Summing Up

We have seen that rigorous and convincing experiments force us to accept the truth of the theory of relativity, which reveals some of the amazing properties of the world around us—properties that escape us in initial (or, to be more precise, superficial) study.

We have seen what deep, radical changes the theory of relativity has wrought in some of man’s basic notions and ideas. Does this not signify the complete collapse of the old, familiar ideas? Does it mean that the whole of the physics in existence before the emergence of the principle of relativity should be scrapped and thrown away, like an old boot that has served its useful time but is no longer of use to anybody?

If that were so, it would be futile to pursue scientific investigation. We would never be sure that in the future a new doctrine might not turn up, completely overthrowing everything that had gone before.

Let us imagine a passenger traveling in an ordinary train who decided to introduce corrections for relativity, fearing that otherwise his watch would be slow compared to the station clock. We would laugh at such a passenger. For the realistic correction would amount to only an infinitesimal part of a second—far less than the effect of a single jerk in the motion of the train upon his watch.

A chemical engineer who doubted whether the quantity of water he was heating retained a constant mass would need to have his head examined. But a physicist who failed to take into account the change of mass in nuclear transmutations would be sacked for incompetence.

Engineers will continue to plan their machines on the basis of the laws of classical physics, because the corrections for the theory of relativity have a much smaller influence on their engines than a single microbe settling on a flywheel. But a physicist observing fast electrons must certainly take into account the change of the mass of the electrons as they accelerate.

Thus the theory of relativity does not contradict but only deepens the ideas and concepts created in older science. It determines the limits within which these older ideas can be applied without leading to incorrect results. None of the laws of nature discovered by physicists before the birth of the theory of relativity are changed, but the limits of their application are now clearly marked out.

The relationship between the physics that takes into account the theory of relativity—which is called relativistic physics—and the older physics—which is called classical—is comparable to that between higher geodesy, which takes into account the spherical shape of the Earth, and lower geodesy, which neglects the spherical shape. Higher geodesy must start out from the relativity of the concept of the vertical; relativistic physics must take into account the relativity of the dimensions of a body and of time intervals between two events. Just as higher geodesy is a development of lower geodesy, so is relativistic physics a development and widening of classical physics.

We can perform the transition from the formulae of spherical geometry—the geometry on the surface of a sphere—to the formulae of plane geometry if we assume that the radius of the Earth is infinitely large. Then the Earth is no longer taken to be a sphere but an infinite plane; the vertical assumes an absolute meaning, and the sum of the angles of a triangle proves to be exactly two right angles.

Similarly, we can make a transition from relativistic to classical physics by assuming that the speed of light is infinitely large—i.e., that light spreads instantaneously. If light spreads instantaneously, then, as we have seen, the notion of simultaneous events becomes absolute. Time intervals between events and sizes of objects acquire an absolute meaning, without reference to the laboratories from which they are observed. In this way all classical concepts can be preserved. And in our ordinary affairs, we can take the speed of light to be infinite, for all practical purposes.

However, any attempt to reconcile the actually finite speed of light with the old notions of space and time would put us in the position of the person who knows that the Earth is a sphere but is certain that the vertical in his native city is the absolute vertical and who therefore is afraid of moving far from his home for fear of falling head over heels into empty space.