Category Archives: Physics

Einstein 1938: Light Spectra

Reference: Evolution of Physics

This paper presents Chapter IV section 4 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.


Light Spectra

We already know that all matter is built of only a few kinds of particles. Electrons were the first elementary particles of matter to be discovered. But electrons are also the elementary quanta of negative electricity. We learned furthermore that some phenomena force us to assume that light is composed of elementary light quanta, differing for different wave-lengths. Before proceeding we must discuss some physical phenomena in which matter as well as radiation plays an essential role.

The sun emits radiation which can be split into its components by a prism. The continuous spectrum of the sun can thus be obtained. Every wave-length between the two ends of the visible spectrum is represented. Let us take another example. It was previously mentioned that sodium when incandescent emits homogeneous light, light of one colour or one wave-length. If incandescent sodium is placed before the prism, we see only one yellow line. In general, if a radiating body is placed before the prism, then the light it emits is split up into its components, revealing the spectrum characteristic of the emitting body.

The discharge of electricity in a tube containing gas produces a source of light such as seen in the neon tubes used for luminous advertisements. Suppose such a tube is placed before a spectroscope. The spectroscope is an instrument which acts like a prism, but with much greater accuracy and sensitiveness; it splits light into its components, that is, it analyses it. Light from the sun, seen through a spectroscope, gives a continuous spectrum; all wave-lengths are represented in it. If, however, the source of light is a gas through which a current of electricity passes, the spectrum is of a different character. Instead of the continuous, multi-coloured design of the sun’s spectrum, bright, separated stripes appear on a continuous dark background. Every stripe, if it is very narrow, corresponds to a definite colour or, in the language of the wave theory, to a definite wavelength. For example, if twenty lines are visible in the spectrum, each of them will be designated by one of twenty numbers expressing the corresponding wavelength. The vapours of the various elements possess different systems of lines, and thus different combinations of numbers designating the wave-lengths composing the emitted light spectrum. No two elements have identical systems of stripes in their characteristic spectra, just as no two persons have exactly identical finger-prints. As a catalogue of these lines was worked out by physicists, the existence of laws gradually became evident, and it was possible to replace some of the columns of seemingly disconnected numbers expressing the length of the various waves by one simple mathematical formula.

All that has just been said can now be translated into the photon language. The stripes correspond to certain definite wave-lengths or, in other words, to photons with a definite energy. Luminous gases do not, therefore, emit photons with all possible energies, but only those characteristic of the substance. Reality again limits the wealth of possibilities.

Atoms of a particular element, say, hydrogen, can emit only photons with definite energies. Only the emission of definite energy quanta is permissible, all others being prohibited. Imagine, for the sake of simplicity, that some element emits only one line, that is, photons of a quite definite energy. The atom is richer in energy before the emission and poorer afterwards. From the energy principle it must follow that the energy level of an atom is higher before emission and lower afterwards, and that the difference between the two levels must be equal to the energy of the emitted photon. Thus the fact that an atom of a certain element emits radiation of one wave-length only, that is photons of a definite energy only, could be expressed differently: only two energy levels are permissible in an atom of this element and the emission of a photon corresponds to the transition of the atom from the higher to the lower energy level.

But more than one line appears in the spectra of the elements, as a rule. The photons emitted correspond to many energies and not to one only. Or, in other words, we must assume that many energy levels are allowed in an atom and that the emission of a photon corresponds to the transition of the atom from a higher energy level to a lower one. But it is essential that not every energy level should be permitted, since not every wave-length, not every photon-energy, appears in the spectra of an element. Instead of saying that some definite lines, some definite wave-lengths, belong to the spectrum of every atom, we can say that every atom has some definite energy levels, and that the emission of light quanta is associated with the transition of the atom from one energy level to another. The energy levels are, as a rule, not continuous but discontinuous. Again we see that the possibilities are restricted by reality.

