Does a Hidden Detector Affect the Double-Slit Experiment?

[PositiveGoo]

Double Slit and "The Observer"

Hi! First of all, I am just getting started in Physics, so I apologize if this is a silly question.

I was talking with my boyfriend (who has a degree in physics) about the double slit experiment. Obviously, if you perform the experiment one electron (or photon?) at a time, an interference pattern results. However, if you try to measure which slit the electron (or photon) goes through, the interference pattern disappears. Cool. Uncertainty Principle. I'm down.

My boyfriend then said, however, "If you put the detector (that monitors which slit the particle is traveling through) in a black box so that you can't see the results, the interference pattern reappears." I called bulls*#t.

Let's say you have an experiment where the detector is going through all the normal operations of detecting which slit the particle travels through, BUT it does not record or display the results in any way. Will an interference pattern result on the screen? I say no. He says yes.

I'm sorry if this is a really stupid question, but my boyfriend is really smart and knows tons about Physics. But I can't find anywhere (reliable) that supports this argument.

Thanks so much,
PositiveGoo

 

[PositiveGoo]

I found this, and it seems to support my argument.

http://boards.straightdope.com/sdmb/archive/index.php/t-126916.html

 

[JesseM]

Yeah, you're right, even if you kept the detectors hidden and had them not keep records of any of their measurements, the interference pattern would still be destroyed. For some sources, you could use p. 2 of http://www.phy.duke.edu/~hsg/212/misc/expt-and-foundations-of-quantum.pdf.gz which says:

Thus the interference pattern is really collected one by one and this suggests the particle nature. Then the famous question can be posed: through which of the two slits did the particle actually pass on its way from source to detector? The well-known answer according to standard quantum physics is that such a question only makes sense when the experiment is such that the path taken can actually be determined for each particle. In other words, the superposition of amplitudes in Eq. (1) is only valid if there is no way to know, even in principle, which path the particle took. It is important to realize that this does not imply that an observer actually takes note of what happens. It is sufficient to destroy the interference pattern, if the path information is accessible in principle from the experiment or even if it is dispersed in the environment and beyond any technical possibility to be recovered, but in principle still ‘‘out there.’’ The absence of any such information is the essential criterion for quantum interference to appear.

This is related to a phenomena called decoherence which you might suggest he read a little about (the linked article is a good place to start), it basically means that if a quantum system isn't kept sufficiently isolated from its environment, interactions with the environment can act much the same as "observations". For an example, look at http://www.mpipks-dresden.mpg.de/~klh/research/decoherence/collisionaldeco/index.html in which a particle called a "fullerene" was used in a double-slit experiment, and if the region it was traveling through was filled with gas, interactions between the fullerene and the gas molecules were sufficient to partly or totally destroy the interference pattern. Similarly in this experiment the fullerenes in another double-slit experiment were heated with lasers, and the heated molecules would give off small numbers of photons, if enough photons were emitted it would in principle be possible to determine which slit the fullerene went through by measuring the emitted photons, even though the experimenters did not attempt to do this. They found that they could gradually go from a regular interference pattern to no interference pattern by varying the temperature that the fullerenes were heated to.

 

[billschnieder]

Maybe you could point your boyfriend to the following experiment in which the path of the particle was known and interference was still observed even though the particle went through only one slit at a time and the experimenters did see clearly which slit it went through.

http://www.physorg.com/news78650511.html
Single-Particle Diffraction and Interference at a Macroscopic Scale
Yves Couder and Emmanuel Fort, Phys. Rev. Lett. 97, 154101 (2006)

 

[unusualname]

Maybe you could point your boyfriend to the following experiment in which the path of the particle was known and interference was still observed even though the particle went through only one slit at a time and the experimenters did see clearly which slit it went through.

http://www.physorg.com/news78650511.html
Single-Particle Diffraction and Interference at a Macroscopic Scale
Yves Couder and Emmanuel Fort, Phys. Rev. Lett. 97, 154101 (2006)

Or maybe not. The fact that some clever macroscopic setup can simulate what is impossible at the quantum level is irrelevant.

