Matveev Mechanics And Theory Of Relativity by A. N. Matveev

Author:A. N. Matveev
Language: eng
Format: epub
Tags: physics, mechanics, theory of relativity, special relativity, newtons laws, conservation laws, angular momentum
Published: 1989-03-08T05:00:00+00:00

Fig. 66. Calculating red shift.

This question cannot be answered proceeding from general considerations since we are unaware of the action of gravity on frequency. We can make use of the equivalence principle to answer this question by considering that in the absence of gravitational field, the frequency of light does not change during its propagation.

We shall consider such an experiment in a reference frame falling freely in a uniform gravitational field. There are no forces in this reference frame, and all the processes occurring in it take place in the same way as in an inertial reference frame. Hence the frequency of light does not change upon propagation, and a stationary person at a point at height h in this reference frame must receive the same frequency that was emitted at point O in the same reference frame.

Let us now analyze the same experiment in the laboratory reference frame fixed to the Earth, in which a noninertial reference frame falls freely. We shall assume that at the instant of emission of the ray at point 0, the velocity of this reference frame is zero (the acceleration, however, is not zero and is equal to the free fall acceleration). In time At = h/c during which the ray of light propagates from point 0 to the point of observation at height A, the freely falling reference frame acquires a velocity v = g At — gh/c. Consequently, on account of the Dopplcr effect, an observer must receive in this reference frame a ray whose frequency is higher than that of the light emitted at point O by Aco = <£>(v/c). However, an analysis of the phenomena in the noninertial reference frame showed that there was no change in frequency. Hence it can be concluded that during the propagation of light from point 0 to the point at height h, the frequency of the emitted light has decreased by Aco = — wgh/c 2 . For visible light, this means a shift of the frequency towards the red colour of the spectrum. Hence the effect of decrease in the frequency during the propagation of light against the force of gravity is called red shift.

The magnitude of the red shift under terrestrial conditions is very small. For a difference of 10 m in height, we obtain the following estimate for the red shift:

Aco

CO

10 x 10 (3 x 10 8 ) 2

10"

(29.3)

To note such a change in frequency is equivalent to observing a loss of one second in about 100 million years. However, the red shift, which is negligibly small under terrestrial conditions, was reliably detected in 1960 by using the Mossbauer effect according to which photons are emitted by a nucleus under

29. Zero Gravity. Equivalence Principle

205

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