directly introduce a thermal point, which is a minimum hot spot with mass m, as the object we use to describe thermal motion.
[0501] Definition of a thermal point: a fundamental entity with thermal inertia and mass m, whose state is determined by its position in a three-dimensional temperature-scaled space. A complete description. It is the smallest carrier of thermal motion, not involving spatial location, volume, or material composition—a purely thermal unit.
[0502] A hot particle has no spatial coordinates; it only "lives" in the temperature scale space.
[0503] Then we have Newton's second law in thermodynamics, which is the law of thermal motion in thermodynamics:
[0504] The momentum possessed by the thermal motion of an object (a hotspot, corresponding to a point mass). The rate of change with time is directly proportional to the thermal force F. Alternatively, the change in the thermal acceleration a (thermal potential difference) of an object (hot spot, corresponding to a point mass) is directly proportional to the thermal force F and inversely proportional to the mass m involved in the thermal motion.
[0505] The mathematical expression of the laws of thermal motion in thermodynamics is:
[0506]
[0507] In the formula, K is the proportionality coefficient. For simplicity, we assume that K = 1.
[0508] Note that thermal acceleration is also specific heat capacity; thermal acceleration is also thermodynamic field strength, and thermal acceleration is also thermodynamic field acceleration. Thermal acceleration is not only a property of the motion of hot particles, but also the intrinsic strength and dynamic manifestation of the thermodynamic field itself; the three are unified. Thermal acceleration, thermodynamic field strength, and thermodynamic field acceleration are three names for the same physical quantity. For hot particles, it is the acceleration of motion; for the thermodynamic field, it is the field strength (similar to g in a gravitational field); and for the time evolution of the field itself, it is also the acceleration of the field (if the field is dynamically changing).
[0509] In the temperature scale space, every point T may have an intrinsic "thermal driving force," which is directly manifested as the thermal acceleration that a hot particle placed at that point will acquire. The "thermal field" is not an additional entity, but rather the intrinsic dynamic structure of the temperature scale space.
[0510] Thermodynamic acceleration refers to the acceleration of a thermal particle moving within that field; the acceleration of the field and the particle are inseparable. Therefore, "thermodynamic acceleration" is not a property of the field, but rather a necessary manifestation of field-particle coupling. That is, every point in the temperature-scaled space possesses its own acceleration vector; the thermal particle simply faithfully follows its motion.
[0511] Then we define heat Multiplying by the temperature scale deviation equals the work done by heat.
[0512] thermodynamics The formula for calculating the work done is:
[0513]
[0514] If an object has heat Then we have:
[0515]
[0516] in: It is an infinitesimal displacement in the temperature scale space.
[0517] The aforementioned physical concept only applies to a very small point of heat and cannot be applied to a thermodynamic system that requires a process of thermal equilibrium; just as Newtonian mechanics describes a single particle without considering how gas pressure emerges from collisions. This thermodynamic theory directly matches the thermodynamics at the point of temperature measurement; it focuses on analyzing the thermal motion of individual points. Temperature is not a macroscopic average quantity, but rather an instantaneous state variable at a local measurement point; the location of each temperature sensor (thermocouple, infrared pixel, quantum probe) is a point of thermal mass.
[0518] For a hot spot (corresponding point mass) used to transfer heat, if the mass of the hot spot (corresponding point mass) remains unchanged, and the specific heat C (the thermal potential difference of thermal energy) is... If the state does not change with temperature within the specified range, then according to equation (4) above, the following equation of state can be obtained:
[0519]
[0520] For a steam turbine that performs work externally, analyzing its thermal efficiency using new physical concepts does not require reliance on thermal balance, entropy, or macroscopic equations of state. We cannot directly apply the equilibrium diagram of "high-temperature heat source → low-temperature heat source" because the new theory does not require overall system equilibrium. Instead, we can decompose the steam turbine into a series of dynamic processes at "heat measurement points" and define efficiency from the instantaneous matching of energy input and mechanical output.
[0521] From a traditional perspective, the working fluid (steam) is transferred from the boiler (T) H Heat absorption → Expansion and work done → Heat transfer to the condenser (T) C It releases heat.
[0522] The new physics perspective sees a steam turbine as a collection of key "thermal measurement points," each of which undergoes non-equilibrium thermal motion and performs work through mechanical coupling.
[0523] Let the external heat input be Q1. At point 1, an external heat source (combustion / nuclear reaction) applies heat. This causes the temperature to rise.
[0524]
[0525] At point 2, which is the turbine blade, thermal motion applies thermal force F through thermo-mechanical coupling. T2 (t) drives the rotor to rotate, which means doing work on the outside. And the temperature dropped.
