Method and apparatus for measuring the interaction of light with gravitational fields

Abstract

This invention relates to experimental methods and apparatus for measuring the interaction between light and gravitational fields, particularly for measuring changes in the frequency and propagation speed of photons under gravitational influence. Regarding the detection of light frequency changes, the method involves splitting a single-frequency laser beam into two beams, each entering a different Earth gravitational field. After traveling through the two fields for the same distance, the two beams are recombined, forming an asymmetric interferometer. Since different optical path lengths result in different redshifts, the differential redshift is measured by detecting the beat signal. Regarding the detection of changes in light propagation speed, the method involves splitting a pulsed laser beam into two beams, each entering a different Earth gravitational field. The beams travel the same distance under the influence of the two gravitational fields. Two photodetectors detect the changes and compare the time delay between the two signals to determine and detect whether and by what amount the light propagation speed changes under the interaction of different gravitational fields.

Description

Technical Field

[0001] This invention relates to experimental methods and apparatus for measuring the interaction between light and a gravitational field, particularly experimental methods and apparatus for measuring the changes in energy and propagation speed of photons under the influence of gravity, belonging to the fields of fundamental physics and optical measurement and sensing technology. Background Technology

[0002] Gravity is a fundamental force in nature that causes objects to attract each other due to their mass. From everyday objects to celestial bodies and everything in the universe, gravity is everywhere. Newton's law of universal gravitation tells us that there is a gravitational force between any two objects, the magnitude of which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Einstein's theory of general relativity further reveals the nature of gravity. According to general relativity, gravity is not a "force," but rather an effect produced by the curvature of spacetime caused by mass and energy. Massive celestial bodies (such as stars and black holes) cause the surrounding spacetime to curve, and other objects move along this curved trajectory.

[0003] Gravity research is a core topic in physics and scientific exploration. It serves as a fundamental and crucial tool for understanding the basic laws of nature and revealing and exploring the mechanisms of celestial bodies and the universe. Furthermore, gravity research will drive scientific and technological progress, providing vital support for future exploration and development. From the microscopic to the macroscopic, from basic theory to practical applications, the study of gravity holds irreplaceable significance, embodying humanity's boundless pursuit of understanding nature and itself.

[0004] Another seemingly ordinary yet still incompletely understood physical phenomenon in physics is the photon. Current theories posit that light is composed of photons, which are quantized excitations of the electromagnetic field and are the fundamental particles that mediate electromagnetic interactions. They are a core subject of quantum electrodynamics (QED). Photons are generally considered to have no rest mass but carry energy, momentum, and angular momentum. Photons play a crucial role in modern physics; light is both a wave and a particle, embodying the core idea of ​​quantum mechanics—wave-particle duality. Light and photons are vital tools for humanity's exploration of the mysteries of nature and the universe. Research on light and photons not only deepens our understanding of the nature of matter and energy but also provides limitless possibilities for scientific and technological innovation. Currently, light and photons play important roles in fields such as communication, computing, energy, and astronomy.

[0005] Although photons have no rest mass, they carry energy and momentum, properties that, according to general relativity, make light subject to gravity. In a strong gravitational field, light behaves according to the geometry of curved spacetime, rather than the linear propagation laws of classical mechanics. Einstein predicted that light would bend its path when passing near celestial bodies like the Sun. This prediction was first confirmed by scientists during the 1919 total solar eclipse, a classic verification of general relativity. A gravitational field can bend the path of light, just as a lens can refract light. This effect is called "gravitational lensing." Another consequence of the interaction between light and a gravitational field is that light traveling outward from a strong gravitational field has a lower frequency and a longer wavelength; this is called "gravitational redshift," also known as Einstein's redshift. The energy of a photon is proportional to its frequency; a strong gravitational field consumes some of the photon's energy, resulting in redshift. In 1960, through the Pound-Rebka experiment (Pound, RV; Rebka Jr. GA (April 1, 1960). "Apparent weight of photons". Physical Review Letters. 4(7): 337–341), the gravitational redshift phenomenon was successfully observed in the Earth's gravitational field. Summary of the Invention

[0006] The purpose of this invention is to provide an experimental method and apparatus for measuring the interaction between light and a gravitational field, based on the gravitational-optical effects (see the theoretical foundation section below), particularly an experimental method and apparatus for measuring the changes in the frequency and propagation speed of photons under the influence of gravity.