It was Bohr who showed for the first time why just these and no other lines appear in the spectra. His theory, formulated twenty-five years ago, draws a picture of the atom from which, at any rate in simple cases, the spectra of the elements can be calculated and the apparently dull and unrelated numbers are suddenly made coherent in the light of the theory.

Bohr’s theory forms an intermediate step toward a deeper and more general theory, called the wave or quantum mechanics. It is our aim in these last pages to characterize the principal ideas of this theory. Before doing so, we must mention one more theoretical and experimental result of a more special character.

Our visible spectrum begins with a certain wavelength for the violet colour and ends with a certain wave-length for the red colour. Or, in other words, the energies of the photons in the visible spectrum are always enclosed within the limits formed by the photon energies of the violet and red lights. This limitation is, of course, only a property of the human eye. If the difference in energy of some of the energy levels is sufficiently great, then an ultraviolet photon will be sent out, giving a line beyond the visible spectrum. Its presence cannot be detected by the naked eye; a photographic plate must be used.

X-rays are also composed of photons of a much greater energy than those of visible light, or in other words, their wave-lengths are much smaller, thousands of times smaller in fact, than those of visible light.

But is it possible to determine such small wavelengths experimentally? It was difficult enough to do so for ordinary light. We had to have small obstacles or small apertures. Two pinholes very near to each other, showing diffraction for ordinary light, would have to be many thousands of times smaller and closer together to show diffraction for X-rays.

How then can we measure the wave-lengths of these rays? Nature herself comes to our aid.

A crystal is a conglomeration of atoms arranged at very short distances from each other on a perfectly regular plan. Our drawing shows a simple model of the structure of a crystal. Instead of minute apertures, there are extremely small obstacles formed by the atoms of the element, arranged very close to each other in absolutely regular order. The distances between the atoms, as found from the theory of the crystal structure, are so small that they might be expected to show the effect of diffraction for X-rays. Experiment proved that it is, in fact, possible to diffract the X-ray wave by means of these closely packed obstacles disposed in the regular three-dimensional arrangement occurring in a crystal.

Suppose that a beam of X-rays falls upon a crystal and, after passing through it, is recorded on a photographic plate. The plate then shows the diffraction pattern. Various methods have been used to study the X-ray spectra, to deduce data concerning the wavelength from the diffraction pattern. What has been said here in a few words would fill volumes if all theoretical and experimental details were set forth. In Plate III we give only one diffraction pattern obtained by one of the various methods. We again see the dark and light rings so characteristic of the wave theory. In the centre the non-diffracted ray is visible. If the crystal were not brought between the X-rays and the photographic plate, only the light spot in the centre would be seen. From photographs of this kind the wave-lengths of the X-ray spectra can be calculated and, on the other hand, if the wave-length is known, conclusions can be drawn about the structure of the crystal.



If a radiating body is placed before the prism, then the light it emits is split up into its components, revealing the spectrum characteristic of the emitting body. The spectrum of the light from the Sun is continuous throughout the visible range. Most elements, however, emit light that produce discrete lines as their spectra.

Each spectral line is produced by a light of a characteristic wavelength. It was possible to express these wavelengths through one simple mathematical formula. These wavelengths could be related to the energy of corresponding photons; and from there to characteristic energy levels of atoms emitting those photons. From this data, Bohr could then develop a model of the atom.

Photons of energies beyond the visible spectra also exist, such as, those of x-rays. Ingenious experiments have been devised to measure the energy of such photons.


Einstein 1938: The Quanta of Light

Reference: Evolution of Physics

This paper presents Chapter IV section 3 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 Quanta of Light

Let us consider a wall built along the seashore. The waves from the sea continually impinge on the wall, wash away some of its surface, and retreat, leaving the way clear for the incoming waves. The mass of the wall decreases and we can ask how much is washed away in, say, one year. But now let us picture a different process. We want to diminish the mass of the wall by the same amount as previously but in a different way. We shoot at the wall and split it at the places where the bullets hit. The mass of the wall will be decreased and we can well imagine that the same reduction in mass is achieved in both cases. But from the appearance of the wall we could easily detect whether the continuous sea wave or the discontinuous shower of bullets has been acting. It will be helpful, in understanding the phenomena which we are about to describe, to bear in mind the difference between sea waves and a shower of bullets.

