Reference: Evolution of Physics
This paper presents Chapter III, section 11 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.
.
Outside and Inside the Lift
The law of inertia marks the first great advance in physics; in fact, its real beginning. It was gained by the contemplation of an idealized experiment, a body moving forever with no friction nor any other external forces acting. From this example, and later from many others, we recognized the importance of the idealized experiment created by thought. Here again, idealized experiments will be discussed. Although these may sound very fantastic, they will, nevertheless, help us to understand as much about relativity as is possible by our simple methods.
Fundamentally substance varies in terms of inertia and uniform velocity. At the lower end inertia appears as a spread out wave with a frequency and high velocity. At the upper end inertia appears as concentrated particle with mass and small velocity. Inertia and velocity are perceived when we compare the waves and particles. There is equivalence between inertia and velocity.
We had previously the idealized experiments with a uniformly moving room. Here, for a change, we shall have a falling lift.
Imagine a great lift at the top of a skyscraper much higher than any real one. Suddenly the cable supporting the lift breaks, and the lift falls freely toward the ground. Observers in the lift are performing experiments during the fall. In describing them, we need not bother about air resistance or friction, for we may disregard their existence under our idealized conditions. One of the observers takes a handkerchief and a watch from his pocket and drops them. What happens to these two bodies? For the outside observer, who is looking through the window of the lift, both handkerchief and watch fall toward the ground in exactly the same way, with the same acceleration. We remember that the acceleration of a falling body is quite independent of its mass and that it was this fact which revealed the equality of gravitational and inertial mass (p. 37). We also remember that the equality of the two masses, gravitational and inertial, was quite accidental from the point of view of classical mechanics and played no role in its structure. Here, however, this equality reflected in the equal acceleration of all falling bodies is essential and forms the basis of our whole argument.
In a gravitational field the force is proportional to the mass, and the proportionality constant is the acceleration. The gravitational field is defined by its acceleration, which is the same for all masses.
Let us return to our falling handkerchief and watch; for the outside observer they are both falling with the same acceleration. But so is the lift, with its walls, ceiling, and floor. Therefore: the distance between the two bodies and the floor will not change. For the inside observer the two bodies remain exactly where they were when he let them go. The inside observer may ignore the gravitational field, since its source lies outside his c.s. He finds that no forces inside the lift act upon the two bodies, and so they are at rest, just as if they were in an inertial c.s. Strange things happen in the lift! If the observer pushes a body in any direction, up or down for instance, it always moves uniformly so long as it does not collide with the ceiling or the floor of the lift. Briefly speaking, the laws of classical mechanics are valid for the observer inside the lift. All bodies behave in the way expected by the law of inertia. Our new c.s. rigidly connected with the freely falling lift differs from the inertial c.s. in only one respect. In an inertial c.s., a moving body on which no forces are acting will move uniformly for ever. The inertial c.s. as represented in classical physics is neither limited in space nor time. The case of the observer in our lift is, however, different. The inertial character of his c.s. is limited in space and time. Sooner or later the uniformly moving body will collide with the wall of the lift, destroying the uniform motion. Sooner or later the whole lift will collide with the earth, destroying the observers and their experiments. The c.s. is only a “pocket edition” of a real inertial c.s.
Within a freely falling lift the acceleration cancels out the gravitational field, leaving an inertial c.s. This shows the equivalence between acceleration and gravity.
This local character of the c.s. is quite essential. If our imaginary lift were to reach from the North Pole to the Equator, with the handkerchief placed over the North Pole and the watch over the Equator, then, for the outside observer, the two bodies would not have the same acceleration; they would not be at rest relative to each other. Our whole argument would fail! The dimensions of the lift must be limited so that the equality of acceleration of all bodies relative to the outside observer may be assumed.
With this restriction, the c.s. takes on an inertial character for the inside observer. We can at least indicate a c.s. in which all the physical laws are valid, even though it is limited in time and space. If we imagine another c.s., another lift moving uniformly, relative to the one falling freely, then both these c.s. will be locally inertial. All laws are exactly the same in both. The transition from one to the other is given by the Lorentz transformation.
Let us see in what way both the observers, outside and inside, describe what takes place in the lift.
The outside observer notices the motion of the lift and of all bodies in the lift, and finds them in agreement with Newton’s gravitational law. For him, the motion is not uniform, but accelerated, because of the action of the gravitational field of the earth.