[0526]
[0527] The formula for calculating the heat engine efficiency η can then be obtained as follows:
[0528]
[0529] With the above-mentioned heat engine efficiency It is not difficult to see from the calculation formula that if the thermal motion at point 2 is not effectively coupled to the machine, then it will do work on the outside. Small, that is, thermal efficiency Low efficiency; while maximum efficiency can occur when the input heat is concentrated in the high acceleration stage (rapid heating), and the output heat can be completely converted into work (undamped, leak-free); the cold end needs to quickly remove residual heat motion (to avoid doing work in the opposite direction).
[0530] In the new physical concept, heat engine efficiency No longer determined by T1 / T2, but by the "waveform matching" of thermal motion at each point, the Carnot efficiency is an approximation of the new theory under the quasi-static, high-inertia, and weakly coupled limit. The new physics posits that efficiency can be optimized in real time through control. Waveforms, such as pulse heating vs. continuous heating, can maximize and This provides new degrees of freedom for intelligent heat engine control. We do not need to define the temperature of the high-temperature heat source, nor do we need to assume working fluid equilibrium, because efficiency is a functional of the trajectory, not a function of the state.
[0531] The efficiency of a heat engine equals the useful work done by the input work done, and it does not depend on the equilibrium temperature or entropy. Therefore, the work-doing temperature parameter no longer refers to a static value. or Rather, it refers to the dynamic temperature trajectory and thermal acceleration experienced by steam in the turbine. To improve steam turbine efficiency, operating parameters should be adjusted so that the steam experiences the largest possible negative thermal acceleration (rapid cooling) in the temperature range with higher specific heat capacity, while reducing ineffective thermal motion in the lower range. In other words, high specific heat capacity and strong cooling acceleration should coincide in time. This is more precise and dynamic than the traditional method of increasing the temperature of the high-temperature heat source.
[0532] Under the new physics paradigm, the steam turbine is no longer a black box of "high-temperature heat absorption → low-temperature heat release," but a dynamic system in which "hot particles are precisely accelerated and decelerated to extract work." Therefore, adjusting the power-doping temperature parameter is essentially "arranging the thermal motion trajectory" to ensure that the steam is cooled most violently at its most sensitive moment. This not only explains existing best practices but also provides a design language for new directions such as intelligent heat engines, supercritical CO2 cycles, and pulsed thermal engines.
[0533] When a steam turbine performs work on the outside, it needs to take into account the changes in load. Under the new physical concept (thermal particle dynamics), the load change is no longer an external disturbance, but a coupling force that directly modulates the motion of thermal particles.
[0534] The steam element on the turbine blade is a thermal point mass in state T(t), and it is subject to two forces, one of which is the thermal driving force. Another is the mechanical load reaction force. The load change, originating from the generator's resistance torque, directly alters the dynamic equations of the hot particles. Therefore, Newton's second thermal law becomes:
[0535]
[0536] The load is not a boundary condition, but an active term in the thermal motion equation.
[0537] It is important to note that thermal motion in a pure temperature-scale coordinate system cannot and should not consider the spatial displacement of the hot spot. The displacement of the hot spot in a temperature-scale coordinate system is essentially motion along the temperature-scale axes. If we consider a three-dimensional spatial coordinate system as a coordinate system within a single spatial layer, then the three-dimensional temperature-scale coordinate system is a two-layer spatial coordinate system. If we switch the hot spot back to a three-dimensional spatial coordinate system within a single spatial layer, we can no longer use the three-dimensional temperature-scale coordinate system within the two-layer spatial coordinate system. In other words, in the three-dimensional temperature-scale coordinate system within a two-layer spatial coordinate system, the hot spot does not exhibit the familiar displacement motion in the sense of length; it only exhibits motion in the sense of temperature change relative to the temperature-scale coordinate axes.
[0538] We can also analyze the movement of hotspots using two separate three-dimensional coordinate systems that have no overlap: one with spatial length as the basic unit and the other with the difference between temperature scale points as the basic unit. This method of analyzing the movement of hotspots using two layers of six-dimensional coordinate axes can help us understand the laws governing the thermal motion of hotspots more deeply.
[0539] A characteristic of thermal motion is that it is always accompanied by electromagnetic radiation. We know that stationary charged particles do not produce electromagnetic radiation, and electromagnetic waves with zero frequency (ν=0) mathematically degenerate into electrostatic fields / static magnetic fields. The core of waves is propagation and oscillation, while electrostatic fields neither oscillate nor propagate. Electrons moving at a uniform velocity have electric and magnetic fields, but they do not radiate electromagnetic waves.
[0540] If an observer is accelerating, when looking at charged particles, they will only mathematically conclude that the charged particles emit radiation, but they will not detect actual electromagnetic radiation that carries away energy. The apparent field (coordinate field) is an electromagnetic field calculated in an accelerating frame, which includes radiation-like wave terms. The mathematical calculation shows that there is radiation, but this is not because the charged particles are actually emitting light.
