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1996年1997年陈老師等人发表在北大学报的实验论文没有电子文档贴不出来，只能去图书馆查阅，反正北大学报任何图书馆都有。我把陈老師在英文书《Relativity and Quantum Mechanics without Hypothesis and Origin of Gravitation 不带假设的相对论和量子力与引力作用的起源》的介绍贴出来来。还涉及到下述章节： 1.2 Self-Inconsistent Test Theory of Special Relativity 1.2.1 Classical ether theory……………………………………………… 1.2.2 Robertson’s theory………………………………………………… 1.2.3 Mansouri–Sexl’s theory… 1.3 Doppler Effect of Absolute Velocities………………………… ………… 1.3.1 Exclusive self-consistent selection…………………………………1.3.2 Preferred vacuum frame and absolute velocity…………………1.3.3 Doppler effect of absolute velocity in Michelson type interferometer 1.3.4 Doppler effect of absolute velocity in Sagnac interferometer……... 1.3.5 Doppler effect of fiber’s absolute velocity in generalized Sagnac interferometer…….. 1.4 Experiments for Testing Special Relativity 1.4.1 Method of heterodyne beat frequency with common mode restraint technique The phase difference measured by the interferometry> has a theoretic uncertainty for the phase difference depending on the changes in speed, wavelength and frequency of the light wave. The integral time of the changes in speed, wavelength and frequency is restricted by the size of the interferometer. As a result, it makes it difficult to improve the sensitivity of the interferometer. For instance, the arm length L = 400km, the phase difference distinguishing to 10– 4 π, the δν/ν can reach the level of about 10–15. It is not suitable for the interferometry> to test the Doppler frequency shift of absolute velocity in Eq.(16) or Eq.(18). Chen & Liu [4] proposed a method to test Eq.(16) or Eq.(18), in which by means of the common mode restraint technique, and via the dual beat-frequency based on the laser heterodyne frequency shift technique,the sensitivity of δν/ν can reach the level of 10–19. 1. Dual beat frequency based on laser heterodyne frequency shift technique We do not let two light waves ẼA and ẼB return from two arms to directly do the zero beat-frequency, but arrange ẼA and ẼB respectively with the third light wave ẼC to do the heterodyne beat-frequency. Set up the electric field intensities of the three light waves respectively as: ẼA =EA cos (ωA t+φA), ẼB =EB cos (ωB t+φB), ẼC =EC cos (ωC t+φ), Ẽ’C =E’C cos(ωC t +φ’ ) (28) Two light beams ẼC and Ẽ’C come from one beam by the beam splitter. These two beams still keep parallel and equidistant (error<1cm) to transmit, and their frequencies keep exactly at the same ωC , but there are only some slight differences in their phases and their electric field intensities. Let ẼA with ẼC beat-frequency, ẼB with Ẽ’C beat-frequency, the intensities of two beat-frequency interference light beams receipted by two photoelectric detectors are respectively: Ĩ A∝(ẼA + ẼC)2=E 2A cos 2 (ωA t+ φA) + E 2C cos 2 (ωC t+ φ)+ EA EC cos( (ωA+ωC) t + φA+ φ) + EA EC cos( (ωA－ ωC) t + φA－ φ ) Ĩ B∝(ẼB +Ẽ’C)2=E 2B cos 2 (ωB t+ φB) + E’ 2C cos 2 (ωC t+ φ’ )+ EB E’C cos( (ωB+ωC) t + φB+ φ’ ) + EB E’C cos( (ωB－ωC) t + φB－ φ’ )Because of the limit on the responding speed of the photoelectric detector, the electric signals exported by the two photoelectric detectors are only the components of difference-frequency (ωA－ωC) and (ωB－ωC), and the component of light-frequency appears to be in a form of direct average voltage Ū: ŨA=ŪA+UA cos( (ωA－ ωC) t + φA－ φ ) ŨB=ŪB+UB cos( (ωB－ ωC) t + φB－ φ’ ) (29) Let: 2πƒA=ΩA=ωA－ωC=2π(νA－νC), 2πƒB=ΩB=ωB－ωC=2π(νB－νC). To sieve the DC voltage, only the AC voltage signals are taken: ŨA (t)= UA cos(2π ƒA t + φA－ φ ) = UA cos(ΩA t + ΨA－Ψ) ŨB (t)= UB cos(2π ƒB t + φB－ φ’ ) = UB cos(ΩB t + ΨB－Ψ’ )Thus it can be seen that two voltage signals ŨA (t) and ŨB (t) obtained by the heterodyne beat-frequency have already inherited the frequency difference and the phase difference of the two light waves ẼA and ẼB: Δƒ= ƒA－ƒB= (ωA－ ωB)/2π = νA－νB = δθ ν, ΔΩ = (ΩA－ΩB) = (ωA － ωB) = Δ ω ΔΨ=ΨA－ΨB + Ψ’－Ψ= φA－ φB + φ’－ φ=Δ φ (30)There is no frequency ωC of the third light wave ẼC in Eq. (30), the result of ŨA (t) and ŨB (t) electric beatfrequency. Thereby, the frequency difference (νA－νB) of two light beams in different directions ẼA and ẼB can be replaced by the frequency difference (ƒA－ƒB) of two AC