An impingement can be continuous or discontinuous with the same overall effect.

We said, previously, that a heated wire emits electrons. Here we shall introduce another way of extracting electrons from metal. Homogeneous light, such as violet light, which is, as we know, light of a definite wave-length, is impinging on a metal surface. The light extracts electrons from the metal. The electrons are torn from the metal and a shower of them speeds along with a certain velocity. From the point of view of the energy principle we can say: the energy of light is partially transformed into the kinetic energy of expelled electrons. Modern experimental technique enables us to register these electron-bullets, to determine their velocity and thus their energy. This extraction of electrons by light falling upon metal is called the photoelectric effect.

Light impinges on metal surface to extract electrons. Is that impingement of light continuous or discontinuous?

Our starting-point was the action of a homogeneous light wave, with some definite intensity. As in every experiment, we must now change our arrangements to see whether this will have any influence on the observed effect.

Let us begin by changing the intensity of the homogeneous violet light falling on the metal plate and note to what extent the energy of the emitted electrons depends upon the intensity of the light. Let us try to find the answer by reasoning instead of by experiment. We could argue: in the photoelectric effect a certain definite portion of the energy of radiation is transformed into energy of motion of the electrons. If we again illuminate the metal with light of the same wave-length but from a more powerful source, then the energy of the emitted electrons should be greater, since the radiation is richer in energy. We should, therefore, expect the velocity of the emitted electrons to increase if the intensity of the light increases. But experiment again contradicts our prediction. Once more we see that the laws of nature are not as we should like them to be. We have come upon one of the experiments which, contradicting our predictions, breaks the theory on which they were based. The actual experimental result is, from the point of view of the wave theory, astonishing. The observed electrons all have the same speed, the same energy, which does not change when the intensity of the light is increased.

Increase in the intensity of light increases the number of electrons emitted. It does not increase the velocity of the electrons emitted. If we consider that as an increase in the intensity of the electron beam then that intensity depends on the number of electrons and not on their velocity.

This experimental result could not be predicted by the wave theory. Here again a new theory arises from the conflict between the old theory and experiment.

Here the confusion is between energy and momentum. Total energy may be looked upon as increasing because of increase in the number of particles of same velocity. Or increase in velocity of the same number of particles. Basically we have confusion between inertia and velocity.

Let us be deliberately unjust to the wave theory of light, forgetting its great achievements, its splendid explanation of the bending of light around very small obstacles. With our attention focused on the photoelectric effect, let us demand from the theory an adequate explanation of this effect. Obviously, we cannot deduce from the wave theory the independence of the energy of electrons from the intensity of light by which they have been extracted from the metal plate. We shall, therefore, try another theory. We remember that Newton’s corpuscular theory, explaining many of the observed phenomena of light, failed to account for the bending of light, which we are now deliberately disregarding. In Newton’s time the concept of energy did not exist. Light corpuscles were, according to him, weightless; each colour preserved its own substance character. Later, when the concept of energy was created and it was recognized that light carries energy, no one thought of applying these concepts to the corpuscular theory of light. Newton’s theory was dead and, until our own century, its revival was not taken seriously.

Energy is the capacity to create effect. Substance can create affect through its substantiality (inertia) and its activity (velocity). In both cases the affect is created through impact. Both inertia and velocity contribute to this impact as momentum. A wave is mostly velocity, but it cannot exist without some substantiality.