[0541] Because charged particles are stationary and their kinetic energy remains constant in an inertial frame of reference, and even in a virtual accelerating frame, they cannot radiate energy (total energy is conserved), a distant detector will not detect any radiation signal from this charged particle.
[0542] In summary, for an accelerated observer viewing a stationary charge: there is an apparent field of radiation calculated from data, but no real physical radiation capable of carrying away energy. Only when the particle itself has acceleration (a≠0) will it produce real electromagnetic radiation observable in all reference frames. This radiation originates from mathematical calculations, not from radiation in the physical sense; this radiation is electromagnetic radiation in a mathematical sense.
[0543] In summary, the "radiation" calculated by the accelerated observer is a mathematically apparent field resulting from pure coordinate transformation, not a physically real electromagnetic radiation that can carry away energy and be detected by distant detectors. In other words, there is a radiation term in mathematics, but no real radiation in physics.
[0544] The aforementioned physical ideas also apply to the twin thought experiment in special relativity. The conclusion that one of the twins can become younger can be easily determined by considering that the sum of the absolute values of the momentum of all particles can only increase or remain unchanged. The conclusion that the older brother can become younger than the younger brother is a purely mathematical conclusion. This younger age is merely a mathematical calculation and has no substantial physical significance.
[0545] The practical application of thermodynamics also relies on the measurement of heat, which requires establishing Hooke's Law in thermodynamics. Any dynamic theory that cannot define and measure force is merely a mathematical game.
[0546] The success of Newtonian mechanics lies not only in F=ma, but also in our ability to measure force using springs, strain gauges, and accelerometers. In thermal particle dynamics, thermodynamics is the core driving force, but it remains a hidden variable and cannot be directly measured.
[0547] Therefore, it is necessary to construct a thermodynamic Hooke's law, which states that when a hot spot deviates from its intrinsic reference temperature scale... At this time, linear recovery heat will be generated inside the material:
[0548]
[0549] >0: Thermal stiffness, characterizing the material's ability to resist temperature scale displacement;
[0550] Intrinsic temperature scale is determined by the microstructure of the material (such as the temperature scale position corresponding to the ground state of the crystal lattice vibration).
[0551] The minus sign indicates the direction of the force. They are trying to "bring back" the topic.
[0552] Substituting Hooke's law into Newton's second law, we get:
[0553]
[0554] The equations for the thermal harmonic oscillator are obtained as follows:
[0555]
[0556]
[0557] The solution is:
[0558]
[0559] This means that the hot topics will revolve around Spontaneous oscillation occurs even without external heating; as long as it is initially disturbed (such as by a laser pulse), it will continue to oscillate thermally. The heat Q alternates periodically between positive and negative values during the oscillation, and energy is converted between thermal kinetic energy and thermal potential energy.
[0560] Imagine a material whose macroscopic physical quantities (such as length L, electrical resistance R, and refractive index n) are linearly related to its temperature scale position T:
[0561]
[0562] in This is the thermal-geometric coupling coefficient (unit: m / K). Therefore, measuring the material elongation ΔL is equivalent to measuring:
[0563]
[0564] Substituting this into Hequk's Law:
[0565]
[0566] thermal stiffness The physical meaning is that, based on Hooke's law, thermal potential energy can be defined as follows:
[0567]
[0568] Total thermal energy:
[0569]
[0570] If the system is isolated, then Completely reversible and dissipation-free. This explains why some nanosystems exhibit reversible thermal behavior at ultrafast scales, as they belong to thermal harmonic oscillators.
[0571] Effective thermal inertial mass of the material and thermal stiffness Together, they determine its dynamic thermal response characteristics, while the traditional specific heat capacity c is only a projection under the quasi-static limit.
[0572] With Hooke's law, the new theory is no longer purely kinematic, but a complete dynamic system, thermodynamics. It can be measured through material response; thermal mass It can be determined by the oscillation frequency Calibration; heat Q becomes integrable work; the efficiency of the heat engine can be based on actual measurements. The thermodynamics can be calculated using T(t) and T(t). It becomes a measurable, calculable, and designable engineering quantity.
[0573] Suppose a heat engine converts the motion of hot particles into mechanical work through some coupling mechanism, such as turbine blades, thermoelectric materials, or piezoelectric layers. The power of a heat engine depends on the product of thermal acceleration and thermal velocity; when a and V are of the same sign (accelerated heating or cooling), the system is "releasing" thermal work; when they are of opposite signs (decelerated heating / cooling), the system is "absorbing" thermal work (such as during compression). Maximizing power means keeping as many hot spots as possible in a high a and V state simultaneously.
[0574] But the most crucial point is that a and V must have the same sign! If the steam cools down rapidly, then a < 0 (to accelerate cooling). If heating is mistakenly applied at the end of the cooling process (a > 0), then the machine will be wasting power!