[0007] The inventors, applying the fundamental principles of general relativity, have theoretically proven that when a photon propagates through curved spacetime, its momentum is not necessarily conserved in a locally stationary observer's frame of reference along the photon's geodesic, thus producing an additional redshift. The inventors call this redshift "supergravitational redshift," a phenomenon entirely different from conventional gravitational redshift (i.e., Einstein's redshift), which is determined by the gravitational potential difference between the source and receiver. Supergravitational redshift, however, is caused by the change in momentum resulting from the curvature of the photon's trajectory in curved spacetime.

[0008] Theoretical basis of the present invention

[0009] Assuming a photon moves within the Schwarzschild geometry produced by an object of mass M (Fundamentals of General Relativity, Zhao Zheng & Liu Wenbiao, Tsinghua University Press, October 2010), we first construct the Lagrangian and, through variational and Lagrangian methods, derive a universal geodesic equation applicable to both massive and massless particles. For a particle moving along a static Schwarzschild spacetime geodesic (whether massive or massless), its energy and angular momentum are conserved. It is important to emphasize that these energy and angular momentum are quantities measured by a stationary observer at infinity, which differs from the results measured by a locally stationary observer. Mathematically, it can be proven that a particle moving within the equatorial plane will remain within that plane. Since the Schwarzschild metric is a solution to Einstein's field equations outside a spherically symmetric mass distribution, a polar axis can always be chosen to ensure that the particle's motion lies within the equatorial plane; therefore, we can assume that the photon moves within the equatorial plane of Schwarzschild coordinates. Due to the curvature of spacetime described by the Schwarzschild metric, the world line of a photon is curved and propagates along the zero geodesic. Previous theoretical studies and experimental observations have demonstrated that the difference in radial coordinates (denoted by r) between the emitter and receiver introduces a redshift. This redshift is caused by time dilation in curved spacetime and is well-known in general relativity. Based on the equivalence principle, this relationship can also be directly derived and is usually interpreted as the gravitational potential difference between the emission and reception points. This redshift is often called the "Einsteinian redshift." Crucially, any change in the momentum of the photon between the emitter and receiver (denoted by Δp) contributes to the total redshift. The momentum of a photon is a vector, always tangent to its geodesic, so any change in its amplitude (denoted by p0) or direction (or both) must be considered. For a weak gravitational field, i.e., Δp / p0 << 1, 2GM / r << 1 (where G is the gravitational constant), the inventors' theoretical derivation yields the expression for the total redshift z as:

[0010]

[0011] Where c is the speed of light, r E r R These are the radial coordinates of the photon emission and reception points, respectively.

[0012] As can be seen from the above equation, the total redshift expression contains two terms. The second term is the Einstein gravitational redshift related to the gravitational potential difference; the first term is the additional redshift introduced by the change in photon momentum (Δp), which the inventors call the supergravity redshift. This is one of the gravitational-optical effects involved in this invention.

[0013] It can be further proven that for the case where both the transmitting and receiving points are at infinity (i.e., r... E →∞,r R→∞), the Einstein gravitational redshift in the total redshift expression disappears, and the additional redshift introduced by the change in photon momentum (Δp) is exactly equal to the ray deflection angle, i.e.

[0014]

[0015] In the above formula, b is the shortest distance from the ray to the center of mass. For the Sun, both theory and observation show that the angle of deflection is 1.75 arcseconds, approximately 5E⁻⁶ radians. This means that light rays from infinity will experience a redshift of 5E⁻⁶ when passing by the Sun. This value will be confirmed by future astronomical observations.

[0016] For Earth, this redshift would be about three orders of magnitude smaller than the redshift produced by the Sun, making it extremely weak. Therefore, measuring this redshift on Earth is extremely difficult.

[0017] Technical solution of the present invention

[0018] One of the objectives of this invention is to provide an experimental method and apparatus for measuring the changes in the energy, i.e. frequency, of photons under the influence of gravity.

[0019] To achieve the above objectives, this invention first provides an experimental method for measuring frequency changes caused by the interaction of light with a gravitational field. This method includes the following steps: a single-frequency laser beam is split into two beams, which enter two different Earth gravitational fields. After passing through the two different gravitational fields for a certain length, the two beams are recombined, thus forming an asymmetric interferometer. Since different optical path lengths will produce different redshifts, the differential redshift is measured by detecting the beat signal. The "differential redshift" is the difference in redshift produced by the two arms of the interferometer, specifically Z1 and Z2, obtained from the aforementioned redshift calculation formula. The differential redshift is equal to Z2 - Z1.

[0020] The optical path of the asymmetric interferometer can be a free-space optical path or an optical fiber path composed of optical waveguides.

