The Meaning of Relativity

Albert Einstein

• Publisher: Routledge
• Year: 2003
• ISBN:
  9781134449781
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

The world would be a very different place if it were not for Albert Einstein. Like Newton and Galileo before him, this remarkable scientist changed forever mankind's understanding of the universe. In 1921, five years after proclaiming his general theory of relativity, Einstein was awarded the Nobel Prize for Physics in recognition of his remarkable achievements. In the same year he travelled to the United States to give four lectures that consolidated his theory and sought to explain its meaning to a new audience. These lectures were published the following year as The Meaning of Relativity, which he revised with each new edition until his death. It remains a key work for anyone wishing to discover at first hand the workings of one of the most inspiring minds of the twentieth century.

THE GENERAL THEORY OF RELATIVITY

All of the previous considerations have been based upon the assumption that all inertial systems are equivalent for the description of physical phenomena, but that they are preferred, for the formulation of the laws of nature, to spaces of reference in a different state of motion. We can think of no cause for this preference for definite states of motion to all others, according to our previous considerations, either in the perceptible bodies or in the concept of motion; on the contrary, it must be regarded as an independent property of the space-time continuum. The principle of inertia, in particular, seems to compel us to ascribe physically objective properties to the space-time continuum. Just as it was consistent from the Newtonian standpoint to make both the statements, tempus est absolutum, spatium est absolutum, so from the standpoint of the special theory of relativity we must say, continuum spatii et temporis est absolutum. In this latter statement absolutum means not only ‘physically real’, but also ‘independent in its physical properties, having a physical effect, but not itself influenced by physical conditions’.

As long as the principle of inertia is regarded as the keystone of physics, this standpoint is certainly the only one which is justified. But there are two serious criticisms of the ordinary conception. In the first place, it is contrary to the mode of thinking in science to conceive of a thing (the space-time continuum) which acts itself, but which cannot be acted upon. This is the reason why E. Mach was led to make the attempt to eliminate space as an active cause in the system of mechanics. According to him, a material particle does not move in unaccelerated motion relatively to space, but relatively to the centre of all the other masses in the universe; in this way the series of causes of mechanical phenomena was closed, in contrast to the mechanics of Newton and Galileo. In order to develop this idea within the limits of the modern theory of action through a medium, the properties of the space-time continuum which determine inertia must be regarded as field properties of space, analogous to the electromagnetic field. The concepts of classical mechanics afford no way of expressing this. For this reason Mach’s attempt at a solution failed for the time being. We shall come back to this point of view later. In the second place, classical mechanics exhibits a deficiency which directly calls for an extension of the principle of relativity to spaces of reference which are not in uniform motion relatively to each other. The ratio of the masses of two bodies is defined in mechanics in two ways which differ from each other fundamentally; in the first place, as the reciprocal ratio of the accelerations which the same motive force imparts to them (inert mass), and in the second place, as the ratio of the forces which act upon them in the same gravitational field (gravitational mass). The equality of these two masses, so differently defined, is a fact which is confirmed by experiments of very high accuracy (experiments of E

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s), and classical mechanics offers no explanation for this equality. It is, however, clear that science is fully justified in assigning such a numerical equality only after this numerical equality is reduced to an equality of the real nature of the two concepts.

That this object may actually be attained by an extension of the principle of relativity, follows from the following consideration. A little reflection will show that the law of the equality of the inert and the 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 Newton’s equation of motion in a gravitational field, written out in full, is

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, fre...

Table of contents

• COVER PAGE
• TITLE PAGE
• COPYRIGHT PAGE
• A NOTE ON THE SIXTH EDITION
• SPACE AND TIME IN PRE-RELATIVITY PHYSICS
• THE THEORY OF SPECIAL RELATIVITY
• THE GENERAL THEORY OF RELATIVITY
• APPENDIX I: ON THE ‘COSMOLOGIC PROBLEM’
• APPENDIX II: RELATIVISTIC THEORY OF THE NON-SYMMETRIC FIELD