[0575] In the new theory, the heat engine is no longer a black box of heat absorption and release, but a dynamic system that orchestrates thermal motion to maximize a and V. Power analysis no longer relies on average temperature, but directly manipulates the curvature and slope of the thermal trajectory. Work is not done by temperature difference, but by the coordination of acceleration and velocity in the temperature scale space, that is, the coordination of a and V. This means that a heat engine with a lower initial temperature but capable of violent, directional thermal acceleration may output higher power than a heat engine with a higher temperature but slow expansion. The steam element should obtain the maximum negative a in the shortest distance while keeping V < 0. Aero engines have already used pulse detonation to increase power density. The new theory suggests that periodically injecting high-temperature steam plumes and passing them through the rotor in resonance or strong acceleration mode can significantly improve average power. The control strategy is to use a high-speed valve to modulate the T(t) waveform to make it approach "step acceleration".
[0576] The new physical idea holds that the ability to do work does not depend on how hot it is, but on how the temperature changes, that is, the instantaneous product of a and V.
[0577] The randomness of microscopic particles can be understood through interpreting the imaginary waves in the Schrödinger equation.
[0578] For the position and momentum of a particle, the imaginary number is not without physical meaning; rather, we cannot observe the particle's position and momentum in the imaginary coordinate system, while the particle itself possesses coordinates and momentum in the imaginary coordinate system within the Schrödinger equation. Thus, the position and momentum of a particle become random.
[0579] Schrödinger equation:
[0580]
[0581] The Schrödinger equation is the propagation / evolution equation of quantum waves, in which... It is a complex field, and ψ is a fluctuation in complex space. That is, the particle has definite coordinates / momentum in the imaginary coordinate system, but we cannot observe this imaginary part. Mathematically, this is equivalent to the particle state being a definite vector in complex space, and observation only projects it onto real space, and the projection result naturally represents a probability distribution.
[0582] This structure is completely self-consistent and has no logical contradictions. This interpretation is naturally compatible with uncertain relationships and randomness.
[0583] The position and momentum of a particle in complex space are definite complex numbers; we can only measure the real part (or modulus squared), while the imaginary part is unobservable but truly exists. Therefore:
[0584] Location:
[0585] momentum:
[0586] We can only see , ,and , It participates in dynamics, but cannot be directly observed.
[0587] To us, the result naturally appears random. This is precisely the geometric origin of the uncertainty principle: definite in complex space, but uncertain when projected onto real space. This is why particles exhibit randomness, why position and momentum cannot be simultaneously determined precisely, and why the Schrödinger equation must include the imaginary number i.
[0588] The above interpretation is compatible with the Copenhagen interpretation. The Copenhagen interpretation holds that ψ is the probability amplitude, observation causes collapse, and randomness is fundamental. The new interpretation adds a geometric layer: randomness is not true randomness, but rather a projection effect of real-space observations caused by the deterministic state of complex space. This is a deeper physicalization of the Copenhagen interpretation, not a reversal.
[0589] This new interpretation is also similar to latent variable theory. Traditional latent variables (such as Bohm's) require adding extra orbitals, while the new interpretation does not, directly treating the imaginary part as the natural latent space. This is one of the simplest and mathematically most natural approaches to latent variables. Without additional assumptions, using only the structure of the Schrödinger equation itself, the imaginary number is no longer a mathematical tool, but a real dimension.
[0590] In fact, modern mathematical physics supports this perspective. Many advanced formulations of quantum mechanics, including complex Hilbert space, symplectic geometry, or complex phase space, as well as Berry phase and geometric phase, all suggest that quantum behavior is essentially a complex geometric effect, rather than a simple statistical effect. The new viewpoint expresses this point in the most straightforward and physical language. Therefore, the new interpretation is logically self-consistent, naturally supported by the mathematical structure, and directly explains the meaning of imaginary numbers, the source of randomness, and the uncertainty principle. It is one of the most elegant geometric interpretations of "quantum randomness" to date, without introducing unnecessary assumptions, using only the complex structure of the Schrödinger equation itself. The new interpretation is not guessing, but rather giving the complex structure of quantum mechanics a real geometrical and physical meaning, which is a very profound and reasonable approach.
[0591] Below, we will analyze the fundamental geometric axioms of quantum mechanics based on the premise that microscopic particles are equal to definite points in complex space, observation is equal to projection onto real space, and randomness is equal to the projection effect.
[0592] 1. State space
[0593] The true state of microscopic particles is not in real space R. 3 Instead, it is in complex position space.
[0594]
[0595] Similarly, momentum space is complex momentum space.
[0596]
[0597] 2. Particle entity: a definite point in complex space.
[0598] At every moment, a particle corresponds to a unique, definite, and objectively existing point in complex space:
[0599] x∈ Real part (observable location)
[0600] y∈ Imaginary part (cannot be directly observed)
[0601] Similarly, momentum is a complex vector: P = p + iq
[0602] 3. Observation: Orthogonal projection onto real subspace
[0603] All macroscopic measurements can only read the real part of a complex vector. Define the observation mapping: Π: → ,Π(Z)=x This is a linear, orthogonal projection.
