Development of Our Conception

Beware when the great God lets loose a thinker on this planet.
RALPH WALDO EMERSON, "Circles," Essays 
Quantum mechanics is very impressive but I am convinced that God does not play dice.
ALBERT EINSTEIN 
WHEN IT WAS discovered that light exhibits the phenomena of interference and refraction, it seemed hardly to be doubted that light had to be considered as a wave propagation. Because light is also able to propagate through vacuum one had to imagine also that there is a special kind of matter present which mediates the propagation of light waves. It was necessary for the laws of light propagation in ponderable bodies to assume that this matter, which was called luminiferous ether, was also present in those, and that it was mainly the luminiferous ether which mediates the propagation of light. The existence of that luminiferous ether seemed indubitable. In the introduction about the ether in the first volume of the excellent textbook in physics by Chwolson, published in 1902, this sentence can be found: "The probability of the hypothesis of the existence of this element is extremely close to certainty."
But today we have to regard the ether hypothesis as an outdated point of view. It is undeniable that there exist an extensive group of facts concerning radiation which show that light has some fundamental properties which can be understood more easily from the viewpoint of Newton's corpuscular theory of light rather than the viewpoint of the undulation theory. My opinion is therefore that the next step of the development of theoretical physics will lead us to a theory of light which can be interpreted as a kind of fusion of undulation and corpuscular theory. The purpose of the following exposition is to justify this opinion and to show that a deep change in our conception about the nature and the constitution of light is indispensable.
The biggest step which theoretical optics has achieved since the introduction of the undulation theory likely consists of Maxwell's brilliant discovery of the possibility of conceiving of light as an electromagnetic process. Instead of a mechanical quantity, namely deformation and velocity of the parts of the ether, this theory introduces the electromagnetic state of ether and matter into consideration and thereby reduces the optical problems to electromagnetic ones. The more the electromagnetic theory was developed, the more the question of whether electromagnetic processes could be traced back to mechanical ones was moved into the background; one got used to treating the conception of electric and magnetic field strength, electric charge density, etc. as elementary conceptions, which need not be interpreted mechanically.
The foundations of theoretical optics were simplified by the introduction of the electromagnetic theory; the number of arbitrary hypotheses was diminished. The old question of the direction of the oscillation of polarised light became irrelevant. The difficulties concerning the boundary conditions at the boundary of two media had arisen from the foundations of the theory. There was no longer a need for an arbitrary hypothesis to incorporate longitudinal light waves. Light pressure, which has only been established lately and which plays s~ch an important role in the theory of radiation, came out as a consequence of the theory. I don't want to try to present here a complete list of the wellknown achievements, but stick to the main point with regard to which the electromagnetic theory agrees with the kinematical theory, or better expressed, seems to agree.
According to both theories light waves seem to be mainly an inherent property of states of a hypothetical medium, the ether, which is also to be present in the absence of radiation. It was therefore reasonable that the motion of this medium had an influence on the optical and electromagnetic phenomena. The search for the laws that underlie this influence started a change of our basic conception concerning the nature of radiation, a development we want to examine briefly.
The basic question one was forced to was the following: Does the luminiferous ether follow the motion of matter, or does it move differently in the interior of moving bodies, or, finally, does it perhaps not participate at all in the movement of matter, but stay always at rest? To decide this question Fizeau did an important experiment with interference which is based on the following consideration. If the body is at rest, light propagates in it with velocity V. If the body takes its ether completely with it when it is moved, light propagates relative to the body in the same way in this case as if the body is in rest. In this case the velocity of propagation relative to the body is Valso. Taken absolutely, that is, relative to an observer who does not move with the body, the velocity of propagation of a lightray is equal .to the geometrical sum of V and the moving velocity v of the body. If velocity of propagation and velocity of motion have the same direction and sense, then Vabs is simply the sum of both velocities, that is Vabs = V + v.
