Quantum Mechanics without Measurement

[stevendaryl]

A framework is a choice of observables at certain times. The kind of statements I had in mind is "If the observables of framework F are chosen to be real, O1 has value X1 at time t1, O2 has value X2 at time t2, ..." AND "If the observables of framework F' are chosen to be real, O1' has value X1' at time t1', O2' has value X2' at time t2', ...". Such meta-statements can always be made.

I don't see how it makes any difference whether you are talking statements or meta-statements. Take a very simple case: We have an electron prepared at time t=0 to have spin-up in the z-direction. Framework F1 consists of a single observable, the x-component of spin, at time t=1. Framework F2 consists of a different observable, the y-component of spin at time t=1. You can imagine frameworks for every possible orientation for spin.

Whatever difficulties we have with compound statement "s_x = +1/2 and s_y = +1/2", we'll have exactly the same difficulties with the compound statement: "If F1 is chosen as real, then s_x = +1/2 and if F2 is chosen as real, then s_y = +1/2". In either case, we're talking about a mathematical mapping from orientations to the two-element set \{ +1/2, -1/2 \}. What Bell's theorem shows is that there is no consistent assignment of probabilities to such mappings in a way that agrees with the predictions of quantum mechanics. Calling the mapping a "meta" fact doesn't change this. The same proof shows that there is no consistent assignment of probabilities to the set of all "meta" statements. So you haven't actually changed anything by letting it be "meta". You still have statements that seem to be meaningful in combination, but there is no consistent way to assign likelihoods of their being true.

You might as well have dropped the "meta", and just talked about spins themselves. It's perfectly meaningful to say "The electron has spin +1/2 in the x-direction, and spin +1/2 in the y-direction". There is no contradiction from making such a claim. But there is no consistent way to assess the probability that such a claim is true. Meta versus non-meta doesn't make any difference.

 

[DevilsAvocado]

What prevents us from assuming that there is a master history? Really, it's not logic, it's probability theory. If we assume that there is a definite, but unknown, master history, then it means that we can use ordinary probability theory to reason about this history. That is, we can just use probability to reflect our ignorance about which master history is the real one.

How about the double-slit? Check out Richard Feynman @49:45, in this video from Cornell University 1964. We're forbidden – even in theory – to in advance know about which slit, because if we did, the double-slit would stop working! This is not a matter of ignorance or 'bad tools'; it's an intrinsic property of QM.

Richard Feynman on the Double Slit Paradox: Particle or Wave?
https://www.youtube.com/watch?v=hUJfjRoxCbk
http://www.youtube.com/embed/hUJfjRoxCbk


P.S: I love nice and even numbers!

 

[stevendaryl]

How about the double-slit? Check out Richard Feynman @49:45, in this video from Cornell University 1964. We're forbidden – even in theory – to in advance know about which slit, because if we did, the double-slit would stop working! This is not a matter of ignorance or 'bad tools'; it's an intrinsic property of QM.

To say that we are forbidden to know which slit seems interpretation-dependent. For example, in the Bohm theory, the electron (or photon--I'm not sure if there is a Bohm theory for the photon) has a definite position at all times.

 

[stevendaryl]

Wow! That video plays the Cornell song at the beginning:

Far above Cayuga's waters,
With its waves of blue,
Stands our noble Alma Mater,
Glorious to view

I'm not a Cornell grad, but I do live in Ithaca.

That is a great video. I wish I could have learned physics from Feynman.

 

[craigi]

To say that we are forbidden to know which slit seems interpretation-dependent. For example, in the Bohm theory, the electron (or photon--I'm not sure if there is a Bohm theory for the photon) has a definite position at all times.

Agreed.

I think much of what we're talking about in latter section of this thread is really about level of abstraction.

 

[DevilsAvocado]

To say that we are forbidden to know which slit seems interpretation-dependent. For example, in the Bohm theory, the electron (or photon--I'm not sure if there is a Bohm theory for the photon) has a definite position at all times.

Yes, but in dBB you have the 'magical' unknown initial conditions (of the universe?), that makes it impossible to make any predictions in advance. If it wasn't, dBB would be deterministic all they way through (and someone would get the Nobel Prize in Physics).