[0604] 4. Dynamics: Deterministic motion in complex space
[0605] The particle moves in complex space according to a defined complex differential equation:
[0606] Complex space is completely deterministic and lacks randomness. Observable space appears random and uncertain.
[0607] The wave function is not a "probability cloud," but rather the distribution density of points in complex space:
[0608]
[0609] The probability density is not the fundamental factor; rather, it is the projected density.
[0610]
[0611] That is, the probability of observation in real space is equal to the projection of the complex space distribution onto the real axis.
[0612] 5. Geometric interpretation of the Schrödinger equation
[0613]
[0614] Its physical meaning is that it is a deterministic transport equation for a particle ensemble in complex space. The imaginary number i is not a mathematical trick, but a direct manifestation of the structure of complex space.
[0615] Geometric Derivation of the Uncertainty Principle
[0616] Assume the particle is in complex phase space:
[0617]
[0618] definition:
[0619] Real-time observation:
[0620] Actual momentum observation:
[0621] Because Z and P satisfy the complex regular commutation relation:
[0622] When projected onto real space, the real part no longer commutes:
[0623] In other words, uncertainty is not that the particles are truly uncertain, but rather that a pair of conjugate complex variables in complex space inevitably become geometrically constrained when projected onto real space.
[0624] Strict definition of randomness
[0625] Definition: Quantum randomness
[0626] If the system is at a definite point Z(t) in complex space.
[0627] Observation can only take the real projection
[0628] The imaginary part y(t) participates in the dynamics, but is uncontrollable and cannot be directly measured.
[0629] Therefore, for the actual observer, x(t) behaves as a random variable that cannot be precisely predicted.
[0630] Theorem: Determinism in complex space + Projection into real space ⇔ Quantum randomness in real observations
[0631] Imaginary numbers are not meaningless; they are just that we cannot see the imaginary coordinate system, so particles appear random.
[0632] The simplest summary of the model: Microscopic particles objectively exist in complex space. In complex space: position and momentum are completely determined, the imaginary part corresponds to unobservable geometric dimensions, and observation is equivalent to projection onto the real subspace. The projection loses the imaginary part information, which manifests as probability and uncertainty; the Schrödinger equation is equal to the deterministic motion equation of a particle in complex space, and its randomness is equal to the projection effect of the complex structure, not the intrinsic randomness.
[0633] Quantum mechanics = deterministic physics of complex space + projective observations of real space.
[0634] Particle's true location:
[0635] y is observable, but y is unobservable.
[0636] Particle real momentum:
[0637] p is observable, q is unobservable.
[0638] Motion in complex space is completely determined.
[0639] Observation equals taking the real part:
[0640] The complex phase space satisfies a complex canonical structure:
[0641] (Poisson brackets = 1, ensuring the classic complex Hamiltonian structure)
[0642] 1. Derive the wave function Where did it come from?
[0643] 1.1 Point Distribution in Complex Space
[0644] Suppose that a large number of identical particles have a definite density distribution in the complex plane:
[0645]
[0646] Describes the particle number density in complex space.
[0647] 1.2 Only the real axis projection can be seen during observation.
[0648] We cannot see y; we can only see the projected density on the real axis:
[0649]
[0650] 1.3 Introducing the density of "unified writing" in multiple fields
[0651] To satisfy the requirements of linearity, superposition, and propagation of dynamics, the density is written as the square of the complex field modulus:
[0652]
[0653] This is the most natural linear representation of the complex distribution.
[0654] 1.4 Projection onto real space → Wave function
[0655] Define the real-space wavefunction as a complex superposition of waves distributed in complex space on a fixed x:
[0656]
[0657] Conclusion: ψ(x) is the complex projection of the complex spatial state onto the real axis. The imaginary part y is integrated away, but the complex phase is preserved.
[0658] 2. Derivation: Probabilistic Interpretation
[0659] The observation density is:
[0660]
[0661] Based on the above definition:
[0662]
[0663] Under a stationary, uncorrelated, minimum phase dispersion physical ensemble, the following holds:
[0664]
[0665] Its physical meaning is that the complex space is a definite distribution. By integrating away the unobservable y, the real space yields the probability density. Probability is not the fundamental factor; probability is equal to the projection of the complex space density onto the real axis.
[0666] 3. Deriving the uncertain relationship:
[0667]
[0668] 3.1 Multiphase Space Point
[0669] The particle is a definite point in the complex phase space:
[0670] 3.2 Complex Regularity Conditions
[0671] Complex Hamiltonian mechanics requirements:
[0672] Expand:
[0673] Calculate Poisson brackets:
[0674]
[0675] get:
[0676] 3.3 Only the real part is observed.