To test if this consequence of the hypothesis of the completely comoving luminiferous ether holds true, Fizeau made two coherent monochromatic lightwaves each pass axially through a tube filled with water and afterwards let them interfere. If the water now moved axially through the tubes, through one tube in the direction of the light, through the other in the opposite direction, a displacement of the interference fringes took place, by which he could draw a conclusion about the influence of the velocity of the body on the absolute velocity.
As is well known and expected, he found that there is an influence of the velocity of the body, but always smaller than that expected according to the hypothesis of the completely comoving ether. He finds that
Vabs = V + av,
where a is always smaller than one. By neglecting dispersion it follows that
a = 1  1/n^{2}
From this experiment it follows that a complete comoving of the ether does not take place and therefore in general there is relative motion of the ether with respect to the matter. But the earth is a body which has velocities with different directions during one year, and it was not supposed that the ether in our laboratories participates completely in the movement of our earth, any more than it seemed to participate completely in the movement of the water in Fizeau's experiment. One was therefore to conclude that there exists a relative motion of the ether with respect to our apparatus which changes with the time of day and year and one had to expect that this relative velocity leads to an apparent anisotropy of space in optical experiments, which means that the optical phenomena are dependent on the orientation of the apparatus. The most diverse experiments were carried out to establish this anisotropy without being able to establish the expected dependence of the phenomena upon the direction of the apparatus.
This contradiction was for the most part removed by H. A. Lorentz's pioneering work in the year 1895. Lorentz showed one gets a theory which satisfies almost all phenomena without setting up other hypotheses. In particular the results of the above indicated experiment of Fizeau and the negative result of the mentioned experiments to establish the earth's movement against the ether were explained. Lorentz's theory seemed inconsistent with only one experiment, namely with Michelson's and Morley's interference experiment.
Lorentz has shown that no influence of a common translational movement of the apparatus is present in his theory that affects the raypaths of optical experiments, except for terms which contained the quotient
velocity of the body / velocity of light
to the second or higher powers as a factor. But at that time the MichelsonMorley's interference experiment was already known, which showed that in one special case even terms of second order with respect to the quotient
velocity of the body / velocity of light
are not noticeable as was expected from the viewpoint of the theory of the stationary luminiferous ether. To cover this experiment with the theory, Lorentz and FitzGerald introduced, as is known, the assumption that all bodies, and therefore also those which connected the parts of Michelson and Morley's experimental arrangement, change their shape in a certain way if they are moved relative to the ether.
This situation was now highly unsatisfactory. Lorentz's theory was the only theory which was useful and clear in its foundations. It rested on the assumption of an absolutely motionless ether. The earth had to be regarded as moving relative to this ether. But all experiments to detect this relative motion were without result, and therefore one was forced to set up this quite peculiar hypothesis to be able to comprehend that the relative motion is not noticeable.
Michelson's experiment leads to the assumption that all phenomena relative to a comoving earth coordinate system, or more generally to every unaccelerated system, obey the same laws. In the following we want to call this assumption the "principle of relativity," for short. Before we touch upon the question of whether it is possible to adhere to the principle of relativity, we want to consider briefly what becomes of the ether hypothesis if we adhere to this principle.
With the ether hypothesis as a basis, the experiment led to the assumption of a motionless ether. The principle of relativity then states that, according to a coordinate system.K', moving uniformly relative to the ether, all laws of nature are equivalent to the corresponding laws in a coordinate system K, at rest relative to the ether. If this holds true, then it is as reasonable to think of the ether as being at rest relative to K' as to K. It is then generally unnatural to distinguish one of both coordinate systems K and K' in a way that one introduces an ether which is at rest relative to it. From that it follows that a satisfactory theory is only achieved by re nouncing the ether hypothesis. The electromagnetic fields that constitute light appear not as states of a hypothetical medium but as independent phenomena which are emitted by light sources, the same as in Newton's corpuscular theory of light. According to this theory a space which is not filled by radiation and which is free of ponderable matter appears to be really empty.