 

[DevilsAvocado]

Wow! That video plays the Cornell song at the beginning:

Enjoy!

 

[DevilsAvocado]

That is a great video. I wish I could have learned physics from Feynman.

Yes, he was truly brilliant. Have you seen the Sir Douglas Robb lectures at the University of Auckland (1979)? It's available on YouTube:

QED: The Strange Theory of Light and Matter

https://www.youtube.com/watch?v=LPDP_8X5Hug

The playlist consist of 30 videos between 10-15 min:
http://www.youtube.com/playlist?list=PL4C9818DC43C7E834

The original can be found here:
http://www.vega.org.uk/video/subseries/8

 

[stevendaryl]

Yes, but in dBB you have the 'magical' unknown initial conditions (of the universe?), that makes it impossible to make any predictions in advance. If it wasn't, dBB would be deterministic all they way through (and someone would get the Nobel Prize in Physics).

I'm just objecting to the claim that people are forbidden from knowing the positions of particles. If someone (God, maybe) whispered into your ear what the position of the electron was at time t=0, and told you what the "pilot wave" was, then you would know what the position was at all future times. If you don't have somebody omniscient whispering in your ear, then that calls for probabilities. You assume a probability distribution on initial positions, and on pilot waves, and then you end up getting a probabilistic prediction for future values of the position. That's the way ordinary classical probability works--anything you don't know, you can throw into the probability distributions to reflect your ignorance.

But when it comes to incompatible observables, such as the spins in the x-direction and the y-direction, it's not simply that you don't know enough. There is no consistent way to assign probabilities (and having the same predictions as quantum mechanics).

I don't think, though, that there is a proof that it is impossible to HAVE simultaneous values for incompatible observables. Only that there is no way to assign probabilities to sets of values for incompatible observables. I don't think the double-slit experiment proves otherwise. As I mentioned before, Pitowsky came up with a model for the EPR experiment which did assume that the spin in every direction was defined. His model escaped from the proof of Bell's theorem in that it did not assign probabilities for certain combinations of events (for the probability that the electron is spin-up in the x-direction and spin-down in the y-direction might be undefined). Bell's theorem amounts to a proof that there is no consistent way to assign probabilities to such events.

 

[DevilsAvocado]

I don't think the double-slit experiment proves otherwise.

In the case of the double-slit, we can be certain that knowledge of which slit will destroy interference. It's very hard (impossible) to get pass this simple fact, and the obvious reason is that you need "two sources" to get this kind of interference, whether this "source" is one particle 'splitting' to pass the two slits, or if it is only the wavefunction passing thru (like "water waves"), or if it is one particle guided by a pilot-wave passing thru, is still unknown.

Bell's theorem amounts to a proof that there is no consistent way to assign probabilities to such events.

Einstein was very skeptical about CFD, and maybe we are paying too much attention to this regarding EPR-Bell, I don’t know...

As you are saying, it only becomes a problem when we perform the measurement, i.e. suppose Bell required us to have a 'particle' with 6 incompatible values. Then we could build a model of a real spinning 'dice', that for some (unknown) reason will never let us see these 6 values simultaneously, and when we perform a measurement, we will only get one value, based solely on classical probabilities.

What's the problem!?

The problem is that this model works very fine for the 1935 version of EPR, where we theoretically could utilize a 'common influence' on the two 'twin dices', showing correlated behavior at measurement, i.e. if one shows even numbers, the other always shows odd, and vice versa.

This however is a dead parrot after 1964 and Bell's theorem, which mathematically proves that to have 'real twin dices' spinning at the source, the 'common influence' is not 'strong' enough to explain what happens in QM experiments (and predictions).

The only way to have spinning 'real dices' is to introduce a 'magical synchronization' that must be non-local, since the final parameters, setting the outcome probability for the 'twin dices', are set locally at the very last moment, and this 'new probability' is a combination of Alice local settings + Bob local settings, which makes any 'common source probability' faulty.

This is how it is.

 

[stevendaryl]

In the case of the double-slit, we can be certain that knowledge of which slit will destroy interference.

