Reference: Evolution of Physics
This paper presents Chapter III, section 13 from the book THE EVOLUTION OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original publication of this book by Simon and Schuster, New York (1942).
The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding. Feedback on these comments is appreciated.
The heading below is linked to the original materials.
.
General Relativity and Its Verification
The general theory of relativity attempts to formulate physical laws for all c.s. The fundamental problem of the theory is that of gravitation. The theory makes the first serious effort, since Newton’s time, to reformulate the law of gravitation. Is this really necessary? We have already learned about the achievements of Newton’s theory, about the great development of astronomy based upon his gravitational law. Newton’s law still remains the basis of all astronomical calculations. But we also learned about some objections to the old theory. Newton’s law is valid only in the inertia! c.s. of classical physics, in c.s. defined, we remember, by the condition that the laws of mechanics must be valid in them. The force between two masses depends upon their distance from each other. The connection between force and distance is, as we know, invariant with respect to the classical transformation. But this law does not fit the frame of special relativity. The distance is not invariant with respect to the Lorentz transformation. We could try, as we did so successfully with the laws of motion, to generalize the gravitational law, to make it fit the special relativity theory, or, in other words, to formulate it so that it would be invariant with respect to the Lorentz and not to the classical transformation. But Newton’s gravitational law opposed obstinately all our efforts to simplify and fit it into the scheme of the special relativity theory. Even if we succeeded in this, a further step would still be necessary: the step from the inertial c.s. of the special relativity theory to the arbitrary c.s. of the general relativity theory. On the other hand, the idealized experiments about the falling lift show clearly that there is no chance of formulating the general relativity theory without solving the problem of gravitation. From our argument we see why the solution of the gravitational problem will differ in classical physics and general relativity.
General relativity attempts to integrate gravitation into the laws of physics. Newton’s law of gravitation is valid only in the inertial c.s. in which inertia and characteristics of space remain constant, but that is not the case on a broader scale. We need to update the Gravitational law not only for the basis of motion used in special relativity, but also for the non-inertial c.s. In other words, we need to update the gravitational law for changing absolute value of inertia.
We have tried to indicate the way leading to the general relativity theory and the reasons forcing us to change our old views once more. Without going into the formal structure of the theory, we shall characterize some features of the new gravitational theory as compared with the old. It should not be too difficult to grasp the nature of these differences in view of all that has previously been said.
(1) The gravitational equations of the general relativity theory can be applied to any c.s. It is merely a matter of convenience to choose any particular c.s. in a special case. Theoretically all c.s. are permissible. By ignoring the gravitation, we automatically come back to the inertial c.s. of the special relativity theory.
A coordinate system is defined by its level of inertia and the rate at which that inertia is changing.
(2) Newton’s gravitational law connects the motion of a body here and now with the action of a body at the same time in the far distance. This is the law which formed a pattern for our whole mechanical view. But the mechanical view broke down. In Maxwell’s equations we realized a new pattern for the laws of nature. Maxwell’s equations are structure laws. They connect events which happen now and here with events which will happen a little later in the immediate vicinity. They are the laws describing the changes of the electromagnetic field. Our new gravitational equations are also structure laws describing the changes of the gravitational field. Schematically speaking, we could say: the transition from Newton’s gravitational law to general relativity resembles somewhat the transition from the theory of electric fluids with Coulomb’s law to Maxwell’s theory.
The gravitational field is a field of substance that is varying in inertia. Inertia is a measure of substantial-ness of the substance. Inertia affects the motion of the substance in the field. There are laws describing the changes in the field.
(3) Our world is not Euclidean. The geometrical nature of our world is shaped by masses and their velocities. The gravitational equations of the general relativity theory try to disclose the geometrical properties of our world.
The geometrical properties in a gravitation field are really the relationships among inertia, space, time and motion. The space and time characteristics are changing according to the laws of inertia and motion.
Let us suppose, for the moment, that we have succeeded in carrying out consistently the programme of the general relativity theory. But are we not in danger of carrying speculation too far from reality? We know how well the old theory explains astronomical observations. Is there a possibility of constructing a bridge between the new theory and observation? Every speculation must be tested by experiment, and any results, no matter how attractive, must be rejected if they do not fit the facts. How did the new theory of gravitation stand the test of experiment? This question can be answered in one sentence: The old theory is a special limiting case of the new one. If the gravitational forces are comparatively weak, the old Newtonian law turns out to be a good approximation to the new laws of gravitation. Thus all observations which support the classical theory also support the general relativity theory. We regain the old theory from the higher level of the new one.