If you detect a quantum particle going through a double slit you have to interact with it in such a way as to obtain a position measurement, this will always prevent that particle from contributing to any subsequent interference pattern. There are no clever ways around the uncertainty principle for individual particles at the quantum level, even if ingenious macroscopic experiments might fool people like billschnieder into thinking otherwise.

 

[PositiveGoo]

Thanks guys. Nothing better than giving your super fancy smart boyfriend a good kick in ye old physics crotch.

 

[Demystifier]

My boyfriend then said, however, "If you put the detector (that monitors which slit the particle is traveling through) in a black box so that you can't see the results, the interference pattern reappears."

That part is wrong.

 

[ecker]

If you detect a quantum particle going through a double slit you have to interact with it in such a way as to obtain a position measurement, this will always prevent that particle from contributing to any subsequent interference pattern.

This ^. Once you operate on the wave function by making an observation of position you collapse its state. Now there IS some contention about making weak measurements on the system to perform a partial collapse which would then allow you to "uncollapse" it back again but that would require further discussion.

 

[BruceW]

If the detector is a classical object (i.e. a cat, a computer, a person), then the wavefunction collapses, and there is no inteference pattern.

If the detector is non-classical, then all bets are off.

 

[ASD16]

There will be no interference pattern...for sure...becoz as soon as u measure the electron passing through the slit and not the screen...the probabilistic path reduces to definite paths irrespective whether u view the results or not... :-)

 

[StevieTNZ]

I'm quite interested in what 'Ring' has to say, in the link you provided PositiveGoo. Most of what has been said (the detector collapses the wavefunction) conforms to the Copenhagen Interpretation right?

 

[2jays]

It was my understanding that the probability wave function extended outwards to the extent that there aren't any observers left to collapse each successive new probability. Wasn't this one the points with the "Schrodinger's Cat" thought experiment? The cat collapses his own probability field, but the outside observer doesn't see what happened, hence his field is still in a superposition until he lifts the lid to the box and collapses his own, "new", field. Yes?

 

[BruceW]

No. Collapse happens for everyone when any single classical object (i.e. the cat) detects the particle.
The point of the Schrodinger's cat thought experiment is that the cat definitely is either dead or alive (not in a quantum superposition), from the perspective of the cat and the perspective of the person, even when the box is still closed.
This seems to be a common source of confusion.

 

[JesseM]

No. Collapse happens for everyone when any single classical object (i.e. the cat) detects the particle.

If the cat is completely isolated from the outside world, can it be considered classical? The Copenhagen interpretation doesn't really give any definite criteria AFAIK. Suppose we have a large quantum computer where all the qubits remain isolated from the environment until the computation is complete, and suppose the computer involves something like a simulation of an A.I. observing some quantum event, but then "forgetting" the results so that when we actually measured the state of all the qubits at the end we wouldn't be able to determine the outcome of the event, even in principle. In this case, if we assumed a "collapse" on measurement I think we would actually get slightly different predictions then if we assumed the A.I. had simply become entangled with the event, but no "collapse" until we measured the state of all the qubits at the end. David Deutsch has actually proposed this thought-experiment as a way to distinguish the many-worlds interpretation from the Copenhagen interpretation (see the description here), but my feeling is that most advocates of the Copenhagen interpretation would agree that the correct prediction is the one that assumes no "collapse" until the end when we make the measurement...do you disagree?

 

[BruceW]

Collapse occurs when the original wavefunction cannot practically be reformed. This is my interpretation, and I think it is the most generally held one.
In the example of the quantum robot, when the robot 'detects' the particle, the robot+particle are still in a combined state that can go back to the original state, therefore collapse has not occurred and the 'detection' the robot made is not a classical measurement. If the robot reforms the original particle, then the robot must also go back to its own original state, therefore its the same as if the robot never 'detected' the particle at all. In fact, there must be no way for the robot (or anyone else) to know whether the robot did or didn't 'detect' the particle.

