A discovered "paradox" in the double slit experiment

[befj0001]

Consider the classical double slit experiment where we are shooting electrons trough a double slit and then capture them on a photographic plate. We know that the pattern of electrons on the plate will differ depending on the state of knowledge of the observer. If he make a measurement to find out witch slit the electron passed through, the interferens pattern will dissapear. This is a well known fact.

Now consider a more complicated situation which have the above situation as a special case:

Assume the condition is like before, we have the classical experiment with an observer. But now assume that this first observer (person 1) is contained in a box, so that no one outside the box will know whether the person in the box observes the electron passing through the slit or not. The person outside (person 2) will only see the photographic plate. Person 1 in the box will see the whole experiment including the photographic plate.

Consider now the situation when person 1 make a measurement to figure out what slit the electron passed through. As a consequense of this the interferens pattern will disappear and he is all satisfied with that. From person 2's perspective, he will not know which slit the electron passed through and so he should see an interferens pattern on the plate. But this contradicts the fact that person 1 did not see interference.

One could argue that once person 2 outside the box sees the interference he will conclude that person 1 did an observation, and so he knows that person 1 knows what slit the electrons passed through. But that doesn't resolve the fact that person 2 didn't know at the time the electron passed through the slit whether person 1 made an observation or not.

I don't know, but at first sight this situaion seems paradoxical!

 

[PeterDonis]

Consider now the situation when person 1 make a measurement to figure out what slit the electron passed through. As a consequense of this the interferens pattern will disappear and he is all satisfied with that. From person 2's perspective, he will not know which slit the electron passed through and so he should see an interferens pattern on the plate.

No, this is not correct. It doesn't matter whether person 2 "knows" which slit the electron passed through, because the fact that person 1 made a measurement means that the experimental setup has changed: person 1 had to put some measuring device at the slits to measure which slit the electron passed through, and this measuring device interacts with the electron and changes its behavior. That interaction is what makes the interference pattern disappear.

In other words, it can never be the case that person 2 sees interference but person 1 does not; if both people make observations, those observations must be consistent.

 

[DrChinese]

And just to add to PeterDonis' excellent comment:

No person needs to be involved at all. No method to determine "which slit" the particle went through is required either. It is the ability, in principle, to know "which slit" information which is required in order to cause interference to disappear. This can be accomplished by placing crossed polarizers or other spin alignment devices near each slit.

 

[phinds]

Any observation kills the interference. You can do it with a mechanism that has no human intervention and it kills the interference. The electrons just KNOW

EDIT: oops ... I had this post sitting on my screen for 1/2 hour and didn't realize that there had already been responses that made mine unnecessary.

 

[DrChinese]

EDIT: oops ... I had this post sitting on my screen for 1/2 hour and didn't realize that there had already been responses that made mine unnecessary.

I have done that once or twice...

 

[atyy]

No, this is not correct. It doesn't matter whether person 2 "knows" which slit the electron passed through, because the fact that person 1 made a measurement means that the experimental setup has changed: person 1 had to put some measuring device at the slits to measure which slit the electron passed through, and this measuring device interacts with the electron and changes its behavior. That interaction is what makes the interference pattern disappear.

In other words, it can never be the case that person 2 sees interference but person 1 does not; if both people make observations, those observations must be consistent.

I'm not sure I agree. The reason is that in a Copenhagen-like interpretation a measurement is something that is made by a macroscopic non-quantum device, and which parts of the universe are considered quantum and which parts non-quantum depend on a common sense which depends on the observer. So if observer 2 wants to consider everything in the box quantum until he opens it, there wouldn't be any contradiction with quantum mechanics, ie. observer 1 and his experiment is in a superposition until observer 2 opens the box and makes his measurement.

 

[atyy]

I think the OP's scenario is similar to Schroedinger's cat, which illustrates that there is a conceptual question raised by quantum mechanics, which is termed the "measurement problem". There is discussion of Schroedinger's cat and the measurement problem in Bell's http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf (p38 of the original page numbering).

As far as I know, one solution to the measurement problem is a form of Bohmian mechanics, for non-relativistic quantum mechanics. I believe the question of whether Bohmian mechanics can be extended to relativistic quantum mechanics is still being researched. Another leading approach to solving the measurement problem is many-worlds, but I think it is still not completely clear whether all technical problems in a many-worlds approach can be taken care of.

