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I'm still struggling a bit with some ideas around double slit experiments. One that keeps cropping up for me is the role of observers.

Imagine a classic double slit experiment with a hidden observer who has arraigned an apparatus to detect which slit the electron's are passing through. This person and their measurements are hidden to you and you have no interaction with them.

So the question is, do you see an interference pattern or not?

Additionally: And if the answer is Not, then is the reason because they "disturbed" the electron (by say firing photons at them) or is it for another reason? And if it is because they "disturbed" the electron, then how is it that unobserved electron's are not disturbed since they certainly interact with other objects, for example other atoms in the matter around the slit(s) will feel a slight gravitational tug as it passes through.

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"and you have no interaction with them" - Yes, I do: Both the hidden observer and I interact with the electrons. The hidden observer by bombarding them with photons, and I by watching their pattern on the screen. Thus, there is an "effective" interaction between myself and the observer –  Lagerbaer Nov 26 '11 at 18:44
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6 Answers

In response to Luboš's answer, Fraggle writes

The issue for me is this. What causes an electron to "shift" from having position probabilities which are somewhat spread out in space to having position probabilities which are much more localized and not as spread out (localized to one slit or the other)? The answer, since it does not depend on consciousness, must only depend on the kinds of interactions the electron encounters. What kinds of interactions will cause its position to become more definite (less spread out) and what kind won't?

The position probabilities are localized by the electron's collision with the barrier that contains the slits. It can only get through the slits, so the wavefunction coming out the other side will start out looking like it arises from two point sources, one slit and the other slit.

But this isn't the issue. The issue is, what happens to that wavefunction as the two wavefronts from the slits spread out and combine? If electrons go through the slits unobserved, you will see interference effects in the impact pattern that builds up on the other side; but if they are being observed, there won't be interference effects. The "wave" nature will appear to have vanished, and you will just have "particle" behavior, a spray of bullet-like impacts.

The explanation for this has nothing to do with the existence of a hidden observer. All that is required is that there is some physical trace of which slit the electron went through. For example, there could be a microscopic magnetized object near each slit, which flips its polarity when an electron passes by.

The reason this removes the interference is that ultimately, quantum probabilities are joint probabilities. A quantum probability is associated with a total physical configuration, and interference of quantum probabilities occurs when two or more histories converge on the same total configuration. In the scenario I just described, which way the little magnets are pointing is an extra degree of freedom, and you don't just have a "wavefront from slit 1" and "wavefront from slit 2" which will then overlap and interfere on their way to the impact screen. You actually have one set of probabilities for "electron passed through slit 1, and the magnet at slit 1 flipped", and another set of probabilities for "electron passed through slit 2, and the magnet at slit 2 flipped". This is why, when it seems that the wavefronts from the slits should be combining and interfering, they don't: because they are actually probability waves for different configurations, when you look at the whole picture, including the state of the magnets, and so they never arrive at the same "point" in "configuration space": one wavefront is confined to the space of configurations in which magnet 1 flipped, the other wavefront is confined to the space of configurations in which magnet 2 flipped.

This is why some people end up believing in parallel worlds or in nonlocality: quantum probabilities look like they keep track of possible total states of the physical world, and allow for probability waves from "different histories" to converge and interfere. So they reason that either there are parallel worlds and they interact somehow, or there's a nonlocal coordination of probabilities within a single world.

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+1 because it is a simple explanation in words. The only reservation I have is in "For example, there could be a microscopic magnetized object near each slit," : microscopic should be orders of magnitude larger than hbar measures. If one reaches hbar measures then the quantum mechanical setup for a solution changes. –  anna v Nov 27 '11 at 6:12
    
I have found that there exists an experiment with minimal interference where the slit the electron has passed through is known and still there is an interference pattern after statistical accumulation. en.wikipedia.org/wiki/… –  anna v Jan 4 '13 at 9:20
    
In those works, they are measuring neither which way the particle went, nor what the interference pattern on the screen was, but some third observable which is correlated with both of those properties, but so weakly that some quantum coherence is preserved. They call it an "unsharp observable" and it has some similarity to the idea of a "weak-valued measurement", a pointer variable which has the right expectation value to track the property it represents, but whose variance is enormous... –  Mitchell Porter Jan 5 '13 at 6:06
    