[0021] For a free-space optical path, the device for measuring the frequency change generated by the interaction of light with a gravitational field includes: a single-frequency laser, the laser beam emitted by the single-frequency laser is split into two beams by an optical beam splitter, the two beams enter two different Earth gravitational fields respectively, and a set of total reflection mirrors is set in each of the two different Earth gravitational fields. After passing through the two different gravitational fields and different interaction lengths, the two beams are recombined, and the light is detected by a photodetector and outputs an electrical signal with a difference frequency for detection by a corresponding frequency measuring instrument or timing instrument.

[0022] For an optical fiber path composed of optical waveguides, the device for measuring the frequency change generated by the interaction of light with the gravitational field includes: a single-frequency laser, the light emitted by the single-frequency laser is split into two paths by an optical fiber beam splitter, the two paths of light pass through two optical fibers of different lengths located in different gravitational fields of the Earth, and are then connected to an optical fiber combiner. The combined optical signal interferes with the photodetector and outputs an electrical signal with a difference frequency for detection by a corresponding frequency measuring instrument or timing instrument.

[0023] Another aspect of this invention relates to the change in the speed of photon propagation under the influence of gravity. The constancy of the speed of light is one of the core assumptions of Einstein's special theory of relativity. It states that the speed of light, *c*, in a vacuum is constant for all inertial observers and is independent of the relative motion between the light source and the observer. This speed is approximately 299,792,458 m / s. Another objective of this invention is to provide an experimental method and apparatus for verifying whether the speed of photon propagation changes under the influence of Earth's gravity.

[0024] The experimental method for detecting changes in the propagation speed of light under the interaction of gravitational fields, as described in this invention, includes the following steps: a pulsed laser beam is split into two beams, which enter two different Earth gravitational fields respectively. The beams travel the same optical path length under the action of the two different Earth gravitational fields. After detection by two photodetectors, the time delay between the two signals is compared, thereby determining and detecting whether and how much the propagation speed of light changes under the interaction of different gravitational fields.

[0025] The apparatus for detecting the change in the propagation speed of light under the interaction of gravitational fields, as described above, includes: a pulsed laser; the light pulse signal generated by the pulsed laser is split into two beams by a beam splitter; the two light pulses enter two different Earth gravitational fields respectively; a set of total reflection mirrors is set in each of the two different Earth gravitational fields; after passing through the two different gravitational fields and with different interaction lengths, the outgoing light pulses are detected by photodetectors to obtain two pulse signals; by comparing the timing relationship between the two pulse signals, it can be determined whether the propagation speed of light is the same under the action of different gravitational fields.

[0026] Advantages and beneficial effects of the present invention:

[0027] The Pound-Rebka experiment is currently the only experiment on Earth studying the interaction between light and a gravitational field. This experiment involves the phenomenon where light's frequency decreases and its wavelength lengthens as it propagates outward from a gravitational field; this is known as "gravitational redshift," or Einstein redshift, caused by the difference in gravitational potential at different altitudes within Earth's gravitational field. The experimental method and apparatus involved in this invention, for measuring the change in the energy (i.e., frequency) of photons under gravitational influence, provide a theoretical basis and experimental technique for detecting the additional redshift introduced by changes in photon momentum under constant Earth's gravity. The experimental method and apparatus involved in this invention make it possible to detect extremely small redshifts (1E-9). Another experimental method and apparatus involved in this invention for measuring the interaction between light and a gravitational field provides a technical means to verify whether the propagation speed of photons changes under different Earth's gravitational influences. Compared with existing methods for measuring the speed of light, the significant advantage of the experimental method and apparatus involved in this invention is that it does not require measuring the absolute value of the speed of light, but only requires measuring the time difference between two light pulses after they have traveled the same optical path. Therefore, it has the advantages of high precision and high sensitivity. Attached Figure Description

[0028] Figure 1 A schematic diagram of an experimental setup for detecting the redshift of light under the influence of Earth's gravitational field.

[0029] 101 is a single-frequency laser; 102 is an optical beam splitter; 103, 105, 107, and 108 are the first to fourth optical total reflection mirrors; 104 is the first gravitational field with g1; 106 is the second gravitational field with g2; 109 is a beam combiner; and 110 is a photodetector.

[0030] Figure 2 A schematic diagram of another experimental setup for detecting the redshift of light under the influence of Earth's gravitational field.

[0031] 201 is a single-frequency laser; 202 is an optical fiber beam splitter; 203 is a gravitational field; 204 is an optical fiber disk; 205 is an optical fiber combiner; 206 is a photodetector.