In a superficial consideration it seems to be impossible to bring the essence of Lorentz's theory into harmony with the principle of relativity. If a light ray propagates in vacuum then, according to Lorentz's theory, with respect to the coordinate system K at rest in the ether, it always does so with the fixed velocity c, independent of the state of motion of the emitting body. We wish to call this statement the principle of constant light speed. According to the addition theorem for velocities the same light ray is not propagated with the same velocity c in a coordinate system K', uniformly translated relative to the ether. The laws of light propagation seem to be different in both coordinate systems and therefore it seems to follow that the principle of relativity is incompatible with the laws of light propagation.
The addition theorem for velocities, however, is based on the arbitrary presupposition that the statements about time and about the shape of moving bodies have a meaning which is independent of the state of motion of the coordinate system used. But one convinces oneself that the introduction of clocks that are at rest relative to the coordinate system used is needed to define the time and the shape of moving bodies. These conceptions have to be therefore specially fixed for each coordinate system and it is not selfevident that this definition leads to the same time t and t' for single events for two coordinate systems, K and K', moving relative to each other; likewise one cannot say a priori that every statement about the shape of bodies which is valid in a coordinate system K is also valid in the frame K' moving relative to K.
From this it follows that the transformation equations used till now for the transition from one coordinate system to another coordinate system moving uniformly relative to it are based on arbitrary assumptions. Giving these up, it can be shown that the basis of Lorentz's theory, or more general, the principle of constant light speed can be brought into harmony with the principle of relativity. In this way new equations of the coordinate transformation are obtained which are definitely determined by the two principles and which are, with a suitable choice of the origin of coordinates and time, characterized by making an identity of the equation
Here c is the velocity of light in vacuum, x, y, z, t are the spacetime coordinates with respect to K, x', y', z', t' with respect to K'.
This path leads to the socalled theory of relativity, from which I only want to cite one consequence, because it leads to a certain modification in the field of physics. It can be shown that the initial mass of a body decreases by L / c^{ 2} if the body emits the energy of radiation L. One can obtain this in the following manner.
We consider a motionless free suspending body which emits the same amount of energy by radiation in two opposite directions. Yet the body remains at rest. If we characterize the energy of the body before the emission with E_{0}, the energy after the emission with E_{1}, the amount of emitted radiation with L, according to the principle of energy conservation it follows that
E_{0} = E_{1} + L.
Let us consider now the body and the radiation emitted by it with respect to a coordinate system to which the body is moved with the velocity v. The theory of relativity gives us then the tools to calculate the energy of the emitted radiation with respect to the new coordinate system. One obtains for it the value
Because the principle of conservation of energy also has to be true in the new coordinate system, by an analogous consideration one gets
By subtracting and neglecting terms in v / c of fourth and higher order, one gets
But E'_{0}  E_{0} is nothing but the kinetic energy of the body before the emission of light, and E' _{l}  E _{l} is nothing but the kinetic energy after the emission of light. If we call M_{0 } the body's mass before the emission, M_{1} the body's mass after the emission, then by neglecting terms of higher order than the second we can set
or
Hence the inertial mass of a body is diminished by light emission. The emitted energy figures as part of the body's mass. We can draw the further conclusion that every absorption and emission of energy goes with an increase or decrease, respectively, of the mass of the body concerned. Energy and mass appear as equivalent quantities just as do heat and mechanical energy.
The theory of relativity has therefore changed our conception of the nature of light insofar as it no longer conceives light as a consequence of the states of a hypothetical medium but as an independent entity like matter. Furthermore, this theory has in common with the corpuscular theory of light the feature that it transfers inertial mass from the emitting body to the absorbing body. The theory of relativity does not change anything in our conception about the structure of radiation, in particular about the distribution of energy in the volume being radiated. However it is my opinion that we are standing at the beginning of a not yet transparent, but nevertheless highly important, development with respect to this side of the question. What I will put forward in the following is mostly bare personal opinion and also the results of reflections which have not yet passed a sufficient check by others. I still put them forward here, not because I have an excessive trust in my own view but because I hope that one or another of you will be motivated to deal with the questions concerned.