voltage signals ŨA (t) and ŨB(t). The integral time of δθ ν is restricted by the size of the interferometer, but the integral time of Δƒ is not restricted in principle by the digital phasemeter of the microcomputer technique. Even if we observe the rotation of Lissajous figure with the ordinary oscillograph, we can also distinguish the frequency difference of 10– 4Hz. From δθ ν/ν=Δƒ/ν,δθ ν/ν can be distinguished to the level of 10–19. When ƒ is several hundred Hz, ν/ƒ≈1012. Thus this so high sensitive method works in a way in which the wavelength looks as if it were “elongate” 1012 times or the phase difference looks as if it were “magnified” 1012 times. Both the heterodyne beat-frequency method and the heterodyne interference method change the total phasedifference (Δ ω t + Δ φ)of two light waves into the total phase difference (Δ Ω t + Δ Ψ) of two electric signals. It is much easier to measure the latter. When measuring the frequency-difference with the heterodyne beat-frequency method, from the records of (Δ Ω t + Δ Ψ) in the total phase-difference we eliminate Δ Ψ which can not change with time, but only take Δ Ω t which can change with time to get the frequency-difference Δ Ω＝Δ ω. When measuring the phase-difference with the heterodyne interference method, from the records of (Δ Ω t + Δ Ψ) in the total phase-difference we eliminate Δ Ω t which can change with time, but only take Δ Ψ which can not change with the time to get the phase-difference Δ Ψ＝Δ φ.Obviously, Δ ω measured by heterodyne beat-frequency and Δ φ measured by heterodyne interference are not the instantaneous values of the light wave, because the time of one period of an electric signal includes about 1012 periods of light wave (ω / Ω ≈ 1012), the stability of light waves ẼA, ẼB, ẼC and Ẽ’C is the necessary precondition. ΔΩ and ΔΨ are equivalent to the “average” values of Δ ω and Δ φ respectively in about 1012 periods of light wave. In principle, the interferential distance of the heterodyne interference method (the unidirectional length of the overlapping paths of two interferential lights in the same direction of the space) is only one wavelength. In fact, the unidirectional interferential length can be made in the range of several mm ~ several cm (time about 10–11~10–10s) due to the technical reason, and the unidirectional interferential length will include the wave-number of 103 ~104, but it does not affect the aforesaid conclusion, because in the interval of 10–11~10–10s the stability of light waves is sufficient. 2. Common mode restraint technique The dual beat frequency based on laser heterodyne frequency shift technique can distinguish the relative frequency difference δθ ν/ν of 10–19. The metrical precision is mainly restricted by the instrumental noise and the environmental interference. The common mode restraint technique in the laser beat frequency is to be shifted from the electronics domain into the optical measurement one and to be generalized. Its principle is that let the frequency emitted by laser change freely, but let the frequencies νA (t) and frequency νB (t) of two laser beams ẼA and ẼB with beat-frequency change along with the time in the same mode (common mode), the frequency difference ((νA (t)－νB (t)) will not change with time. When the frequencies of two light beams in the interferometer with two strictly equal length arms do not change on the way, i.e., there is no any mechanical vibration or thermal displacement velocity of the reflectors as well as no the Doppler frequency shift of absolute velocity, and the frequencies of two returning light beams will still keep change in the common mode.As an example, the frequency shift of the non-steady frequency He-Ne laser is caused mainly by the change in the length of the laser cavity, and excluding the mechanical vibration, the change in the cavity length is caused mainly by the change in the temperature. When the thermal equilibrium between the laser and the milieu is basically reached by warming up the laser for about 4h, the change rate in the temperature of the laser tube is less than 1°C/h=3×10–4 °C/s, then it cause the relative elongation of the glass cavity of laser: ΔL/L<3×10–9/s. When the difference between these