What does Copenhagen interpretation tell about Mach-Zehnder interferometer with single photons?

Question

Reading many sources on the net it is not clear what Bohr et al. says concretely about MZI. Maybe they say that the particle doesn't exist during this flight and appears only on the detectors? Maybe they say that the particle splits somehow and goes two ways? Maybe the particle goes one way and the wavefunction goes both ways but only as information (ghost as Einstein would put it)? Are there some rules for the particle in the MZI at all like that it must not disentegrate, be in two places (or all places) at once, follow a continuos path or it can do any nonphysical things?

Answer 1

The Copenhagen Interpretation introduces the notion of a 'classical apparatus'. A classical apparatus is something like a measuring device, or a permanent mark, or an irreversible process like an avalanche in a gas, etc. One asserts that a quantum amplitude is a quantity whose modulus squared gives the probability of the corresponding state of the classical apparatus, as long as one has carefully included all relevant systems in the analysis. If one asks about the quantum amplitude at spacetime locations where no classical apparatus is present (e.g. in an arm of an ordinary interferometer before the final beam-splitter) then the Cophenhagen Interpretation (CI) does not invite you to take its modulus squared or to interpret it at all. In such a case the CI says 'ok you have a quantum amplitude there, but it is not describing a classical apparatus so you should regard it as part of a calculation which is not yet complete. Keep going.' Eventually the quantum amplitude you are dealing with does describe a situation where a classical apparatus is in one state or another. In this situation the CI says 'ok, that's what the formalism is telling you; the modulus-squared of that number is the probability for the corresponding state of the classical apparatus.'

Thus the whole of quantum theory is seen as a framework which yields statements about probabilities for classical apparatuses.

Within that framework you can interpret as you like; you can talk about wavefunctions as if they were waves, if you wish. You can talk about particles as if they can be in two places at once, if you wish. If that helps your intuition about the physics and associated maths, then it is all allowed (though not required). But ultimately the CI places the classical apparatus 'front and centre', as it were, and says it is the probabilities of developments of such apparatuses which the physical world determines by its process.

If you now say 'but isn't that classical apparatus quantum really?' then the CI says: 'if you can frame that question in terms of an experiment, then you will merely have postponed the moment at which the modulus-square has to be interpreted as a probability, but that moment must inexorably arrive for all well-posed questions in physics.'

Answer 2

Copenhagen Interpretation, from what I understand, is a bit "agnostic" about the reality of a particle when it is not being measured. When it is not being measured there is no statement about what the reality of the state is. When it is not being measured there is a wavefunction that describes how the probabilities will behave when it is measured, and that's all there is to it.

Your MZI example is no different from Schrodinger's cat. The particle is in a superposition of both paths when it is not being measured. Copenhagen interpretation simply says that it is in a superposition -- and all a superposition means is that it specifies what the probabilies are when measured. Thinking too hard about the reality of the superposition itself leads to the Schrodinger's cat paradox where states are in two positions simultaneously.

I've typically encountered two types of people that are in this "Copenhagen" category. Those who are fairly insistent that there's no meaning in trying to understand more than what the model specifies (somewhat "nihilistic"). And those who think that the actual wavefunction is something that is "real" in the sense that things really become waves of probability amplitudes in all possible states that slosh around until you measure them.

Answer 3

This is about probability. A beam splitter has split beam into ratio of transmission and reflection. By changing some parameters like coating we can change the ratio or probability or intensity of light in the path. So even in single photon (it's hypothetical), there is certain chances of it goes to given path, but it doesn't split and join if it particle which is everything only dimension varies. Suppose coefficient of transmission is 0.25, then there are chances that 1 out of 4 photon is transmitted, or maybe none or all. But if we increase the number of photons or trial then we get nearly 25% of photons are transmitted.

In case of a coin, probability of either head or tail on tossing is half. If we toss same coin for large number of times then may be due to wear and taer it develops some biasness. So it is good to say number of similar coins are tossed and gives probability in this terms. At smaller level, there are chances that small disturbances cause variation, which is indeterminacy. To remove it, it is said that wavefunction collapse after measurement. Also, intensity of few photons from source is not possible, so filters are used. But that raise question that this is in itself measurement.