June 21, 2023 started, August 15, 2023 revised, January 13, April 19, 2024 revised.

Takanori Senoh

1. Introduction

Because the light has no weight, it is not affected by any other's motion. Its speed of 300,000(km/s) on the absolute rest coordinate never changes even on the moving Earth. However, because the light-pass length changes when the Earth moves, the light propagation time changes on a distance L fixed on the Earth. Because the light speed C(m/s) is very fast, the propagation time to a mirror at L=1(m) away is just about T=3.5(ns). If the Earth motion is slow, we can't measure the change of the light propagation time. Because the Earth revolution speed V = about 30(km/s), which is 1/10,000 of the light speed C, the propagation time difference is about 0.35(ps), 

1-1. Failed Michelson's Experiment

Michelson (USA) noticed he could measure the round-trip time of the light with the scale of the light-wavelength, which is about 500(nm), by dividing the light into two lights (one is parallel to the Earth motion and the other is perpendicular to it) with a half-mirror and generating their fringe pattern from the reflected lights. He reported the results in the famous Michelson-Morley's experiment (1881). The fringe pattern is generated by the interference of these two light waves if they are crossing to each other. The light becomes bright where their phases are the same to each other and becomes dark where their phases are opposite to each other.  As small as the crossing angle of these lights, the fringe pattern interval becomes large. Hence, a very small phase difference is magnified in the fringe pattern and becomes visible. In his experiment, the round-trip time T of the light perpendicular to the Earth motion was thought to be T=2L/C(sec), where L (m) = distance to the mirror and C (m/s) = light speed. The other light takes a time of T1=L/(C-V)(sec) on the outward-trip because the mirror escapes with the Earth speed V(m/s). The reflected light takes another time of T2=L/(C+V)(sec) because the half-mirror is approaching with the Earth speed. Hence the round-trip time is T1+T2=(2L/C)/(1-(V/C)2)(sec). This amount is a little larger than T=2L/C(sec). The difference is ΔT= about Tx(V/C)2=7x10-17(sec).  During this time, the light goes CxΔT=21(nm)= 1/25 of the green light wavelength, λ=500(nm). At first, the fringe edge position is memorized by pointing one light to the Earth motion direction (Ex. East-West at midday on summer solstice). Next, measure the displacement of the edge after rotating the system by 90 degrees.  This time, the two lights swap to each other, their crossing angle is inversed, and the displacement becomes twice of the time difference.  Hence, the half of the fringe edge displacement becomes the path-difference of two lights. Unfortunately, the measured half fringe edge displacement was about 1/50 of the fringe interval. Lator, he noticed the predicted amount 1/25 was wrong and the correct amount was 1/50 because the light perpendicular to the Earth motion must travel diagonally compensating the Earth motion.  Although the measured amount was correct, because it was comparable to the measurement error, he repeated the experiment in 1887, extending the light-path to 10(m) by reflecting the light many times, and expecting the displacement of 1/2.5 fringe interval. Unfortunately, this time also, the measured displacement was less than 1/100 fringe interval. After his trials, some scientists retested and got the same results of measurement error order. 

Michelson’s Result:   ΔT=0,   that is  (T1+T2) = (T3+T4)

1-2. Premise of Relativity Theory

From these experimental results, people seem believed "the light travel-time to the motion direction is same as the time perpendicular to the motion." To explain these results, in 1892, Lorentz made "Shrink-Hypothesis", where "Every object shrinks to the motion direction", or in 1905, Einstein made "Special-Relativity-Theory" where "There is no common absolute time and each relative time flies slowly if on the moving objects". Einstein augmented this theory to "Generalized Relativity Theory", where "Gravity delays the time and warps even a vacant no-weight space, hence bends no-weight light". Because this theory has mathematically no-error and is difficult to confirm in  experiments, it has been believed as a truth for 100 years until now.

Lorentz' Length Contraction Hypothesis:  Any material shrinks  along to its motion direction.

Einstein's Relativity Theory:  There is no common absolute time. 

Relative time of a moving object becomes slow.

1-3. Truth of Michelson's Experiment

However, we must be careful here, because Michelson seems have done a mistake in 1887's experiment, too.  Although the fringe pattern needs two crossing wavefronts, he converted the sphere wavefront to flat by the lens behind the lamp and reflected both lights exactly along the incoming paths and made the path-lengths long. Consequently, the wavefronts became flat and parallel to each other. Hence, the visible fringe pattern seems never generated. What worse, because the light was directly observed through a telescope, a Newton-ling might be generated in the telescope, by the interference between the incoming light and the reflected light between the eye-catch lens and the cross-marker plate placed close to the lens, which is used to measure the fringe pattern position. It seems he might mistake this Newton ling as the fringe pattern generated by the Earth motion. Because its light-path difference was short, the pattern seems never affected by its direction, time, nor even the Earth motion.

 Consequently, the experiments done by Michelson and others seem simply "incorrect" and never be the evidence of "the light propagation times are same, affected or not by the Earth motion". Hence, the Relativity theory made on this wrong premise seems same as the Geo-centrism, which was made based on the no-evidence faith "God made the universe centering the Earth."

Truth of Michelson's Experiment:   The experiment was done incorrectly.

1-4. Better Modern Experiment

Nowadays, because a stable fringe pattern is generated by a single-mode laser, it seems the difference can be measured, even though it is very small, if the experiment is done correctly. Originally this experiment aimed to investigate the effect (V/C=10-4）) of the Earth motion V(m/s) to the light travel time T(sec). However, because it was decided to measure the difference between the round-trip times of the lights, ΔT=T(V/C)2=7x10-17(sec) and because the Earth motion effect is almost cancelled, it became 104 times difficult, and a mathematically correct theory was created to explain the wrong results. This ratio of the Earth motion speed and the light speed (V/C) will be easily measured by comparing the arrival times L/(C-V) to the mirror placed along the Earth motion, by a pulse light source and a high-speed oscilloscope, and the arrival time L/C by rotating the measurement system by 90°. Because the resolution of currently available oscilloscope is about 10Ghz (100ps), the difference (100ps) will be observed on the oscilloscope screen by measuring the light arrival time on a tanker of L=300m long, with changing the ship direction 90 degrees. However, because there were no such tools, nor the enough knowledge about the fringe patterns at that time, it might be inevitable that no one noticed this mistake.

Correct Experiment:    Time difference can be measured by a fast oscilloscope.

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