Without going deeper into any theoretical considerations, one notices that our theory of light is not able to explain certain fundamental properties of the phenomena of light. Why is the occurrence of a certain photo chemical reaction only dependent on the color, but not on the intensity of light? Why are shortwave rays in general more effective than longwave rays? Why is the velocity of the photoemitted cathoderays independent of the intensity of light? Why are high temperatures needed, or high molecular energies, to get shortwave components in the radiation emitted by bodies?
The undulation theory in today's version gives no answer to any of these questions. In particular it is not yet comprehensible why cathoderays, created by xrays or photoemitted, attain such a remarkable velocity independent of beam intensity. Competent physicists have been forced to take refuge in a quite remote hypothesis by the appearance of such huge amounts of energy at a molecular structure under the influence of a source in which the energy is distributed so much less densely, as we must presuppose for light and xrays according to the undulation theory. They have assumed that light plays only an initiatory role during this process, that the molecular energy that appears is of radioactive nature. But since this hypothesis is already as good as abandoned I do not wish to bring up any arguments against it.
The basic properties of the undulation theory which cause these difficulties seem to lie in the following. While in the kinetic theory of molecules for every process in which only a few elementary particles participate, for instance, in every molecular collision, there exists the inverse process, this is not the case for the elementary processes of radiation according to the undulation theory. An oscillating ion produces a spherical wave propagating outwardly according to the current theory. The inverse process does not exist as an elementary process. The spherical wave propagating inwardly is mathematically realizable but one needs for its approximate realization an incredible number of elementary emitting structures. Hence the elementary process of light emission does not have the character of invertibility. I think in this case our undulation theory does not describe the truth. It seems that Newton's corpuscular theory of light contains more truth than the undulation theory, because according to the former the energy that a corpuscle is given during emission is not dispersed over infinite space but remains available for an elementary absorption process. Think of the laws for the generation of secondary cathoderays by xrays.
If primary cathoderays hit a metal plate P_{ 1'} they produce xrays. If these hit another metal plate P_{ 2}, they again produce cathoderays whose velocities are of the same order as the velocities of the primary cathode rays. As far as we know today the velocity of the secondary cathoderays is neither dependent on the distance of the plates P_{ 1} and P_{2 } nor of the intensity of the primary cathoderays, but exclusively on the velocity of the primary cathoderays. Suppose this is strictly correct. What will happen if we let the intensity of the primary cathoderays, or the size of the plate P_{1} upon which they impinge, decrease in such a way that one can interpret the collision of an electron of the primary cathoderays as an isolated process? If the preceding is really true, we will have to suppose, because the velocity of the secondary rays is independent of the intensity of the primary cathoderays, that either nothing is created at P_{2} (as a consequence of the collision of this electron on P_{1}) or there occurs a secondary emission of an electron on P_{2} with a velocity which is of the same order as the one of the electron which hits P_{1}. In other words, the elementary process of radiation seems to happen in such a way that the energy of the primary electron is not distributed and dispersed by a spherical wave propagating in all directions, as the undulation theory requires. On the contrary, at least a large part of this energy seems to be available at any point of P_{2} or elsewhere. The elementary process of radiation emission seems to be directed. Furthermore I have the impression that the processes of creation of the xray at P_{1} and creation of the secondary cathoderay at P_{2} are essentially inverse processes. The constitution of radiation seems to be different than what follows from the undulation theory. The theory of heat radiation has provided us with important hints about this, and it was primarily that theory on which Mr. Planck has based his formula for radiation. Because I cannot assume this theory to be generally known I will briefly present the main points.