That sounds like a "wave function collapse" interpretation. I don't think it's unambiguously true that knowledge destroys the interference. What you can say is that the normal ways that one might attempt to detect which slit the particle goes through destroys the inference. That's because setting up such a detector changes the complete situation. (From the point of view of dBB, each electron is influenced nonlocally by the complete setup, not just the facts about what's happening along its own path).

Einstein was very skeptical about CFD, and maybe we are paying too much attention to this regarding EPR-Bell, I don’t know...

CFD as in contrafactual definitess? I'm not sure I understand the relevance.

As you are saying, it only becomes a problem when we perform the measurement, i.e. suppose Bell required us to have a 'particle' with 6 incompatible values. Then we could build a model of a real spinning 'dice', that for some (unknown) reason will never let us see these 6 values simultaneously, and when we perform a measurement, we will only get one value, based solely on classical probabilities.

What's the problem!?

The problem is that this model works very fine for the 1935 version of EPR, where we theoretically could utilize a 'common influence' on the two 'twin dices', showing correlated behavior at measurement, i.e. if one shows even numbers, the other always shows odd, and vice versa.

This however is a dead parrot after 1964 and Bell's theorem, which mathematically proves that to have 'real twin dices' spinning at the source, the 'common influence' is not 'strong' enough to explain what happens in QM experiments (and predictions).

Bell's theorem has an essential step, which is the assumption that whatever hidden variables there are have an associated measure, or probability. I don't completely know what the physical meaning of nonmeasurable hidden variables would be, but it certainly is a necessary assumption for Bell's proof to go through.

 

[kith]

Whatever difficulties we have with compound statement "s_x = +1/2 and s_y = +1/2", we'll have exactly the same difficulties with the compound statement: "If F1 is chosen as real, then s_x = +1/2 and if F2 is chosen as real, then s_y = +1/2".

Ok, now I see. What you and atyy have in mind is to combine statements about the "real" histories in the frameworks. I agree with your view on this. What I was thinking when talking about meta-statements are statements about probabilities in frameworks. A combined statement of this sort would be "In framework F1, s_x = +1/2 has the probability p1 and in framework F2, s_y = +1/2 has the probability p2".

 

[stevendaryl]

Ok, now I see. What you and atyy have in mind is to combine statements about the "real" histories in the frameworks. I agree with your view on this. What I was thinking when talking about meta-statements are statements about probabilities in frameworks. A combined statement of this sort would be "In framework F1, s_x = +1/2 has the probability p1 and in framework F2, s_y = +1/2 has the probability p2".

Yes, I agree with that.

 

[DevilsAvocado]

That sounds like a "wave function collapse" interpretation. I don't think it's unambiguously true that knowledge destroys the interference. What you can say is that the normal ways that one might attempt to detect which slit the particle goes through destroys the inference. That's because setting up such a detector changes the complete situation. (From the point of view of dBB, each electron is influenced nonlocally by the complete setup, not just the facts about what's happening along its own path).

Yes, of course any type of detection will destroy inference. But think of it like this:

• If you close/measure one slit, we will know which slit.
• If you close/measure one slit, inference is gone.
• To get inference we must have two undisturbed slits open.

And this because no matter of interpretation CI, dBB, Path integral, etc, they all rely on the fact that one particle is generating interference with itself, by the difference in path length between two slits, as in any wave interference:

There is no other way for one particle to interfere with itself (in this setup).

Now, imagine you had a "Perfect Theory" that is extremely precise, down to the size of the particle, and every time you prepared a particle, you would have full deterministic information on what it will do once you push the button and let it go, including which slit it will pass through.

So, what exactly would you see on the screen in a case with a "Perfect Theory"?

Well, if the theory is correct, you could close the slit you knew on beforehand it will not pass through, and still get interference on the screen!

But it doesn't work that way, does it? "Perfect Theories" don't change the outcome of empirical experiments, do they?

"Perfect Theories" are doomed to fail in the double-slit...

CFD as in contrafactual definitess? I'm not sure I understand the relevance.

