Reviewing Michelson Interferometer Experiment and Measuring the Speed of Starlight

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.


Introduction
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 [1] [2] [3] [4]. Among them, the wave-aether model attracts most attention, because this model satisfies many light propagation characteristics such as polarization, refraction, diffraction, interference, stellar aberration, etceteras. However, this model involved the existence and drag effect of aether [1] [3] [4] [5] [6]. Michelson-Morley used an interferometer to test the aether wind and they obtained a null result of interference pattern shift [1] [3] Because the Michelson-Morley experiment is an important milestone in modern physics, it still attracts some attention recently [6] [7] [8].
Lorentz and others proposed a hypothesis that the length of a moving object along its motion direction contracted by the factor of ( ) 1 v c − , then the original Michelson's calculation interference pattern shift value agreed with the measured data [1]. In 1932, Kennedy and Thorndike performed an experiment using different arm lengths of an interferometer to test the Lorentz-Fizeau contraction [9]. The result showed the contraction might exist. Most people therefore gradually forgot and even abandoned this model. We may say that the wave-aether model is well-suited for describing the light propagation.
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 [10]. He concluded that the speed of light is independent of the speed of the light source and therefore the speed of light is constant. The wave-aether model explains his first conclusion.
However, he did not consider the motion of the earth. The constancy of the speed of light conclusion conflicts with the wave-aether model and further evaluation is needed.
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-Morley Experiment and Aether Wind
Michelson invented the interferometer to test the aether wind. Figure 1 shows the sketch of Michelson interferometer [1].
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 where v is velocity of the aether wind [1].
Similarly the round trip time along the second arm is ( ) 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 ( ) As shown in Figure 1, the aether wind blows along l 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 1 ' t and 2 ' t . Now the time difference is ( ) The difference ' ∆ − ∆ would yield an interference pattern shift by δ fringes where λ is the wavelength, v is the orbit speed of the earth [1].
Michelson used light with  [1]. In about next three decades, many physicists used various arm lengths and still observed no significant interference pattern shift [1] [3] [4]. In those days, many physicists including Lorentz, etceteras believed that the aether might exist and the earth truly moved in the aether [1]. The mother nature had a magical power thus that the length of a moving object along its moving direction with respect to the aether contracted by a factor of ( ) Then (1) became ( ) and t 2 remained unchange as ( ) The theoretical value agreed with the experimental data.
In 1727, Bradley discovered the stellar aberration of γ-Draconis [11]. In 1871, Airy used a telescope in which the whole tube was filled with water, to observe the stellar aberration then he found the light drag effect, and gave the drag coef- Imagine that if we fill the tubes of Fizeau's apparatus by a luminiferous medium with unit refractive index, such as aether, then f = 0.
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)  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.

Measuring the Speed of Starlights
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 [12]. We compare the arrival times of the starlight pulses and the local light pulses at the receiver. Then we can obtain the speeds of the starlights. delays may be caused by the system errors from temperature, humidity, and air dispersion [16], but the trends remain the same over the years.

Conclusions
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 Journal of Modern Physics 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.