To keep the principal idea of Newton’s theory, we must assume that homogeneous light is composed of energy-grains and replace the old light corpuscles by light quanta, which we shall call photons, small portions of energy, travelling through empty space with the velocity of light. The revival of Newton’s theory in this new form leads to the quantum theory of light. Not only matter and electric charge, but also energy of radiation has a granular structure, i.e., is built up of light quanta. In addition to quanta of matter and quanta of electricity there are also quanta of energy.

For homogenous light to be composed of energy-grains there must be an absolute definition of energy, which is not the case for energy in material domain. Kinetic energy is defined in terms of velocity, which is conceived in relative terms only. We are then left with the “innate force” concept of inertia. It is possible that light is composed of force-grains, or by “lines of force”. This will make Faraday happy.

The idea of energy quanta was first introduced by Planck at the beginning of this century in order to explain some effects much more complicated than the photoelectric effect. But the photo-effect shows most clearly and simply the necessity for changing our old concepts.

In my opinion, Einstein’s reference to “energy quanta” can be better understood as “force quanta”. I truly respect Faraday’s insight here. And I greatly respect Einstein.

It is at once evident that this quantum theory of light explains the photoelectric effect. A shower of photons is falling on a metal plate. The action between radiation and matter consists here of very many single processes in which a photon impinges on the atom and tears out an electron. These single processes are all alike and the extracted electron will have the same energy in every case. We also understand that increasing the intensity of the light means, in our new language, increasing the number of falling photons. In this case, a different number of electrons would be thrown out of the metal plate, but the energy of any single one would not change. Thus we see that this theory is in perfect agreement with observation.

The frequency of photons remains the same. The kinetic energy of the electrons remains the same. Increase in light intensity results in increased number of extracted electrons. Therefore, increase in light intensity increases the number of impinging photons and not their energy.

What will happen if a beam of homogeneous light of a different colour, say, red instead of violet, falls on the metal surface? Let us leave experiment to answer this question. The energy of the extracted electrons must be measured and compared with the energy of electrons thrown out by violet light. The energy of the electron extracted by red light turns out to be smaller than the energy of the electron extracted by violet light. This means that the energy of the light quanta is different for different colours. The photons belonging to the colour red have half the energy of those belonging to the colour violet. Or, more rigorously: the energy of a light quantum belonging to a homogeneous colour decreases proportionally as the wave-length increases. There is an essential difference between quanta of energy and quanta of electricity. Light quanta differ for every wave-length, whereas quanta of electricity are always the same. If we were to use one of our previous analogies, we should compare light quanta to the smallest monetary quanta, differing in each country.

The photon is absorbed in the process of extracting the electron. The quantum of the photon depends on the color of light. The lesser is the “inertial energy” of the absorbed photon, the lesser is the “kinetic energy” of the extracted electron. Therefore, its “inertial energy” is changing and not the “kinetic energy”. This means that “inertial energy” of photon is converting into the “kinetic energy” of electron. In other words, “mass” is converting into “energy” in the photoelectric process. 

Let us continue to discard the wave theory of light and assume that the structure of light is granular and is formed by light quanta, that is, photons speeding through space with the velocity of light. Thus, in our new picture, light is a shower of photons, and the photon is the elementary quantum of light energy. If, however, the wave theory is discarded, the concept of a wave-length disappears. What new concept takes its place? The energy of the light quanta! Statements expressed in the terminology of the wave theory can be translated into statements of the quantum theory of radiation. For example:

The state of affairs can be summarized in the following way: there are phenomena which can be explained by the quantum theory but not by the wave theory. Photo-effect furnishes an example, though other phenomena of this kind are known. There are phenomena which can be explained by the wave theory but not by the quantum theory. The bending of light around obstacles is a typical example. Finally, there are phenomena, such as the rectilinear propagation of light, which can be equally well explained by the quantum and the wave theory of light.

The wave theory and the quantum theory can both exist together if the light quantum is a “line of force” and not a ball like particle. A line of force can have wavelength as postulated by Faraday. A line of force can also be a discrete quantum as postulated by Einstein.

