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On the Phenomenon of Red Shifted Star Light

 

According to the Equivalence Principle, radiation emitted upward from the bottom of the celebrated box in deep, gravity-free space will be Doppler shifted toward the red when it is absorbed at the accelerating top of the box. Equivalently, radiation emitted from a point at rest and low in a gravitational field should have a longer wavelength when absorbed at a resting point higher up in the field a result shown experimentally to occur by Pound, Rebka et al. In this article it is demonstrated that the wavelength shift is a function of how far apart a massive emitter and a less massive receiver are. (Any Doppler shift that occurs when the emitter and absorber move toward or away from one another can only augment this shift.)

 

In order to demonstrate the assertion mathematically, let us begin by imagining that there are two resting bodies, one emitting radiation and the other absorbing it. Let the two bodies have gravitational masses m1 and m2. There is a point on the line between the two at which gravity is zero. If that zero point is r1 distant from m1 and r2 distant from m2, then

 

Gm1/r12 = Gm2/r22                  (1)

 

whence

 

r1 = (m1/m2)1/2r2.           (2)

 

If m1=m2 then r1=r2.

 

Let us say that the total distance between m1 and m2 is

 

L = r1+r2.                        (3)

 

Then

 

L = (m1/m2)1/2r2+r2.                           (4)

 

If m1=m2, then r1=r2=L/2. But If m1>>m2, then r1>>r2. This would typically be the case if m1 is a star and m2 is the Earth.

 

Now if m1 equaled m2 then the zero point would be midway between them. Light from m1 would be red shifted from m1 to the zero point, and blue shifted by the same amount from the zero point to m2. There would be no net red or blue shift. But if m1>>m2 then r1>>r2. There will be a net red shift in propagating from m1 to m2. And this net red shift will become greater as L is increased.  

 

It is noteworthy that the effect is reversible; radiation emitted from m2 would be blue shifted when absorbed by m1.

 

In view of the above, a rather solid case can be made that the red shift of starlight measured on Earth becomes more pronounced with increasing Earth-star distance, even when the star and Earth are at rest in the same frame. In particular, the red shift is not because the Universe is expanding (although the red shift could be augmented by expansion).