In the interior of a cavity of temperature T there is radiation of definite composition that is independent of the nature of the body. Per unit volume the amount of radiation present in the cavity whose frequency varies between v and v + dv is pdv. The problem consists in seeking p as a function of v and T. If the cavity contains an electric resonator of eigen frequency r_{0 } and negligible damping, the electromagnetic theory of radiation allows us to calculate the temporal mean of the energy (E) of the resonator as a function of p(r_{0 }). The problem is therefore reduced to that of calculating E as a function of temperature. But the latter problem can be again reduced to the following. Suppose very many (N) resonators of the frequency V_{0 } are present in the cavity. How does the entropy of this resonator system depend on its energy? To solve this question, Mr. Planck applies the general relation between entropy and probability which was obtained by Boltzmann from his research on gas theory. In general
entropy = k * log W,
where k is a universal constant and W is the probability of the chosen state. This probability is measured by the "number of complexions," a number which indicates in how many different ways the chosen state is realizable. In the case of the above problem, the state of the resonator system is defined by its total energy, so that the question to be solved is: In how many possible ways can the given total energy be distributed among the N resonators? To solve this, Mr. Planck divided the total energy into equal quanta of given size E. A complexion is determined by the number of particles E which belong to each resonator. The number of such complexions which give the total energy has to be determined and will be set equal to W. By use of Wien's displacement law, which can be derived from thermodynamics, Mr. Planck then further concludes that we must set E = hv, where h is a number independent of v. He finds in this way his radiation formula
which coincides so far with all previous experience. According to this derivation it might appear that Planck's formula has to be regarded as a consequence of today's electromagnetic theory of radiation. However, this is not the case, in particular because of the following reason. One can regard the number of complexions under discussion as an expression for the multiplicity of possible distributions of the total energy among N resonators only if every possible distribution of the energy appears, at least with a certain approximation, among the complexions used to calculate W. A necessary condition is that for all v which correspond to a reasonable energy density p, the energy quantum is small compared with the mean energy E of the resonator. By a simple calculation, one finds, however, that for the wavelength 0.5 micrometer and an absolute temperature T = 1700, is not only not small compared to 1 but even very large compared to 1. It has a value of about 6.5 * 10^{ 7}. In the given numerical example of the counting of the complexions one proceeds as if the energy of the resonator can take only the values zero, 6.5 * 10^{7} times this mean energy, or a multiple of that. It is clear that with this procedure only an infinitely small part of the theoretically possible distributions of the energy is used for the calculation of the entropy. The number of these complexions is therefore, according to the basic theory, not an expression for the probability of the states in the sense of Boltzmann. To take over Planck's theory means, in my opinion, to give up the foundations of our theory of radiation.
I have already tried to show you that we have to abandon our present foundations of the theory of radiation. In any case, one cannot think of denying Planck's theory because it does not fit in these foundations. This theory has led to a determination of the elementary quanta which is brilliantly confirmed by the latest measurement of this value on the basis of counting alphaparticles. For the elementary quantum of electricity Rutherford and Geiger got the mean value 4.65 * 10^{ 10}, Regener 4.79 * 10^{10}, while Mr. Planck calculated the intermediate value 4.69 * 10^{10} out of the constants of his formula by means of his theory of radiation.
Planck's theory leads to the following assumption. If it is really true that a radiating resonator can take up only such values of energy that are multiples of hv, then we are led to the assumption that emission and absorption of radiation take place only in quanta of this energy size. On the basis of this hypothesis, the hypothesis of light quanta, the above mentioned questions about absorption and emission of radiation can be answered. As far as our knowledge extends, the quantitative predictions of this hypothesis are verified. But the following question comes up. Is it possible, that Planck's formula is correct, but that there exists a derivation which is not based on such incredibleseeming assumptions as Planck's theory? Is it possible to replace the hypothesis of light quanta by another assumption which can explain the known phenomena just as well? If it is necessary to modify the elements of the theory, is it still possible to keep the equation for the propagation of radiation and to change our conception about the elementary processes of emission and absorption?
To clarify this we want to try to proceed in the direction inverse to what Mr. Planck did with his theory of radiation. We regard Planck's formula as correct and ask if something can be concluded from it with respect to the constitution of the radiation. I want to sketch here only one of two considerations which I have carried out in this sense because I found it especially convincing due to its intuitive nature.