But what is light really? Is it a wave or a shower of photons? Once before we put a similar question when we asked: is light a wave or a shower of light corpuscles? At that time there was every reason for discarding the corpuscular theory of light and accepting the wave theory, which covered all phenomena. Now, however, the problem is much more complicated. There seems no likelihood of forming a consistent description of the phenomena of light by a choice of only one of the two possible languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do!

How is it possible to combine these two pictures? How can we understand these two utterly different aspects of light? It is not easy to account for this new difficulty. Again we are faced with a fundamental problem.

This fundamental problem of wave-particle arises from the assumption that a light quantum is ball-like and it can have no wavelength. But a light quantum can be string-like and it can have wavelength. The contradiction is only because of a wrong assumption.

For the moment let us accept the photon theory of light and try, by its help, to understand the facts so far explained by the wave theory. In this way we shall stress the difficulties which make the two theories appear, at first sight, irreconcilable.

We remember: a beam of homogeneous light passing through a pinhole gives light and dark rings (p. 118). How is it possible to understand this phenomenon by the help of the quantum theory of light, disregarding the wave theory? A photon passes through the hole. We could expect the screen to appear light if the photon passes through and dark if it does not. Instead, we find light and dark rings. We could try to account for it as follows: perhaps there is some interaction between the rim of the hole and the photon which is responsible for the appearance of the diffraction rings. This sentence can, of course, hardly be regarded as an explanation. At best, it outlines a programme for an explanation holding out at least some hope of a future understanding of diffraction by interaction between matter and photons.

The diffraction rings are explained when we consider the light quantum to be a string-like line of force. It is continuous in one dimension and discrete in another.

But even this feeble hope is dashed by our previous discussion of another experimental arrangement. Let us take two pinholes. Homogeneous light passing through the two holes gives light and dark stripes on the screen. How is this effect to be understood from the point of view of the quantum theory of light? We could argue: a photon passes through either one of the two pinholes. If a photon of homogeneous light represents an elementary light particle, we can hardly imagine its division and its passage through the two holes. But then the effect should be exactly as in the first case, light and dark rings and not light and dark stripes. How is it possible then that the presence of another pinhole completely changes the effect? Apparently the hole through which the photon does not pass, even though it may be at a fair distance, changes the rings into stripes! If the photon behaves like a corpuscle in classical physics, it must pass through one of the two holes. But in this case, the phenomena of diffraction seem quite incomprehensible.

A photon is a wavy string-like particle that can cause diffraction.

Science forces us to create new ideas, new theories. Their aim is to break down the wall of contradictions which frequently blocks the way of scientific progress. All the essential ideas in science were born in a dramatic conflict between reality and our attempts at understanding. Here again is a problem for the solution of which new principles are needed. Before we try to account for the attempts of modern physics to explain the contradiction between the quantum and the wave aspects of light, we shall show that exactly the same difficulty appears when dealing with quanta of matter instead of quanta of light.



In the photoelectric effect, an increase in the intensity of light only increased the number of electrons emitted and not their energy (velocity). This implies an increase in the same type of interactions between light and electrons. Hence, light must also be composed of particles like electrons.

When the wavelength of light was increased, it lowered the energy of the electrons emitted, and not their number. This implies that the energy was supplied by the composition of light particles and not by their kinetic energy. In other words, the inertia (innate force) of light particles converted into the velocity of the electrons. It is like a conversion from “mass” into “energy”.

A constant velocity is an outcome of balanced forces. Inertia is the innate force of the substance It balances the acceleration of the quantum particle. As this balance shifts, so does the velocity. Thus, underlying the exchange of energy there is a balance of forces in terms of momentum.

Einstein refers to these light and electricity particles as “energy quanta”, but, much earlier, Faraday referred to them as lines of force. These lines of force may be viewed as string-like “force quanta”. This view explains the wave properties of light and generates no conflict with its quantum properties.  