 

[DrChinese]

atyy,

I get your analogy to the Many Worlds-like quality in OP's example (due to the person 1 and person 2 references). Of course, something has to be in a superposition for that to be relevant, and there isn't anything in this case. I guess it could somehow be reformulated to make that happen, if you can have a cat in a superposition.

The example states: "no one outside the box will know whether the person [1] in the box observes the electron passing through the slit or not." That gives it away there: person 1 and person 2 will BOTH always know whether any which slit observation has occurred. Obviously, person 1's decision will be visible on the plate via the pattern, which person 2 has access to at all times - "The person outside (person 2) will only see the photographic plate." There is no isolated and "un-collapsed" system to consider.

 

[befj0001]

atyy,

I get your analogy to the Many Worlds-like quality in OP's example (due to the person 1 and person 2 references). Of course, something has to be in a superposition for that to be relevant, and there isn't anything in this case. I guess it could somehow be reformulated to make that happen, if you can have a cat in a superposition.

The example states: "no one outside the box will know whether the person [1] in the box observes the electron passing through the slit or not." That gives it away there: person 1 and person 2 will BOTH always know whether any which slit observation has occurred. Obviously, person 1's decision will be visible on the plate via the pattern, which person 2 has access to at all times - "The person outside (person 2) will only see the photographic plate." There is no isolated and "un-collapsed" system to consider.

Yes, I agree with you that once the electrons get to the plate person 2 will know about the state of the observer inside the box. But what confuses me is that, at the time the electron passes through the slit person 2 doesn't know, and so from his perspective the electron is still in a state of superposition! From his perspective the wavefunction doesn't collapse until he observes the electron pattern on the plate.

 

[Jilang]

I would think that any kind of intervention whether you know the results of it or not would destroy the correlations and the interference pattern.

 

[PeterDonis]

if observer 2 wants to consider everything in the box quantum until he opens it, there wouldn't be any contradiction with quantum mechanics, ie. observer 1 and his experiment is in a superposition until observer 2 opens the box and makes his measurement.

Observer 1 and his experiment will be in a superposition, yes, but it won't be a superposition of having an interference pattern and not having one, because, by the OP's hypothesis, in the case under discussion, observer 1 *does* make a measurement of the electron's position--in other words, the physical configuration inside the box is such that there *is* an interaction at each slit between the electron and a measuring device. That alone is sufficient to destroy the interference pattern.

In order to have a "Schrodinger's cat" situation, we would have to set things up inside the box such that observer 1 only measures which slit the electron goes through if, for example, a radioactive atom decays (i.e., the interaction with the electron at each slit is only "turned on" if the atom decays). Then observer 2 would model observer 1 as being in a superposition of measuring the electron position and not measuring it, and the detector as being in a superposition of having an interference pattern and not having one, until he opens the box and collapses the superposition.

But even in the latter situation, after the box is opened, observer 1 and observer 2 would agree on whether there was an interference pattern or not; whichever alternative observer 2 sees must be consistent with what observer 1 sees in that alternative.

 

[WannabeNewton]

There is discussion of Schroedinger's cat and the measurement problem in Bell's http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf (p38 of the original page numbering).

That is quite an article. I should print out several copies of it and hand it out to passers-by while preaching in the arts quad at my university.

 

[atyy]

atyy,

I get your analogy to the Many Worlds-like quality in OP's example (due to the person 1 and person 2 references). Of course, something has to be in a superposition for that to be relevant, and there isn't anything in this case. I guess it could somehow be reformulated to make that happen, if you can have a cat in a superposition.

The example states: "no one outside the box will know whether the person [1] in the box observes the electron passing through the slit or not." That gives it away there: person 1 and person 2 will BOTH always know whether any which slit observation has occurred. Obviously, person 1's decision will be visible on the plate via the pattern, which person 2 has access to at all times - "The person outside (person 2) will only see the photographic plate." There is no isolated and "un-collapsed" system to consider.

Observer 1 and his experiment will be in a superposition, yes, but it won't be a superposition of having an interference pattern and not having one, because, by the OP's hypothesis, in the case under discussion, observer 1 *does* make a measurement of the electron's position--in other words, the physical configuration inside the box is such that there *is* an interaction at each slit between the electron and a measuring device. That alone is sufficient to destroy the interference pattern.