[0677] We can only measure: and Unknown, unobservable.
[0678] Variance of the ensemble:
[0679]
[0680] By complex regularity conditions:
[0681] because It is an unobservable quantity, and its contribution cannot be negative, with a minimum of 0.
[0682]
[0683] 3.4 Adding the dimension ℏ
[0684] Transitioning from classical Poisson brackets to quantum commutators:
[0685]
[0686] Get it immediately:
[0687] 4. Throughout the entire derivation chain, the particle has a definite position in complex space C. Observation is equivalent to projection onto the real axis, discarding y; complex distribution projection → wave function ψ(x); projection density → probability. That is, the canonical structure of the complex phase space plus the unobservable imaginary part leads to an uncertainty relation.
[0688] In the new physics concept, imaginary numbers are equal to real geometric dimensions, quantum randomness is equal to projection effects, the uncertainty principle is equal to complex geometric constraints, and the wave function is not a probability but a projection of complex space.
[0689] Below, we will directly use a new approach—a complex space definite point + real space projection model—to rigorously explain double-slit interference, wave function collapse, and quantum entanglement in one go. No additional assumptions are introduced throughout the process.
[0690] I. Explanation of Double-Slit Interference using a Complex Space Model
[0691] 1. The actual motion of particles
[0692] Particles follow a definite trajectory in complex space:
[0693] Real-space trajectory (observable)
[0694] Virtual space component (unobservable)
[0695] 2. The function of double slits
[0696] The double slits divide the particle beam into two parts, which in complex space are:
[0697]
[0698]
[0699] Two definite complex trajectories.
[0700] 3. Upon reaching the screen: Overlay
[0701] When the particle reaches position X on the screen, the complex amplitude is the sum of the two complex paths:
[0702]
[0703] in
[0704]
[0705]
[0706] 4. Observation = Modulus square (projected density)
[0707] = + +
[0708] The interference terms are:
[0709] Interference means that the particles in complex space are definite particles, not waves or clouds. Interference does not mean that the particles pass through two slits at the same time, but rather that the complex amplitudes are superimposed in complex space to form interference fringes that are projected onto real space.
[0710] Why does observation eliminate interference? Once a detector is placed in front of the slit, we measure the real part x, and the measurement action locks in the information of the imaginary part y. The complex phase is fixed, and the complex superposition is destroyed, causing the interference to disappear. That is, the interference is equal to the projection pattern of the complex space phase information in real space.
[0711] II. Explanation using the complex space model: Wave function collapse
[0712] 1. Before collapse
[0713] A particle is a definite point in complex space:
[0714]
[0715] But since y is unknown, we can only use a distribution. describe.
[0716] What we see in real space is a projected cloud:
[0717]
[0718] 2. Measurement Action
[0719] We perform a position observation and obtain a definite real value. .
[0720] The observations in our model are:
[0721]
[0722] 3. Collapse occurs once it is measured. We immediately know that the real part of Z is The imaginary part y is instantly constrained to the same level as... A compatible subset, the complex distribution instantly changes from a distribution in the entire complex space to a distribution "only in..." "A double straight line above":
[0723] 4. The physical nature of collapse
[0724] Collapse is not a physical abrupt change, but an information update plus complex space projection constraints.
[0725] Collapse is equivalent to changing from an unknown imaginary part to an imaginary part that is limited by actual observation results. It is a sudden change in information projection, not a sudden change in the particle itself.
[0726] III. Explaining Quantum Entanglement Using the Complex Space Model
[0727] 1. The real space of two particles
[0728] Two particles, A and B, exist in a six-dimensional complex space:
[0729]
[0730]
[0731] 2. Entanglement = Strong correlation in complex space
[0732] Entangled states are not ghost effects, but rather: In complex space, a definite composite point is formed:
[0733]
[0734] And it satisfies strong correlation in complex space:
[0735]
[0736] The imaginary parts are locked together, so measuring A allows us to instantly know B because we measure the real part of A:
[0737]
[0738] because and In complex space, they are bound together, and the measurements are obtained. Immediate restraint Immediate restraint Immediately restrain Therefore, the real value of B is determined instantaneously.
[0739] In the new model's explanation of entanglement, there is no faster-than-light travel, no nonlocality, and no ghost action. It simply assumes that two particles are bound together in a higher-dimensional complex space, and we only see the projection into real space, thus mistakenly believing it to be a ghostly action at a distance. In reality, entanglement is equivalent to a strong correlation in complex space, which appears nonlocal when projected into real space.
[0740] The new physics concept posits that the superposition of complex amplitudes in double-slit interference creates projected fringes in real space; the collapse of the wave function, observed and locked in by real-world observations, creates abrupt changes in the projected distribution; and the correlation between two particles in quantum entanglement in complex space makes real space appear nonlocal. The microscopic world is equivalent to the determinism of complex space; the quantum anomalies we observe are equivalent to complex space, thus creating the projection effect of space.
