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The wave-aether model was proposed long time ago. We study Michelson interferometer experiment and find that its theoretical calculation erroneously neglected the aether drag effect. We take the drag effect into account and reanalyze the theoretical interference pattern shift. The result is null because the drag coefficient of aether is zero. Such that the wave-aether model fulfills all light propagation characteristics. We design and implement a system to measure the starlight speed by comparing to that from a local source. We observe that the arrival times are different. It implies the apparent speeds of starlights are not equal to
*c*.

The speed and the propagation model of light are interesting subjects. The speed of light was considered as a very important physical parameter which is used to estimate the distance, mass etceteras. A few propagation models have been proposed since the ancient days [

Lorentz and others proposed a hypothesis that the length of a moving object along its motion direction contracted by the factor of ( 1 − v 2 / c 2 ) 1 2 , then the original Michelson’s calculation interference pattern shift value agreed with the measured data [

In 1818, Fresnel predicted that the light would be dragged by the luminiferous medium [

According to the wave-aether model, the motion of a light source will not communicate to the light speed i.e. the velocity of the light source is irrelevant to the speed of light but it will change the spectrum and wavelength.

Many observations and experiments have used moving light sources to test or prove the constancy of the speed of light.

In 1913, W. de Sitter observed some binary stars [

Around spring equinox each year, the earth is leaving away from Capella, Aldebaran, and Betelgeuse but approaching to Vega. We assume that the earth is moving in the aether, the starlight propagates with speed c in the aether. We setup a system including a transmitter and a receiver. The transmitter simultaneously modulates starlight and light from a local source into pulses. These pulses are detected by a distant receiver. We compare the arrival times of these two kinds of pulses. However, the receiver has relative motion with respect to the aether, the apparent speed of starlight may be related to the motion of the earth according to the wave-aether model. We find the arrival times are different. The system setup and measurement will be described in Section 3.

Michelson invented the interferometer to test the aether wind.

The two arms of Michelson interferometer are perpendicular. The length of the first arm is l_{1} and a second one is l_{2}. The light from the source is incident upon the beam splitter B which splits the light into two parts. Assume that the thickness of the beam splitter is zero. One part of light travels along the first arm and is reflected back by the mirror M1. Then it travels along the same path and partially reflected by the beam splitter B incident upon the observer. According to Michelson calculation, the round trip time is

t 1 = l 1 c − v + l 1 c + v = 2 l 1 c 2 − v 2 (1)

where v is velocity of the aether wind [

Similarly the round trip time along the second arm is

t 2 = 2 l 2 ( c 2 − v 2 ) 1 2 (2)

Note that in the nineteenth century, the fluid mechanics was well developed and understood. The velocity of wave propagating in a fluid current, e.g. flowing water in a river, is vector addition. Probably, Michelson adopted the concept of fluid mechanics to formulate the light wave travelling times expressed as (1) and (2) which had neither theoretical basis nor experimental evidence.

The time difference of t_{1} and t_{2} is

Δ = t 1 − t 2 ≈ 2 ( l 1 − l 2 ) c + 2 l 1 v 2 c 3 − l 2 v 2 c 3 (3)

As shown in _{1}, we turn the interferometer 90˚, the aether wind will blow along l_{2}, such that the round trip times along l_{1} and l_{2}, i.e. t_{1} and t_{1}, will be reversed and become t 1 ' and t 2 ' . Now the time difference is

Δ ' = t 1 ' − t 2 ' ≈ 2 ( l 1 − l 2 ) c + l 1 v 2 c 3 − 2 l 2 v 2 c 3 (4)

The difference Δ − Δ ' would yield an interference pattern shift by δ fringes

δ = c ( Δ − Δ ′ ) λ = ( l 1 − l 2 ) v 2 λ c 2 (5)

If l 1 = l 2 , then

δ = 2 ( v / c ) 2 λ / l (6)

where λ is the wavelength, v is the orbit speed of the earth [

Michelson used light with λ = 6 × 10 − 7 m , l = 1.2 m .

Then according to (6) [

δ = 0.04 fringes.

However, Michelson didn’t observe this interference pattern shift. Later Michelson and Morley extended the arm length to 11.0 m to have more accurate result. They obtained 0.01 fringes. The theoretical interference shift is 0.40 fringes i.e. the difference of the theoretical value and the experimental data is ever bigger [

Then (1) became

t 1 = 2 l 1 ( c 2 − v 2 ) 1 2 (7)

and t_{2} remained unchange as

t 2 = 2 l 2 ( c 2 − v 2 ) 1 2 (8)

Therefore

Δ = Δ ' (9)

The theoretical value agreed with the experimental data.