In order to have a "Schrodinger's cat" situation, we would have to set things up inside the box such that observer 1 only measures which slit the electron goes through if, for example, a radioactive atom decays (i.e., the interaction with the electron at each slit is only "turned on" if the atom decays). Then observer 2 would model observer 1 as being in a superposition of measuring the electron position and not measuring it, and the detector as being in a superposition of having an interference pattern and not having one, until he opens the box and collapses the superposition.

But even in the latter situation, after the box is opened, observer 1 and observer 2 would agree on whether there was an interference pattern or not; whichever alternative observer 2 sees must be consistent with what observer 1 sees in that alternative.

OK, yes, I agree completely.

 

[befj0001]

From the article above:

"What exactly qualifies some physical systems to play the role of "measurer"?"

 

[WannabeNewton]

From the article above:

"What exactly qualifies some physical systems to play the role of "measurer"?"

The article provides several quotes from Landau's QM book that serve to clarify that question. Keep reading.

 

[atyy]

From the article above:

"What exactly qualifies some physical systems to play the role of "measurer"?"

As Dr Chinese (post #8) and Peter Donis (post #11) have explained above, the way your question is set-up is ambiguous, since it allows Person 2 to designate Person 1 as his measurer, because you have said that Person 1 does measure the particle's position.

In order to have the question illustrate the "measurement problem", you have to set it up differently, like what Peter Donis suggested (part of post #11):

In order to have a "Schrodinger's cat" situation, we would have to set things up inside the box such that observer 1 only measures which slit the electron goes through if, for example, a radioactive atom decays (i.e., the interaction with the electron at each slit is only "turned on" if the atom decays). Then observer 2 would model observer 1 as being in a superposition of measuring the electron position and not measuring it, and the detector as being in a superposition of having an interference pattern and not having one, until he opens the box and collapses the superposition.

But even in the latter situation, after the box is opened, observer 1 and observer 2 would agree on whether there was an interference pattern or not; whichever alternative observer 2 sees must be consistent with what observer 1 sees in that alternative.

 

[DrChinese]

Yes, I agree with you that once the electrons get to the plate person 2 will know about the state of the observer inside the box. But what confuses me is that, at the time the electron passes through the slit person 2 doesn't know, and so from his perspective the electron is still in a state of superposition! From his perspective the wavefunction doesn't collapse until he observes the electron pattern on the plate.

We will have to make up our mind whether this is about double slit or superposition. These are 2 different issues.

If the question is about superposition, it needs to be set up differently. As stated, there is no superposition. It doesn't matter whether person 1 or person 2 knows anything about what's on the plate (detector), as long as person 1 makes a decision about whether to observe which-slit info.

 

[Nugatory]

That is quite an article. I should print out several copies of it and hand it out to passers-by while preaching in the arts quad at my university.

That's one of the two articles that were added in the second edition of "Speakable and unspeakable in quantum mechanics"; the other is "La Nouvelle Cuisine". Even if you already have the first edition, it's worth buying the second edition for those two articles.

 

[bhobba]

What exactly qualifies some physical systems to play the role of "measurer"?"

A deep question indeed.

In modern times measurement is deemed to have occurred once decoherence has taken place. This is a purely quantum phenomena not dependant on dividing the world into classical and quantum.

But some issues such as the so called factoring problem do remain.

If you would like a discussion of such issues check out Omnes book:
https://www.amazon.com/dp/0691004358/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

That is quite an article. I should print out several copies of it and hand it out to passers-by while preaching in the arts quad at my university.

Good one.

Check out heavy boots:
http://www.phys.ufl.edu/~det/phy2060/heavyboots.html

Thanks
Bill

 

[bhobba]

That's one of the two articles that was added to the second edition of "Speakable and unspeakable in quantum mechanics"; the other is "La Nouvelle Cuisine". Even if you already have the first edition, it's worth buying the second edition for those two articles.

Like Ballentine every serious QM student should have a copy of Bells "Speakable and unspeakable in quantum mechanics"

Such a pity he died prematurely - a 100% certainty for a Nobel prize otherwise.

