# гЂгяТлЮФЭј

### СЊЯЕЗНЪН

##### ЙигкЪВУДЪЧАЎвђЫЙЬЙЕФЕШаЇд­Рэ 

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ciple is a dynamic principle. To appreciate EinsteinЁЏs ingenuity, it would be easier to start from his paper of 1911, where he found that his equivalence principle is compatible with the Doppler effects and even the notion of p hoton. Thus, EinsteinЁЏs equivalence principle has been firmly established on the ground of universality of physics. Since the notion of curved space would produce a second order effect in his consideration of the effect of gravitational red shifts , EinsteinЁЏs 1911 derivation of the red shifts is valid. Einstein assumed that the mechanical equivalence of an inertial system K under a uniform gravitational field, which generates a gravitational acceleration g (but, system K is free from acceleration), and a system K' accelerated by g in the opposite direction, can be extended to other physical processes. He considered two material systems S1 and S2 which are situated initially at rest on the z-axis of system K and are separated by a distance h so the gravitation potential in S2 is greater that S1 by gh. If a definite radiation energy E2 be emitted from S2 to S1 at the moment that system K' has zero velocity relative to an inertial system K0, the radiation will arrive at S1 when the time h/c has elapsed (to a first order approximation); and at this moment the velocity of S1 relative to K0 is gh/c = v. According to special relativity, the radiation arrives S1 with a greater energy E1 which (to a first order approximation) is related to E2 by E1 = E2(1 + v/c) = E2(1 + gh/c2) (2) The above is consistent with, E = mc2 in the sense of mass-energy conservation . By assumption, exactly the same relation holds if the same process takes place in the system K, which is not accelerated, but is provided with a gravitational field. Then, gravity must act also on radiation, and we may replace gh by the gravitational potential F and obtain E1 = E2(1 + F/c2) = E2 + F(E2/c2). (3) Thus, the energy increment of radiation due to gravity is resolved by the equivalence of the K and K' systems. If the radiation emitted in the uniformly accelerated system K' in S2 towards S1 had the frequency n2 relatively to the clock in S2, then at the arrival of radiation in S1, it has a greater frequency n1 relatively to S1, such that to a first approximation n1 = n2(1 + g h/c2) (4a) If the radiation is emitted at time that K' has no velocity, S1 at the time of arrival of the radiation, has relative to K, the velocity gh/c. Eq. (4a) is an immediate result of the Doppler's principle. If gh is substituted by the gravitational potential F of S2 - that of S1 being taking as zero - then the equivalence principle, to the first order approximation gives n1 = n2(1 + F /c2). (4b) If on the surface of a star (where S2 is located) the light is emitted to the Earth (S1) where the frequency of the arriving light is measured, then eq. (4b) implies n = n0(1 + F/c2), where F is the (negative) difference of gravitational potential between the surface of the star and the Earth. Also, if (3) and (4) are compared, then one would conjecture that the energy of a photon be E = k n, &nb sp; БОТлЮФгЩгЂгяТлЮФЭјЬсЙЉећРэЃЌЬсЙЉТлЮФДњаДЃЌгЂгяТлЮФДњаДЃЌДњаДТлЮФЃЌДњаДгЂгяТлЮФЃЌДњаДСєбЇЩњТлЮФЃЌДњаДгЂЮФТлЮФЃЌСєбЇЩњТлЮФДњаДЯрЙиКЫаФЙиМќДЪЫбЫїЁЃ

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