In 1727, Bradley discovered the stellar aberration of γ-Draconis [

f = 1 − 1 n 2 (10)

which is known as Fresnel’s drag coefficient, n is the refractive index.

Fizeau designed the apparatus as shown in

Based on previous discussion, readers may be aware of that using interferometer to test aether wind will yield a null result. Bearing the drag effect in mind i.e. n = 1, f = 0, we rewrite (1) and (2) as

t 1 = l 1 c n − v f + l 1 c n + v f = 2 l 1 c (11)

and

t 2 = l 1 ( c 2 n 2 − v 2 f 2 ) 1 / 2 = 2 l 2 c (12)

(11) and (12) show that the round trip times of lights travelling along the two arms are irrelevant to the velocity of aether wind. The theoretical value and the experimental data are consistent. The wave-aether model therefore fulfills all light propagation characteristics such as interference, polarization, stellar aberration, especially the null result of Michelson interferometer experiment.

In other words, the wave-aether model should be valid. Based on the wave-aether model, we design a system and perform the experiment to measure the speed of starlight.

In the wave-aether model, the speed of light is irrelevant to the speed of the source but is influenced by the motion of the observer. The principle of our measurement system is simple. We use a chopper to modulate the continuous starlight ray and a local light ray into pulses. The speed of the local light, c, is known [

The details of the measurement setup, operation, data analysis, calibration, are described in References [

Date | The delays of the starlight pulses (ns) | |||
---|---|---|---|---|

Capella | Betelgeuse | Aldebaran | Vega | |

2010/3/15 | 1.61 | |||

2010/3/16 | 2.1/1.5 | |||

2010/3/18 | 3.9 | 1.2 | −3.2 | |

2011/2/28 | 3.0/2.7 | 1.8 | −7.4 | |

2011/3/4 | 2.5 | |||

2011/3/12 | 3.8 | |||

2012/2/18 | 4.6 | |||

2013/3/8 | 2.1 | −1.3 | ||

2013/3/9 | 2.2 | −1.9 | ||

2013/3/12 | 1.2 | |||

2014/1/20 | 1.4 | 1.8 | ||

2014/1/22 | 1.9/2.2 | |||

2014/1/23 | 2.1 |

We study Michelson interferometer experiment and search the causes of disputation between the experimentally measured null interference pattern shift and the significant theoretical calculation value. We find that Michelson formulated the light travelling times along the two arms of the interferometer neglecting the drag effect. We take the drag coefficient into account to reanalyze the theoretical interference pattern shift value and obtain a null result. We prove that the measured data and the theoretical value match very well. Previously the disputation of Michelson interference pattern shift is a major concern of the validation of the wave-aether model for light propagation. Now this issue is solved and the wave-aether model satisfies all light propagation characteristics such as straight line transmission, polarization refraction, etceteras. We can conclude that the wave-aether model is valid.

Based on the wave-aether model, we consider that the earth moves in the aether. We setup a system on the earth to measure the speed of starlight i.e. the system moves in the stationary aether. Because the system including the observer is moving, the apparent measured speed of the starlight may not be equal to c. we design a transmitter to modulate the starlight and the light from a local source into pulses. Note that the speed of the local light pulses is c, these starlight and the local light pulses travel over a distance and reach the receiver. We compare the arrival times of these two kinds of pulses. We find that the arrival time of the starlight pulse is different with that of the local light pulse. It indicates that the apparent measured speeds of the starlight vary from the well known c. In general, our experiment fits the wave-aether model well qualitatively.

The authors are grateful for Prof. Hong T. Young, Prof. Wen-Ping Chen, Director Hung-Chin Lin, Prof. San-Liang Lee, Mr. Chong-Tsong Chang, the staff of the Lulin Observatory of National Central University and the Experimental Forest of National Taiwan University to provide the facilities and necessary help. We also thank assistance from Miss Hui-Ting Tsao, and many our assistants and students who were involved in this project in the last two decades.

This work was supported in part by Excellent Research Projects of National Taiwan University and National Science Council, Taiwan under Grants 98R0062-06, NSC 97-2221-E-002-146-MY3, NSC100-2221-E-002-035, and NSC 101-2221-E-002-002.

The authors declare no conflicts of interest regarding the publication of this paper.

Wu, J., Tsao, H.-W. and Huang, Y.-R. (2019) Reviewing Michelson Interferometer Experiment and Measuring the Speed of Starlight. Journal of Modern Physics, 10, 539-547. https://doi.org/10.4236/jmp.2019.105037