Quantum weirdness, or not?

How can you test something without touching it with anything, even a single photon? Here is one of the weirder aspects of quantum mechanics. First, we need a tool, and we use the Mach-Zehnder interferometer, which is illustrated as follows:

There is a source that sends individual photons to a beam splitter (BS1), which divides the beam into two sub-beams, each of which proceed to a mirror that redirects them to meet at another beam splitter (BS2). The path lengths of the two sub-beams are exactly the same (in practice a little adjustment may be needed to get this to work). Each sub-beam (say R and T for reflectance and transmitted at BS1) is reflected once by a mirror. When reflected, they sustain a phase shift of π, and R sustains such a phase shift at BS1. At BS2, the waves going to D1 both have had two reflections, so both have had a phase shift of 2π and they interfere constructively, therefore D1 registers the photon arrival. However, it is a little more complicated at D2. The original beams T and R that would head towards D2 have a net phase difference of π within the beam splitter, so they destructively interfere and the original beam R continues in the direction of net constructive interference hence only detector D1 registers. Now, suppose we send through one photon. At BS1, it seems the wave goes both ways but the photon, which acts as a particle, can only go one way. You get exactly the same result because it does not matter which way the photon goes; the wave goes both ways but the phase shift means only D1 registers.

Now, suppose we block one of the paths? Now there is no interference at BS2 so both D1 and D2 register equally. That means we can detect an obstruction on the path R even if no photon goes along it.

Now, here is the weird conclusion proposed by Elitzer and Vaidman [Foundations of Physics 23, 987, (1992)]. Suppose you have a large supply of bombs, but you think some may be duds. You attach a sensor to each bomb wherein if one photon hits it, it explodes. (It would be desirable to have a high energy laser as a source, otherwise you will be working in the dark setting this up.) At first sight all you have to do is shine light on said bombs, but at the end all you will have are duds, the good ones having blown up. But suppose we put it in the arm of such an interferometer so that it blocks the photon. Half the time a photon will strike it and it will explode if it is good, but consider the other half. When the photon gets to the second beam splitter, the photon has a 50% chance of going to either D1 or D2. If it goes to D1 we know nothing, but if it goes to D2 we know the photon went to the bomb. If the bomb was any good it exploded, so if it did not explode we know it was a dud. So if the bomb is good, the probability is ¼ that we shall learn without destroying it, ½ that we destroy it, and ¼ that we don’t know. In this case we send a second photon and continue until we get a hit at D2, then stop. The probability that we can detect the bomb without sensing it with anything now ends up at 1/3. So we end up keeping 1/3 of our bombs and locate all the duds.

Of course, this is a theoretical prediction. As far as I know, nobody has ever tested bombs, or anything else for that matter, this way. In standard quantum mechanics this is just plain weird. Of course, if you accept the pilot wave approach of de Broglie or Bohm, or for that matter my guidance wave version, where there is actually a physical wave other than the wave being a calculating aid, it is rather straightforward. Can you separate these versions? Oddly enough, yes, if reports are correct. If you have a version of this with an electron, the end result is that any single electron has a 50% chance of firing each detector. Of course, one electron fires only one detector. What does this mean? The beam splitter (which is a bit different for particles) will send the electron either way with a 50% probability, but the wave appears to always follow the particle and is not split. Why would that happen? The mathematics of my guidance wave require the wave to be regenerated continuously. For light, this happens from the wave itself, from Maxwell’s theory of light being an oscillation of electromagnetic waves. The oscillation of the electric field causes the next magnetic oscillation, and vice versa. But an electron does not have this option, and the wave has to be tolerably localised in space around the particle.

Thus if the electron version of this Mach Zehnder interferometer does do what the reference I say claims it did (unfortunately, it did not cite a reference) then this odd behaviour of electrons shows that the wave function for particles at least cannot be non-local (or the beam splitter did not work. There is always an alternative conclusion to any single observation.)