In dx.doi.org/10.1007/BF00734319 they say that "transparency of the mirror" or "visibility of the interference pattern" can serve as the third observable, but I do not understand what concrete measurement is involved. –  Mitchell Porter Jan 5 '13 at 6:07
    
In my opinion if they can tag which slit an electron went through it clears that what one is observing is an interference pattern in the probability /wavefunction even if it is a complicated wavefunction. The electron is in a probability wave, not a mass/energy wave which people imagine; the effect: if I observe it it disappears is refuted. –  anna v Jan 5 '13 at 6:52
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Of course that the interference pattern disappears whether or not you are aware of the experimenter who has bombarded the electrons with other particles.

The quantum mechanical predictions are surely independent of the "consciousness" of the other objects, which is what may lead some people to the same question as yours. Quantum mechanics is valid for predictions of any observed phenomena, whether they incorporate macroscopic objects and humans or not.

The electron is being entangled with some additional particles (photons?) that someone uses to bombard the electrons. These photons won't be detected again. We will only observe electrons, so it's enough to describe them by the density matrix for electrons only. Mathematically: $$ |\psi\rangle = a |{\rm left}\rangle + b |{\rm right}\rangle \to a |{\rm left}\rangle \otimes |{\rm left\,\,photons}\rangle + b |{\rm right}\rangle \otimes |{\rm right\,\,photons}\rangle $$ and $$ |\psi\rangle \to \rho ={\rm Tr}_{\rm partial\,\,over\,\,photons} |\psi\rangle \langle \psi| = |a|^2 |{\rm left}\rangle \langle {\rm left}| + |b|^2 |{\rm right}\rangle \langle {\rm right}| $$

That's why we're allowed to trace the density matrix over the photons' Hilbert space, and by doing so, the information about the relative phase of the left-slit and right-slit portions of the electron's wave function disappears (because these two portions are entangled with different, orthogonal wave functions of the photons) which is why interference is not possible anymore.

So the interference pattern disappears even if no one else is observing the reflected photons at all.

Where quantum mechanics "requires" consciousness or active knowledge is when you ask whom the predictions of QM are made for. They're not made for an objective world: at the fundamental level, none exists. Predictions of QM are meant to be used by a "conscious observer" who may observe the actual outcomes of experiments – whose probabilities are calculated as expectation values of the projection operators corresponding to the Yes/No questions.

But once you are such an observer, you may treat all objects in the world on par – as blind systems of particles that universally obey the laws of quantum mechanics. Their "humanity" or "knowledge" or "plan to exploit an observation" or "consciousness" is totally irrelevant for your predictions and their verification.

The real "paradox" about an observer knowing about another observer is that observer A may observe observer B who observes system S. According to B, the outcomes of measurements are known as long as B "perceives" them. However, A may evolve B+S into Schrödinger cat-like superpositions and only "collapse them" i.e. interpret them once A perceives his observations. So A,B may disagree when "facts became facts". But this question "when a fact became a fact" isn't measurable: any observer may "delay" this moment up to the moment when he actually perceives the outcomes, and there won't be any contradictions in the final perceptions of A,B. (Of course, A may also uniquely calculate the earlier moment when B says "now I know the result": this moment is before A observes the situation, and it is earlier because it's independent on the actual outcome that B perceives. However, B is still just a part of the physical dull world for A.)

