Quantum Mechanics without Measurement

[kith]

However, I believe it is not possible to explain EPR-Bell experiments outcome, using only classical logic and classical probability.

If the statement A is true in history H₁ and the statement B is true in history H₂ the statement A AND B may be meaningless because the histories themself are not compatible. In this sense, you could say that Griffiths abandons classical logic but I don't think this is a very accurate description of the situation.

Like stevendaryl, I don't see the quotes you gave regarding Bell's theorem as controversial. The "third way" is simply not to introduce hidden variables. The only thing in CH which could be called a hidden variable is which history belongs to our world. But such a history is a history of observations and doesn't include simultaneous sharp values of incompatible observables.

/edit: As far as the measurement problem is concerned, it is not obvious to me if and how CH eliminates measurements as primitives but I haven't read the paper yet

 

[atyy]

Regarding "classical logic": would it be it would be more accurate to say, like Devils Avocado's comment above, that the usual rules of probability to classical reality are not applied?

Is Bell's theorem meaningless in CH simply because P(A,B,a,b), where A,B are measurement outcomes and a,b are measurement settings, is declared not to exist? A,B,a,b are all classical realities, and we can certainly form P(A,B,a,b) over them without any problem. Or does CH obtain locality by some other means?

 

[Jilang]

It would appear that if you can live with negative probabilities there should be no problem. This is the only concession to realism that is really necessary. Rather than meaningless perhaps it would be better to think of the amplitude as being imaginary, so the probability is negative. Of course we measure that as a zero hence the violation of the inequality.
http://drchinese.com/David/Bell_Theorem_Negative_Probabilities.htm

 

[DevilsAvocado]

@atyy, kith, Jilang

I think the key to all this is:

http://quantum.phys.cmu.edu/CQT/chaps/cqt24.pdf]This[/PLAIN] seems a rather high price to pay just to have a theory which is more “classical” than ordinary quantum mechanics.

And the "high price" is to abandon either locality or realism, which Griffiths obviously is not willing to do.

Problem: No one in this thread seems to be sure on how Griffiths actually preserves this "new" local realism.

Hint: Since Bell was nominated for the Nobel Prize for 'destroying' local realism, I'm pretty sure Griffiths now will get the Nobel Prize for 'restoring' the darned thing, i.e. if we just can get hold of the actual proof...

To-Do: Someone must email Zeilinger & Aspect, and warn them that their experiments will stop working as soon as we have found Griffiths proof!

 

[atyy]

@atyy, kith, Jilang

I think the key to all this is:
And the "high price" is to abandon either locality or realism, which Griffiths obviously is not willing to do.

Problem: No one in this thread seems to be sure on how Griffiths actually preserves this "new" local realism.

Hint: Since Bell was nominated for the Nobel Prize for 'destroying' local realism, I'm pretty sure Griffiths now will get the Nobel Prize for 'restoring' the darned thing, i.e. if we just can get hold of the actual proof...

To-Do: Someone must email Zeilinger & Aspect, and warn them that their experiments will stop working as soon as we have found Griffiths proof!

Regardless of whether CH is local, I think it is nonrealistic because there are multiple incompatible frameworks, and you can choose anyone of these frameworks to describe "reality". To me the question is whether CH is nonlocal and nonrealistic, or local and nonrealistic. And if it is the latter, why exactly does it evade the Bell theorem? Is it just that P(A,B,a,b) where A,B are classical measurement outcomes and a,b are classical measurement choices?

 

[bhobba]

I think it is nonrealistic because there are multiple incompatible frameworks, and you can choose anyone of these frameworks to describe "reality".

They consider it realistic, but have their own peculiar version of realism - weak property realism:
http://www.siue.edu/~evailat/pdf/qm12.pdf

Things like this make me laugh - like I say its defining your way out of problems. In doing that I believe it complicates things unnecessarily.

I don't want to be too hard on it however - I have Griffiths book - Consistent Quantum Theory - and its actually quite good. Certainly an excellent source for coming to grips with some of these issues and seeing how CH handles it.

Thanks
Bill

 

[atyy]

According to Laloe http://arxiv.org/abs/quant-ph/0209123 (p86, p50), Griffiths's version of CH is local because it rejects counterfactual definiteness, which is an assumption in the proof of Bell's theorem. But if I reject counterfactual definiteness, isn't even dBB local, since the Bell inequality doesn't exist?

 

[Demystifier]

But if I reject counterfactual definiteness, isn't even dBB local, since the Bell inequality doesn't exist?

No. First, you can see that dBB is non-local even without Bell inequality. Indeed, Bell FIRST noted that dBB is non-local, and only AFTER discovered his inequality, as a tool to see non-locality of QM without referring to dBB.
Second, I don't see how one might accept dBB and reject counterfactual definiteness at the same time.

 

[Demystifier]

Hint: Since Bell was nominated for the Nobel Prize for 'destroying' local realism, I'm pretty sure Griffiths now will get the Nobel Prize for 'restoring' the darned thing, i.e. if we just can get hold of the actual proof...