[0032] Figure 3 A schematic diagram of an experimental setup for detecting changes in the propagation speed of photons under the influence of gravity.

[0033] 301 is a pulsed laser; 302 is an optical beam splitter; 303, 304, 306, 307, and 309 are the fifth to ninth optical total reflection mirrors; 308 is the first gravitational field with g1; 305 is the second gravitational field with g2; and 310 and 311 are the second and first photodetectors, respectively. Detailed Implementation

[0034] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0035] To detect the extremely small redshift of light under the influence of Earth's gravitational field, this invention utilizes the principle of coherent heterodyne. The method involves splitting a single-frequency laser beam into two beams. Under the influence of Earth's gravitational field, the two beams are allowed to rejoin after passing through different lengths of interaction with the gravitational field, thus forming an asymmetric interferometer. Since different optical path lengths will produce different redshifts, the differential redshift can be measured by detecting the beat signal.

[0036] The interaction force (ΔG) between light and the gravitational field can be given by the following formula:

[0037]

[0038] Where g1 and g2 are the first and second gravitational field strengths, respectively; l1 and l2 are the optical path lengths of the two arms of the interferometer, respectively; θ1 and θ2 are the angles (acute angles) between the optical path and g1 and g2, respectively. The differential redshift of the interference signal is linearly related to ΔG.

[0039] Example 1

[0040] As attached Figure 1 As shown, the laser beam emitted by the single-frequency laser 101 is split into two beams by the optical beam splitter 102. The reflected beam is reflected by the first total internal reflection mirror 103 and enters the second gravitational field 106. This beam travels back and forth multiple times between the second and third total internal reflection mirrors 105 and 107, which increases the interaction length between the beam and the second gravitational field 106 (this method is a commonly used existing technique, and its function can also be achieved by other existing methods). The outgoing beam is reflected by the fourth total internal reflection mirror 108. The other transmitted beam, after passing through the optical beam splitter 102 and the first gravitational field 104, is combined with the beam reflected by the fourth total internal reflection mirror 108 at the beam combiner 109. The beam is detected by the photodetector 110, which outputs an electrical signal with a difference frequency for detection by a corresponding frequency measuring instrument or timing instrument. The first gravitational field 104 can be the same as or different from the second gravitational field 106.

[0041] In laboratory conditions, a horizontal light path is typically used, and the gravitational field at the Earth's surface is uniform within a certain range. Therefore, in the expression for ΔG, g1 = g2, θ1 = θ2 = 90°. Therefore, using an attached... Figure 1 The differential redshift obtained from the experimental setup shown is proportional to the optical path difference between the two arms of the asymmetric interferometer. Therefore, a long optical path difference is required to detect the differential redshift caused by Earth's gravity.

[0042] Example 2

[0043] exist Figure 2In another experimental setup shown, which uses a fiber optic interferometer to detect the redshift of light under the influence of Earth's gravitational field, the light emitted by the single-frequency laser 201 is split into two paths by the fiber optic beam splitter 202. These paths are connected by optical fibers to the fiber optic disk 204 and the straight-through fiber located in the gravitational field 203, respectively, and then connected to the fiber optic combiner 205. The combined light signal interferes at the photodetector 206 and outputs an electrical signal with a difference frequency for detection by the corresponding frequency measuring instrument or timing instrument.

[0044] Compared with the method used in Example 1 Figure 1 Compared to the experimental setup shown, the one used is... Figure 2 The fiber optic interferometer shown has advantages such as simple structure and easy adjustment. In particular, it is easy to realize a detection system with long optical path difference by using a fiber optic interferometer.

[0045] In the experiment, laser 201 was a 1550nm single-frequency laser with a frequency of 1.935E14Hz and a coherence length greater than 50km. Under the condition of an optical path difference of 40km, the measured differential redshift was 5Hz.

[0046] Example 3

[0047] To detect changes in the propagation speed of photons under the influence of gravity, the present invention involves splitting a pulsed laser beam into two beams, which are then transmitted with the same optical path length under different gravitational fields. The time delay between the two signals is compared after detection by two photodetectors, thereby determining and detecting whether and by what amount the propagation speed of light changes under the interaction of different gravitational fields.

