Einstein’s insight ánd blind spot

Einstein’s opposition to the quantum state wave interpretation of Bohr

Despite his contribution to quantum physics with his explanation of the photoelectric effect with Planck’s quantum, Einstein strongly opposed the quantum mechanics interpretation of Bohr, Heisenberg, Pauli, Born and von Neumann. According to Einstein, despite the successes achieved, the theory still lacked a few essential parts. Einstein was a materialistic thinker who still thought completely in the spirit of classical physics with real hard particles with mass, speed and energy. In his view, photons were real permanently existing particles with an energy and momentum that depended directly on their frequency, although the philosophical question still remains what the frequency of such a particle actually means. On the opposite side, Bohr’s group advocated the idea that there existed only a non-material state wave before measurement which only changed into a material particle upon measurement.

Einstein was an excellent inventor of thought experiments (gedanken experimenten), which is also the way he developed his theory of relativity. He therefore devised a number of thought experiments with which he hoped to convince Bohr and his colleagues that their quantum theory was still far from complete. In his first quantum thought experiment, which he presented on a Solway conference in 1927, he wondered what would happen if you knew which slit a photon passed through in a double-slit experiment. According to him, quantum theory, as it was at the time, predicted two contradictory outcomes, namely an interference pattern on the screen behind the double slit and at the same time no interference pattern.

Gedanken experiment with recoiling slit and photons

Light can give a push

Einstein’s reasoning went like this:

  • A photon has a momentum. Momentum is a physical quantity that indicates the thrust a particle can deliver on collision. A photon’s momentum is proportional to its frequency. Although the photon has no rest mass and always moves at the speed of light, it can still push an object it hits. Watch the YouTube video above if you want to know more about that.
  • We fire single photons – monochromatic, so all will have the same frequency, energy and wavelength – with a photon gun on a double slit. But those photons have to pass first a movable slit of which we can measure its up and down movement. After the movable slit, the photons must travel up or down to pass through the upper respectively the lower slit of the double slit. We measure the recoil of that movable slit brought on by the hit of each passing photon. The photon has then a speed and a direction that is influenced by the recoiling slit, which classically means that the slit must also recoil in turn. Action equals reaction and is oppositely directed. We measure – in principle, it’s a thought experiment – the recoil movement of the single slit.
Einstein’s Recoiling Slit Thought Experiment – Version 1. There is no interference. Each photon travels through only one slit because we can know its path from the recoiling slit.
  • Behind the recoiling slit the normal double slit and screen are positioned. The recoiling slit shown in the figure is a drawing which was actually made by Bohr in finding an answer to Einstein’s challenge. He even drew the nuts and bolts with which the slit holder should be fastened to the support of the whole set-up and also a pointer and a scale that would indicate the recoil.
  • From the recoil of the movable slit we know which slit the photon passed. As the slit recoils downwards, the photon must travel upwards and thus pass through the upper slit. If the slit recoils upwards, the photon must travel the lower path and thus go through the lower slit.
  • In this way we know which slit the photon passed through. According to quantum theory, the state wave of the photon will now only extend from that slit. However, from the other slit there will now no state wave be extending. There is therefore no possibility of double slit interference, so we will not see any interference pattern on the screen. The result of shooting a large number of equal energetic photons will now look like a single spread-out spot on the screen with the greatest intensity in the center behind the double slits.
  • So far excellent reasoning by Einstein and nothing to argue really against.
  • However, you can also think of the photon gun together with that single slit, Einstein says, as a single device, a composite source of photons, so that the experiment now becomes an ordinary double slit experiment where we fire photons at a double slit.
Mechanically the same recoiling slit experiment – just envisioned differently. The recoiling slit is now considered as a part of the photon gun. We don’t know which path the photon takes. We now will see interference.

With this alternative design of the experiment, which is actually exactly mechanically the same, but only envisioned in another way in terms of components, we will now expect interference. The reason for this is that it shouldn’t matter how the photon source is composed of its parts. It only matters that the photons all have the same frequency.

A disturbing contradiction for quantum physics

With the same set-up, only arranged differently in mind, we therefore expect both interference and no interference. Quantum theory predicts two conflicting outcomes and that means there is something wrong with it, it is probably not complete.