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 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 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 elementary quantum of hydrogen is an atom. This atom may be stripped off an electron, which is the elementary quantum of electricity. This leaves a positively charged nucleus behind. The electron has hardly any mass compared to the nucleus.

The electron, therefore, appears to be a surface phenomenon of outward radiating mass. When it is removed, it seems to leave an inward radiating groove on the surface of the nucleus.

This outward radiating mass seems to form the negative charge. The inward radiating groove seems to form the positive charge for the lack of better explanation. They have a tendency to join back together.


Einstein 1938: Continuity—Discontinuity

Reference: Evolution of Physics

This paper presents Chapter IV section 1 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.



A map of New York City and the surrounding country is spread before us. We ask: which points on this map can be reached by train? After looking up these points in a railway timetable, we mark them on the map. We now change our question and ask: which points can be reached by car? If we draw lines on the map representing all the roads starting from New York, every point on these roads can, in fact, be reached by car. In both cases we have sets of points. In the first they are separated from each other and represent the different railway stations, and in the second they are the points along the lines representing the roads. Our next question is about the distance of each of these points from New York, or, to be more rigorous, from a certain spot in that city. In the first case, certain numbers correspond to the points on our map. These numbers change by irregular, but always finite, leaps and bounds. We say: the distances from New York of the places which can be reached by train change only in a discontinuous way. Those of the places which can be reached by car, however, may change by steps as small as we wish, they can vary in a continuous way. The changes in distance can be made arbitrarily small in the case of a car, but not in the case of a train.

The output of a coal mine can change in a continuous way. The amount of coal produced can be decreased or increased by arbitrarily small steps. But the number of miners employed can change only discontinuously. It would be pure nonsense to say: “Since yesterday, the number of employees has increased by 3.783.”

Asked about the amount of money in his pocket, a man can give a number containing only two decimals. A sum of money can change only by jumps, in a discontinuous way. In America the smallest permissible change or, as we shall call it, the “elementary quantum” for American money, is one cent. The elementary quantum for English money is one farthing, worth only half the American elementary quantum. Here we have an example of two elementary quanta whose mutual values can be compared. The ratio of their values has a definite sense since one of them is worth twice as much as the other.

A quantum is a definite, discrete amount.

We can say: some quantities can change continuously and others can change only discontinuously, by steps which cannot be further decreased. These indivisible steps are called the elementary quanta of the particular quantity to which they refer.

We can weigh large quantities of sand and regard its mass as continuous even though its granular structure is evident. But if the sand were to become very precious and the scales used very sensitive, we should have to consider the fact that the mass always changes by a multiple number of one grain. The mass of this one grain would be our elementary quantum. From this example we see how the discontinuous character of a quantity, so far regarded as continuous, can be detected by increasing the precision of our measurements.

If we had to characterize the principal idea of the quantum theory in one sentence, we could say: it must be assumed that some physical quantities so far regarded as continuous are composed of elementary quanta.

The region of facts covered by the quantum theory is tremendously great. These facts have been disclosed by the highly developed technique of modern experiment. As we can neither show nor describe even the basic experiments, we shall frequently have to quote their results dogmatically. Our aim is to explain the principal underlying ideas only.



Some quantities can change only by steps which cannot be further decreased. These indivisible steps are called the elementary quanta of the particular quantity to which they refer.

Some physical quantities so far regarded as continuous are composed of elementary quanta. This is the principle idea of quantum theory.


Einstein 1938: Field and Matter

Reference: Evolution of Physics

This paper presents Chapter III, section 14 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).

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Field and Matter

We have seen how and why the mechanical point of view broke down. It was impossible to explain all phenomena by assuming that simple forces act between unalterable particles. Our first attempts to go beyond the mechanical view and to introduce field concepts proved most successful in the domain of electromagnetic phenomena. The structure laws for the electromagnetic field were formulated; laws connecting events very near to each other in space and time. These laws fit the frame of the special relativity theory, since they are invariant with respect to the Lorentz transformation. Later the general relativity theory formulated the gravitational laws. Again they are structure laws describing the gravitational field between material particles. It was also easy to generalize Maxwell’s laws so that they could be applied to any c.s. like the gravitational laws of the general relativity theory.