And I don't blame you; maybe no one knows exactly what went on in Einstein's head after the EPR paper...

In the 1935 EPR paper (which was written in English by Podolsky and Einstein didn't see the final draft) the first premise was "either quantum theory is incomplete or there can be no simultaneously real values for incompatible quantities", and then they went on trying to prove that incompatible quantities indeed could have simultaneous real values, by measuring them separately via entanglement, i.e. quantum theory is incomplete (according to EPR).

But after the EPR publication, Einstein started to work on a clearer version of the EPR argument, where both the criterion of reality and elements of reality was dropped out... and instead he focused entirely on locality/separability vs. completeness (in the state function).

You can read more about it here: http://plato.stanford.edu/entries/qt-epr/#1.3

Bell's theorem has an essential step, which is the assumption that whatever hidden variables there are have an associated measure, or probability. I don't completely know what the physical meaning of nonmeasurable hidden variables would be, but it certainly is a necessary assumption for Bell's proof to go through.

According to the 1935 EPR criterion of reality, your (LHV) theory must be able to predict, with certainty, the value of the physical quantity. However, one could claim that there are real values indeed, but with current technology we can't reach them (and meanwhile we are 'fine-tuning' the theory ).

The ingenious of Bell is that he handles this 'exception' as well (as in my 'dice example').

 

[stevendaryl]

Yes, of course any type of detection will destroy inference. But think of it like this:

• If you close/measure one slit, we will know which slit.
• If you close/measure one slit, inference is gone.
• To get inference we must have two undisturbed slits open.

The implication is

We close one of the slits \Rightarrow we know which slit it went through \Rightarrow no interference pattern. But it doesn't follow that the interference pattern would be destroyed if we knew in some other way which slit it went through.

Now, imagine you had a "Perfect Theory" that is extremely precise, down to the size of the particle, and every time you prepared a particle, you would have full deterministic information on what it will do once you push the button and let it go, including which slit it will pass through.

So, what exactly would you see on the screen in a case with a "Perfect Theory"?

Well, if the theory is correct, you could close the slit you knew on beforehand it will not pass through, and still get interference on the screen!

First, in dBB, knowing which slit the particle will pass through requires knowing which slits are open, so closing a slit will change the answer, even if the particle doesn't go through that slit.

But that's a nonlocal theory, so let's confine ourselves to local theories.

My first thought was that any argument against hidden variables must make use of probabilities, because Bell's proof makes use of them. But the nice thing about interference is that there are certain cases where the interference makes a 100% certain difference. In your case, there is a spot on the screen that has zero chance of a particle landing on it if both slits are open, and nonzero chance if only one slit is open (and vice-versa). So opening or closing a slit can potential make an observable difference without assuming anything about probabilities.

My original statement was motivated by EPR and Bell's proof, and there I know (because Pitowsky wrote a paper about it) that nonmeasurability can avoid the conclusion. But the two slit experiment is not obvious to me. Maybe you're right, but I'll have to think about it some more.

 

[atyy]

At the end of http://arxiv.org/abs/1105.3932, Griffiths says "Sensible quantum descriptions can be constructed from the perspective of someone outside the system being considered."

Does this mean that CH still has a measurement problem? Is what is outside and inside subjective? Is the observer still a primitive notion in CH?

 

[bhobba]

To say that we are forbidden to know which slit seems interpretation-dependent. For example, in the Bohm theory, the electron (or photon--I'm not sure if there is a Bohm theory for the photon) has a definite position at all times.

It does - but you can't know what it is. That's because its guided by this pesky pilot wave that has things like interference effects etc. That's why its a hidden variable theory. The particle is really common sense classical but it is intrinsically hidden.

Note I am not an expert on BM - that pretty close to the limit of my knowledge about it. If you want to go into it deeper I am sure guys like Dymistifyer will only be too happy to help.

Thanks
Bill

 

[craigi]

...

There is no other way for one particle to interfere with itself (in this setup).

...

You know that that's not strictly true, right?

We do still see an interference pattern from a single slit, but I think you know this already.

 

[stevendaryl]

You know that that's not strictly true, right?

