Einstein 1938: Relativity and Mechanics

Reference: Evolution of Physics

This paper presents Chapter III, section 8 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.

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Relativity and Mechanics

The relativity theory arose from necessity, from serious and deep contradictions in the old theory from which there seemed no escape. The strength of the new theory lies in the consistency and simplicity with which it solves all these difficulties, using only a few very convincing assumptions.

Although the theory arose from the field problem, it has to embrace all physical laws. A difficulty seems to appear here. The field laws on the one hand and the mechanical laws on the other are of quite different kinds. The equations of electromagnetic field are invariant with respect to the Lorentz transformation and the mechanical equations are invariant with respect to the classical transformation. But the relativity theory claims that all laws of nature must be invariant with respect to the Lorentz and not to the classical transformation. The latter is only a special, limiting case of the Lorentz transformation when the relative velocities of two c.s. are very small. If this is so, classical mechanics must change in order to conform with the demand of invariance with respect to the Lorentz transformation. Or, in other words, classical mechanics cannot be valid if the velocities approach that of light. Only one transformation from one c.s. to another can exist, namely, the Lorentz transformation.

The classical transformation is only a special, limiting case of the Lorentz transformation when the relative velocities of two c.s. are very small. No material object can reach the velocity of light unless its inertia is reduced to almost zero.

It was simple to change classical mechanics in such a way that it contradicted neither the relativity theory nor the wealth of material obtained by observation and explained by classical mechanics. The old mechanics is valid for small velocities and forms the limiting case of the new one.

It would be interesting to consider some instance of a change in classical mechanics introduced by the relativity theory. This might, perhaps, lead us to some conclusions which could be proved or disproved by experiment.

The relative theory works because of the reciprocal relationship between inertia and motion.

Let us assume a body, having a definite mass, moving along a straight line, and acted upon by an external force in the direction of the motion. The force, as we know, is proportional to the change of velocity. Or, to be more explicit, it does not matter whether a given body increases its velocity in one second from 100 to 101 feet per second, or from 100 miles to 100 miles and one foot per second or from 180,000 miles to 180,000 miles and one foot per second. The force acting upon a particular body is always the same for the same change of velocity in the same time.

Is this sentence true from the point of view of the relativity theory? By no means ! This law is valid only for small velocities. What, according to the relativity theory, is the law for great velocities, approaching that of light? If the velocity is great, extremely strong forces are required to increase it. It is not at all the same thing to increase by one foot per second a velocity of about 100 feet per second or a velocity approaching that of light. The nearer a velocity is to that of light the more difficult it is to increase. When a velocity is equal to that of light it is impossible to increase it further. Thus, the changes brought about by the relativity theory are not surprising. The velocity of light is the upper limit for all velocities. No finite force, no matter how great, can cause an increase in speed beyond this limit. In place of the old mechanical law connecting force and change of velocity, a more complicated one appears. From our new point of view classical mechanics is simple because in nearly all observations we deal with velocities much smaller than that of light.

A body at rest has a definite mass, called the rest mass. We know from mechanics that every body resists a change in its motion; the greater the mass, the stronger the resistance, and the weaker the mass, the weaker the resistance. But in the relativity theory, we have something more. Not only does a body resist a change more strongly if the rest mass is greater, but also if its velocity is greater. Bodies with velocities approaching that of light would offer a very strong resistance to external forces. In classical mechanics the resistance of a given body was something unchangeable, characterized by its mass alone. In the relativity theory it depends on both rest mass and velocity. The resistance becomes infinitely great as the velocity approaches that of light.

Einstein’s math works, but his interpretation of why it works does not pan out. No body is absolutely at rest except the body of infinite inertia. The velocity increases only when the inertia of particle decreases. Therefore, the proportionality constant between force and change in velocity also decreases. The nearer a velocity is to that of light the easier it is to increase. Einstein’s interpretation of his relativity theory is just the opposite.

The results just quoted enable us to put the theory to the test of experiment. Do projectiles with a velocity approaching that of light resist the action of an external force as predicted by the theory? Since the statements of the relativity theory have, in this respect, a quantitative character, we could confirm or disprove the theory if we could realize projectiles having a speed approaching that of light.

A projectile being a material object can never reach the velocity of light unless, somehow, its inertia is reduced to almost zero.

Indeed, we find in nature projectiles with such velocities. Atoms of radioactive matter, radium for instance, act as batteries which fire projectiles with enormous velocities. Without going into detail we can quote only one of the very important views of modern physics and chemistry. All matter in the universe is made up of elementary particles of only a few kinds. It is like seeing in one town buildings of different sizes, construction and architecture, but from shack to skyscraper only very few different kinds of bricks were used, the same in all the buildings. So all known elements of our material world from hydrogen the lightest, to uranium the heaviest are built of the same kinds of bricks, that is, the same kinds of elementary particles. The heaviest elements, the most complicated buildings, are unstable and they disintegrate or, as we say, are radioactive. Some of the bricks, that is, the elementary particles of which the radioactive atoms are constructed, are sometimes thrown out with a very great velocity, approaching that of light. An atom of an element, say radium, according to our present views, confirmed by numerous experiments, is a complicated structure, and radioactive disintegration is one of those phenomena in which the composition of atoms from still simpler bricks, the elementary particles, is revealed.

The velocity of an elementary particle is as great as its inertia is small.