In a cavity let there be an ideal gas and also a plate made of a rigid substance that can be moved freely only perpendicular to its plane. Because of the irregularity of the collisions between gas molecules and plate, the latter will start moving in such a way that its mean kinetic energy is equal to one third of the mean kinetic energy of a monatomic gas molecule. This is a prediction of statistical mechanics. Let's suppose now that besides the gas, which we can think of as consisting of only a few molecules, radiation is present in the cavity and that this so called heat radiation has the same temperature as the gas. This will be the case if the walls of the cavity have the definite temperature T, are not permeable to the radiation, and are not everywhere completely reflecting toward the cavity. Furthermore we suppose for the moment that our plate is completely reflecting on both sides. With these preliminaries not only the gas but also the radiation will effect the plate. The radiation will exhibit a pressure on both sides of the plate. The pressure forces of both sides are equal to one another if the plate is in rest. But if it is moved, the area which precedes the movement (the front surface) will reflect more radiation than the back surface. The pressure force acting on the front surface in a backward direction will be larger than the pressure force acting on the back surface. As a resultant of the two, there remains a force which opposes the movement of the plate and which increases with the velocity of the plate. Let us call this resultant "radiation friction" for short.
If we suppose for a moment that we have taken into account all of the mechanical influences of the radiation on the plate, then we come to the following conclusion. Through collisions with the gas molecules the plate is imparted momenta at irregular intervals into irregular directions. Between two such collisions the velocity of the plate decreases because of the radiation friction, whereby kinetic energy is converted into radiation energy. We would have the consequence that the energy of the gas mole cules is constantly converted into energy of radiation by the plate, up to the moment when all the energy present is converted into energy of radiation. There would not be an equilibrium of temperature between gas and radiation.
This consideration is erroneous because one cannot regard the pressure forces exerted by the radiation on the plate as temporally constant and free of irregular fluctuations any more then the pressure force exerted by the gas on the plate. To allow thermal equilibrium these fluctuations of the pressure forces of the radiation have to be constituted in such a way that they compensate in the mean for the losses of velocity of the plate by radiation friction, where the mean kinetic energy of the plate is equal to one third of the mean kinetic energy of a monatomic gas molecule. If the law of radiation is known, the radiational friction can be calculated, and hence the mean value of the momentum that the plate has to receive because of the fluctuations of the radiation pressure in order that statistical equilibrium can exist.
The consideration gets still more interesting if we so choose the plate that it reflects only radiation in the range of frequencies dv, but allows radiation of different frequencies to pass without any absorption; one obtains then the fluctuations of the pressure of the radiation in the range of frequencies dv. For this case I want to give the result of the calculation. If I denote by 1:1 the value of the quantity of motion [momentum] which gets transferred to the plate during the time T because of the irregular fluctuations of the pressure of radiation, I get the expression [f = surface area]
for the mean value of the square of delta.
First of all notice the simplicity of this expression. There cannot be any radiation formula that coincides with the experiments within observational error and gives such a simple expression for the statistical properties of the radiation pressure as Planck's formula.
As for the interpretation, notice first that the expression for the mean square of the fluctuations is a sum of two terms. It is as if there are two independent different causes present that produce the fluctuations of the radiation pressure. Out of the proportionality of 1:12 to f one concludes that the fluctuations of the pressure for parts of the plate that are side by side and whose linear size is large compared to the wavelength of the reflected radiation, give results which are independent of each other.
The undulation theory gives an explanation only for the second term of the expression for delta squared. According to the undulation theory bunches of rays that differ only infinitesimally in direction, frequency and state of polarization, have to interfere, and the sum of these interferences, which arise in the most disordered fashion, has to correspond to a fluctuation of the radiation pressure. By a simple consideration of dimensions one can see that these fluctuations must have a form like the second term of our formula. It is seen that the undulating structure of the radiation indeed gives rise to the expected fluctuations of the radiation pressure.
But how can the first term of the formula be explained? This is not at all negligible but on the contrary in the range of validity of the socalled Wien radiation law it is solely dominant. For a wavelength of 0.5 micrometer and T = 1700 this term is about 6.5 X 10^{7 } times bigger than the second term. If the radiation consists only of very few extended complexes of energy hv, that propagate independently through space and are reflected independently of each otheran assumption which is the crudest picture of the hypothesis of light quantathen our plate would be effected due to fluctuations of the radiation pressure by an amount given by the first term of our formula.
