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Binary Star and Special Relativity

In the figure  below, star 1 and star 2 circle each other, connected by gravity, in what is called a binary star. The three arrows closer to the binary star show how one might picture the light coming off of this system, if one assumed that the motion of the source of light changed the velocity of light originating from that source. At the top of the orbit star 1 is moving towards the observer, at its orbital velocity V, emitting light at the combined velocity of  C + V. At the next position it is moving down, meaning it is not headed away from or towards the observer, so its light's velocity is just C. When it reaches the bottom of the circle, star 1 is headed directly away from the observer, its light's velocity in the observers frame should be C - V. If the light's velocity, with respect to the observer ( who is not moving with respect to the center of this binary system) changed according to the source's motion, the image in the observer's telescope would be scrambled. In fact it is coherent

The light from the top of the orbit would reach the observer ahead of light from the bottom of the orbit. In fact a binary star in a telescope looks as is should, meaning that the second set of arrows, with light from all points on the orbit traveling at the same velocity, C, represents what happens in nature. The terms of special relativity fit with what the binary star shows us.

Here is another representation of a binary star system:

The notations "blue" and  "red" refer to a change in color towards the shorter wavelengths when the star is heading towards us, "blue shift" this is called, and towards the longer wavelengths when the  star is going away from us, which is "red shift". So, even if the speed of light is unchanged, the wavelength and frequency change. This is like the "Doppler shift" with sound waves. The whistle of a train coming towards you goes from a higher to lower pitch as the train passes you and goes away from you. The higher pitch in sound is the blue shift in light, the lower pitch in sound is the red shift i light.

 The binary star issue is the same as the one depicted here: one source is moving towards the observer, the other source is moving away from the observer.

It may be noted that under the "ether" hypothesis light waves from differently moving sources would travel at the same velocity with respect to the ether, as do sound waves with respect to the air. So the intact binary star image would be expected under the ether hypothesis. But if we accept that light travels in a vacuum, then one would expect the motion of a light  source to be imparted to a pulse of light, so that the light from and spacecraft moving towards us would pass us at a higher rate than light from a spacecraft moving away from us.  Nevertheless, is is not that hard to imagine that light from two differently moving sources would assume the same velocity in space. For one thing the fixed reference of space can be imagined as all the light passing through any given cubic inch of space, which is akin to the ether notion...... But when there is one light source and two observers (see figure below), one moving toward the pulse of light, the other away from it, and Relativity says both observers measure the light as having the same velocity, the issue is different from the binary star issue (two sources one observer).  It is impossible to imagine how two differently moving observers could measure the same wave front as having the same velocity, and it is much harder to accept than the claim Relativity makes for two sources and one observer.  And, in the case of the two sources and one observer, we have the binary star to show us that the light signals travel at the same velocity, even though the sources of those two signals are moving towards and away from the observer.

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