[0048] In the appendix Figure 3 In the experimental setup shown for detecting the change in photon propagation speed under gravity, the light pulse signal generated by the pulsed laser 301 is split into two beams by the optical beam splitter 302. The reflected beam is reflected by the fifth total internal reflection mirror 303 and enters the second gravitational field 305 (gravitational field strength g2). This beam travels back and forth multiple times between the sixth and seventh total internal reflection mirrors 304 and 306, increasing the interaction length between the beam and the second gravitational field 305. The outgoing beam is detected by the second photodetector 310, yielding pulse signal 2. The beam passing through the optical beam splitter 302 passes through the first gravitational field 308 (gravitational field strength g1). This beam travels back and forth multiple times between the eighth and ninth total internal reflection mirrors 307 and 309, and the outgoing beam is detected by the first photodetector 311, yielding pulse signal 1. By comparing the timing relationship between pulse signal 1 and pulse signal 2, it is possible to detect whether the propagation speed of light is the same under different gravitational fields. On the Earth's surface, the gravitational field varies at different altitudes, so this is achieved by utilizing the gravitational field at different altitudes. Figure 3 The experimental setup shown can achieve precise measurement of Earth's gravity or gravitational gradient.

[0049] In the experiment, laser 301 used a pulsed laser with a pulse width of 1 ps and a repetition frequency of 80 MHz. With the first gravitational field 308 at the ground and the second gravitational field 305 at a height of 10 meters, the time delay between the two pulse signals was measured to be 1 ps. The experimental results show that the same light pulse, after being split, travels the same distance in different gravitational fields, resulting in a 1 ps time delay. Since the speed of light equals the propagation distance divided by the propagation time, the existence of this time delay proves that the propagation speed of the light pulse is different in different gravitational fields.

[0050] Those skilled in the art will understand that the ideas of this invention can be implemented in ways other than the specific embodiments listed above.

Claims

1. An experimental method for measuring frequency changes caused by the interaction of light with a gravitational field, characterized by the following steps: A single-frequency laser beam is split into two beams and sent into two different gravitational fields of Earth. After passing through two different gravitational fields for a certain length, the two beams are reunited, thus forming an asymmetric interferometer. Since different optical paths will produce different redshifts, the differential redshift can be measured by detecting the beat signal.

2. The experimental method for measuring frequency changes caused by the interaction of light with a gravitational field according to claim 1, characterized in that... The optical path of the asymmetric interferometer is a free-space optical path.

3. The experimental method for measuring frequency changes caused by the interaction of light with a gravitational field according to claim 1, characterized in that... The optical path of the asymmetric interferometer is an optical fiber path composed of optical waveguides.

4. An apparatus for measuring frequency changes generated by the interaction of light with a gravitational field to implement the method of claim 2, characterized in that... The device includes a single-frequency laser, the laser beam emitted by the single-frequency laser is split into two beams by an optical beam splitter, the two beams enter two different Earth gravitational fields respectively, and a set of total reflection mirrors is set in each of the two different Earth gravitational fields. After passing through the two different gravitational fields and different action lengths, the two beams are recombined, and the difference frequency electrical signal is detected by a photodetector and output for detection by a corresponding frequency measuring instrument or timing instrument.

5. An apparatus for measuring frequency changes generated by the interaction of light with a gravitational field to implement the method of claim 3, characterized in that... The device includes a single-frequency laser. The light emitted by the single-frequency laser is split into two paths by an optical fiber beam splitter. The two paths pass through two optical fibers of different lengths located in different gravitational fields of the Earth, and are then connected to an optical fiber combiner. The combined optical signal interferes with the photodetector and outputs an electrical signal with a difference frequency for detection by a corresponding frequency measuring instrument or timing instrument.

6. An experimental method for detecting changes in the speed of light propagation under gravitational field interaction, characterized by the following steps: A pulsed laser beam is split into two beams, which enter two different Earth gravitational fields. The beams travel the same optical path length under the influence of the two different gravitational fields. The time delay between the two signals is compared by two photodetectors to determine and detect whether the speed of light changes and the amount of change under the interaction of different gravitational fields.

7. An apparatus for detecting changes in the propagation speed of light under gravitational field interaction, implementing the method of claim 6, characterized in that... The device includes a pulsed laser. The optical pulse signal generated by the pulsed laser is split into two beams by an optical beam splitter. The two optical pulses enter two different Earth gravitational fields respectively. A set of total reflection mirrors is set in each of the two different Earth gravitational fields. After passing through the two different gravitational fields and with different action lengths, the outgoing optical pulses are detected by photodetectors to obtain two pulse signals. By comparing the timing relationship between the two pulse signals, it can be determined whether the propagation speed of light is the same under the action of different gravitational fields.

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