Meaning of Relativity [Paperback]

On page 92, Einstein states that the rate of a clock is slower
the greater is the masse of the ponderable matter in the
neighborhood. This comports with the theory and computation
of inertia. As the base and height increases, the inertial
computation is geometrically greater in accordance with the
formulas of inertia [ ((b x h^3)/12) ]. In the discussion of
Mach, Einstein states that the inertia of a body must increase
when ponderable masses are piled in the neighborhood. This is
proven by computing inertia utilizing more massive bases and
heights. As the base and height increases, the inertial
computation is geometrically greater thereby proving that the
inertia of a body must increase when ponderable masses are
piled up in the neighborhood.

Einstein discusses the theory of Mach in relation to inertia
and the mutual action of bodies. The actual measurement of
Mach has at least 3 different levels; namely, subsonic,
sonic and supersonic measurements

Einstein argues that the hypothesis that the universe is
infinite and Euclidean at infinity is complicated from the
relativistic point of view. The universe expands and contracts .
Accordingly, the nature tends to approximate non-Euclidean
or quasi-Euclidean objects in the evolution toward the
expansive and infinite state which Einstein postulates as
potentially Euclidean in order.

The author begins this book with a discussion of the origin of the concepts of space-time, the emphasis being partly philosophical and partly psychological, and the reader can see the origin of the author's operationalism in reading this introduction. He is clearly against the philosophers who attempt to remove concepts from experience and put them in his words "in the intangible heights of the a priori". The motion of rigid bodies is used to set up a discussion of Euclidean geometry and linear orthogonal transformations. The author emphasizes the role of the physicist in discerning whether a system of geometry is true or not, contrary to the pure mathematician. Examples of geometrical invariants, such as the Cartesian line element and the volume element are discussed, along with the role of vectors and tensors. Both of these are used as means by which one can give expression to the independence of Cartesian coordinates. Maxwell's equations are put in tensor notation as an example of covariance with respect to Cartesian coordinate transformations. All of this is done to motivate the theories of special and general relativity.

The theory of spectial relativity is treated in chapter 2, the author introducing his famous principle of special relativity. The author poses the problem of calculating the coordinates and time in an inertial system moving with uniform translation relative to another. He shows how this problem is solved by assuming that time and space are absolute, and if the coordinate axes of the systems are parallel to one another, the Galilean transformations result. Newton's equations of motion are covariant under these transformations, but Maxwell equations are not (but the author chooses not to show this explicitly). He then gives an in-depth discussion of how the Lorentz transformations arise as being those that guarantee the covariance of the Maxwell equations. The author also discusses the signature of the Lorentz metric and how it is related to the light cone. He ends the chapter by developing the energy tensor of the electromagnetic field and matter.

The author's rejection of inertial frames as being priveleged leads him in the beginning of the next chapter to a short philosophical critique of the principle of inertia. This leads to a discussion of the principle of equivalence and to the origin of the general theory of relativity, a theory which the author developed, amazingly, single-handedly, and which he clearly believes is very much superior to classical mechanics. The intuition to be gained by reading this chapter is invaluable for serious students of general relativity. One can see the simplicity and power of the author's arguments, relying on keen physical intuition and sound use of mathematics. In particular, the author's heuristic derivation of the gravitational field equations from Poisson's equation is briliant. In addition, he is not ashamed to interject philosophical argumentation into his writing, particularly in his discussion of Mach's principle. Such discussions are becoming more rare among physicists at the present time.