Einstein 1938: The First Clue

Reference: Evolution of Physics

This paper presents Chapter I, section 2 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.


The First Clue

Attempts to read the great mystery story are as old as human thought itself. Only a little over three hundred years ago, however, did scientists begin to understand the language of the story. Since that time, the age of Galileo and Newton, the reading has proceeded rapidly. Techniques of investigation, systematic methods of finding and following clues, have been developed. Some of the riddles of nature have been solved, although many of the solutions have proved temporary and superficial in the light of further research.

Science really took off three hundred years ago with the age of Galileo and Newton.

A most fundamental problem, for thousands of years wholly obscured by its complications, is that of motion. All those motions we observe in nature that of a stone thrown into the air, a ship sailing the sea, a cart pushed along the street are in reality very intricate. To understand these phenomena it is wise to begin with the simplest possible cases, and proceed gradually to the more complicated ones. Consider a body at rest, where there is no motion at all. To change the position of such a body it is necessary to exert some influence upon it, to push it or lift it, or let other bodies, such as horses or steam engines, act upon it. Our intuitive idea is that motion is connected with the acts of pushing, lifting or pulling. Repeated experience would make us risk the further statement that we must push harder if we wish to move the body faster. It seems natural to conclude that the stronger the action exerted on a body, the greater will be its speed. A four-horse carriage goes faster than a carriage drawn by only two horses. Intuition thus tells us that speed is essentially connected with action.

A fundamental problem is motion. Intuition tells us that push is needed to generate motion. The harder is the push the greater is the speed.

It is a familiar fact to readers of detective fiction that a false clue muddles the story and postpones the solution. The method of reasoning dictated by intuition was wrong and led to false ideas of motion which were held for centuries. Aristotle’s great authority throughout Europe was perhaps the chief reason for the long belief in this intuitive idea. We read in the Mechanics, for two thousand years attributed to him:

The moving body comes to a standstill when the force which pushes it along can no longer so act as to push it.

The discovery and use of scientific reasoning by Galileo was one of the most important achievements in the history of human thought, and marks the real beginning of physics. This discovery taught us that intuitive conclusions based on immediate observation are not always to be trusted, for they sometimes lead to the wrong clues.

But intuition can be wrong. Scientific reasoning supersedes it.

But where does intuition go wrong? Can it possibly be wrong to say that a carriage drawn by four horses must travel faster than one drawn by only two?

Let us examine the fundamental facts of motion more closely, starting with simple everyday experiences familiar to mankind since the beginning of civilization and gained in the hard struggle for existence.

Suppose that someone going along a level road with a pushcart suddenly stops pushing. The cart will go on moving for a short distance before coming to rest. We ask: how is it possible to increase this distance? There are various ways, such as oiling the wheels, and making the road very smooth. The more easily the wheels turn, and the smoother the road, the longer the cart will go on moving. And just what has been done by the oiling and smoothing? Only this: the external influences have been made smaller. The effect of what is called friction has been diminished, both in the wheels and between the wheels and the road. This is already a theoretical interpretation of the observable evidence, an interpretation which is, in fact, arbitrary. One significant step farther and we shall have the right clue. Imagine a road perfectly smooth, and wheels with no friction at all. Then there would be nothing to stop the cart, so that it would run for ever. This conclusion is reached only by thinking of an idealized experiment, which can never be actually performed, since it is impossible to eliminate all external influences. The idealized experiment shows the clue which really formed the foundation of the mechanics of motion.

Scientific reasoning tells us that in the absence of external influences motion continues.

Comparing the two methods of approaching the problem, we can say: the intuitive idea is the greater the action, the greater the velocity. Thus the velocity shows whether or not external forces are acting on a body. The new clue found by Galileo is: if a body is neither pushed, pulled, nor acted on in any other way, or, more briefly, if no external forces act on a body, it moves uniformly, that is, always with the same velocity along a straight line. Thus, the velocity does not show whether or not external forces are acting on a body. Galileo’s conclusion, the correct one, was formulated a generation later by Newton as the law of inertia. It is usually the first thing about physics which we learn by heart in school, and some of us may remember it:

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

Thus, the scientific reasoning leads us to the law of inertia.

We have seen that this law of inertia cannot be derived directly from experiment, but only by speculative thinking consistent with observation. The idealized experiment can never be actually performed, although it leads to a profound understanding of real experiments.

From the variety of complex motions in the world around us we choose as our first example uniform motion. This is the simplest, because there are no external forces acting. Uniform motion can, however, never be realized; a stone thrown from a tower, a cart pushed along a road can never move absolutely uniformly because we cannot eliminate the influence of external forces.

