On the Phenomenon of Red Shifted Star
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.)
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
m1=m2 then r1=r2.
us say that the total distance between m1 and m2 is
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.
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.
is noteworthy that the effect is reversible; radiation emitted from m2
would be blue shifted when absorbed by m1.
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).