Relativity: The Special and the General Theory

by Albert Einstein

May the book bring someone a few happy hours of suggestive thought!

In the first place we entirely shun the vague word ‘space’, of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by ‘motion relative to a practically rigid body of reference’.

But in view of the more recent development of electrodynamics and optics, it became more and more evident that classical mechanics affords an insufficient foundation for the physical description of all natural phenomena.

Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

“If we pick up a stone and then let it go, why does it fall to the ground?” The usual answer to this question is: “Because it is attracted by the earth.” Modern physics formulates the answer rather differently for the following reason.

Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body.

fundamental property of the gravitational field of giving all bodies the same acceleration,

But no person whose mode of thought is logical can rest satisfied with this condition of things. He asks: “How does it come that certain reference-bodies (or their states of motion) are given priority over other reference-bodies (or their states of motion)? What is the reason for this preference? In order to show clearly what I mean by this question, I shall make use of a comparison.

It is now high time that we remedy this defect, but I would mention at the outset, that this matter lays no small claims on the patience and on the power of abstraction of the reader.

It is a veritable wonder that we can carry out this business without getting into the greatest difficulties.

the velocity of light must always depend on the co-ordinates when a gravitational field is present.

general laws of nature;

Now let us refer this domain to a random Gauss co-ordinate system or to a ‘mollusc’ as reference-body K’. Then with respect to K’ there is a gravitational field G (of a particular kind).

Hereupon we introduce a hypothesis that the influence of the gravitational field on measuring rods, clocks and freely-moving material points continues to take place according to the same laws, even in the case where the prevailing gravitational field is not derivable from the Galileian special care, simply by means of a transformation of co-ordinates.

curvature of light rays by the gravitational field of the sun,

Considerations on the Universe as a Whole

As regards space (and time) the universe is infinite.

universe should have a kind of centre in which the density of the stars is a maximum, and that as we proceed outwards from this centre, the group-density of the stars should diminish, until finally, at great distances, it is succeeded by an infinite region of emptiness. The stellar universe ought to be a finite island in the infinite ocean of space.

This conception is in itself not very satisfactory.

We thus free ourselves from the distasteful conception that the material universe ought to possess something of the nature of a centre.

According to the general Theory of Relativity, the geometrical properties of space are not independent, but they are determined by matter.

Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of the matter as being something that is known.