2-The first hints
In an attempt to explain Mystery 2 in the previous chapter Planck realized that such a behavior was understandable if one made the strange assumption that atoms could absorb or emit electromagnetic radiation energy only in certain portions where portion of energy was proportional to the frequency. Planck calculated the value of the proportionality factor that corresponded to the best fit of the experiment.
This proportionality factor is known as Planck’s constant and noted by symbol h.
However Planck himself was not satisfied with his own work at that time . It appeared to him as too artificial and unfounded to put such an assumption into the model just to fit the theoretical curve to the experimental data. It appeared to him that his work didn’t reveal a deeper understanding about what happened at atomic scales.
Trying to explain the photoelectric effect (Mystery 3 in previous chapter) Einstein realized that it could be understood if one accepts that electromagnetic radiation exchanges energy with electrons in portions, contrary to the expectations of classical radiation theory where electric and magnetic fields of electromagnetic radiation exert a continuous accelerating or decelerating force on the charges. The exchanged energy portion was proportional to the frequency of incident radiation. The proportionality factor that was calculated for the photoelectric effect was in a very good agreement with the value that was obtained by Planck to explain the spectral distribution of purely thermal (black body) radiation.
All these hints led the physicists to suggest that the electromagnetic field, which behaved as a continuous field in macroscopic phenomena, was in fact made of indivisible portions at very small energy scales. These portions were given the name photon. If n is the frequency of the electromagnetic radiation, the energy of a single photon is given by hn . This energy is so small that it is natural that it didn’t affect the validity of Maxwell equations at macroscopic scales.
Here we should pause and think a little. The idea of the photon emerged by investigation of the interaction of radiation with charges in atoms. The experimental facts suggest that the charges exchange energy with the electromagnetic field in indivisible portions. However this fact alone doesn’t help us decide if these portions are an intrinsic property of the electromagnetic field; namely if they exist even in the absence of charges or if this behavior appears only in interaction with charges.
The tendency was towards the first alternative since there were no theories developed at that time how these phenomena could be explained in terms of a system of charges and their interaction with an electromagnetic field obeying Maxwell’s equations. It was known that oscillating/vibrating systems exchange energy with oscillating external forces more effectively when the frequency of the external force is closer to the proper frequency or eigenfrequency1 of the oscillating system. The concept of resonance catastrophe was already known at that time. This is what happens when the external force that feeds the system with energy has the eigenfrequency of the vibrating system. The external force feeds the oscillating system steadily with energy until the oscillation amplitude exceeds the limits of elastic (reversible) vibration and the system breaks down. You may have seen films of oscillating bridges that broke down. You may know also that a glass can be brought to vibrate and can be shattered just by human voice with the right note. That frequency could play a role in transferring energy between two different coupled systems was known at that time. Thus the role of frequency in the photoelectric effect is not completely surprising, contrary to the statements in some text books. But in most of the phenomena with frequency dependent coupling there are one or more eigenfrequencies or some frequency region where the effect is maximum . Far outside of these frequency regions, whether in lower or higher frequency regions, the system doesn't respond to the external stimulus. In the case of photo electric effect however the strange fact was that as if all frequencies above a lower limit were able to pick up electrons. There was no decrease of the effect at higher frequencies. On the contrary the transferred energy was directly proportional to the frequency.
This behavior of electrons was not easily explainable using the model of a vibrating system interacting with continuous external stimuli at that time. The knowledge about the electrons in atoms was extremely insufficient. It was the simpler choice to accept the first view, namely to assume that the portions are an intrinsic property of electromagnetic radiation itself.
This development notes an important point in the history of physics . It is the emergence of the concept of duality. Electromagnetic field seemed to poses a dual nature. On the one hand it seemed to be a continuous field that covers a space, but at the same time it was made up of very small packets, namely quanta, of energy. Was the wavelike behavior present for even a single quantum ? Whether a single photon possessed wavelike properties or not were open questions at that time. Physicists had no idea how these pictures could consistently fit together. There were no methods to try to test models of a single photon.
Einstein wrote to Lorenz on 23 may 1909 2
I conceive of the light quantum as a point that is surrounded by a greatly extended vector field that somehow diminishes with distance. Whether or not when several light quanta are present with mutually overlapping fields one must imagine superposition of vector fields I cannot say.
Apparently what brought Einstein to this idea was an analogy with the electrostatic Coulomb field around a charge. An electric charge takes its own static electric field wherever it goes.
However please notice here an important point :
There was no forcing reason to accept the existence of a pointlike entity so far. What was known at this point was only that the energy exchange occurs in indivisible portions as if charges sip energy from the electromagnetic field in small gulps when absorbing energy and spit them back to the electromagnetic field in discrete portions when radiating.
Today the dominant view is that electromagnetic field not only interacts in portions but that it is itself made up of quanta. We know however today that we don’t need the concept of a pointlike entity in order to understand why the electromagnetic field exists in the form of indivisable quanta as we will discuss in coming chapters3.
1. Eigenfrequency is the frequency with which the system vibrates naturally.
2. Belousek 1996, p. 450
3. In theories of field quantization the quanta/portions of the field emerge as a natural consequence of the field properties.