Erk's Relativity Pages: ae_prgrx.htm

The General Theory of Relativity (extract) part of a lecture by Albert Einstein (1921) (Princeton University, May)

(Inert mass) * (Acceleration) = (Intensity of the gravitational field) * (Gravitational mass)

It is only when there is numerical equality between the inert and gravitational mass that the acceleration is independent of the nature of the body. Let now K be an inertial system. Masses which are sufficiently far from each other and from other bodies are then, with respect to K, free from acceleration. We shall also refer these masses to a system of co-ordinates K', uniformly accelerated with respect to K . Relatively to K' all the masses have equal and parallel accelerations, with respect to K' they behave just as if a gravitational field were present and K' were unaccelerated. Overlooking for the present the question as to the 'cause' of such a gravitational field, which will occupy us later, there is nothing to prevent our conceiving this gravitational field as real, that is, the conception that K' is 'at rest' and a gravitational field is present we may consider as equivalent to the conception that only K is an 'allowable'' system of co-ordinates and no gravitational field is present.
The assumption of the complete physical equivalence of the systems of co-ordinates, K and K', we call the 'principle of equivalence'; this principle is evidently intimately connected with the law of the equality between the inert and the gravitational mass, and signifies an extension of the principle of relativity to co-ordinate systems which are in non-uniform motion relatively to each other. In fact, through this conception we arrive at the unity of the nature of inertia and gravitation. For, according to our way of looking at it the same masses may appear to be either under the action of inertia alone (with respect to K ) or under the combined action of inertia and gravitation (with respect to K' ).
The possibility of explaining the numerical equality of inertia and gravitation by the unity of their nature gives to the general theory of relativity, according to my conviction, such a superiority over the conceptions of classical mechanics, that all the difficulties encountered in development must be considered as small in comparison with this progress.

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U / D = pi

But if K' rotates we get a different result. Suppose that at a definite time t , of K we determine the ends of all the rods. With respect to K all the rods upon the periphery experience the Lorentz contraction, but the rods upon the diameter do not experience this contraction (along their lengths!). *note It therefore follows that

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U / D > pi

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* These considerations assume that the behaviour of rods and clocks depends only upon velocities, and not upon accelerations, or, at least, that the influence of acceleration does not counteract that of velocity.

LECTURE CONTINUED ON PAGE 59 OF "THE MEANING OF RELATIVITY" -== ==-

The Meaning of Relativity
Chapman and Hall, starting at page 54
ISBN 0-412-20560-2