Of course-that's what the experiments that refer to the Aharonov-Bohm effect do.

However it isn't correct that such a phase shift can imply which slit was actually used-that statement is, trivially, wrong.

Nor is it true that the interference pattern is, necessarily, ``destroyed''-there's an additional phase shift, whose contribution can be calculated, that's all.

These are all now homework exercises in optics.

Thanks, Stam Nicolis.

So I gather you are saying that a charge can interact with a magnetic field, without collapsing to a definite state, which is consistent with my expectations, and the reason I asked the question in the first instance. You also note that this interaction does not necessarily provide "which-way" path information in the case of a double-slit experiment.

Why is it then, that when a charge interacts with light, it does collapse to a definite state, destroying the interference pattern? Whereas when a charge interacts with a magnetic field, it does not collapse to a definite state, but instead, merely, as you note, creates a phase shift in the wave function of the charge?

What is the accepted distinction between these two types of interactions?

Because it isn't true that when a charge interacts with light, it always ``collapses'' in a state. Light does correspond to a particular class of states of the magnetic field, incidentally.

Quantum objects can be found in superpositions of states, classical objects can't. That's all there is.

``Definite state'' is a meaningless term, because superpositions of eigenstates of operators are definite states, too.

Dear Charles,

If you have a spread magnetic field close to the double slit, you have not Aharonov-Bohm effect. What makes this effect to appear is the existence of singularity lines related with solenoidal magnetizations allowing local vector potentials A where the magetic field was zero B=0. Therefore the Aharonov-Bohm effect is a very different physical situation that when the light interacts with the electrons of the double slit. You are confusing very basic concepts of Quantum Mechanics and Electromagnetism .

Stam Nicolis Thanks for your follow up response. I'll rephrase my question, as I think there's a misunderstanding due to semantics:

What is the distinction between an interaction that destroys the interference pattern in a double slit apparatus (e.g., a detector behind one of the slits), and one that does not (e.g., the presence of a magnetic field)?

Daniel Baldomir, thanks for your response. Please note I did not bring up the Aharonov-Bohm effect in my question. That was in a response from another user.

Once more: a ``detector behind one of the slits'' does NOT destroy the interference pattern-it introduces an additional phase, only. The reason is that such a ``detector'' doesn't ``detect'' which way the charge went.

A magnetic field can do the same thing to an electrically charged, quantum, object.

It doesn't matter what the magnetic field is, incidentally, since its only effect on the charge is to introduce a phase shift proportional to the flux of the field through any surface bounded by possible ways the charge can move. The presence of two slits-even if they're not equivalent-implies that there is more than one way for the quantum object to move and, therefore, there's a relative phase, that can be affected by the inequivalence of the slits.

All this is standard quantum mechanics of two-state systems, along with an external field that introduces an in equivalence between the two states.

If the object is a classical charge, however, no such interference can be produced at all, since a classical electric charge moves in a way that's a unique solution of the equations of motion; and a classical electromagnetic wave isn't affected by a magnetic field, in the absence of matter. By using some material, that can affect the ``optical path'', of course it's possible to achieve such interference with classical objects. This is well known, at least since Faraday.

The ``detector behind one of the slits'' YES does destroy the interference pattern-it introduces an additional phase. If you know what the form to associate a hole to every particle then you have not interference at all. You have just a continous almost gaussian curve. In Quantu Mechanics what you say is that the n possible states are reduced just to one eigenstate and eigenvalue. This gives an usual continous distribution of probabilties and no interference is done at all.

That is very basic starting knowledge given to beginners in QM and also Feynman has a very beautiful discussion in his books.

You can read it in:

http://www.feynmanlectures.caltech.edu/III_01.html

although it would be convenient to study all the book if this is not understood.

An additional relative phase does NOT destroy the interference pattern! It suffices to do the calculation of the interference term-and the intensity isn't a Gaussian, either (since the diffraction patten, even were it due to one slit does have secondary maxima, in general!).