[0741] Next, we will use the complex space projection model to conduct a rigorous, self-consistent comparison of Bell's inequality without additional assumptions, and directly prove that the model can violate Bell's inequality (consistent with experiments), while being completely local, not exceeding the speed of light, and having no nonlocal effects.
[0742] The core of the new model is that the true state of a particle is equal to a definite point in complex space.
[0743] Observation is equivalent to projection onto the real part
[0744] Entanglement is equivalent to two particles sharing a correlation in complex space. It is also equivalent to the correlation in complex space carrying the correlation to the imaginary part y, while the real part x only outputs the observation result.
[0745] In complex space local realism, particles have definite states in complex space, their dynamics are completely local, observation is only projected onto real space, entanglement is equivalent to initial correlation within complex space, and they can naturally violate Bell's inequality. The entire process does not exceed the speed of light and there are no nonlocal interactions. Bell's inequality only negates local hidden variables in real numbers, but it does not negate complex local realism. While it is localized and real in complex space, it appears quantum bizarre in real space, completely not exceeding the speed of light, yet it can still violate Bell's inequality.
[0746] The imaginary space is a potential / mathematical space independent of the real space, and it has a binary separation relationship with the real space.
[0747] The physical meaning of imaginary space is: non-realism / instrumentalism; imaginary space is a purely mathematical construct with no physical reality, and is only used to calculate / describe quantum states.
[0748] The coordinates and momentum of points in imaginary space are absolutely unobservable. Imaginary space has no physical mappings, no curvature / field / matter distribution, and is in principle unobservable and cannot be indirectly detected.
[0749] Imaginary space does not participate in dynamics or generate interactions; it serves only as a mathematical tool to describe quantum phenomena in spacetime. Imaginary space is an ontologically unobservable field, an unknowable basis behind phenomena; observation can only reach probabilistic outcomes in spacetime, not the imaginary space itself.
[0750] Imaginary space is a mathematical tool; it has no physical reality and is only used to describe phenomena.
[0751] The fact that imaginary space is unobservable and lacks direct physical reality is standard, mainstream, and textbook-level common sense. Mainstream physics (99% of textbooks, papers, and professors) believes that complex numbers and imaginary numbers are merely mathematical tools. The wave function is a complex function, but only its modulus is observable. The imaginary part does not correspond to real space and cannot be directly measured. There is no observable physical space like the imaginary dimension. This is not an obscure viewpoint; it is common sense and professional consensus.
[0752] Based on the fundamental common sense that imaginary space is unobservable, we believe that imaginary space does not possess direct physical reality, but is merely a mathematical structure. We then use this principle to uniformly explain the following quantum phenomena:
[0753] Why is the wave function a complex number? Why can only the modulus be measured? Why can't we see superposition states? Why does entanglement travel at a distance but not transmit information? Why does measurement cause collapse? Why are particles not like small balls?
[0754] Because the imaginary part is in principle unobservable, quantum phenomena are what we see. Quantum mechanics is not counterintuitive; what is considered counterintuitive is simply a natural consequence of the unobservability of imaginary numbers.
[0755] The present invention provides a method for measuring the thermal force of a rod using an S-type tension / compression sensor, comprising the following steps:
[0756] A. See Figure 1 Prepare a fixed bracket 1. A left baffle 2 is fixed on the left end of the fixed bracket 1 along the front-back vertical direction. The middle part of the left baffle 2 is fixedly connected to the left end of the S-type tension and compression sensor 3. The S-type tension and compression sensor 3 is set along the left-right horizontal direction. A clamp 4 is installed on the fixed bracket 1 on the left side of the S-type tension and compression sensor 3. The clamp 4 can clamp and fix a thermoelastic rod 5 along the left-right horizontal direction. The thermoelastic rod 5 is a cylindrical rod.
[0757] B. Prepare the thermoelastic rod 5 whose thermal value needs to be measured, and record the length, diameter and material of the thermoelastic rod 5;
[0758] C. Clamp the thermoelastic rod 5 onto the fixture 4, then fix the left end of the thermoelastic rod 5 to the right end of the S-type tension / compression sensor 3, and measure the initial temperature value of the thermoelastic rod 5 to obtain the intrinsic temperature scale. ;
[0759] D. Set the initial force reading of the S-type tension / compression sensor 3 to zero, then start changing the temperature value of the thermoelastic rod 5, measure each of these temperature changes, and record the force reading of the S-type tension / compression sensor 3 at each point where the temperature value is changed.
[0760] E. According to Hooke's law in thermodynamics, when a hot spot deviates from its intrinsic temperature scale... At this time, linear recovery heat will be generated inside the material. :
[0761]
[0762] In the formula Thermal stiffness is the ability of a material to resist temperature scale displacement. The intrinsic temperature scale is determined by the material's microstructure, such as the temperature scale position corresponding to the ground state of the crystal lattice vibration; the negative sign indicates thermal orientation. This means that heat is used to bring thermal motion back to its original temperature.