We do still see an interference pattern from a single slit, but I think you know this already.

As I said, the real point is to pick some spot where the intensity of the interference pattern is 0 for one slit and nonzero for two slits. Then seeing anything at that spot means that both slits are open. So it seems that if the particle only takes one slit, then it must be influenced by the nonlocal information that the other slit is open.

 

[stevendaryl]

It does - but you can't know what it is. That's because its guided by this pesky pilot wave that has things like interference effects etc. That's why its a hidden variable theory. The particle is really common sense classical but it is intrinsically hidden.

Note I am not an expert on BM - that pretty close to the limit of my knowledge about it. If you want to go into it deeper I am sure guys like Dymistifyer will only be too happy to help.

Thanks
Bill

I was actually talking about something other than Bohmian mechanics, which is, the possibility of explaining QM through the use of local interactions, but using nonmeasurable sets. In the specific case of spin-1/2 EPR, I read an article where nonmeasurable sets were used to construct a model that reproduced the predictions of quantum mechanics (and evaded Bell's theorem, because he assumed that certain probabilities were always well-defined).

But in the case of the two slit experiment, I don't see how something similar could be made to work. It sure seems like the appearance of a particle at a particular point depends on nonlocal information--whether both slits are open. So a model with local hidden variables using nonmeasurable sets doesn't seem possible.

 

[craigi]

As I said, the real point is to pick some spot where the intensity of the interference pattern is 0 for one slit and nonzero for two slits. Then seeing anything at that spot means that both slits are open. So it seems that if the particle only takes one slit, then it must be influenced by the nonlocal information that the other slit is open.

Nonlocal to what though? Nonlocal to an arbitrary slit, that the light seen at your observation point must have passed through, at some point in the past? It's not nonlocal to your observation point though.

Even then, it's certaintly not clear from a standard double slit experiment that a point at an arbitrary slit must gather information from the second slit in a nonlocal manner in order to display the interference that we observe.

Why is any of this important? Because if we don't consider it, we fall into using presumptions from Bohmian mechanics in our interpretation.

 

[stevendaryl]

Nonlocal to what though? Nonlocal to an arbitrary slit, that the light seen at your observation point must have passed through, at some point in the past? It's not nonlocal to your observation point though.

Even then, it's certaintly not clear from a standard double slit experiment that a point at an arbitrary slit must gather information from the second slit in a nonlocal manner in order to display the interference that we observe.

Why is any of this important? Because if we don't consider it, we fall into using presumptions from Bohmian mechanics in our interpretation.

This thread has taken lots of twists and turns. The specific issue that the double slit experiment is relevant to is whether it is possible to explain QM in terms of a particle having a definite position at all times and being influenced by only local factors (that is, forces and so forth that are present along the path that the particle takes). It's hard to see how that is possible, because closing the slit that the particle doesn't go through seems to have an effect on the particle. Bohmian mechanics explicitly is nonlocal in this sense; even though the particle takes one path, its motion is affected by conditions along the other path.

 

[craigi]

This thread has taken lots of twists and turns. The specific issue that the double slit experiment is relevant to is whether it is possible to explain QM in terms of a particle having a definite position at all times and being influenced by only local factors (that is, forces and so forth that are present along the path that the particle takes). It's hard to see how that is possible, because closing the slit that the particle doesn't go through seems to have an effect on the particle. Bohmian mechanics explicitly is nonlocal in this sense; even though the particle takes one path, its motion is affected by conditions along the other path.

Yeah, to my mind, in dBB the CFD particle "feels" out the geometry using a non-local pilot wave.

It's worth looking at the Transactional Interepretation too, which gives CFD, but is also explicitly non-local.

All the other interpretations abandon CFD so it becomes meaningless to talk of a single point particle between measurement events, but I think there is a lot of merit in understanding the double slit experiment in these contexts too.

So in answer to your question, I think it's safe to say that there is an overwhelming consensus that if you want an objectively real, single, point particle between measurement events then you have to have an interpretation with non-local influences.

 

[atyy]

But does the pilot wave have to be nonlocal in the double slit? After all, light already shows diffraction.