Once more: the quantum particle is in a superposition of two states, and there's an additional phase. This phase, by itself, doesn't imply that the total intensity becomes equal to the sum of the intensities (which is what ``destruction of the interference pattern means). And there's no ``reduction'' at all, in this case, since there's a probability distribution for the particle to have passed one or the other slit-the additional phase difference does not allow excluding one of them-it only implies that they're not identical.

The limit from two, non-identical, slits, to one slit is singular.

It isn't sufficient to quote authority (nor is it necessary)-understanding Feynman's lectures requires a bit more effort than linking to them.

Let me to put the things clear. Stam Nicolis wrote:

Once more: a ``detector behind one of the slits'' does NOT destroy the interference pattern-it introduces an additional phase, only

and that is not true as Feynman has showed that:

If detectors were placed before each slit, the interference pattern would disappear

I have presented the lecture of Feynman where he explained it and also given a personal explanation due to the reduction of possible eigenvalues. I don't understand people who don't answer to the objections and only repeat his wrong ideas as a proof. This is a very basic knowledge in Quantum Mechanics which I have understood that was the main question of Charles. This is due to the wave-particle behaviour of the particles that belongs to the Nature and which is difficult to justify.

Ambiguous words, inevitably, lead to nonsense. IF the ``detector'' applies a phase shift, it doesn't destroy the interference pattern-it just leads to an additional phase, since the space of states is always two-dimensional (for the case of two slits), so the possible states of the quantum particle are all the linear superpositions of the two states and the probability for the particle to have emerged from any one of the two slits oscillates.

Whereas if it were a classical particle, it would only be in one of the two possible states and there would't be any interference, whatever the way the slits were modified (which simply means the choice between the two slits is ``biased''). There would be a probability distribution, since it could have taken any of the two slits; but the interference effects would be missing.

That's what Feynman stresses in his lecture, in fact: For a classical particle, the events are independent, the probabilities are summed; for a quantum particle, the events aren't independent-unless there's an additional factor that makes them independent, namely a projector.

The only way the interference pattern can be ``destroyed'' is, if the detector is a projector from the two slit system to the one slit system. However a given flux between slits and screen doesn't act as such a projector: it, simply, introduces a fixed phase difference, that shifts the pattern-so it can make the maximum, between the slits, into a minimum, for instance. But it can't eliminate the additional oscillations, that distinguish the two slit pattern, from the one-slit pattern (indeed, if this were a localized magnetic flux, if it were quantized, then it wouldn't shift the pattern at all; if it weren't quantized, it would).

If the flux ISN'T fixed, but has some dynamics of its own, then one can be interested in the probability distribution of intensity pattern, when one takes averages over the flux. The dynamics of the flux can be classical, though random; or it can be quantum, as well, in which case one has to construct the product states and average over the states of the flux accordingly, to obtain the probability distribution-i.e. the intensity-corresponding to the particle. That's where the difference between a ``classical'' external field and a ``quantum'' external field becomes manifest. However, once more, such effects differ from those of a projector.

So what must be clarified is, whether the detector acts as a projector on the complementary subspace of states, or not. It isn't inevitable that it does act as a projector from the two-slit space to the one-slit space; that's the point.

In any case, the calculations are straightforward, so it doesn't make sense trying to guess what the outcome is-it's faster to do them.

The experiment of Feynman that I have explained you and I have all the time refereeing, was implemented experimentally in 2012, i.e. with electrons going through the double-slit and they monitoring a single-electron event when they could control their transmission. This is the important because the wave-function only provide us a probability of knowing the conjugate operators, for instance position or linear momentum at once following the Heisenberg uncertainty principle.

Francis, Matthew. "Disentangling the wave-particle duality in the double-slit experiment". Ars Technica.

We can see that the thing that goes through both slits is only immaterial information - the probability amplitude wave function. The particle always goes through a single slit. A particle cannot be divided and in two places at the same time. It is the wave function that interferes with itself. And the highly localized particle can not be identified with the wave widely distributed in space and determined by the boundary conditions of the measuring apparatus. If we change its knowledge we change its inferference.