Thanks
Bill

 

[PeterDonis]

Check out heavy boots:
http://www.phys.ufl.edu/~det/phy2060/heavyboots.html

Oy. Of course, the obvious rejoinder to the "heavy boots" response is to point out that (a) heavy objects don't fall faster than light ones on Earth, once you correct for air resistance, and (b) on one of the Apollo missions, they actually did the classic experiment of dropping a feather and a heavy object (it was a geologist's hammer) and watching them fall with the same acceleration:

http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html

 

[Demystifier]

I'm not sure I agree. The reason is that in a Copenhagen-like interpretation a measurement is something that is made by a macroscopic non-quantum device, and which parts of the universe are considered quantum and which parts non-quantum depend on a common sense which depends on the observer. So if observer 2 wants to consider everything in the box quantum until he opens it, there wouldn't be any contradiction with quantum mechanics, ie. observer 1 and his experiment is in a superposition until observer 2 opens the box and makes his measurement.

I disagree. Decoherence theory (which does not depend on interpretation, meaning that even Copenhagenians should accept it) teachs us that coherent superposition of a subsystem is destroyed by quantum interaction described by the many-particle Schrodinger equation, irrespective of whether there are observers, collapse, Bohmian particles, etc.

See also
http://lanl.arxiv.org/abs/1406.3221

 

[atyy]

I disagree. Decoherence theory (which does not depend on interpretation, meaning that even Copenhagenians should accept it) teachs us that coherent superposition of a subsystem is destroyed by quantum interaction described by the many-particle Schrodinger equation, irrespective of whether there are observers, collapse, Bohmian particles, etc.

I'm not sure I understand exactly what you are saying, but yes, I was confused in the original scenario, which as Dr Chinese and Peter Donis pointed out, does indicate that Person 2 knows that Person 1 makes a position measurement.

See also
http://lanl.arxiv.org/abs/1406.3221

"In particular, we assume that it encodes some classical information, the evolution of which may be considered irreversible at the macroscopic level." That seems to me the same as assuming a classical measuring apparatus in the Copenhagen sense, since there should be no irreversibility if time evolution is unitary.

Reading quickly, it does look like decoherence as you say, because you integrate over degrees of freedom and cancel the off-diagonal terms. The difference is that in decoherence it is usually explicitly shown that unitary evolution removes the off-diagonal terms in the density matrix, whereas here you used the assumption of an irreversible classical record. I don't think I agree with your conclusion about what it feels like to be a Schrodinger cat. In the Copenhagen viewpoint, decoherence does not solve the measurement problem, or the problem of when a definite outcomes occurs. Until there is a definite outcome, quantum mechanics says nothing about what it is like to be a Schroedinger cat, since presumably "feeling like a cat" is a sequence of definite classical outcomes.

 

[Demystifier]

"In particular, we assume that it encodes some classical information, the evolution of which may be considered irreversible at the macroscopic level." That seems to me the same as assuming a classical measuring apparatus in the Copenhagen sense, since there should be no irreversibility if time evolution is unitary.

Concerning the reversibility/irreversibility issue, there is no much difference between quantum and classical physics. Both quantum and classical physics are reversible at the fundamental microscopic level. But at a practical macroscopic course-grained level, both look irreversible when a large number of mutually interacting particles is involved. And this does not depend on whether you adopt Copenhagen or some other interpretation of QM. Therefore you can understand the claim above in a Copenhagen sense if you like, but also in other senses as well.

 

[Demystifier]

I'm not sure I understand exactly what you are saying, but yes, I was confused in the original scenario, which as Dr Chinese and Peter Donis pointed out, does indicate that Person 2 knows that Person 1 makes a position measurement.

Person 2 does not need to know that Person 1 makes a position measurement. It is sufficient that Person 1 does make a position measurement.

The knowledge in QM is potentially (depending on the interpretation) only relevant for explanation of the wave function collapse, because some interpretations assert that collapse is nothing but a Bayesian update of knowledge. However, the presence or absence of interference does not depend on collapse, so in this sense it does not depend on the knowledge either. It depends only on the wave function. As long as wave function before the collapse is considered to be an objective entity, the presence or absence of interference is objective too.

 

[Demystifier]

That's one of the two articles that were added in the second edition of "Speakable and unspeakable in quantum mechanics"; the other is "La Nouvelle Cuisine". Even if you already have the first edition, it's worth buying the second edition for those two articles.

Alternatively, you can buy the book
https://www.amazon.com/dp/9810246889/?tag=pfamazon01-20
containing the reprints of all these Bells papers in the original format.

 

[atyy]

Person 2 does not need to know that Person 1 makes a position measurement. It is sufficient that Person 1 does make a position measurement.

The knowledge in QM is potentially (depending on the interpretation) only relevant for explanation of the wave function collapse, because some interpretations assert that collapse is nothing but a Bayesian update of knowledge. However, the presence or absence of interference does not depend on collapse, so in this sense it does not depend on the knowledge either. It depends only on the wave function. As long as wave function before the collapse is considered to be an objective entity, the presence or absence of interference is objective too.

I think that's right, because I haven't come up with a counterexample. But I think I can set up a situation where Person 2's knowledge is important for him to see the same interference that Person 1 sees. Let Person 1 prepare state A with probability P_A and state B with probability P_B. At the end of each run of the experiment, there is a single spot on the plate. Persons 1 and 2 accumulate plates after many runs, and build up interference patterns from the results of many runs. State A gives the single slit pattern, and state B gives the double slit pattern. If Person 1 knows which runs were state A and which were state B, then he will be able to separate out the sub-ensemble corresponding to state B and get a double slit pattern. If Person 2 doesn't know which runs were which, then he will see a pattern that is a mixture of single and double slit patterns. This is not a counterexample, since it is indeed enough for Person 1 to have prepared state B for the double slit pattern to be seen. But it seems to show that Person 2 needs some knowledge to see the same pattern.

 

[bhobba]

Alternatively, you can buy the book
https://www.amazon.com/dp/9810246889/?tag=pfamazon01-20
containing the reprints of all these Bells papers in the original format.

Well worth the dosh IMHO. I forked out for it and certainly didn't regret it - a man of great insight.

I disagree. Decoherence theory (which does not depend on interpretation, meaning that even Copenhagenians should accept it) teachs us that coherent superposition of a subsystem is destroyed by quantum interaction described by the many-particle Schrodinger equation, irrespective of whether there are observers, collapse, Bohmian particles, etc.

:thumbs::thumbs::thumbs::thumbs::thumbs::thumbs:

Thanks
Bill

 

[Demystifier]

I think that's right, because I haven't come up with a counterexample. But I think I can set up a situation where Person 2's knowledge is important for him to see the same interference that Person 1 sees. Let Person 1 prepare state A with probability P_A and state B with probability P_B. At the end of each run of the experiment, there is a single spot on the plate. Persons 1 and 2 accumulate plates after many runs, and build up interference patterns from the results of many runs. State A gives the single slit pattern, and state B gives the double slit pattern. If Person 1 knows which runs were state A and which were state B, then he will be able to separate out the sub-ensemble corresponding to state B and get a double slit pattern. If Person 2 doesn't know which runs were which, then he will see a pattern that is a mixture of single and double slit patterns. This is not a counterexample, since it is indeed enough for Person 1 to have prepared state B for the double slit pattern to be seen. But it seems to show that Person 2 needs some knowledge to see the same pattern.

Here the crucial statement is "Let Person 1 prepare state A with probability P_A and state B with probability P_B". This corresponds to a state which is not described by a wave function. Instead, it is described by a mixed density matrix. Even if wave functions are viewed as objective entities not depending on knowledge, mixed states are generally viewed as objects which do depend on knowledge. That's why in your case the visibility of interference does depend on knowledge, and why it does not contradict my claim that interference described by a wave function does not depend on knowledge.

In fact, your example is not much different from the following one. Let there be two laboratories, one in which the interferometer is set up correctly, and another in which the interferometer is set up incorrectly. Obviously, whether you will see interference depends on whether you know which laboratory contains a correct set up.

Or even more trivially, whether you will see interference depends on whether you know how to correctly set up the interferometer. (For instance, I myself am a theorist who does not know how to set up the interferometer in the true laboratory, so in this sense I am not able to see interference.)

These examples clearly show that dependence on knowledge is nothing but a common sense. Formally, this common sense can always be expressed elegantly in the language of density matrices.

 

[rkastner]

At this point, there is actually no answer to the measurement problem ('Schrodinger's Cat') in the many-worlds picture since the 'Einselecton' program that would allow for splitting of worlds does not work: http://arxiv.org/abs/1406.4126
Among other things, this means that 'Quantum Darwinism' does not work either as an explanation for the emergence of the macroscopic world.