Interference experiments illustrate many of the weird features for which quantum mechanics is rightly famous. One of the weirdest is that the fact that an event could have happened, but did not actually happen, can affect future observable events (the so-called "observability of counterfactuals"). This leads to the possibility of obtaining information about a system without interacting with it physically at all. This is described and explained in detail in the first pdf below.
A characteristic feature of interference experiments is that particles are able to travel via alternative paths to the point at which they interfere. The interference is destroyed if we are able, in principle, to tell by which path the particle travelled. There are many specific illustrations of this in texts, but why should this always be true? The first pdf below explains how this arises as a simple consequence of the state algebra.
The second pdf addresses an issue raised by Wheeler. If the choice as to whether to observe which path the particle takes is delayed until after the particle is (classically speaking) already committed to one path or the other, will we observe interference? The answer is "yes", but of course only in those cases for which the choice is not to measure.
The third pdf below addresses a set of related issues which are much discussed in popular accounts. They relate to what happens when interference experiments are carried out on pairs of entangled particles. There is a greatly illuminating conundrum regarding whether a measurement on one of the entangled pair will destroy the interference observed for the other. Since the entanglement means that a measurement carried out on one of the pair is effectively also a measurement on the other, this should destroy the interference. But this appears to create the opportunity for faster-than-light (FTL) communication. Of course this is not so, but the reason why is important.
The third pdf also discusses quantum erasure. This is the phenomenon whereby a 'measurement', which would destroy an interference pattern, can be erased and the interference regained. Such erasures become even more intriguing when coupled with experiments on entangled particles - and hence when the erasure is carried out after the interference data has already been obtained. This is often presented in popular accounts as posing a challenge to the correct temporal order of causality. It does not, and the pdf explains why. The pdf also points out a crucial ambiguity in the meaning of "measurement" in such experiments.
Unfortunately the popular accounts of these issues are desperately inaccurate. Indeed I am tempted to say that, "when I hear of delayed erasure I reach for my gun". I have attempted to clarify the situation in the rather long account in the third pdf. The key to a sound understanding is the Hilbert state algebra – which is virtually trivial and far easier to follow than accounts of detailed experimental arrangements.
One source of confusion is the distinction between local interference and correlated interference. Popular accounts are guilty of failing to distinguish the two - perhaps because they do not appreciate that there is a distinction. But the distinction is crucial and resolves the causality problem (i.e., the FTL issue).
Another confusion may be caused by the lazy assertion that, "entangled particles cannot cause interference". Whether or not this is true depends upon the situation. It clearly cannot always be true because, in the real world, particles will always be entangled with things you know nothing of - by virtue of their history. So, if it were true, no interference would ever be observed. More accurate guidance is that entanglement between specified degrees of freedom will prevent interference between these same degrees of freedom. But the fact that my particle happens to be entangled with another particle, currently in the vicinity of Alpha Centauri, will not prevent it creating interference fringes when incident upon a double slit screen.
The third confusion results from the great play that is made in popular accounts of the weirdness of the outcome of delayed erasure experiments. One particle, it is claimed, appears to 'know' that a measurement will be carried out in the future on its entangled partner. Hence an interference pattern is created due to erasure being carried out after the interference data has already been collected (they say).
But these protestations of weirdness tend to forget the crucial issue - that an interference pattern is found in delayed erasure experiments only when the detector counts are vetoed according to whether there is a corresponding count in the entangled channel. Purely local interference in one channel is not observed, but only a correlated interference. Only when the signal from a detector on the entangled channel is used as a mask to retain or veto individual counts in the signal channel does the interference pattern emerge. But this 'masking' data must be communicated classically and is not available FTL. The directly observed, un-edited, local signal contains no interference pattern.
Nevertheless, these experiments are of considerable importance in verifying, yet again, that the predictions of quantum mechanics are borne out. And, of course, quantum mechanics is weird. The weirdness lies in the fact that alternative outcomes are not deterministic (there are no hidden variables) and yet, despite that, causally unconnected measurements contrive to be correlated. It's weird all right, but not as weird as popular accounts of delayed erasure generally suggest.
Read the pdf Observability of Counterfactuals: you can get information about a system without interacting with it physcially at all - not even a little bit
Read the pdf Wheeler's Delayed Choice Interference Experiment: you can't trick the interferometer - if you delay the choice as to whether to make a measurement to destroy the interference until after the particle is already committed, there will still be interference in those cases when no measurement is made
Read the pdf Interference, Entanglement and Quantum Erasure: clarification of the conundrums misrepresented in popular accounts - the state algebra explains it all
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