In January of this year I started a series of posts based on an article in Angew. Chem. Int Ed. 52: 118 – 122, where van Gunsteren mentioned the seven deadly sins of chemists. I commented on the first one (inadequate descriptions of methodology), inspired in part by an example that help up progress on my PhD when an eminent chemist left out a very critical piece of the experimental methodology and I was not smart enough to pick it, but then I got distracted by a series of what I thought were important announcements, coupled with one or two things that were happening in my life.
The second sin was "Failure to perform obvious, cheap tests that could repudiate or confirm a model, theory or measurement." The defence, of course, is that the experimenter did not think of it, and I am far from thinking that one should blame an experimenter for failing to do the "obvious". The problem with "obvious" is it is always so when pointed out in retrospect, but far from it at the time. Nevertheless late in my career I have an example that is a nuisance, and in this case, it is not even chemistry, but rather physics. My attempts at understanding the chemical bond, and, for that matter, some relationships I found relating to atomic orbitals (I. J. Miller, 1987. Aust. J. Phys. 40 : 329 -346) led me to an alternative interpretation of quantum mechanics. It is a little like de Broglie's pilot wave, except in this case I assume there are only physical consequences when the wave is real, which, for a travelling wave, from Euler, is once per period. (Twice for certain stationary states.) As with the Schrödinger equation, the wave here is fully deterministic. (For the Schrödinger equation, if you know ψ for any given set of conditions, you know ψ for any changed conditions, hence the determinism. The position of the particle is NOT deterministic. The momentum is in as much as it is conserved, but not at a specific point in space.) Now, my interpretation of quantum mechanics has a serious disagreement with standard QM in terms of the delayed quantum eraser. Let me explain the experiment, details of which can be found at Phys. Rev. Lett. 84: 1 – 5.
But first, for those who do not know of it, the two slit experiment. Suppose you fire electrons at two slits spaced appropriately. On the screen behined, eventually you get a diffraction pattern. Now, suppose on the other side, you shine light on the screen. As the electrons emerge from a slit, and an electron only goes through one slit, the electron scintillates, and you know through which slit the electron passed, however, now the diffraction pattern disappears, and the resultant pattern is of two strips, and if the photomultiplier can assign the signal to a specific electron (requiring low intensity) then it is shown that a given strip is specific to a given slit. Standard quantum mechanics states that it is because you know the passage, there is no diffraction. By knowing the path, you have converted the experiment into a particle experiment, and all wave characteristics are lost. You can know particle properties or wave properties, but not both.
Now, this experiment starts the same way, but at the back of the slits there are two down converters, each of which turns a given photon into two photons of half energy. One of these, called the signal photon, goes to the photomuliplier, while the other photon, called an idler photon, sets off on a separate path from each down converter, so at this point, there are two streams that define which slit the photon went through. Accordingly, by recording the signal photons paired to one of these streams, it is known which path the signal photon took, and there should be no diffraction pattern if standard quantum mechanics is correct on this issue. What was actually done was that each stream was directed at a beam splitter, and half of each stream of idler photons went to a separate photomultiplier, and when the paired signal electrons were studied, there was no diffraction pattern. If, on the other hand, the the other half went to two further beam splitters such that the beams were mixed, and knowledge of which slit the parent photon went through was lost, the paired signal photons gave a diffraction pattern. Weirder still, the path lengths were such that what the idler photons did occurred after the signal photons had been recorded, i.e. the diffraction pattern either occurred or did not occur depending on a future event.
So where is the sin? Do you see what should have been done? The alternative explanation may seem a bit hard to swallow, but is it harder than believing the photons would give a diffraction pattern or not depending totally on what was going to happen in the future? Remember, the idler photons could have been sent to Alpha Centauri to do the critical mix/not mix and the theory states clearly that the signal photons will, er, what? Rearrange the records eight years years later if the physicist does something different at the other end?
What I would have liked to see was that one stream of the idler photons heading to the mixing was blocked. The theory is, in the down converter, it would be possible that only one of the photons carried diffraction information, and that would go equally to signal or idler photons by chance. However, the next beam splitter could split idler photons not on chance but by whether they carried diffraction information, or appropriate polarization. The difference is, the separation is causal, and nothing to do with what the experimenter knows. If the partners of these two streams of idler photons heading to the mixing step carry the diffraction information, cutting out one of those streams will merely delete half of the information (because only hald the signal photons are now counted) if the patterns arise deterministically (and recall in terms of wave properties the Schrödinger equation is deterministic.) If the experimenter's knowledge is critical, then the diffraction pattern will go because the experimenter knows which path the photons have taken.
The point is, if physicists over the last decade have not commented on this, then maybe it is not that obvious. Maybe it is not a sin not to do the "obvious", because it is seldom obvious at the time. Hindsight is great, but if you did not see the sin before I told you, maybe you will be more generous when others appear to have sinned.