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I downvoted because if the OP doesn't get the double slit experiment, then talking about the partial trace of a density matrix will be pretty worthless to him. –  Colin K Nov 26 '11 at 18:47
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Dear Colin K, I am writing the answer not only for the OP but for everyone who asks the same question which may be asked, believe me, even if one has been exposed to double-slit experiment. Fraggle, nothing "causes" probabilities to shrink. Probabilities by definition always describe "shrunk" outcomes. For example, if you throw a dice, the probability distribution is spread over the numbers 1,2,3,4,5,6. It is completely spread. But it doesn't prevent "3" from being the result. In fact, it is guaranteed that one sharp number will be the result if you throw dice. –  Luboš Motl Nov 27 '11 at 8:07
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@Fraggle: Any interaction which is stronger if the photon goes through the first slit than if it went through the second slit, or vice versa, will cause the electron to shirt. The interaction has to be stronger by at least one unit of action to destroy the interference pattern. –  Peter Shor Nov 28 '11 at 2:54
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@Lubos: the issue with quantum mechanics is that only probabilities are allowed to shrink this way, because only probabilities have a consistent ignorance interpretation. But quantum amplitudes are not probabilities, and they are shrunk in this way after a measurement. The idea then is that probability is emergent from quantum mechanics, and this is philosophically difficult, because probability is so fundamental looking. –  Ron Maimon Nov 28 '11 at 2:56
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"But quantum amplitudes are not probabilities, and they are shrunk in this way after a measurement." Dear @Ron, quantum amplitudes and probabilities are related in a straightforward way: probabilities are squared amplitudes (in absolute value), or sums of such squared terms. Because this is a purely mathematical operation, it's clear that one must assign the same qualitative interpretation to both. So quantum amplitudes are (quantum-completed) probabilities. They surely can't be "more tangible" than probabilities - you couldn't get an "untangible" thing by squaring a tangible one. –  Luboš Motl Dec 15 '11 at 6:57
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I'm a little unsatisfied by all the other answers because they don't have any units in them. In order to measure which slit the electron goes through, you have to disturb it by at least the order of one unit of action (that's ħ). If you disturb it enough to measure it, you destroy the interference pattern. You can disturb it less than that, and get a small amount of statistical information on which slit it went through, and this will only blur the interference pattern slightly. So there's a tradeoff between how much information you gain, and how blurry the interference pattern gets. I'm not going to work this out in detail.

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Dear @Peter, you seem to refer to Bohr's quantitative "complementarity" which allows a "partly wave-like" and "partly particle-like" behavior of a quantum of the field. That's OK and you're right but that's not really what the original question was about. The original question talked about the situation when some apparata are completely able to measure the which-slit information (so the action change is very large, in your language), but this measurement isn't accessible to "us". So your answer is arguably off-topic. –  Luboš Motl Dec 12 '11 at 11:16
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Dear @Lubos, I was addressing the last part of the question, that you seem to have overlooked ... why does the gravitational tug of the electron on the apparatus (say) not count as a measurement? It's because it's too weak, and once you bring "too weak" into it, you need have some quantitative measure for it to make sense. –  Peter Shor Dec 12 '11 at 11:59
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What Luboš Motl said. But I want to address the second part:

then how is it that unobserved electron's are not disturbed since they certainly interact with other objects, for example other atoms in the matter around the slit(s) will feel a slight gravitational tug as it passes through.

When one is thinking of a double slit experiment, one is in the quantum mechanical region, i.e. the energies and wavelengths within the sizes of hbar. We do not have a double slit of macroscopic size with respect to the particles and expect to see interference.

The "slight gravitational tug as it passes through" is inconsistent with the quantum mechanical framework. One would have to solve the total quantum mechanical problem, including the gravitational tug from matter, which would affect infinitesimally the interference pattern, but would still work as a QM probability amplitude for passing through either slit.

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Surely you don't mean wavelengths within the sizes of hbar; they're not even measured in the same units. –  Peter Shor Nov 28 '11 at 13:50
    
That is why I used the word sizes, meaning measured in appropriate units, depending on what one measures: energy h*nu, or space deltap*deltax~hbar, etc. –  anna v Nov 28 '11 at 15:15
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Leonard Susskind explains this well in lectures 6 and 7 of quantum entanglement. These lectures can be viewed online (see Stanford continuing education lectures; Leonard Susskind).

There he explains how any record of which way the particle went destroys the interference pattern no matter whether you as observer are aware of the record or not.

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Is it about dual state of the matter, interference, or collision with the interiors surfaces and the corners of the wall thickness??? The wall thickness is huge by comparison with the particles size.

Think about!!!

You say: "One that keeps cropping up for me is the role of observers". They say: "when we put sensors near slits", not " if we look at the experiment from a distance corner of the room"...

I've make a short movie explain this, hope you find it useful: http://www.youtube.com/watch?v=gBm6Y82Mz3g

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