In a good mystery story the most obvious clues often lead to the wrong suspects. In our attempts to understand the laws of nature we find, similarly, that the most obvious intuitive explanation is often the wrong one.

Human thought creates an ever-changing picture of the universe. Galileo’s contribution was to destroy the intuitive view and replace it by a new one. This is the significance of Galileo’s discovery.

But a further question concerning motion arises immediately. If the velocity is no indication of the external forces acting on a body, what is? The answer to this fundamental question was found by Galileo and still more concisely by Newton, and forms a further clue in our investigation.

Inertia is the property of the internal forces, which keeps the motion uniform in the absence of external forces.

To find the correct answer we must think a little more deeply about the cart on a perfectly smooth road. In our idealized experiment the uniformity of the motion was due to the absence of all external forces. Let us now imagine that the uniformly moving cart is given a push in the direction of the motion. What happens now? Obviously its speed is increased. Just as obviously, a push in the direction opposite to that of the motion would decrease the speed. In the first case the cart is accelerated by the push, in the second case decelerated, or slowed down. A conclusion follows at once: the action of an external force changes the velocity. Thus not the velocity itself but its change is a consequence of pushing or pulling. Such a force either increases or decreases the velocity according to whether it acts in the direction of motion or in the opposite direction. Galileo saw this clearly and wrote in his Two New Sciences:

… any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of acceleration or retardation are removed, a condition which is found only on horizontal planes; for in the case of planes which slope downwards there is already present a cause of acceleration; while on planes sloping upwards there is retardation; from this it follows that motion along a horizontal plane is perpetual; for, if the velocity be uniform, it cannot be diminished or slackened, much less destroyed.

The action of an external force changes the velocity. The new uniform velocity is then rigidly maintained by internal forces.

By following the right clue we achieve a deeper understanding of the problem of motion. The connection between force and the change of velocity and not, as we should think according to our intuition, the connection between force and the velocity itself is the basis of classical mechanics as formulated by Newton.

We have been making use of two concepts which play principal roles in classical mechanics: force and change of velocity. In the further development of science both of these concepts are extended and generalized. They must, therefore, be examined more closely.

Force and change in velocity are the keynotes of classical mechanics.

What is force? Intuitively, we feel what is meant by this term. The concept arose from the effort of pushing, throwing or pulling from the muscular sensation accompanying each of these acts. But its generalization goes far beyond these simple examples. We can think of force even without picturing a horse pulling a carriage! We speak of the force of attraction between the sun and the earth, the earth and the moon, and of those forces which cause the tides. We speak of the force by which the earth compels ourselves and all the objects about us to remain within its sphere of influence, and of the force with which the wind makes waves on the sea, or moves the leaves of trees. When and where we observe a change in velocity, an external force, in the general sense, must be held responsible. Newton wrote in his Principia:

An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uniformly forward in a right line.

This force consists in the action only; and remains no longer in the body, when the action is over. For a body maintains every new state it acquires, by its vis inertiae only. Impressed forces are of different origins; as from percussion, from pressure, from centripetal force.

Force is present wherever there is change in velocity (acceleration or deceleration).

If a stone is dropped from the top of a tower its motion is by no means uniform; the velocity increases as the stone falls. We conclude: an external force is acting in the direction of the motion. Or, in other words : the earth attracts the stone. Let us take another example. What happens when a stone is thrown straight upward? The velocity decreases until the stone reaches its highest point and begins to fall. This decrease in velocity is caused by the same force as the acceleration of a falling body. In one case the force acts in the direction of the motion, in the other case in the opposite direction. The force is the same, but it causes acceleration or deceleration according to whether the stone is dropped or thrown upward.

The definition of force seems to be evolving still. Please see the final comments below.


A more fundamental problem than motion is the recognition of substance. Substance precedes motion because there cannot be motion with nothing to move. This substance was assumed to be matter. But we attribute velocity to light without recognizing it as a substance. This is contradictory. Therefore, light must be recognized as a fast moving substance, instead of being referred to simply as “energy”.

Substance is perceived because it has force. In other words, force is the core characteristic of substance. Even Newton recognized the innate force of matter and attributed to it the property of inertia. Not only is there external force, but there is also the internal force that influences the motion of the body. Light has force and it exerts force.

Scientific reasoning tells us that beyond making the motion uniform, the internal force must also determine the magnitude of uniform velocity. Thus the new uniform velocity induced by external forces is not rigidly maintained as stated by Newton’s laws of motion. The uniform velocity most likely adjusts itself to a value in balance with the mass of the body, when there are no external forces.


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