By very ingenious and intricate experiments we can find out how the particles resist the action of an external force. The experiments show that the resistance offered by these particles depends on the velocity, in the way foreseen by the theory of relativity. In many other cases, where the dependence of the resistance upon the velocity could be detected, there was complete agreement between theory and experiment. We see once more the essential features of creative work in science: prediction of certain facts by theory and their confirmation by experiment.

This result suggests a further important generalization. A body at rest has mass but no kinetic energy, that is, energy of motion. A moving body has both mass and kinetic energy. It resists change of velocity more strongly than the resting body. It seems as though the kinetic energy of the moving body increases its resistance. If two bodies have the same rest mass, the one with the greater kinetic energy resists the action of an external force more strongly.

It is difficult to change inertia, so it is difficult to change velocity also. Normally, the particle we move by pushing have a much greater natural velocity than the velocity they have on earth. By pushing we are only overcoming the forces of friction and gravity that are stopping these objects from moving.

But in case of quanta, the particles are moving at their natural uniform velocities. Changing these velocities is more difficult because it means changing their inertia (frequency).

Imagine a box containing balls, with the box as well as the balls at rest in our c.s. To move it, to increase its velocity, some force is required. But will the same force increase the velocity by the same amount in the same time with the balls moving about quickly and in all directions inside the box, like the molecules of a gas, with an average speed approaching that of light? A greater force will now be necessary because of the increased kinetic energy of the balls, strengthening the resistance of the box. Energy, at any rate kinetic energy, resists motion in the same way as ponderable masses. Is this also true of all kinds of energy?

The farther is the velocity from its natural uniform velocity the greater shall be the resistance to increasing that gap.

The theory of relativity deduces, from its fundamental assumption, a clear and convincing answer to this question, an answer again of a quantitative character: all energy resists change of motion; all energy behaves like matter; a piece of iron weighs more when red-hot than when cool; radiation travelling through space and emitted from the sun contains energy and therefore has mass; the sun and all radiating stars lose mass by emitting radiation. This conclusion, quite general in character, is an important achievement of the theory of relativity and fits all facts upon which it has been tested.

Einstein sates, “All energy behaves like matter,” because a particle of higher energy resists harder. That means velocity converts into inertia, or there is some equivalency between motion and inertia.

Classical physics introduced two substances: matter and energy. The first had weight, but the second was weightless. In classical physics we had two conservation laws: one for matter, the other for energy. We have already asked whether modern physics still holds this view of two substances and the two conservation laws. The answer is: “No”. According to the theory of relativity, there is no essential distinction between mass and energy. Energy has mass and mass represents energy. Instead of two conservation laws we have only one, that of mass-energy. This new view proved very successful and fruitful in the further development of physics.

Both matter and energy reduce to force. Thus, force is conserved as originally stated by Faraday.

How is it that this fact of energy having mass and mass representing energy remained for so long obscured? Is the weight of a piece of hot iron greater than that of a cold piece? The answer to this question is now “Yes”, but on p. 43 it was “No”. The pages between these two answers are certainly not sufficient to cover this contradiction.

The difficulty confronting us here is of the same kind as we have met before. The variation of mass predicted by the theory of relativity is immeasurably small and cannot be detected by direct weighing on even the most sensitive scales. The proof that energy is not weightless can be gained in many very conclusive, but indirect, ways.

The reason for this lack of immediate evidence is the very small rate of exchange between matter and energy. Compared to mass, energy is like a depreciated currency compared to one of high value. An example will make this clear. The quantity of heat able to convert thirty thousand tons of water into steam would weigh about one gram! Energy was regarded as weightless for so long simply because the mass which it represents is so small.

The conversion ratio between matter and energy (motion) is very, very large.

The old energy-substance is the second victim of the theory of relativity. The first was the medium through which light waves were propagated.

The influence of the theory of relativity goes far beyond the problem from which it arose. It removes the difficulties and contradictions of the field theory; it formulates more general mechanical laws; it replaces two conservation laws by one; it changes our classical concept of absolute time. Its validity is not restricted to one domain of physics; it forms a general framework embracing all phenomena of nature.

Yes, the theory of relativity forms a general framework embracing all phenomena of nature.

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FINAL COMMENTS

The theory of relativity forms a general framework embracing all phenomena of nature. It works because of the reciprocal relationship between inertia and motion. At one end of this range we have light with zero inertia and infinite velocity. At the other end of this range we have black holes with infinite inertia and zero velocity. Lorentz transformation seems to cover this whole range. It reduces to classical transformation when the velocities are in the material domain.

Einstein’s math works, but his interpretation is questionable. The reciprocal relationship between inertia and motion tells us that (a) the velocity of an elementary particle is as great as its inertia is small, (b) no material object can reach the velocity of light unless its inertia is reduced to almost zero, and (c) no body is absolutely at rest except the body of infinite inertia.

The velocity increases only when the inertia of particle decreases. Therefore, the proportionality constant between “force” and “change in velocity” also decreases. The nearer a velocity is to that of light the easier it is to increase. Einstein’s interpretation is just the opposite.

It is difficult to change inertia, so it is also difficult to change velocity. For quanta, its inertia is equivalent to its frequency; so change in inertia would mean change in frequency. The greater is the gap between an object’s natural velocity and the forced velocity, the greater is the resistance to increasing that gap further.

Einstein states, “All energy behaves like matter,” because a particle of higher energy resists harder. That means velocity converts into inertia, or there is some equivalency between motion and inertia. The conversion ratio between matter and energy (motion) is very, very large.

Both matter and energy reduce to force. Thus, force is conserved as originally postulated by Faraday.

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