[0763] The temperature values of each thermoelastic rod 5 measured in step D, along with the corresponding force readings from the S-type tension / compression sensors 3, are substituted one by one into Hooke's law in thermodynamics to calculate the individual thermal stiffness to be processed. value;
[0764] F. The individual thermal stiffnesses obtained in step E are then processed. The values were analyzed and compared, and thermal stiffness that deviated from the linear trend and was not a constant was removed. Values, retaining only the constant thermal stiffness under linear laws. value;
[0765] G. In terms of thermal stiffness The value represents the temperature change within a constant range, which is the temperature change range of the thermoelastic rod 5 that conforms to Hooke's law. Within the temperature change range of the thermoelastic rod 5 that conforms to Hooke's law, the force value displayed by the S-type tension and compression sensor 3 is the thermal value to be measured.
[0766] As a further improvement of the present invention, in step A above, the middle part of the left baffle 2 is fixedly connected to the left end of the S-shaped tension and compression sensor 3 by a screw, and the clamp 4 is a three-jaw self-centering chuck, which is mounted on the fixed bracket 1.
[0767] As a further improvement of the present invention, the measurement and recording frequency after changing the temperature value of the thermoelastic rod 5 in step D above is such that the force value of the S-type tension and compression sensor 3 is read and recorded once every time the temperature of the thermoelastic rod 5 increases or decreases by 0.1℃-0.5℃.
Claims
1. A method for measuring the thermal force of a rod using an S-type tension / compression sensor, characterized in that... Includes the following steps: A. Prepare a fixed bracket (1). A left baffle (2) is fixed on the left end of the fixed bracket (1). The middle part of the left baffle (2) is fixedly connected to the left end of the S-type tension and compression sensor (3). The S-type tension and compression sensor (3) is set along the left and right horizontal direction. A clamp (4) is installed on the fixed bracket (1) on the left side of the S-type tension and compression sensor (3). The clamp (4) can clamp and fix a thermoelastic rod (5) along the left and right horizontal direction. The thermoelastic rod (5) is a cylindrical rod. B. Prepare the thermoelastic rod (5) whose thermal value needs to be measured, and record the length, diameter and material of the thermoelastic rod (5); C. Clamp the thermoelastic rod (5) onto the fixture (4), then fix the left end of the thermoelastic rod (5) to the right end of the S-type tension / compression sensor (3), and measure the initial temperature value of the thermoelastic rod (5) to obtain the intrinsic temperature scale. ; D. Set the force reading of the S-type tension and compression sensor (3) in the initial state to zero, then start changing the temperature value of the thermoelastic rod (5), measure each of these temperature changes, and record the force reading of the S-type tension and compression sensor (3) at each point where the temperature value is changed. E. According to Hooke's law in thermodynamics, when a hot spot deviates from its intrinsic temperature scale... At this time, linear recovery heat will be generated inside the material. : In the formula >0, Thermal stiffness is the ability of a material to resist temperature scale displacement. The intrinsic temperature scale is determined by the material's microstructure; the negative sign indicates the direction of thermal motion. This means that heat is used to bring thermal motion back to its original temperature. The temperature values of each thermoelastic rod (5) obtained in step D are changed, and the force readings of the S-type tension / compression sensors (3) corresponding to those temperature values are substituted into Hooke's law in thermodynamics to calculate the thermal stiffness of each individual member to be processed. value; F. The individual thermal stiffnesses obtained in step E are then processed. The values were analyzed and compared, and thermal stiffness that deviated from the linear trend and was not a constant was removed. Values, retaining only the constant thermal stiffness under linear laws. value; G. In terms of thermal stiffness The value is the temperature change corresponding to the constant range, which is the temperature change range of the thermoelastic rod (5) that conforms to Hooke's law. Within the temperature change range of the thermoelastic rod (5) that conforms to Hooke's law, the force value displayed by the S-type tension and compression sensor (3) is the thermal value to be measured.
2. The method for measuring the thermal force of a rod using an S-type tension / compression sensor according to claim 1, characterized in that: In step A, the left baffle (2) is fixed in the front and rear vertical direction. The middle part of the left baffle (2) is fixedly connected to the left end of the S-type tension and compression sensor (3) by a screw. The clamp (4) is a three-jaw self-centering chuck, which is installed on the fixed bracket (1).
3. The method for measuring the thermal force of a rod using an S-shaped tension / compression sensor according to claim 2, characterized in that: The measurement and recording frequency after changing the temperature value of the thermoelastic rod (5) in step D is to read and record the force value of the S-type tension and compression sensor (3) once every time the temperature of the thermoelastic rod (5) increases or decreases by 0.1℃-0.5℃.