In my opinion, the following must be concluded from the above formula, which itself is a consequence of Planck's formula. Besides the spatial irregularities in the distribution of the quantity of motion of radiation which arise out of the undulation theory, there are also other irregularities in the spatial distribution of the quantity of motion present, which greatly exceed the first mentioned irregularities at low energy densities of the radiation. I would like to add that a different treatment considering the spatial distribution of the energy gives the same result as above with respect to the spatial distribution of the quantity of motion.
As far as I know nobody has succeeded in setting up a mathematical theory of radiation which yields both the undulational structure and the structure that follows from the first term of the above formula (quantized structure). The difficulties are mainly that the properties of the fluctuations of radiation, as they are expressed in the above formula, give few formal hints for setting up a theory. Suppose the phenomena of refraction and interference were still unknown, but one knew that the mean value of the irregular fluctuations of the radiation pressure were determined by the second term of the above equation, where v is a parameter of unknown meaning which determines the color. Who would have enough imagination to build up the undulation theory of light on this basis? To me, the most natural concept is that the occurrence of the electromagnetic fields of light is bound to singular points in the same way as the occurrence of electrostatic fields according to electron theory. It cannot be excluded that in such a theory the total energy of the electromagnetic field has to be regarded as being localized in these singularities, in the same way as in the old theory of action at a distance. I think of every singular point as being surrounded by a force field, which has in essence the character of a plane wave and whose amplitude decreases with the distance to the singular point. If many such singularities are present at distances which are small compared to the size of the force field of a singular point, then the force fields will start to superimpose and the sum will give rise to an undulational force field, which probably differs only slightly from an undulational field in the sense of the present electromagnetic theory of light. I do not have to emphasize that such a picture has no worth as long as it does not lead to an exact theory. I only wished to illustrate briefly that the two structural phenomena (undulational structure and quantized structure) that the radiation possesses according to Planck's formula, do not have to be regarded as incompatible with each other.
DISCUSSION
Planck: I would like to add some comments about the lecture, but before doing so I can only join in the gratitude of all participants who listened with the greatest interest to that which Mr. Einstein has presented, and who were inspired to further investigation whenever a contradiction perhaps emerged. I will restrict myself naturally to the points where I have a different opinion than that of the speaker. Most of what the speaker has pointed out will not be opposed. I too stress the introduction of some kind of quanta. We do not get on with the whole theory of radiation without splitting energy in some sense into quanta, which ought to be thought as "atoms of action." There is now the question of where to look for these quanta. According to the latest explanations of Mr. Einstein it would be necessary to think of free radiation in vacuum, that is the light waves themselves, as atomistically constituted, and therefore to give up Maxwell's equations. This seems to me to be a step that is in my opinion not yet necessary. I do not want to go into details but just state the following: in his last consideration Mr. Einstein infers fluctuations of free radiation in pure vacuum from the movement of matter. This reasoning seems to me totally unobjectionable only if one knows completely the interaction between radiation in the vacuum and the motion of matter. If this is not the case then there is lacking the bridge that is necessary in order to go from the motion of the mirror to the intensity of the incident radiation. But to me this interaction between free electric energy in vacuum and the motion of the atoms of matter seems to be known very poorly.
Essentially it is based on emission and absorption of light. The radiation pressure too consists essentially of this, at least according to the generally accepted theory of dispersion, which reduces also reflection to absorption and emission. But emission and absorption is exactly the dark spot we know very little about. We might know perhaps something about absorption, but what about emission? It is thought to be caused by the acceleration of electrons. But this is the weakest point of the whole theory of electrons. The electron is considered to possess some definite volume and a specific finite charge density, be it spatial density or surface density; without this one does not get along. But this contradicts the atomistic conception of electricity in some sense. These are not impossibilities but problems and I am almost astonished that there did not arise more opposition to this.
