Einstein 1938: Elementary Quanta of Matter and Electricity

Reference: Evolution of Physics

This paper presents Chapter IV 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.


Elementary Quanta of Matter and Electricity

In the picture of matter drawn by the kinetic theory, all elements are built of molecules. Take the simplest case of the lightest element, that is hydrogen. On p. 66 we saw how the study of Brownian motions led to the determination of the mass of one hydrogen molecule. Its value is:

0.000 000 000 000 000 000 000 0033 gram.

This means that mass is discontinuous. The mass of a portion of hydrogen can change only by a whole number of small steps each corresponding to the mass of one hydrogen molecule. But chemical processes show that the hydrogen molecule can be broken up into two parts, or, in other words, that the hydrogen molecule is composed of two atoms. In chemical processes it is the atom and not the molecule which plays the role of an elementary quantum. Dividing the above number by two, we find the mass of a hydrogen atom. This is about

0.000 000 000 000 000 000 000 0017 gram.

Mass is a discontinuous quantity. But, of course, we need not bother about this when determining weight. Even the most sensitive scales are far from attaining the degree of precision by which the discontinuity in mass variation could be detected.

The mass variation in a portion of hydrogen is discontinuous. The elementary quanta of the mass of an element are called atoms.

Let us return to a well-known fact. A wire is connected with the source of a current. The current is flowing through the wire from higher to lower potential. We remember that many experimental facts were explained by the simple theory of electric fluids flowing through the wire. We also remember (p. 82) that the decision as to whether the positive fluid flows from higher to lower potential, or the negative fluid flows from lower to higher potential, was merely a matter of convention. For the moment we disregard all the further progress resulting from the field concepts. Even when thinking in the simple terms of electric fluids, there still remain some questions to be settled. As the name “fluid” suggests, electricity was regarded, in the early days, as a continuous quantity. The amount of charge could be changed, according to these old views, by arbitrarily small steps. There was no need to assume elementary electric quanta. The achievements of the kinetic theory of matter prepared us for a new question: do elementary quanta of electric fluids exist? The other question to be settled is: does the current consist of a flow of positive, negative or perhaps of both fluids?

The idea of all the experiments answering these questions is to tear the electric fluid from the wire, to let it travel through empty space, to deprive it of any association with matter and then to investigate its properties, which must appear most clearly under these conditions. Many experiments of this kind were performed in the late nineteenth century. Before explaining the idea of these experimental arrangements, at least in one case, we shall quote the results. The electric fluid flowing through the wire is a negative one, directed, therefore, from lower to higher potential. Had we known this from the start, when the theory of electric fluids was first formed, we should certainly have interchanged the words, and called the electricity of the rubber rod positive, that of the glass rod negative. It would then have been more convenient to regard the flowing fluid as the positive one. Since our first guess was wrong, we now have to put up with the inconvenience. The next important question is whether the structure of this negative fluid is “granular”, whether or not it is composed of electric quanta. Again a number of independent experiments show that there is no doubt as to the existence of an elementary quantum of this negative electricity. The negative electric fluid is constructed of grains, just as the beach is composed of grains of sand, or a house built of bricks. This result was formulated most clearly by J. J. Thomson, about forty years ago. The elementary quanta of negative electricity are called electrons. Thus every negative electric charge is composed of a multitude of elementary charges represented by electrons. The negative charge can, like mass, vary only discontinuously. The elementary electric charge is, however, so small that in many investigations it is equally possible and sometimes even more convenient to regard it as a continuous quantity. Thus the atomic and electron theories introduce into science discontinuous physical quantities which can vary only by jumps.

The charge variation in a portion of electricity is discontinuous. The elementary quanta of negative electricity are called electrons.

Imagine two parallel metal plates in some place from which all air has been extracted. One of the plates has a positive, the other a negative charge. A positive test charge brought between the two plates will be repelled by the positively charged and attracted by the negatively charged plate. Thus the lines of force of the electric field will be directed from the positively to the negatively charged plate. A force acting on a negatively charged test body would have the opposite direction. If the plates are sufficiently large, the lines of force between them will be equally dense everywhere; it is immaterial where the test body is placed, the force and, therefore, the density of the lines of force will be the same. Electrons brought somewhere between the plates would behave like raindrops in the gravitational field of the earth, moving parallel to each other from the negatively to the positively charged plate. There are many known experimental arrangements for bringing a shower of electrons into such a field which directs them all in the same way. One of the simplest is to bring a heated wire between the charged plates. Such a heated wire emits electrons which are afterwards directed by the lines of force of the external field. For instance, radio tubes, familiar to everyone, are based on this principle.