 

[2jays]

The point of the Schrodinger's cat thought experiment is that the cat definitely is either dead or alive (not in a quantum superposition), from the perspective of the cat and the perspective of the person, even when the box is still closed.

Bruce: Are you saying that the point of the thought experiment is to demonstrate that NO superposition exists before the lid is opened?

 

[JesseM]

Collapse occurs when the original wavefunction cannot practically be reformed.

What do you mean "reformed"? In the experiment involving the AI that Deutsch suggested, there's no suggestion that the state of the system goes back to exactly what it was at the beginning, just that the specific memory of what happened with a single quantum event is lost. Similarly if we could really have an isolated cat in a box that lived or died based on a radioactive decay, but we waited a billion years before opening the box, then by the time we opened it the cat would already be dead either way and its molecules so scrambled that it would probably be impossible in principle to determine whether the cat had died due to the radioactive decay causing poison release or if it just died of old age. In this case the ends state (scrambled molecules of a long-dead cat) is quite different from the initial state when the box was sealed (live cat), but information about whether that decay occurred has been "erased". In these cases would you say there was any collapse of the wavefunction of the system in the box (or in the isolated quantum computer) before the time that we measured it?

 

[BruceW]

The collapse happens when the cat died. By definition, a classical object can't be in a superposition. It doesn't matter if you can't tell (in principle) which state it collapsed into.
For example: imagine a quantum state collapse happened in a far away galaxy. Then by the restriction of the speed of light, we could not know the outcome in principle, but the collapse still happens when they made the measurement. (In other words, I'm saying that if collapse of a state happens somewhere, then it happens everywhere, instantaneously).

Of course, the question 'what is a classical object?' is a grey area. The definition 'cannot practically be put into superposition' is sturdy, but what objects that includes is vague. For example, Buckyball molecules have been made to interfere. So even though they are molecules, they can still be counted as non-classical objects!

 

[BruceW]

When I say a classical object can't be in superposition, I mean it can't be a superposition of a small number of known states.

 

[JesseM]

The collapse happens when the cat died. By definition, a classical object can't be in a superposition.

Why do you assume the cat is "classical" if it's in isolation? Keeping a macroscopic object in complete isolation from its environment would be a very unusual state that we've never observed in reality. If we could build a large quantum computer with as many qubits as there are particles in a "macroscopic" object, would you predict that the quantum computer's state will self-collapse even if it has no interaction with the environment, so it won't work as predicted? Do you agree with Deutsch's claim that the Copenhagen interpretation and the many-worlds interpretation are in principle experimentally distinguishable in an experiment where we "erase" the memory of a large A.I. with a simulated brain as complex as a cat's (or a person's)?

It doesn't matter if you can't tell (in principle) which state it collapsed into.

But consider the double-slit experiment. If you assume a "collapse" happened at the slits, but you don't know which state it collapsed into (i.e. you don't know which slit it went through), then you should predict the total probability distribution at the screen will just be a sum of the two single-slit patterns with no interference between them. Now consider the "delayed choice quantum eraser" variant on the double-slit experiment (see the thread here if you're not familiar with the setup, the link to the actual paper in that thread is outdated but here is a working link). Since the idler photon is entangled with the signal photon in a way that would in principle allow you to determine which slit the signal photon went through immediately after both photons were created, this does destroy the interference pattern in the total pattern of signal photons, but if the idler is measured in a state where the which-path information has been "erased" and is unrecoverable (at either the D1 or D2 detectors), then if you do a coincidence count of only that subset of signal photons whose idlers were detected in this state, then you recover an interference pattern, something that would be impossible if you assume there was a true "collapse" at the slits.