I think that the quantum theory can set to work usefully at that point. We can express the laws only for large times. But for short times and high accelerations one still stands in front of a gap, whose filling requires new hypotheses. Perhaps one may assume that an oscillating resonator does not possess a constant variable energy range but that its energy is a multiple of an elementary quantum. I think that one can achieve a satisfactory theory of radiation if one uses this statement. There is now always the question: how to picture such a thing? That means, one requires a mechanical or electrodynamical model of such a resonator. But we have no discrete "action elements" in mechanics and present electrodynamics and therefore cannot produce such a mechanical or electrodynamical model. This appears now to be mechanically impossible and we have to get accustomed to this fact. Our trials to describe the luminiferous ether mechanically have also failed completely. One wished to picture the electric current mechanically too and one thought about the analogy of a water current, but this had to be abandoned too, and as we got used to this we have to get used to such a resonator also. Of course, the new theory has to be worked out in much greater detail than has been done until now. Perhaps someone else will be more lucky than I. In any case I think that we should first try to transfer the problem of quantum theory into the area of interaction between matter and radiating energy. The processes in the pure vacuum could then still be explained by Maxwell's equations.
H. Ziegler: If one thinks about the basic particles of matter as invisible little spheres which possess an invariable speed of light, then all interactions of matter like states and electrodynamic phenomena can be described and thus we would have erected the bridge between the material and immaterial world that Mr. Planck wanted.
This profound fact was recognized by H. Ziegler in 1906, two hundred years before it would finally be realized by the funded Physicists.
We now know that this is the correct cause
of the phenomena of relativity.
Vernon Brown PTE 1995 
Stark: Mr. Planck has pointed out that so far we have no reason to go over to Einstein's conclusion that we should regard radiation in space, where it occurs separated from matter, as concentrated. Originally I too was of the opinion that one can restrict oneself for the present to tracing the elementary law back to a certain behavior of the resonators. I think, however, that there is one phenomenon which forces us to think of electromagnetic radiation as separated from matter and concentrated in space. This is the phenomenon that electromagnetic radiation that emerges from a Rontgentube into the surrounding space can still come concentratedly to act on a single atom, even at large distances of up to ten meters. I think that this phenomenon is reason enough to investigate the question of whether electromagnetic radiation energy has to be conceived as concentrated even where it occurs separated from matter. The conception as advocated by Mr. Einstein would result in a practical consequence, which can be verified experimentally. As is well known not only alpharays but also betarays give rise to scintillations on a fluorescent screen. According to the developed concept the same has also to hold true for gammarays and Rontgenrays.
Planck: There is something unique to Rontgenrays, and I do not wish to claim too much in this case. Stark has mentioned something in favor of the quantum theory, I wish to add a remark against it, that is, the interferences at the enormous path differences of hundreds of thousands wave lengths. If a quantum interferes with itself it must have a spatial extension of hundreds of thousands wavelengths. This is also a definite difficulty.
Stark: Interference phenomena can easily be contraposed to the quantum theory. But I would like to express the hope that, if one will treat them with greater care for the quantum hypothesis, one will also attain an explanation. Concerning the experimental part, it has been emphasized that the experiments that Mr. Planck referred to were performed with very dense radiation so that very many quanta of the same frequency were concentrated in the light bundle. That has to be taken into consideration in dealing with those interference phenomena. The interference phenomena would probably be different with very low radiation density.
Einstein: The interference phenomena would probably not be so difficult to arrange as one imagines, and that for the following reason: One should not think that radiation consists of quanta that do not interact with each other; this would be impossible for an explanation of the interference phenomena. I think of a quantum as a singularity, surrounded by a large vector field. With a large number of quanta a vector field can be composed that differs little from the one we presume for radiation. I can imagine that when radiation hits a boundary there occurs a separation of the quanta by processes at the boundary, say according to the phase of the resulting field at which the quanta reach the separating surface. The equations for the resulting field would differ little from those of the previous theory. It is not asserted that we have to change very many of our conceptions about the phenomena of interference. I wish to compare this with the process of molecularisation of the carriers of the electrostatic field. The field as produced by atomistic electric particles is not very essentially distinguished from the previous conception, and it is not to be excluded that something similar will take place in the radiation theory. I do not see a difficulty of principle with the phenomena of interference.