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If a particle (photon) goes through a Mach-Zehnder interferometer it is accepted in quantum mechanics texts that in passes in both channels after first beam splitter BS1 and propagates there until BS2. This is at least my impression though it is not stated explicitly in textbooks I've seen.

The channels could be practically at any length. If observation is made in one of channel before BS2 a photon will be found. This implies that

  • A) the other channel was empty or

  • B) The particle which has been an extended object like chewing gum and it went in both channels but then after observation retrieved back to BS1 and to the point of observation in 0 time.

  • C) particle is destroyed to vacuum state and only it's Wave function traverse further. At the observation point the particle is reborn again.

I can't see other possibilities. Can you tell? Of course B and C are rather weird and break many physical classical laws. Then only A) can be true. But that means that an empty wave exists in say channel 2. Nevertheless I've never met any statement about empty waves except of course in de Broglie-Bohm. Maybe in many-worlds interpretation (MWI) also are empty waves. So my question is what is the status of empty waves in Copenhagen interpretation and in MWI? How they will deny empty waves in the aforementioned case. What does quantum field theory (QFT) say? The particles there are excitations which must be propagating in both channels?

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  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. $\endgroup$
    – ACuriousMind
    Commented Apr 7 at 10:25

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In the MWI what is happening in reality is described by quantum equations of motion. In the pilot wave theory reality is described by the same equations of motion with point particles sprinkled on top. In the Copenhagen interpretation (CI), you just do calculations using quantum equations of motion and if you ask about what's happening in reality you're a heretic, so the CI sez nothing about empty waves or anything else.

In the pilot wave theory a particle may go along one of the possible paths and then follow the other in an interferometer, hence the empty wave:

https://arxiv.org/abs/quant-ph/0312227

In the MWI the description of the world in terms of particles is an approximate description of quantum waves that only works under decoherence:

https://arxiv.org/abs/2303.00831

https://arxiv.org/abs/1111.2189

In addition, in QFT particles can only emerge when interactions between particle fields are weak enough

http://philsci-archive.pitt.edu/15296/1/qm-continuum%20revised.pdf

As such there are no empty waves in the MWI because particles are only an approximate description of quantum waves in the weak interaction and decoherent regime.

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  • $\begingroup$ @Mercury The EM field can propagate virtual fields. $\endgroup$ Commented Apr 5 at 12:46
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I'm glad you called the photon a particle and that's the main thing you need to remember. There is no wave unless your talking about millions of individual coherent photons radiating from a common source, but your still only talking about groups of individual photons resembling a wave. Wave functions are not real so there's no wave actually traversing anywhere. A single photon can only enter one arm of the experiment or the other, and cannot be split in two, so that it can travel both ways at once. If that single photon travels through an arm of the experiment and into the second splitter, then again it can only go one way or the other. If by empty wave you mean no photon, then the answer to your question should be YES.

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  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. $\endgroup$
    – Buzz
    Commented Apr 9 at 1:09
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It is the EM field that you are interested in here ... not just any field. The EM field propagates many virtual fields even before the photon is created. Virtual fields are your "empty waves".

If you ignore the EM field you will never understand the photon experiments.

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  • $\begingroup$ how do you explain/describe/model an EM field without resorting to photons? You can't just say fields without explaining what they are physically. $\endgroup$ Commented Apr 5 at 22:08
  • $\begingroup$ @BillAlsept The field is underlying fundamental constitent in QFT particles are excitatons. But as I asked in my question they are very strange. I discuss here how they spread as spheres and than collapse in a point. Just the same way as WF. But WF is not real whereas excitations are thought to be real. And maybe they are as weak measurements show there was something in both channels of MZI before BS2. (Lemmel Quantification ...) $\endgroup$
    – Mercury
    Commented Apr 6 at 19:32
  • $\begingroup$ Can u be more clear? Do u mean that the particle travels one channel and in the other there is smth called virtual field. I don't know about virtual field? I know virtual particles but they (if they exist) don't travel in a preferred direction and are always present in vacuum. $\endgroup$
    – Mercury
    Commented Apr 6 at 19:44
  • $\begingroup$ @Mercury You say "field is underlying fundamental constituent in QFT". That's an empty claim that can't even be proven wrong because there is no explanation, model or anything to back it it up. EVERY light phenomenon can be derived with a photon/particle theory, which is the ONLY theory that also offers a physical model to go along with it. Just saying there is an underlying field is like saying there's an underlying spirit or something. $\endgroup$ Commented Apr 6 at 20:50
  • $\begingroup$ Of course the fr.pat. is from many photons and each one interferes with itself only. Even send one by one at a time u get a fr.pat. after 10 tausend. About smth happening I agree. Also about math. That's why I ask the question. About your theory I read it some years ago. U think the photon infr with the wall. That's not the case. Diffraction is not due to interaction at the wall. Explanation is the wave but the matter of fact is that in CI it can not be real or connected with a real process. $\endgroup$
    – Mercury
    Commented Apr 7 at 6:32
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In QM the wave function is the fundamental physical property describing your system. In your case, before you disturb the system by the measurement, it will be an extended object reaching through the entirety of your interferometer. Once you carry out a measurement of the position of the particle, the wave function will collapse and after the measurement be in a state where the wave function will be in a state sharply peaked around the point where you measured it.

So from a standard QM view out of the given options I would claim that answer B is the best description of reality.

Now there is also the De Broglie-Bohm-Theory, which I am not super familiar with. As I am aware following that view one might legitimately claim, that the particle only went 1 way. Since the predictions made by De Broglie-Bohm-Theory are equivalent to the ones made by QM one would then have to describe the extended pilot wave as a separate object, which could be interpreted as resembling something similar to what you called “empty waves".

So in that case one might rather tend to choose option A, though the physical predictions will be the same.

Let me also note that in QM it is very much necessary to describe even single particles using extended wave functions developing over time or equivalently with path integrals or with extended pilot waves. There is a vast amount of experimental proof for that, for example you can produce a double-slit interference patterns by just shooting 1 photon at a time through a double-slit and then measure its place. In that experiment it is clearly shown that even the behavior of singular particles has to be described using a wave function or some of the other extended objects mentioned above. Another impressive example mentioned by Quantum Mechanic in the comments showing that even single particle wave functions can indeed extend through multiple paths is described here. In case that wasn’t clear, this very much implies that Bill Alsept's answer is wrong.

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