 

[stevendaryl]

But does the pilot wave have to be nonlocal in the double slit? After all, light already shows diffraction.

Well, in classical optics, light shows diffraction because the electromagnetic waves really do go through both slits, and recombine (either constructively or destructively). But if the particle intensity is low enough that only one particle (photon or electron) at a time goes through the slits, then it's hard to see how it can possibly go through both slits.

 

[Jilang]

This thread has taken lots of twists and turns. The specific issue that the double slit experiment is relevant to is whether it is possible to explain QM in terms of a particle having a definite position at all times and being influenced by only local factors (that is, forces and so forth that are present along the path that the particle takes). It's hard to see how that is possible, because closing the slit that the particle doesn't go through seems to have an effect on the particle. Bohmian mechanics explicitly is nonlocal in this sense; even though the particle takes one path, its motion is affected by conditions along the other path.

I could imagine that in the frame of reference of the particle everything works out. Shrink yourself down and imagine you are the particle. Would the two slits positions appear fuzzy and not well defined, sometimes overlapping so you could get through both at once? With a single slit it might be possible to make it through and achieve any final angle relative to your initial momentum by timing your transit so impact with a side wall to impart the desired momentum. But with two slits it might be impossible to achieve certain angles and some might be more likely than others.

 

[craigi]

But does the pilot wave have to be nonlocal in the double slit? After all, light already shows diffraction.

Yup. Take a look at Wheeler's delayed choice experiments, if you're not familiar with them.

http://en.wikipedia.org/wiki/Wheeler's_delayed_choice_experiment#Double-slit_version

 

[atyy]

Well, in classical optics, light shows diffraction because the electromagnetic waves really do go through both slits, and recombine (either constructively or destructively). But if the particle intensity is low enough that only one particle (photon or electron) at a time goes through the slits, then it's hard to see how it can possibly go through both slits.

Perhaps it is possible for the pilot wave to go through both slits, but the particle to go through one, just as in Bohmian mechanics. However, because only one particle is involved, the pilot wave can be a local wave like an electromagnetic wave.

In the two particle case, this would be like EPR/Bell again, but then one might hope the nonmeasurable loophole comes into enable local hidden variables.

 

[atyy]

But since this is a thread on consistent histories, does anyone have thoughts on this issue?

CH makes sense for an observer outside the system. Griffiths, http://arxiv.org/abs/1105.3932 (p30): "Sensible quantum descriptions can be constructed from the perspective of someone outside the system being considered." But, at least to me, it doesn't seem clear whether CH makes sense for an observer in the system. So the measurement is not solved, because we still have to define an observer outside the quantum system, with the quantum system being only a subsystem of the universe.

 

[craigi]

Perhaps it is possible for the pilot wave to go through both slits, but the particle to go through one, just as in Bohmian mechanics. However, because only one particle is involved, the pilot wave can be a local wave like an electromagnetic wave.

In the two particle case, this would be like EPR/Bell again, but then one might hope the nonmeasurable loophole comes into enable local hidden variables.

In Bohmian mechanics the CFD particle and the pilot wave are the electromagnetic wave and are non-local.

 

[stevendaryl]

Perhaps it is possible for the pilot wave to go through both slits, but the particle to go through one, just as in Bohmian mechanics. However, because only one particle is involved, the pilot wave can be a local wave like an electromagnetic wave.

In the two particle case, this would be like EPR/Bell again, but then one might hope the nonmeasurable loophole comes into enable local hidden variables.

Wow. That's an interesting option. I always dismissed the pilot wave as an actual wave, precisely because of the fact that for multiple particles, it evolves in 3N dimensional configuration space instead of 3 dimensional physical space. But maybe it's only a real wave for single particles? Hmm. I have to think whether that's possible.

It sounds like a pretty complicated hidden-variables theory, though. But it might just work.

 

[stevendaryl]

But since this is a thread on consistent histories, does anyone have thoughts on this issue?

