The Meaning of Relativity

"Before the development of the theory of relativity it was known the principle of energy and momentum could be expressed in a differential form for the electromagnetic field. The four-dimensional formulation of these principles leads to an important conception, that of the energy tensor, which is important of the further development of the theory of relativity."

"Some try to explain Hubbles shift of spectral lines by means other than the Doppler effect. There is, however, no support for such a conception in the known physical facts."

"One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with a continuum theory, and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory."

"It is the essential achievement of the general theory of relativity that it has freed physics from the necessity of introducing the "inertial system" (or inertial systems). This concept is unsatisfactory for the following reason: without any deeper foundation it singles out certain co-ordinate systems among all conceivable ones. It is then assumed that the laws of physics hold only for such inertial systems (e.g. the law of inertia and the law of the constancy of the velocity of light). Thereby, space as such is assigned a role in the system of physics that distinguishes it from all other elements of physical description. It plays a determining role in all process, without in its turn being influenced by them. Though such a theory is logically possible, it is on the other hand rather unsatisfactory. Newton had been fully aware of this deficiency, but he had also clearly understood that no other path was open to physics in his time. Among the later physicians it was above all Ernst Mach who focussed attention on this point."

"A material particle upon which no force acts moves, according to the principle of inertia, uniformly in a straight line. In the four-dimensional continuum of the special theory of relativity (with real time co-ordinate) this a real straight line. The natural, that is, the simplest, generalization of the straight line which is meaningful in the system of concepts of the general (Riemannian) theory of invariants is that of the straightest, or geodesic, line."

"A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newtons equation of motion in a gravitational field, written out in full, it is: (Inertial mass) \cdot (Acceleration) = (Intensity of the gravitational field) \cdot (Gravitational mass). It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body."