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.
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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.
In the wave theory, the energy of the wave is proportional to the square of the amplitude. But in the case of light, its energy is proportional to its frequency. The frequency of light relates to its substance. The substance of light has a syrupy consistency. In the case of matter, its very high frequency appears as “mass.”
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 (inertial mass) and its activity (velocity). In both cases the affect is created through impact. Both inertial mass and velocity contribute to this impact as momentum. A wave is mostly velocity, but it cannot exist without some substantiality (inertial mass).
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.
How does a light quantum look like. It is certainly not like a material particle as it has no center of mass. A quantum could be a line or sheet of force with a thin consistency. Each frequency shall have its own sheet, and all these sheets shall be wrapped or swirling around each other in a polychromatic light. We may assume any kind of shape for the light quanta. It just imparts a granular feel to light.
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.
The frequency represents consistency of light, which, together with its velocity provides a momentum to light. Since the velocity of light is fixed, this momentum can be changed only by changing light’s frequency. Electrons have fixed consistency but variable velocity. With this exchange of momentum between light and electron, the frequency of light converts into the velocity of the electron.
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” or a “sheet of force” and not a ball like particle. A line or sheet of force can have wavelength as postulated by Faraday. A line or sheet of force can also contain discrete quanta 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 or particle arises from the assumption that a light quantum is like a ball and it can have no wavelength or frequency. But a light quanta can be like a string or a sheet and it can have wavelength, frequency or consistency. The contradiction is only because of a fixed view of a “granular” state in terms of ball-like particles only.
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.
Photons are made up of non-atomic fluid-like substance. They may coalesce together and split as long as they have the same frequency. 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.
Einstein is assuming that an elementary particle of light is indivisible like the elementary particle of matter. But the consistency of light is much thinner than the consistency (or mass) of matter. Light particle is not solid. It is more like a drop of fluid that can split.
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.
The new idea is to examine the assumptions pertaining to the nature of the light quanta. Is there a limit to which it can be divided?
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FINAL COMMENTS
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 that 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.
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