CH makes sense for an observer outside the system. Griffiths, http://arxiv.org/abs/1105.3932 (p30): "Sensible quantum descriptions can be constructed from the perspective of someone outside the system being considered." But, at least to me, it doesn't seem clear whether CH makes sense for an observer in the system. So the measurement is not solved, because we still have to define an observer outside the quantum system, with the quantum system being only a subsystem of the universe.

Somehow, I still don't understand your point here. There is nothing special about the observer in CH, as far as I can see. The observer is subjectively special (in that the observer thinks of himself as special). But there is no special physics involved in the observer, unlike in interpretations where observation collapses the wave function.

 

[atyy]

Somehow, I still don't understand your point here. There is nothing special about the observer in CH, as far as I can see. The observer is subjectively special (in that the observer thinks of himself as special). But there is no special physics involved in the observer, unlike in interpretations where observation collapses the wave function.

But can the observer be in all frameworks?

 

[craigi]

But can the observer be in all frameworks?

The observer has property X from framework Y and property X' from framework Y'?

I think it has a hard enough time being in one framework, completely at least, nevermind them all.

Can it be partly in all of them? That would be omnipresence.

 

[DevilsAvocado]

The implication is

We close one of the slits \Rightarrow we know which slit it went through \Rightarrow no interference pattern. But it doesn't follow that the interference pattern would be destroyed if we knew in some other way which slit it went through.

Of course, some ancient symbols on a paper can't change anything happening in the real world, but if the physical consequence of these symbols are that we will know – with 100% certainty – that the particle we are about to send towards the double-slit will only pass through one slit*, this is will have the same effect as physically closing one slit, except in this case the 'closing' is theoretical.

*I haven't thought this through; but my guess is that it's enough to create a "Perfect Theory" that proves that the particle only goes through one slit (of course without any 'pilot influences'), to make the double-slit experiment 'break down', i.e. you are not required to tell exactly which slit ... I guess, maybe ...

But the nice thing about interference is that there are certain cases where the interference makes a 100% certain difference. In your case, there is a spot on the screen that has zero chance of a particle landing on it if both slits are open, and nonzero chance if only one slit is open (and vice-versa). So opening or closing a slit can potential make an observable difference without assuming anything about probabilities.

True.

My original statement was motivated by EPR and Bell's proof, and there I know (because Pitowsky wrote a paper about it) that nonmeasurability can avoid the conclusion. But the two slit experiment is not obvious to me. Maybe you're right, but I'll have to think about it some more.

Yes, it's a hard nut to crack, please let me know if you find any weakness in the argument.

 

[DevilsAvocado]

It does - but you can't know what it is. That's because its guided by this pesky pilot wave that has things like interference effects etc. That's why its a hidden variable theory. The particle is really common sense classical but it is intrinsically hidden.

Note I am not an expert on BM - that pretty close to the limit of my knowledge about it.

Yes, I'm not an expert on this either (i.e. same status as on the rest of the enchilada ), but I think that besides the pilot wave, Bohmian mechanics needs the quantum equilibrium hypothesis to be compatible to the Born rule (and experiments), as it otherwise would be a fully causal, deterministic model. I think...

 

[atyy]

Yes, it's a hard nut to crack, please let me know if you find any weakness in the argument.

Bell's proof simply fails for nonmeasurable local hidden variables. That doesn't mean they exist, but Bell's proof does not exclude them.

 

[DevilsAvocado]

You know that that's not strictly true, right?

We do still see an interference pattern from a single slit, but I think you know this already.

Yup, that's why I wrote "(in this setup)".

 

[DevilsAvocado]

But does the pilot wave have to be nonlocal in the double slit? After all, light already shows diffraction.

Perhaps it is possible for the pilot wave to go through both slits, but the particle to go through one, just as in Bohmian mechanics. However, because only one particle is involved, the pilot wave can be a local wave like an electromagnetic wave.

This has puzzled me. How is information 'transmitted' between the two 'pilot beams', to make the particle land on the screen in the right place? If a particle is going through one slit, accompanied by only one 'pilot beam', you won't get the correct result, do you?

 

[Doc Al]

This has puzzled me. How is information 'transmitted' between the two 'pilot beams', to make the particle land on the screen in the right place? If a particle is going through one slit, accompanied by only one 'pilot beam', you won't get the correct result, do you?