The mechanical view described simple forces acting between unalterable particles. It broke down because it was limited to a certain level of inertia. The electromagnetic phenomena went beyond that level of inertia. It could be explained better with field concepts. Speed of light in special relativity helped understand absolute motion and its relationship with inertia. Changing inertia in general relativity helped understand the laws of gravity on a broader basis.

We have two realities: matter and field. There is no doubt that we cannot at present imagine the whole of physics built upon the concept of matter as the physicists of the early nineteenth century did. For the moment we accept both the concepts. Can we think of matter and field as two distinct and different realities? Given a small particle of matter, we could picture in a naive way that there is a definite surface of the particle where it ceases to exist and its gravitational field appears. In our picture, the region in which the laws of field are valid is abruptly separated from the region in which matter is present. But what are the physical criterions distinguishing matter and field? Before we learned about the relativity theory we could have tried to answer this question in the following way: matter has mass, whereas field has not. Field represents energy, matter represents mass. But we already know that such an answer is insufficient in view of the further knowledge gained. From the relativity theory we know that matter represents vast stores of energy and that energy represents matter. We cannot, in this way, distinguish qualitatively between matter and field, since the distinction between mass and energy is not a qualitative one. By far the greatest part of energy is concentrated in matter; but the field surrounding the particle also represents energy, though in an incomparably smaller quantity. We could therefore say: Matter is where the concentration of energy is great, field where the concentration of energy is small. But if this is the case, then the difference between matter and field is a quantitative rather than a qualitative one. There is no sense in regarding matter and field as two qualities quite different from each other. We cannot imagine a definite surface separating distinctly field and matter.

Field and matter are split by a wide gulf of inertia and velocity. Both represent substance. Matter has high inertia but low velocity. Field has low inertia but high velocity. Physics views inertia as “mass” and velocity as “energy” but it does not see the reciprocal relationship between “mass” and “energy” as can be seen between inertia and velocity. Physics, however, does recognize some commonality between “mass” and “energy”. When it says, “Matter represents vast stores of energy,” it is comparing them as substance in terms of inertia. “Energy” has the sense of kinetic energy, which is perceived as velocity. Mass and energy equivalence is none other than inertia and velocity equivalence.

The same difficulty arises for the charge and its field. It seems impossible to give an obvious qualitative criterion for distinguishing between matter and field or charge and field.

Charge seems to be a transition phenomenon between matter and field. It has the characteristics of inertia and velocity that fall between matter and field.

Our structure laws, that is, Maxwell’s laws and the gravitational laws, break down for very great concentrations of energy or, as we may say, where sources of the field, that is electric charges or matter, are present. But could we not slightly modify our equations so that they would be valid everywhere, even in regions where energy is enormously concentrated?

We seem to have discontinuity between field and matter in terms of applicable laws.

We cannot build physics on the basis of the matter-concept alone. But the division into matter and field is, after the recognition of the equivalence of mass and energy, something artificial and not clearly defined. Could we not reject the concept of matter and build a pure field physics? What impresses our senses as matter is really a great concentration of energy into a comparatively small space. We could regard matter as the regions in space where the field is extremely strong. In this way a new philosophical background could be created. Its final aim would be the explanation of all events in nature by structure laws valid always and everywhere. A thrown stone is, from this point of view, a changing field, where the states of greatest field intensity travel through space with the velocity of the stone. There would be no place, in our new physics, for both field and matter, field being the only reality. This new view is suggested by the great achievements of field physics, by our success in expressing the laws of electricity, magnetism, gravitation in the form of structure laws, and finally by the equivalence of mass and energy. Our ultimate problem would be to modify our field laws in such a way that they would not break down for regions in which the energy is enormously concentrated.

