The first experiment we will describe is a thought-experiment to begin with, but in due course we should see the equivalent real experiment being performed.
A diagram is shown below. A photon-detector has to be something moveable, such as an electron in a potential well B which the photon can nudge into a second potential well C, maybe a deeper well or something of a more permanent character.
The electron begins and ends in a monochromatic eigenstate, so we propose that in mid-flight between the two wells B and C, it is also in a monochromatic state, or near enough to a monochromatic state to be able to deliver on what will be proposed.
The monochromatic Dirac wave packet is a tachyon. This is usually explained away by pointing to the superluminal wave velocity, but subluminal group velocity. Here we will not explain it away, but note that we are dealing with a transient nonlinear phenomenon. Given the nonlinearity, we will need computer simulation to show it.
Now consider a photon passing through a half-silvered mirror at A, duly splitting into two half-photons according to our realist view. Half the photon encounters the electron at B, and sets it into motion. It is proposed that as a tachyon, the electron can now reach out and grab the other half-photon in the vicinity of D. The electron will then usually fall into the second well C with the re-emission of relocalised electromagnetic energy, but with the entire original photon being 'mopped up'. We would like to show this happening someday by means of computer simulation.
There ought to be some way of capturing the tachyonic electron in mid-flight. Maybe another potential well at D in the vicinity of the other half-photon will occasionally capture the electron, a result which will be very surprising if it happens, and which is what we will predict. Let us call this the
or at least the proposition that the detector cannot be taken for granted. We will work towards a computer simulation which can show us what might happen, and confirm that there is no new censorship principle at work. Then we will urge experimentalists to think up some equivalent experiment before or after the production of the computer simulation.
One alternative view, which may be identified with the Copenhagen Interpretation, is that this talk of half-photons is misleading. The Maxwell and Dirac waves have epistemological rather than physical significance: they are merely 'mathematical objects'. The detecting electron will not turn up anywhere but in the usual expected place at C. The vanishing half-photon does not need any tachyonic electron to deal with it for the simple reason that it never existed.
Well here we have the possibility of settling the matter by experiment. We will try to do computer simulations to demonstrate and quantify the effect being predicted, and ask experimentalists to look for it. The author is expecting surprise, knowing what quantum mechanics is like.
If the Copenhagen view turns out to be correct, it is still a fair complaint that the Copenhagen Interpretation takes the act of detection for granted, a point implicitly made by the paradox of Schroedinger's Cat. We could do with a more rigorous approach which tells us exactly what the act of detection consists of.
The second experiment is also a thought-experiment. In the first experiment, we assumed that the jump between the potential wells at B and C was a classical jump with no quantum tunnelling involved, and that it therefore needed a whole photon to induce it. Now suppose that we have two detectors, as in the diagram below.
If the jumps between B and C and between D and E are classical jumps, then only one of the detectors can detect the photon, this being the standard mystery of quantum mechanics. In other words, there is perfect anti-correlation between the two detectors.
Now suppose we shrink the intervals between B and C and between D and E to allow some quantum tunnelling. Sometimes the detectors will "detect" anyway, even when no photon is present. Let us do the experiment many times without the photon, to quantify and extract this base effect.
With the photon present, there will be an enhanced rate of "detections". It is proposed that with respect to this enhanced rate, the perfect anti-correlation between the two detectors will no longer hold. Sometimes a detector will be triggered by a half-photon, and then with quantum tunnelling the act of detection will be over before the other half-photon can be captured as proposed above. The other half-photon will in the meantime have triggered the other detector.
Let us call the half-photon a "hemiphoton". Note that our experiment is made up of the usual actors of quantum mechanics: half-silvered mirrors and their equivalents in thin potential barriers. It is proposed that either electron can "borrow" the energy of a hemiphoton (a real object in this view) to jump more rapidly through a potential barrier, and that we can be aware of this by studying the correlation between the behaviours of the two electrons.
This experimental arrangement cannot be used for superluminal communication, and we will assume that there is no difficulty with the relativity of simultaneity, which remains to be checked by means of computer simulation. The first experiment may inadvertently lead to a possible, though inefficient, superluminal communications device, and may need to be re-designed to get round this.
This whole area needs to be explored, perhaps firstly by computer simulation, and then by experiment, to find out what is going on. At the present time, as a matter of fact, we do not have any theory which tells us how to do a computer simulation of the encounter between a whole photon and a whole electron sitting in a potential well, which could at random be nudged into a second well. Where does the randomness come in?
Alexandre Chorin has shown us how to inject randomness into a computer simulation of Euler's equation in order to achieve something like a computer simulation of the Navier-Stokes equation, which can deliver on a rich variety of phenomena. Can we achieve something similar in quantum mechanics? This is a simple and obvious question for which it is the author's ambition to find the answer.