two arm-lengths is δL ≤ 1mm, the time difference between the round-trips caused by the light traveling in two arms is about δt ≤7×10–12 s. At the time intervals δ t the relative change in the frequency of the glass tube laser is about: δ ν /ν < 3×10–20. For the quartz tube laser it is δ ν /ν < 3×10–21, which is close to the level of the quanta noise caused by the laser emitting photons and the photoelectric cell receiving photons. Therefore, the main error in the dual beat-frequency with the common mode restraint technique does not come from the inner reason of the laser frequency shift, but comes from the external reason of the non-ideal quakeproof step and the thermal displacement of the mirror and the base etc.Let one light beam be divided into three beams ẼA, ẼB and ẼC by the beam-splitter and then let them transmit in different paths with the same length, the three beams can beautifully satisfy the common mode condition. The frequency of the light beam ẼC is shifted several hundred Hz by the external frequency modulation method such as by the even speed reflector. The beat-frequency ẼA with ẼC and ẼB with Ẽ’C still can satisfy the common mode condition. The frequency ωC of the referenced beam ẼC does not appear in the last result Δ ƒ in Eq.(30), because the two frequencies ωC s in ŨA (t) and ŨB (t) counteract with each other during the course of the electrical beat-frequency. 1.4.2 Twinborn interferometer and experimental test for the isotropy of two-way speed of light With the twinborn laser interferometer we [6] tested the isotropy of two-way speed of light showed in Fig. 4 and obtained the precise value: Δ ν / ν ≤ 1×10–18, or the relative variation of the two-way speed of light Δ c / c ≤ 1×10–18.  In the experiment showed in Fig.4, the light source is the ordinary non-steady frequencies He-Ne laser. The triangle wave voltage on PZT is about 100 V in peak-peak value, its period about 8 ms, and caused the light wave frequency shift about 1kHz. The appropriative digital phasemeter is controled synchronously by the triangle wave voltage on PZT, and its reading is calibrated by the rotation of Lissajous figure, 0→π rotation which corresponds to the reading 0→1024 of the phasemeter. Within each triangle wave voltage period once metrical result is present, and within the real time period 4ms is used to collect samples and make readings, and the other 4ms to deal with signal and to calculate. The average phase difference Ф obtained from 512 times (about 4s) metrical results and ΔФ = Фi+1－Фi are shown on the computer screen. In order to decrease the error caused by the air convection, the whole device with the optical path (including laser) is airproofed in a metal airproofed in a metal box with a vacuum of 13.3Pa. Also in order to decrease the error caused by the vibrating disturbance around, the entire experimental device (including the oscillograph, appropriative digital phasemeter and microcomputer) is set in a big quakeproofed experiment- platform of the Department of Geophysics, Peking University. But the error in the test experiment still mainly comes from the vibratory disturbance around. Just as our expected, the relative error caused by the change in the emission frequency of the non-steady frequency He-Ne laser decreased to 1×10 – 19. As soon as the laser was switched on and started running, an obvious rotation of Lissajou figure was observed by us, and after this running lasted for 4~8 hours the rotation of Lissajou figure couldn’t be seen by us. We found: when the optical paths with common mode are adjusted from δL=1mm to δL=1cm, the experimental results are the same. It shows that by fully warming up the glass tube of the laser, the change rate in its temperature is not over 0.5°C/h. When we make the vacuum degree of the airproof metal box fall to 1 atm. (full air), the experimental results are also the same, and it shows that by full thermal equilibrium the refractive index of the air in the box is in high uniformity and isotropy. The measuring result is: Δ f =ΔФ /4s ≤5×10– 4 Hz. Δ f / ν = δθ ν/ ν ≤ 1×10 – 18. From Eq.(12) the absolute velocity V ≤1×10 – 18 c ≤ 0.3nm/s. From Eq.(14) the absolute velocity V ≤ (3.3×10 – 19)1/2 c ≤ 6×10 – 10 c ≤ 18 cm/s. |