Many very ingenious experiments have been performed on a beam of electrons. The changes of their path in different electric and magnetic external fields have been investigated. It has even been possible to isolate a single electron and to determine its elementary charge and its mass, that is, its inertial resistance to the action of an external force. Here we shall only quote the value of the mass of an electron. It turned out to be about two thousand times smaller than the mass of a hydrogen atom. Thus the mass of a hydrogen atom, small as it is, appears great in comparison with the mass of an electron. From the point of view of a consistent field theory, the whole mass, that is, the whole energy, of an electron is the energy of its field; the bulk of its strength is within a very small sphere, and away from the “centre” of the electron it is weak.

The energy of the electron is its “mass” as determined from its inertial resistance. This “mass” is spread out from a center and becomes weak rapidly.

We said before that the atom of any element is its smallest elementary quantum. This statement was believed for a very long time. Now, however, it is no longer believed! Science has formed a new view showing the limitations of the old one. There is scarcely any statement in physics more firmly founded on facts than the one about the complex structure of the atom. First came the realization that the electron, the elementary quantum of the negative electric fluid, is also one of the components of the atom, one of the elementary bricks from which all matter is built. The previously quoted example of a heated wire emitting electrons is only one of the numerous instances of the extraction of these particles from matter. This result closely connecting the problem of the structure of matter with that of electricity, follows, beyond any doubt, from very many independent experimental facts.

It is comparatively easy to extract from an atom some of the electrons from which it is composed. This can be done by heat, as in our example of a heated wire, or in a different way, such as by bombarding atoms with other electrons.

Suppose a thin, red-hot, metal wire is inserted into rarefied hydrogen. The wire will emit electrons in all directions. Under the action of a foreign electric field a given velocity will be imparted to them. An electron increases its velocity just like a stone falling in the gravitational field. By this method we can obtain a beam of electrons rushing along with a definite speed in a definite direction. Nowadays, we can reach velocities comparable to that of light by submitting electrons to the action of very strong fields. What happens, then, when a beam of electrons of a definite velocity impinges on the molecules of rarefied hydrogen? The impact of a sufficiently speedy electron will not only disrupt the hydrogen molecule into its two atoms but will also extract an electron from one of the atoms.

Let us accept the fact that electrons are constituents of matter. Then, an atom from which an electron has been torn out cannot be electrically neutral. If it was previously neutral, then it cannot be so now, since it is poorer by one elementary charge. That which remains must have a positive charge. Furthermore, since the mass of an electron is so much smaller than that of the lightest atom, we can safely conclude that by far the greater part of the mass of the atom is not represented by electrons but by the remainder of the elementary particles which are much heavier than the electrons. We call this heavy part of the atom its nucleus.

In a hydrogen atom the electron is smeared around its nucleus.

Modern experimental physics has developed methods of breaking up the nucleus of the atom, of changing atoms of one element into those of another, and of extracting from the nucleus the heavy elementary particles of which it is built. This chapter of physics, known as “nuclear physics,” to which Rutherford contributed so much, is, from the experimental point of view, the most interesting. But a theory, simple in its fundamental ideas and connecting the rich variety of facts in the domain of nuclear physics, is still lacking. Since, in these pages, we are interested only in general physical ideas, we shall omit this chapter in spite of its great importance in modern physics.



The mass variation in a portion of hydrogen is discontinuous. This means that mass is “granular” in terms of atoms. Similarly, the charge within an atom appears to be granular in terms of electrons, but is it really so?

The mass is mostly contained in the nuclei of atoms, which are separated from each other by layers of electrons. How are the electrons in atom separated from each other?

A hydrogen atom is made of one proton (the nucleus), which is surrounded by a single electron. Here the electron cannot be assumed to be a spherical particle separate from the proton, another spherical particle. Here an electron is more like a drop of fluid at the center of which the proton is embedded.

Einstein says, “From the point of view of a consistent field theory, the whole mass, that is, the whole energy, of an electron is the energy of its field; the bulk of its strength is within a very small sphere, and away from the ‘centre’ of the electron it is weak.”

That may be so with a free electron, but it is not consistent with the hydrogen atom containing just one electron. There may be a high gradient of change in consistency from proton to electron, but within the electron the change in consistency is not so sharp.

It is possible that the flow of electricity is not granular, and that the electrons are just like the drops of fluid that can coalesce together. Even in a field there is a gradual change in strength, and a continuity is maintained.


Both comments and trackbacks are currently closed.
%d bloggers like this: