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.)

Hi Ian,

This M-Z interferometer is one reason why I believe in nonlocality, bomb or no bomb.

Nonlocality is pretty obvious with a pinhole: the photon/electron “senses” the size of the hole: that’s nonlocal.

And the Quantum formalism, namely waves all over, is intrinsically nonlocal.

And what’s wrong with nonlocality, anyway? I ask Einstein.

Nonlocality is how to get out of the homunculus theory… Namely that smaller is just like big, except smaller, ad infinitum…

Instead nonlocality says that smaller is everywhere…

” it seems the wave goes both ways but the photon, which acts as a particle, can only go one way.” How do we know that? That the photon acts like a “particle”. Received and emitted as a particle: we know that. It does not mean it’s a particle in flight, though… I call that Einstein’s Error:

OK, it has not been demonstrated yet that it is an error stricto sensu… But it is an error to assert as a truth something that drastic, and not experimentally demonstrated. Instead I believe in delocalization…

May I get a version of your guidance theory? (I tried the Kindle, but somehow it didn’t work… And I have never done Kindle… OK, maybe I need to grow up?)

You can get it on kindle, and I can supply a link if you wish, but I am currently working on a second edition so maybe you would prefer to wait. I have tried to get Amazon to offer the second edition free to anyone who buys the first, but, they say, they haven’t got a mechanism to do that. They wouldn’t.

“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.”

Yes, in plain Quantum Mechanics, we get an effect out of nothing.

To make an effect out of something, one needs some sort of REAL guidance wave.

So the M-Z interferometer is close to showing definitively that either Einstein was wrong in 1905 with his idea of particles in flight, or that Quantum Mechanics is not real… as there is nothing real being blocked, according to QM… (This is not a lousy joke about complex vs real numbers; QM NEEDS complex numbers to depict polarization…)

The point real wave partisans should make is that there is *probably* a blockage… We don’t get really something out of nothing, as QM pretends we do.

What is going on is that the Quantum Guiding Wave is blocked along that path.

This being said, the (Particle + Guiding Wave) model has to be demonstrated… These pictures with “Quantum Trajectories” do not prove much in my opinion. They do NOT demonstrate delocalization… as they depend upon localizations! Many localizations!

In SQPR, the photon is the nonlinear part of the Quantum Wave (a kind of soliton). The QGW is linear enough to make Quantum Mechanics, a linear theory, work. No more “particles”! Just nonlinear waves…

In my admittedly biased opinion, the M-Z interferometer effectively demonstrates the existence of the wave, at least for photons. Interestingly, it is claimed that electrons do not demonstrate the same effect. There could be two reasons. First, the wave is confined to a region of the particle and continuously gets regenerated, which implies that to get the complete MZ effect you would have to build a tiny interferometer. The other reason may be that the so-called “electron beam splitter is merely a particle trajectory splitter and doesn’t affect the wave. (I suppose a third could be that reflection does not generate phase shift for the guidance wave but I don’t think that is a desirable thought.)

No Mach Zehnder interferometer for electrons? That would violate the De Broglie Principle of a mass, a wave… https://arxiv.org/abs/2104.09992… And another source: “Electron interferometry is regarded as one of the most promising routes for studying fractional and non-Abelian statistics and quantum entanglement…”

Science progresses, one new bias at a time…

Thanks for the link, Patrice. As for the MZ effect for electrons, that is specifically dependent on the wave being split – if it isn’t with a phase shift of π, and how do you tell? then there will be no interference, even if there is a de Broglie wave.

Reblogged this on Patrice Ayme's Thoughts and commented:

This is a foretaste of my own considerations on the subject of nonlocality.

A particular interferometer is one reason why I believe in nonlocality, bomb or no bomb.

Nonlocality is pretty obvious with a pinhole: the photon/electron spreads after it, it has “sensed” the size of the hole: that’s nonlocal.

The Quantum formalism, namely waves all over, parametrized with time, is intrinsically nonlocal.

And what’s wrong with nonlocality, anyway? I ask Einstein.

Nonlocality is how to get out of the homunculus theory… Namely that smaller is just like big, except smaller, ad infinitum…

Instead nonlocality says that smaller is everywhere…

In the Mach-Zehnder Interferometer, ”it seems the wave goes both ways but the photon, which acts as a particle, can only go one way.” How do we know that? That the photon acts like a “particle”. Received and emitted as a particle: we know that. It does not mean it’s a particle in flight, though… I call that Einstein’s Error:

EINSTEIN’S ERROR: The Multiverse

In 1905, his so-called Wonder Year, Albert Einstein presented a theory of the photoelectric effect. The new idea came in just two lines. However I boldly claim that Einstein’s theory of the photoelectric effect, although crucially correct, was also crucially wrong. I claim that Einstein talked too much. His intuition was not careful enough, though….

My view, of course, is the wave goes through both slits but the particle goes through only one. My guidance wave is like the de Broglie pilot wave, except I have a couple of additions.