If Bell was nominated for the Nobel Prize, it was because he made a new measurable prediction, which was tested by an actual experiment. I don't think that it was the case with Griffiths.

Speaking of nominations for the Nobel Prize, is there an official site where one can see who was nominated and when?

 

[craigi]

According to Laloe http://arxiv.org/abs/quant-ph/0209123 (p86, p50), Griffiths's version of CH is local because it rejects counterfactual definiteness, which is an assumption in the proof of Bell's theorem. But if I reject counterfactual definiteness, isn't even dBB local, since the Bell inequality doesn't exist?

The whole point of dBB is that it is counterfactual definite. If you take dBB and remove counterfactual definiteness then all you're left with is the pilot wave. At this stage you haven't chosen locality or objective realism yet. You could choose either or both but you certainly don't have dBB anymore.

 

[DevilsAvocado]

Regardless of whether CH is local, I think it is nonrealistic because there are multiple incompatible frameworks, and you can choose anyone of these frameworks to describe "reality".

I have to be honest and admit that I don't understand CH well enough to judge if this is the case or not. However if CH is nonrealistic, then Griffiths has paid that "high price" that he rejects in his book and this, to me, makes this story even more inconsistent...

But if we assume that CH is nonrealistic, could you explain – step by step – what happens in an EPR-Bell experiment, according to CH and multiple incompatible frameworks?

To me the question is whether CH is nonlocal and nonrealistic, or local and nonrealistic.

If CH is nonlocal and nonrealistic... Griffiths has paid the "high price" twice, and then maybe we are beyond inconsistent storytelling...

Regarding "classical logic": would it be it would be more accurate to say, like Devils Avocado's comment above, that the usual rules of probability to classical reality are not applied?

To avoid any confusion, maybe I should explain what I mean by "classical probability" (in this allegory):

• Take a coin, and let it spin at very high speed on both vertical and horizontal axes.
  
  
• Initial conditions are completely unknown and the outcome is regarded as 100% random.
  
  
• Send the coin toward a metal plate with vertical and horizontal slit +.
  
  
  [*]The coin will always go through the vertical or horizontal slit with a 50/50 chance.
  
  
  [*]Now we introduce a second coin, with exactly the same properties, and send both coins in opposite direction towards two space-like separated metal plates with a vertical/horizontal slit +.
  
  
  [*]When we check the outcome, the two coins are always correlated, i.e. if they have gone through the same orientation they show the same face, if they have gone through the opposite orientation they show the opposite face.
  
  
  [*]We make the conclusion that "something magical" happened at the source when we created the spin of the two coins, that make them act randomly but correlated.
  
  
  [*]We also make the conclusion that there is no "spooky action at a distance" going on (the source is the explanation) and also make the conclusion that these coins are real, it's just that with current technology we can't inspect all their properties.
  

This is the "classical probability", however now we change the setup:

• We modify the metal plates to tilt randomly between 0° = + and 45° = X, and repeat the experiment.
  
  
  [*]To our surprise it turns out that when metal plates have the same tilting, we get exactly the same results as in previous setup. But when metal plates have the different tilting, we get a random correlation of 50% head or tail, and there is no explanation on how the two space-like separated coins 'knew' they were going through different orientations, none whatsoever, and the "common source explanation" can't save us this time.
  
  
  [*]Now an extensive debate starts – whether the coins are real or not, or if there is some non-local influence on the coins – which is still ongoing...
  

This would be "non-classical probability".

 

[DevilsAvocado]

If Bell was nominated for the Nobel Prize, it was because he made a new measurable prediction, which was tested by an actual experiment. I don't think that it was the case with Griffiths.

Ehh... it was meant more like a 'joke'... sorry, my silly humor again...

Speaking of nominations for the Nobel Prize, is there an official site where one can see who was nominated and when?

I don't think so, they are very secretive in the committee and nominations are kept secret for 50 years.
http://www.nobelprize.org/nomination/physics/

But some (old) data are available in the nomination database (not Physics though??):
http://www.nobelprize.org/nomination/archive/

But there is always 'talk' and I take it for granted that Jeremy Bernstein somehow has gotten the correct information.
(page 13)
http://arxiv.org/abs/1007.0769

 

[kith]

And the "high price" is to abandon either locality or realism [...]

That's not what he says in your quote. He says if we want to construct a hidden variables theory, Bell tells us that we have to embrace either non-locality or backwards causation. His "solution" is simple: like Bohr, he doesn't want to construct a hidden variables theory in the first place. So what he rejects is EPR realism. Calling his theory realistic may be sensible from another point of view but this is certainly not EPR realism which is what Bell's theorem is about.

/edit: I also wrote a statement about locality here but actually, I think this should be discussed in an own thread.

 

[craigi]

I think a lot of confusion arises because there isn't much clarity about the terms realism and locality.

Do we not just consider CH to have the same types of locality and realism as MWI?