However, a generation of physicists born and brought up in the lift would reason quite differently. They would believe themselves in possession of an inertial system and would refer all laws of nature to their lift, stating with justification that the laws take on a specially simple form in their c.s. It would be natural for them to assume their lift at rest and their c.s. the inertial one.
It is impossible to settle the differences between the outside and the inside observers. Each of them could claim the right to refer all events to his c.s. Both descriptions of events could be made equally consistent.
We see from this example that a consistent description of physical phenomena in two different c.s. is possible, even if they are not moving uniformly, relative to each other. But for such a description we must take into account gravitation, building, so to speak, the “bridge” which effects a transition from one c.s. to the other. The gravitational field exists for the outside observer; it does not for the inside observer. Accelerated motion of the lift in the gravitational field exists for the outside observer, rest and absence of the gravitational field for the inside observer. But the “bridge”, the gravitational field, making the description in both c.s. possible, rests on one very important pillar: the equivalence of gravitational and inertial mass. Without this clue, unnoticed in classical mechanics, our present argument would fail completely.
Newton considered a momentary push and a momentary change in uniform motion. Einstein is considering a continuous push and a continuous change in uniform motion.
Now for a somewhat different idealized experiment. There is, let us assume, an inertial c.s., in which the law of inertia is valid. We have already described what happens in a lift resting in such an inertial c.s. But we now change our picture. Someone outside has fastened a rope to the lift and is pulling, with a constant force, in the direction indicated in our drawing. It is immaterial how this is done. Since the laws of mechanics are valid in this c.s., the whole lift moves with a constant acceleration in the direction of the motion. Again we shall listen to the explanation of phenomena going on in the lift and given by both the outside and inside observers.
The outside observer: My c.s. is an inertial one. The lift moves with constant acceleration, because a constant force is acting. The observers inside are in absolute motion, for them the laws of mechanics are invalid. They do not find that bodies, on which no forces are acting, are at rest. If a body is left free, it soon collides with the floor of the lift, since the floor moves upward toward the body. This happens exactly in the same way for a watch and for a handkerchief. It seems very strange to me that the observer inside the lift must always be on the “floor”, because as soon as he jumps the floor will reach him again.
The inside observer: I do not see any reason for believing that my lift is in absolute motion. I agree that my c.s., rigidly connected with my lift, is not really inertial, but I do not believe that it has anything to do with absolute motion. My watch, my handkerchief, and all bodies are falling because the whole lift is in a gravitational field. I notice exactly the same kinds of motion as the man on the earth. He explains them very simply by the action of a gravitational field. The same holds good for me.
Acceleration is zero in an inertial system. The moment acceleration is added as a continuous push we see the manifestation of gravity within the moving system. NOTE: Accelerated motion is in reference to the body itself and not to another body.
These two descriptions, one by the outside, the other by the inside, observer, are quite consistent, and there is no possibility of deciding which of them is right. We may assume either one of them for the description of phenomena in the lift: either non-uniform motion and absence of a gravitational field with the outside observer, or rest and the presence of a gravitational field with the inside observer.
The outside observer may assume that the lift is in “absolute” non-uniform motion. But a motion which is wiped out by the assumption of an acting gravitational field cannot be regarded as absolute motion.
There is, possibly, a way out of the ambiguity of two such different descriptions, and a decision in favour of one against the other could perhaps be made. Imagine that a light ray enters the lift horizontally through a side window and reaches the opposite wall after a very short time. Again let us see how the path of the light would be predicted by the two observers.
The outside observer, believing in accelerated motion of the lift, would argue: The light ray enters the window and moves horizontally, along a straight line and with a constant velocity, toward the opposite wall. But the lift moves upward, and during the time in which the light travels toward the wall the lift changes its position. Therefore, the ray will meet at a point not exactly opposite its point of entrance, but a little below. The difference will be very slight, but it exists nevertheless, and the light ray travels, relative to the lift, not along a straight, but along a slightly curved line. The difference is due to the distance covered by the lift during the time the ray is crossing the interior.
The inside observer, who believes in the gravitational field acting on all objects in his lift, would say: there is no accelerated motion of the lift, but only the action of the gravitational field. A beam of light is weightless and, therefore, will not be affected by the gravitational field. If sent in a horizontal direction, it will meet the wall at a point exactly opposite to that at which it entered.