Couldn't something similar be done with the cat, or the A.I. in Deutsch's experiment? Suppose that although the box is nearly completely isolated, it does have a pair of slits which allow a single electron to escape, then shutters on the slits close and nothing else escapes again until the box is opened. Inside the box, there are detectors at each slit, and if the electron is detected going through the left the cat lives, if the electron is detected going through the right the poison is released killing the cat. But instead of opening the box shortly afterwards, we wait billions or trillions of years, when the cat is long dead, the equipment including the poison bottle has long fallen apart, and all the molecules in the box are thoroughly scrambled into a high-entropy state where it's not possible even in principle to determine if the electron went through the right slit or the left slit. Now at the micro level there are going to be a huge number of different possible high-entropy states we could find at the end, call them S₁, S₂, ..., S_10^100, ..., S_N, but suppose we could repeat this experiment an even huger number of times with cats all prepared in identical initial quantum states at the beginning of the experiment. Then I would expect, analogous to the quantum eraser, that if you picked some particular final state S_X in which the "which-path" information for the electron was unrecoverable, and graphed the positions of the electrons on the screen in the tiny subset of trials where the contents of the box ended up in state S_X, then in this case you would see an interference pattern in this coincidence count. At least, that's what I'd guess would be predicted by QM if you assumed no "collapse" inside the box until it was finally opened. Whereas if you do assume there was a "collapse" at the time the electron was detected going through the left or right slit inside the box, and the cat lived or died as a result, then you should predict no interference even in such a coincidence count, right? So this would suggest that at least in principle, no-collapse interpretations like the MWI or Bohmian mechanics could be distinguished from your version of the Copenhagen interpretation (though again I am not sure if all Copenhagen advocates would agree that an isolated cat should be counted as "classical" and can thus collapse the wavefunction).

Of course, the question 'what is a classical object?' is a grey area. The definition 'cannot practically be put into superposition' is sturdy, but what objects that includes is vague. For example, Buckyball molecules have been made to interfere. So even though they are molecules, they can still be counted as non-classical objects!

But how does this apply to thought-experiments, then? If for the sake of the thought-experiment we are assuming some super-advanced civilization has the technology to practically keep a cat completely isolated from the external world (perhaps slightly more realistic if we just assume they can build a giant quantum computer whose qubits are kept isolated from external influences by methods like lowering their temperature to very near absolute zero, and that this giant quantum computer is used to do a detailed simulation of a cat in a box), then doesn't that mean that for the purposes of the thought-experiment we must treat the cat as a non-classical object?

 

[BruceW]

In the paper you've linked to, classical measurement of the idler photon at some time t_2 means you have effectively also made a classical measurement of the signal photon at t_1 even though t_2 > t_1, and it seems like you don't physically do anything to the signal photon.

When I said earlier:

if collapse of a state happens somewhere, then it happens everywhere, instantaneously

To be accurate, I should say: for a particular inertial reference frame, if a particle wavefunction collapses at a particular time, then it collapses for any observer in that reference frame at that same time. And to calculate the time it collapses for another inertial reference frame, just do a Lorentz transform.

If you could get a cat into a known quantum state, and have the ability to manipulate the quantum state of the cat to get to it into other exact quantum states, then it would no longer be a classical object. The most obvious problem is that the computing power to do this would be insane. Also, we currently have no way to measure or manipulate such a complex quantum state.
Possibly more fundamental obstacles are decoherence due to the fact that even a vacuum doesn't have absolute zero temperature. And the slight curvature of spacetime due to general relativity may cause sufficient decoherence of a large object that needs to be in an exact quantum state.
The cat doesn't strictly need to be in an exactly known quantum state to be able to exhibit quantum effects (since the cat probably wouldn't mind if it lost a few thousand atoms). In this case, the atoms that were not correctly put in superposition would collapse.

My problem with many-worlds theory is that it tells us nothing about the probabilities that we should expect if I do a quantum experiment. And I don't buy the argument 'the state collapses for the person doing the experiment, but if there is another person that hasn't seen the outcome of the experiment, then collapse hasn't happened for him yet.' This argument requires several systems (i.e. one for the experimenter and one for the other guy). But my interpretation is that there is one system, where classical measurements cause collapse. And it is consistent if someday there they make a humanoid with a quantum brain, (as I explained in an earlier post).
What's your interpretation, JesseM?

 

[2jays]

A cat in a box doesn't prevent superposition from occurring no more than it does if he stands in front of a double-slit.