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Two observers – A & B - conduct a single double slit experiment and watch the same detector screen for the appearance of an interference pattern.

A separate detector records which slit each particle passes through, but the data from this detector is only available to observer A.

As I understand it the wave function should therefore collapse for observer A, but not for observer B. Observer A will therefore not see an interference pattern on the detector screen, but observer B will.

How can this be when both observers are watching the same detector screen during the same experiment?

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    $\begingroup$ The detector is the only observer worth talking about in this scenario. It observes which slit the particle passes through, therefore the wave function collapses. Observers A and B are irrelevant $\endgroup$ – Jim Mar 20 '15 at 16:08
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    $\begingroup$ This is a variation on Wigner's friend - en.wikipedia.org/wiki/Wigner%27s_friend $\endgroup$ – innisfree Mar 20 '15 at 16:09
  • $\begingroup$ @Jimnosperm are you assuming an objective collapse of the wavefunction? $\endgroup$ – innisfree Mar 20 '15 at 16:13
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    $\begingroup$ If they both look at the screen, they are both measuring which-path information for the photon (superposition, first slit, second slit). I don't see how observer B could remain ignorant of that which-path information if he's looking at the screen. $\endgroup$ – innisfree Mar 20 '15 at 16:15
  • $\begingroup$ @innisfree I'm not assuming anything. If the detector observes each particle through going through the slits, then it interacts with them and kills the wave-like interference pattern. Once the detector observes, the other observers are just extra fluff $\endgroup$ – Jim Mar 20 '15 at 16:15
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You are wrong, but understandably so given the ridiculous way in which quantum measurement is commonly discussed. A measurement is an interaction that makes a record of the value of some observable. If such an interaction happens during an interference experiment, the interference doesn't take place. What matters is whether there is a record, not whether some observer has looked at it. All this is a consequence of unitary evolution:

http://arxiv.org/abs/1212.3245,

the collapse postulate is entirely unnecessary.

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  • $\begingroup$ A record or just the measurement itself? I mean, if the result of the measurement is lost without trace, it still took place, right? $\endgroup$ – მამუკა ჯიბლაძე Mar 20 '15 at 18:39
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    $\begingroup$ If the measurement is erased by literally being reversed, you undo the interaction, then the measured system can undergo interference again. If you erase the result by wiping a record in the standard way, moving the information into the environment, then the original system can't undergo interference. $\endgroup$ – alanf Mar 23 '15 at 10:31
  • $\begingroup$ This turns out to be deeper than I thought. So then all four combinations are realized: record lost, no interference; record lost, interference possible; record kept, no interference; record kept, interference possible. If this is true, I think it is not quite correct to say that what matters for the interference to be possible is wheterh there is a record. It must be some slightly different condition on the measurement and record of it which is decisive, right? What is it? $\endgroup$ – მამუკა ჯიბლაძე Mar 23 '15 at 10:45
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    $\begingroup$ If you're going to have interference, you can't have a record. Nothing I have said implies otherwise. $\endgroup$ – alanf Mar 23 '15 at 11:56
  • $\begingroup$ Sorry you are absolutely right. One of the four things I listed has to be excluded, and what remains is precisely record kept $\Rightarrow$ no interference, no more, no less. $\endgroup$ – მამუკა ჯიბლაძე Mar 23 '15 at 12:01
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All measurements come from interactions. In our macroscopic world, our intuition is that we can observe things without affecting them, but this is not true at quantum scales. In order for that measurement at the slit to happen, the photon has to interact with something — an electron, say — which couples the state of the photon to the state of the detector, which in turn can be read. This coupling destroys the coherence between the two paths through the slits so that they don't interfere.

The idea of wavefunction collapse is a simplification that we use when we are modelling only part of the total system with our equations. For example, it's common to write down a Scrödinger equation for a single particle, but not include a representation for what detects the particle. Such models work fine as long as one remembers to collapse the wavefunction after a measurement event. It's just a model, though, it doesn't represent all of reality.

In general, remember that quantum mechanics is physics, not philosophy. "Observers" get conflated with conscious beings a lot in popular conversation, but that is not how best to understand them. When physicists speak of an abstract observer, it's really a label in a thought experiment to group together certain physical interactions. In the case of wavefunction collapse, the wavefunction is the simplified representation of a small physical system, and the observer is whatever breaks the boundary between the larger world and that system. In this case this is the slit detector, as @Jimnosperm describes.

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