Even if no additional observation could be quoted in favour of the new theory, if its explanation were only just as good as the old one, given a free choice between the two theories, we should have to decide in favour of the new one. The equations of the new theory are, from the formal point of view, more complicated, but their assumptions are, from the point of view of fundamental principles, much simpler. The two frightening ghosts, absolute time and an inertial system, have disappeared. The clue of the equivalence of gravitational and inertial mass is not overlooked. No assumption about the gravitational forces and their dependence on distance is needed. The gravitational equations have the form of structure laws, the form required of all physical laws since the great achievements of the field theory.
Some new deductions, not contained in Newton’s gravitational law, can be drawn from the new gravitational laws. One, the bending of light rays in a gravitational field, has already been quoted. Two further consequences will now be mentioned.
Light rays bend in a gravitation field because light has a very small amount of inertia. General relativity predicts the amount of bend more accurately.
If the old laws follow from the new one when the gravitational forces are weak, the deviations from the Newtonian law of gravitation can be expected only for comparatively strong gravitational forces. Take our solar system. The planets, our earth among them, move along elliptical paths around the sun. Mercury is the planet nearest the sun. The attraction between the sun and Mercury is stronger than that between the sun and any other planet, since the distance is smaller. If there is any hope of finding a deviation from Newton’s law, the greatest chance is in the case of Mercury. It follows, from classical theory, that the path described by Mercury is of the same kind as that of any other planet except that it is nearer the sun. According to the general relativity theory, the motion should be slightly different. Not only should Mercury travel around the sun, but the ellipse which it describes should rotate very slowly, relative to the c.s. connected with the sun. This rotation of the ellipse expresses the new effect of the general relativity theory. The new theory predicts the magnitude of this effect. Mercury’s ellipse would perform a complete rotation in three million years! We see how small the effect is, and how hopeless it would be to seek it in the case of planets farther removed from the sun.
The deviation of the motion of the planet Mercury from the ellipse was known before the general relativity theory was formulated, and no explanation could be found. On the other hand, general relativity developed without any attention to this special problem. Only later was the conclusion about the rotation of the ellipse in the motion of a planet around the sun drawn from the new gravitational equations. In the case of Mercury, theory explained successfully the deviation of the motion from the Newtonian law.
General relativity successfully explains the path of Mercury around the sun, whereas Newtonian law gives an error. The error occurs due to stronger than usual gravitational forces between Mercury and Sun, which are accounted for in the general relativity equation but not by the Newtonian law.
But there is still another conclusion which was drawn from the general relativity theory and compared with experiment. We have already seen that a clock placed on the large circle of a rotating disc has a different rhythm from one placed on the smaller circle. Similarly, it follows from the theory of relativity that a clock placed on the sun would have a different rhythm from one placed on the earth, since the influence of the gravitational field is much stronger on the sun than on the earth.
We remarked on p. 103 that sodium, when incandescent, emits homogeneous yellow light of a definite wave-length. In this radiation the atom reveals one of its rhythms; the atom represents, so to speak, a clock and the emitted wave-length one of its rhythms. According to the general theory of relativity, the wave-length of light emitted by a sodium atom, say, placed on the sun should be very slightly greater than that of light emitted by a sodium atom on our earth.
Gravitational redshift is also predicted accurately by general relativity.
The problem of testing the consequences of the general relativity theory by observation is an intricate one and by no means definitely settled. As we are concerned with principal ideas, we do not intend to go deeper into this matter, and only state that the verdict of experiment seems, so far, to confirm the conclusions drawn from the general relativity theory.
General relativity has been tested only for higher gravity than earth’s gravity.
.
FINAL COMMENTS
Newton’s law of gravitation is valid only in the inertial coordinate system in which inertia and characteristics of space remain constant. This law needs to be updated for coordinate systems that cover the whole range of inertia. Transformation among such systems must account for change in inertia.
Inertia is a measure of substantial-ness of the substance. The natural uniform motion of a body is reciprocal to its inertia. Gravity being equivalent to acceleration is a field of varying inertia. General relativity seems to provide the law describing the changes in inertia in the gravitational field.
The geometrical properties in a gravitation field are really the relationships among inertia and motion. The space and time characteristics are changing with changes in inertia and motion. General relativity attempts to integrate the laws of physics over the whole range of inertia.
Like special relativity, general relativity works only in the material domain because the basis of light does not exactly represent zero inertia. That approximation, however, is adequate for the material domain.
.
