# Bohr-Kramers-Slater (BKS) theory and energy conservation only on statistically basis

I was reading Wikipedia article on Bohr-Kramers-Slater (BKS) theory, https://en.wikipedia.org/wiki/BKS_theory. I encountered two interesting points and need your help to understand the reasons behind them.

Einstein was awarded Nobel Prize in 1921 [1] primarily for his work on photoelectric effect which used photon model to explain the phenomenon.

BKS theory was put forward around 1924.

The Wikipedia article says the following.

Nevertheless, Bohr and Kramers had two objections to Slater's proposal:

1: The assumption that photons exist. Even though Einstein's photon hypothesis could explain in a simple way the photoelectric effect, as well as conservation of energy in processes of de-excitation of an atom followed by excitation of a neighboring one, Bohr had always been reluctant to accept the reality of photons, his main argument being the problem of reconciling the existence of photons with the phenomenon of interference;

Niels Bohr was one the leading physicist at that time; around 1924. I'm sure there would be others prominent physicists like him who didn't really believe in photons. I understand there are always some persons who tend to oppose or doubt even well established theories or models. In this case, the mention of Bohr really fascinated me. I know that Einstein and Bohr had totally different interpretation of quantum mechanics.

The article also says the following.

However, physically the most provocative element of the theory, that momentum and energy would not necessarily be conserved in each interaction but only overall, statistically, was soon shown to be in conflict with experiment.

You could check the Wikipedia article for little more details. Anyway, I don't really understand what it means. I don't think they were saying that the laws of energy conservation and momentum conservation don't hold at all because these two laws, in my view, were very firmly established by then. I think they were saying that energy conservation doesn't hold when you look at individual interactions but it only holds when you look at the complete system. Could you please help me with it? I'm just a learner so please try to keep it simple if you can.

I also find some articles which I cannot access and even if I were able to, I don't think I would be able to understand!

• I read the article from Dirac (Nature 1936) that you linked, and it does not help much. Dirac is kind of assuming that energy conservation could be violated but he says we should not be worried. Then he gives some summary of the issues of forgetting that electromagnetic waves should be quantized and that most experiments are seen from a non-relativistic approach. But is unclear what is Dirac conclusion and he seems to leave the question open. Aug 28, 2021 at 16:02
• Check this might be of interest: publishing.cdlib.org/ucpressebooks/… Aug 28, 2021 at 16:08
• Even Einstein equivocated on the existence of phtons, saying that it should be reconciled with (well confirmed) classical electrodynamics. BKS suggested that conservation of energy holds like the second law, when averaged over large ensemble of interactions. It is somewhat similar to "virtual particles" in modern physics that briefly violate conservation laws by popping in and out of existence, although most physicists consider them mathematical fictions rather than physical objects. In contrast, BKS violations were real. Aug 30, 2021 at 5:33
• What remains unclear to me (but maybe it is not part of the question) is where was the flaw in the argument? What was the superseding theory? Aug 30, 2021 at 11:29
• That prize was supposed to be for relativity, and photoeffect was a compromise fig leaf chosen to appease the opposition that had as much to do with anti-semitism as with physics, see Why didn't Einstein win a second Nobel Prize, for relativity? In any case, it was formally awarded for the "discovery of the law of the photoelectric effect". The law as such had been experimentally confirmed regardless of how it was derived, so existence of photons was irrelevant as far as the prize was concerned. Aug 30, 2021 at 11:54

From the BKS paper itself (emphasis mine):

On the one hand, the phenomena of interference, on which the action of all optical instruments essentially depends, claim an aspect of continuity of the same character as that involved in the wave theory of light, especially developed on the basis of the laws of classical electrodynamics. On the other hand, the exchange of energy and momentum between matter and radiation, on which the observation of optical phenomena ultimately depends, claims essentially discontinuous features. These have even led to the introduction of the theory of light-quanta, which in its most extreme form denies the wave constitution of light.

So BKS here give a good hint that at that moment there were a variety o views regarding the existence of photons. Still regarding the photons:

Although the great heuristic value of this hypothesis is shown by the confirmation of Einstein's predictions concerning the photoelectric phenomenon, still the theory of light-quanta can obviously not be considered as a satisfactory solution of the problem of light propagation. This is clear even from the fact that the radiation 'frequency' $$\nu$$ appearing in the theory is defined by experiments on interference phenomena which apparently demand for their interpretation a wave constitution of light.

As wikipedia states, the interference phenomena really were a block to accepting the photon, at least for the people involved. In the the second section they start explaining their model of the matter-radiation interaction with a focus on the transistions between stationary states in an atom as described by Bohr's model.

As regards the occurrence of transitions, which is the essential feature of the quantum theory, we abandon on the other hand any attempt at a causal connexion between the transitions in distant atoms, and especially a direct application of the principles of conservation of energy and momentum, so characteristic for the classical theories. The application of these principles to the interaction between individual application principles atomic systems is, on our view, limited to interactions which take place when the atoms are so close that the forces which would be connected with the radiation field on the classical theory are small compared with the conservative parts of the fields of force originating from the electric charges in the atom.

and later:

The cause of the observed statistical conservation of energy and momentum we shall not seek in any departure from the electrodynamic theory of light as regards the laws of propagation of radiation in free space, but in the peculiarities of the interaction between the virtual field of radiation and the illuminated atoms.

So yes, the paper assumes that conservation of energy/momentum would be violated in individual atomic transitions involving atoms far away from each other, being maintained only statistically on macroscopic matter.

• Thanks for the reply! I still have my confusion. Let me give it some time. I've upped your answer. Aug 30, 2021 at 9:34