After probably a night of worrying, Bohr more or less found an answer to Einstein’s challenge. The photon that passes through the recoiling slit and changes its direction there, loses necessarily some of its momentum. That momentum had been transfered to the recoiling slit. This is perfectly consistent with the law of conservation of momentum. That loss of momentum due to the interaction with the recoiling slit, means that the photon loses also some of its energy and frequency . The frequencies of all the photons are now no longer equal, which disrupts the interference pattern because the locations of maximum and minimum probability differ now per photon. The interference pattern weakens, and can even turn into a spread-out spot.

A real recoiling slit experiment

In my eyes a somewhat weak defense from Bohr and still almost completely in a classical physics way reasoned. But that was in 1927, quantum theory was still in full development and the technology was not yet there to really carry out the experiment. But by 2014, the technology had advanced far enough that Einstein’s thought experiment could actually be performed. I describe that experiment in detail in my book, chapter 5.

The double slit has been replaced by the two atoms of an oxygen molecule. Which oxygen atom has been hit by the photon is measured by the captured electron that flies away from the hit atom. It is investigated whether the interference pattern depends on whether or not it is possible to determine which atom has been hit by the photon.

Schematic representation of the principle of the experiment. From the publication ‘Einstein–Bohr recoiling double-slit gedanken experiment performed at the molecular level‘. Click on the figure for the full article on IOPScience.

The outcome of the experiment is that the interference stays away as soon as we can know which oxygen atom was hit by the photon. The article is rather technical, but the ‘Abstract’ does indeed describe the effect on the interference of information being available or unavailable. “This wave-like behavior and corresponding interference is absent if ‘which-slit’ information exists.” However, explicit reference is also made to the momentum transfer of the photon to the recoiling slit as argued by Bohr in his answer to Einstein. So Bohr was proved right and Einstein was wrong. But that’s a bit short sighted in my opinion. I do want to pay attention to something that Einstein saw excellently, after which both he and Bohr were apparently blind to what was really going on.

Einstein & Bohr’s blind spots.

What Einstein and Bohr both missed was that there is an essential but hidden difference between the two ways in which we envision the “double slit with moving slit experiment”. You may have noticed it already, but it took me quite a while before I saw it.

Although an uncompromising and thorough thinker, Einstein did not recognize that when there was no difference in the machinery of the experiment the only remaining difference was that which we can know. In the envision in mind where the recoiling slit is not part of the photon source, we can know which slit the photon passed through. From this ‘being able to know’, Einstein realizes that it can be deduced that the state wave only comes from one slit because the photon is – as we know – only in one slit. This may seem obvious but is a deep and extremely important insight. In the alternative envision in mind where the recoiling slit is seen as part of the photon source, we are supposed no longer to be able to know the recoil; such is more or less tacitly assumed but not explicitly expressed. But it is an extremely important difference. I think that it is not so easily recognized because, mechanistically speaking, both versions are completely identical so that they should therefore behave identically. The difference in the experimental set-up exists purely in the mind. There is still a moving single slit between the primary photon source and the double slit in the envision where slit and photon gun have become a single device. Only in that case it is now tacitly assumed that we cannot observe it. In both envisions Bohr’s argument of loss of impulse would equally apply, so the difference is really only in being able or not being able to know which slit has been chosen.

So you could now perhaps conclude, as the researchers seem to do, that it is indeed the impulse transfer that would make the interference disappear, but there are several arguments against this. First, that argument also applies in the event that the researchers were unable to determine which atom was hit because the atoms stuck together. There was, of course, just as much impulse transfer there, so that can’t make a real difference. Second, this is not the only experiment where the interference disappears once we can know which path the quantum object has taken. I describe two of these experiments in my book: The Delayed Choice Experiment with Single Atoms in Australia at the University of Canberra and The Delayed Choice Experiment with Two Photon Imaging at the University of Maryland, Baltimore.

In short; to measure is to know is to realize

As soon as we can know which path the quantum object has traveled, we see that the state wave has adapted to what we can know. As soon as we can know which slit has been chosen, the state wave will only have passed through one slit. I am speaking here on purpose about the state wave and not about the particle, for the reason that we will never be able to determine the difference between ‘there was a material particle in the slit‘ and ‘the state wave passed through one slit, so the probability of passing the photon measured there was 100%‘. I prefer the latter option as it assumes less concerning the so-called quantum collapse, which only happens in that case on the screen and not in the slit, and therefore has a greater probability of being closer to the truth. Ockham’s Razor.

And last but not least; if it is indeed a question of ‘being able to know‘, then the connection with the consciousness of the observer is of course obvious.

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