Isn't there but a single "pilot wave" that goes through both slits?

 

[DevilsAvocado]

Bell's proof simply fails for nonmeasurable local hidden variables. That doesn't mean they exist, but Bell's proof does not exclude them.

Do you mean completely non-measurable LVH (what use do we have of this? ), or something like my "spinning dices" in post #210?

 

[DevilsAvocado]

Isn't there but a single "pilot wave" that goes through both slits?

You mean like the wavefunction? It will 'automatically' generate a different 'pattern' with one vs. two slits?

 

[atyy]

Do you mean completely non-measurable LVH (what use do we have of this? ), or something like my "spinning dices" in post #210?

"Nonmeasurable" as in "probability distribution cannot be defined over the set". I don't know what use we have of it, but Bell's theorem doesn't exclude local hidden variables over which a probability distribution cannot be defined.

 

[craigi]

Isn't there but a single "pilot wave" that goes through both slits?

That's the normal terminology, but presumably it could be considered a superposition too.

 

[atyy]

This has puzzled me. How is information 'transmitted' between the two 'pilot beams', to make the particle land on the screen in the right place? If a particle is going through one slit, accompanied by only one 'pilot beam', you won't get the correct result, do you?

What I'm trying to say is that there is no Bell inequality violated in the single slit single particle experiment. So if there is nonlocality in this case, it is not proven by Bell's theorem. I can't really construct a case, I was just trying to sketch to stevendaryl what a construction might look like. But mainly the technical thing is no Bell inequality is violated by a single particle.

 

[stevendaryl]

But can the observer be in all frameworks?

I don't know what you mean by being "in" a framework. There might be one framework in which my spatial location is well-defined---I'm either in New York, or I'm in Georgia. In another framework, I might be in a superposition of both locations. I (that is, my body) is in both frameworks. Only one framework is of any use to me, so that's the one I use. But I'm in both of them.

The framework is a choice of which observables have definite values at which times. So I pick the framework that involves whatever observables I'm interested in. It's a subjective choice, it's not part of the physics.

 

[atyy]

I don't know what you mean by being "in" a framework. There might be one framework in which my spatial location is well-defined---I'm either in New York, or I'm in Georgia. In another framework, I might be in a superposition of both locations. I (that is, my body) is in both frameworks. Only one framework is of any use to me, so that's the one I use. But I'm in both of them.

The framework is a choice of which observables have definite values at which times. So I pick the framework that involves whatever observables I'm interested in. It's a subjective choice, it's not part of the physics.

Since you are in both frameworks, the choice of framework which is part of what you are should be in the framework. So in which framework do you make which subjective choice?

 

[stevendaryl]

Do you mean completely non-measurable LVH (what use do we have of this? ), or something like my "spinning dices" in post #210?

In measure theory, you have a set (the sample space, maybe? I forget the terminology) of possibilities. Then you have real numbers (the measures) associated with certain subsets of that set. There is no guarantee that every set of possibilities has an associated measure. (The Banach-Tarskii paradoxical partition of the sphere is an example of the use of nonmeasurable sets). Since Bell's theorem involves probabilities (or correlations, which are defined in terms of probabilities), the terms in the inequality may not be defined if you have nonmeasurable sets. So the proof fails because of a technicality.

 

[DevilsAvocado]

"Nonmeasurable" as in "probability distribution cannot be defined over the set". I don't know what use we have of it, but Bell's theorem doesn't exclude local hidden variables over which a probability distribution cannot be defined.

Wow, this is a crazy world... me just thought you could not find the dar*ed thing.

 

[atyy]

The observer has property X from framework Y and property X' from framework Y'?

I think it has a hard enough time being in one framework, completely at least, nevermind them all.

Can it be partly in all of them? That would be omnipresence.

I suspect this is why Griffiths only claims that CH makes sense for an observer outside the quantum system. But then that seems to me to leave the measurement problem unsolved.

Gell-Mann and Hartle do try to put the observer in all frameworks, but then they end up with one real history in each framework, and the real histories are not connected, and they have to introduce negative probabilities.