Duality & complementarity?

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For example with photons in a double slit, knowing the path of the photon leads to particle-like measurements and not knowing leads to interference (wave-like). In the interference case, is it fair to suppose the photon travels through more than one slit at the same time? Is this accepted thought or just completely naive? What could you argue against it? My understanding of the Copenhagen Interpretation (Griffiths) is that a particle has no position before it is measured, which according to common sense is just as implausible.

Secondly, is there any evidence for the complementarity of wave-particle duality. Can we be sure that a photon doesn't behave like a wave and particle simultaneously? Then a measuring device could 'pick out' the appropriate state.
 
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Nugatory
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In the interference case, is it fair to suppose the photon travels through more than one slit at the same time? Is this accepted thought or just completely naive?
The (most) accepted thought is that the question is not exactly naive, but it is sterile because no experiment or can ever confirm of deny that the photon travels through both slits. So you are free to suppose that it goes through both slits, but someone else is just as free to suppose that it does not (the de Broglie/Bohm theory, for example). There is no way for either of you to prove the other wrong, so eventually you will find yourself agreeing to disagree. (And in the meantime, people who have heard it before will experience a weary exasperation reminescent of what parents listening to bickering siblings feel).

What could you argue against it? My understanding of the Copenhagen Interpretation (Griffiths) is that a particle has no position before it is measured, which according to common sense is just as implausible.
There are a bunch of different variations of "the" Copenhagen interpretation, but yes, your understanding is reasonable. As for whether that interpretation is more or less plausible than going through both slits... Plausibility is somewhat a matter of personal taste and the specific problem at hand. For example, some people find "no definite position" more palatable when trying to reconcile quantum tunneling with conservation of energy than in the classic double-slit experiment.

Secondly, is there any evidence for the complementarity of wave-particle duality. Can we be sure that a photon doesn't behave like a wave and particle simultaneously? Then a measuring device could 'pick out' the appropriate state.
A measuring device measures some property (position, energy, frequency, spin, angular momentum, charge, ....) of a quantum system. It's not clear that there is any single property that, if measured, would demonstrate both waviness and particleness.
 
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Secondly, is there any evidence for the complementarity of wave-particle duality. Can we be sure that a photon doesn't behave like a wave and particle simultaneously? Then a measuring device could 'pick out' the appropriate state.
Just to follow on from Nugatory's excellent response.

The wave-particle duality is pretty much an outmoded idea these days. It really dates back to the rapidly changing state of Quantum theory between 1922 and 1926. QM reached its modern form when Dirac came up with his transformation theory at the end of 1926 - except for some mathematical niceties sorted out by Von-Neumann a bit later:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

In that theory the correct statement of the wave-particle duality is quantum particles sometimes behave like a particle and sometimes like a wave - but most of the time its like neither. The issue here is in order to figure out when that sometimes is and exactly what like means you need to go to the full theory - so why bother with it in the first place? Basically it confuses more than helps IMHO and the opinion of many on this forum. Because of that I think Bohr's complementarity idea is too 'vague' to be of any value.

IMHO the 'essence' of QM isn't complementarity etc etc - its a simple extension of probability theory:
http://www.scottaaronson.com/democritus/lec9.html

It actually turns out that a few reasonable assumptions leads to either standard probability theory or QM:
http://arxiv.org/pdf/quant-ph/0101012.pdf

What separates the two is continuous transformations between pure states - QM allows it - standard probability theory doesn't. But physically if you have some process that transforms a system during one second it is applied for half a second in doing that - so continuous transformations seems unavoidable and you have QM.

This is purely how to look at the formalism - interpretations are another matter.

Thanks
Bill
 

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