It seems from this discussion that there is a possibility of deciding between these two opposite points of view as the phenomenon would be different for the two observers. If there is nothing illogical in either of the explanations just quoted, then our whole previous argument is destroyed, and we cannot describe all phenomena in two consistent ways, with and without a gravitational field.
But there is, fortunately, a grave fault in the reasoning of the inside observer, which saves our previous conclusion. He said: “A beam of light is weightless and, therefore, will not be affected by the gravitational field.” This cannot be right! A beam of light carries energy and energy has mass. But every inertial mass is attracted by the gravitational field, as inertial and gravitational masses are equivalent. A beam of light will bend in a gravitational field exactly as a body would if thrown horizontally with a velocity equal to that of light. If the inside observer had reasoned correctly and had taken into account the bending of light rays in a gravitational field, then his results would have been exactly the same as those of an outside observer.
Near infinite velocity of light indicates the presence of infinitesimal inertia. This inertia is restraining some acceleration because the velocity is constant. Because of the equivalency of acceleration with gravity, we may say that the infinitesimal inertia of light has infinitesimal gravity.
The gravitational field of the earth is, of course, too weak for the bending of light rays in it to be proved directly, by experiment. But the famous experiments performed during the solar eclipses show, conclusively though indirectly, the influence of a gravitational field on the path of a light ray.
We may also say that high inertia of stars shall have high gravity. Gravitational fields interact with each other. Therefore, there shall be interaction between the gravity of light and the gravity of stars.
It follows from these examples that there is a well-founded hope of formulating a relativistic physics. But for this we must first tackle the problem of gravitation.
We saw from the example of the lift the consistency of the two descriptions. Non-uniform motion may, or may not, be assumed. We can eliminate “absolute” motion from our examples by a gravitational field. But then there is nothing absolute in the non-uniform motion. The gravitational field is able to wipe it out completely.
In uniform motion there is no acceleration, since all acceleration has reduced to the gravity of inertia Gravity, then, forms the gradient of uniform velocity or inertia in the spectrum of inertia. The highest gravity shall exist at the interface between particle and void, where the gradient is the highest.
The ghosts of absolute motion and inertial c.s. can be expelled from physics and a new relativistic physics built. Our idealized experiments show how the problem of the general relativity theory is closely connected with that of gravitation and why the equivalence of gravitational and inertial mass is so essential for this connection. It is clear that the solution of the gravitational problem in the general theory of relativity must differ from the Newtonian one. The laws of gravitation must, just as all laws of nature, be formulated for all possible c.s., whereas the laws of classical mechanics, as formulated by Newton, are valid only in inertial c.s.
Newton’s inertial c.s. is an idealized system that deals with uniform motion. But such systems do not really exist in nature. There exist non-inertial systems only where motion manifests itself as gravity.
.
FINAL COMMENTS
Newton considered a momentary push and a momentary change in uniform motion. This gives us the sense of inertia, which keeps the body moving. Einstein, on the other hand, considered a continuous push and a continuous change in motion. This gives us the sense of gravitational field, which keeps the body accelerating.
There is equivalence between inertia and velocity on one hand; and between gravity and acceleration on the other. As velocity changes, inertia changes too and thus acceleration and gravity manifest themselves. External force produces change not only in velocity, but also in inertia.
Increasing inertia is balancing increasing acceleration, which appears as gravity. So, heavier is the mass, the stronger is its gravitational field. With infinite mass there is infinite inertia and infinite gravity. The body acts as a point of fixedness in space relative to which other locations around it are in motion. As inertia decreases, the velocity increases.
In this material region, inertia is so large that any changes in it are imperceptible. But the velocity is small and changes in it are visible. The velocity fluctuates in a narrow range. This material region is wide. It is followed by a very narrow atomic region, which is then followed by a wide field region.
In the narrow atomic region, there is a rapid decline of inertia accompanied by a rapid increase in velocity by many degrees of magnitude. Here we have electromagnetic wave-particles of rapidly declining mass.
Beyond the atomic region there is a wide field region, where, once again, inertia decreases and velocity increases gradually. The velocity in this region is approximated by the velocity of light. This velocity is so high that any changes in it are imperceptible. But the inertia is small and changes in it are visible. The inertia fluctuates in a narrow range.
The inertia appears as mass in the material region, electromagnetic wave-particles in the narrow atomic region, and as frequency in the field region. Inertia is very weak in the field region. Gravity is proportional to inertia.
.