We may look at matter as highly concentrated field. Here field is extremely dynamic, whereas, matter is nearly static. We need laws of physics to cover the structure of both field and matter.

But we have not so far succeeded in fulfilling this programme convincingly and consistently. The decision, as to whether it is possible to carry it out, belongs to the future. At present we must still assume in all our actual theoretical constructions two realities: field and matter.

Fundamental problems are still before us. We know that all matter is constructed from a few kinds of particles only. How are the various forms of matter built from these elementary particles? How do these elementary particles interact with the field? By the search for an answer to these questions new ideas have been introduced into physics, the ideas of the quantum theory.

These problems are taken forward to Quantum theory.


A new concept appears in physics, the’ most important invention since Newton’s time: the field. It needed great scientific imagination to realize that it is not the charges nor the particles but the field in the space between the charges and the particles which is essential for the description of physical phenomena. The field concept proves most successful and leads to the formulation of Maxwell’s equations describing the structure of the electromagnetic field and governing the electric as well as the optical phenomena.

The theory of relativity arises from the field problems. The contradictions and inconsistencies of the old theories force us to ascribe new properties to the time-space continuum, to the scene of all events in our physical world.

The relativity theory develops in two steps. The first step leads to what is known as the special theory of relativity, applied only to inertial co-ordinate systems, that is, to systems in which the law of inertia, as formulated by Newton, is valid. The special theory of relativity is based on two fundamental assumptions: physical laws are the same in all co-ordinate systems moving uniformly, relative to each other; the velocity of light always has the same value. From these assumptions, fully confirmed by experiment, the properties of moving rods and clocks, their changes in length and rhythm depending on velocity, are deduced. The theory of relativity changes the laws of mechanics. The old laws are invalid if the velocity of the moving particle approaches that of light. The new laws for a moving body as reformulated by the relativity theory are splendidly confirmed by experiment. A further consequence of the (special) theory of relativity is the connection between mass and energy. Mass is energy and energy has mass. The two conservation laws of mass and energy are combined by the relativity theory into one, the conservation law of mass-energy.

The general theory of relativity gives a still deeper analysis of the time-space continuum. The validity of the theory is no longer restricted to inertial co-ordinate systems. The theory attacks the problem of gravitation and formulates new structure laws for the gravitational field. It forces us to analyse the role played by geometry in the description of the physical world. It regards the fact that gravitational and inertial mass are equal, as essential and not merely accidental, as in classical mechanics. The experimental consequences of the general relativity theory differ only slightly from those of classical mechanics. Thy stand the test of experiment well wherever comparison is possible. But the strength of the theory lies in its inner consistency and the simplicity of its fundamental assumptions.

The theory of relativity stresses the importance of the field concept in physics. But we have not yet succeeded in formulating a pure field physics. For the present we must still assume the existence of both: field and matter.



Matter and field are two aspects of substance that remind us of particle and void; but there is no absolute void. Matter forms a high inertia and low velocity plateau; whereas, field forms low inertia and high velocity plateau. These two plateaus are separated by a sharp slope as shown in the following picture. Charge seems to be a transition phenomenon between matter and field.

Physics views inertia as “mass” and velocity as “energy”. The theory of relativity establishes equivalence between mass and energy. A very small amount mass is equivalent to a very large amount of energy. A similar relationship appears to exist between inertia and velocity. A large change in velocity in the material region has imperceptible change in mass (inertia).

The picture above shows that there is a reciprocal relationship between inertia and velocity. It will be helpful to find the exact mathematical relationship between them. This also shows that there exist absolute scales for both inertia and velocity.

Equivalence between gravity and acceleration means that a gravitational field shall consist of changing inertia. It will take an extremely small change in inertia to construct a gravitational field. This may help us develop a better understanding between field and matter.