Locality is preserved, though splitting is global and instantaneous.

Realism is preserved in that all observers in the same framework have the same reality.

These concepts are compatible with those which apply to other interpretations too, since they are not concerned with splitting, worlds or frameworks, though in those interpretations it is not possible for both to preserved.

If we follow these, I don't see how Bell Inequality can apply, because there is no hidden variable or information transfer.

Is it not true that in order to calculate the Bell Inequality in this context, we would incorporate quantities outside of the universe?

I don't see how there is a modification to the rules of logic here, simply a clarification that in order to generate inference by combining statements, they must pertain to the same universe.

Not of this undermines the significance of Bell's work, but it's applicability was to information transfer via hidden variables, which neither the MWI nor CH are concerned with.

 

[DevilsAvocado]

That's not what he says in your quote. He says if we want to construct a hidden variables theory, Bell tells us that we have to embrace either non-locality or backwards causation.

And this shows that Griffiths has not gotten the complete picture, since there are other options for non-realism than backwards causation. Shouldn't a professor, claiming to have a new solution to this problem, be better informed?

His "solution" is simple: like Bohr, he doesn't want to construct a hidden variables theory in the first place. So what he rejects is EPR realism. Calling his theory realistic may be sensible from another point of view but this is certainly not EPR realism which is what Bell's theorem is about.

Most of us doesn't care what Griffiths wants, we're more interested in what he can prove (which seems to be nothing, this far). Introducing something as "almost real" and then name this new invention "consistent", would generally be considered a joke.

I don't know how many times I have asked this question:
Could you please explain – step by step – what happens in an EPR-Bell experiment, according to CH and the new "Almost-realism"?

(Even if Griffiths don't acknowledge EPR realism, I sure hope he accept experimental outcomes...)

 

[DevilsAvocado]

Is it not true that in order to calculate the Bell Inequality in this context, we would incorporate quantities outside of the universe?

I don't see how there is a modification to the rules of logic here, simply a clarification that in order to generate inference by combining statements, they must pertain to the same universe.

I could be wrong, but my firm belief is that if we incorporate "stuff" outside this universe to solve scientific problems inside this universe, we have to move to the Vatican and finish our thesis inside these walls.

It's probably even possible to prove the existents of the flying Centaur, if we just have the option to throw any unpleasant data in the "I-Don't-Like-Bin", and just toss it out of this universe.

But I could be wrong, of course...

[Note: strong irony warning]

 

[kith]

And this shows that Griffiths has not gotten the complete picture, since there are other options for non-realism than backwards causation. Shouldn't a professor, claiming to have a new solution to this problem, be better informed?

I'm a bit puzzled by your fixation on this. Why exactly do you think that Griffiths thinks something about Bell's theorem needs to be "solved"? In everything I have read from him, Griffiths says that it doesn't make sense to search for hidden variable theories because Bell's theorem tells us that they are ugly. This is simply the mainstream view. I don't know what he says about the definition of the terms "locality" and "realism", but this is just a semantic sidenote and really not the core issue of this thread.

What Griffiths wants to solve (and what caused stevendaryl to open this thread) is the problem that textbooks assign a special role to the concept of measurement and make it seem like QM can't be used to describe the measurement process.

 

[craigi]

And this shows that Griffiths has not gotten the complete picture, since there are other options for non-realism than backwards causation. Shouldn't a professor, claiming to have a new solution to this problem, be better informed?



Most of us doesn't care what Griffiths wants, we're more interested in what he can prove (which seems to be nothing, this far). Introducing something as "almost real" and then name this new invention "consistent", would generally be considered a joke.

I don't know how many times I have asked this question:
Could you please explain – step by step – what happens in an EPR-Bell experiment, according to CH and the new "Almost-realism"?

(Even if Griffiths don't acknowledge EPR realism, I sure hope he accept experimental outcomes...)

I'm not sure what it about Griffiths' interpretation that's bugging you so much, but none of the interpretations prove any new physics. That is not their purpose. Their goal is epistemological rather than ontological. Some, including myself, believe that an interpretation could hint at something of ontological value, but this hasn't happened yet.

Of course Griffiths understands the EPR experiments very well. He is one of the leading experts in the field of QM and by no means denies the results of the experiments, which are not in the slightest inconsistent with his interpretation.

 

[craigi]

I could be wrong, but my firm belief is that if we incorporate "stuff" outside this universe to solve scientific problems inside this universe, we have to move to the Vatican and finish our thesis inside these walls.

It's probably even possible to prove the existents of the flying Centaur, if we just have the option to throw any unpleasant data in the "I-Don't-Like-Bin", and just toss it out of this universe.

But I could be wrong, of course...

[Note: strong irony warning]

That's the point, we don't incorporate stuff outside of this universe and that is where part of the Bell Inequality calculation lies, under the CH interpretation. I can understand a reactionary attitude to this terminology, I don't like it either, because it does sound like something from science fiction, or perhaps as you suggest, theology. You can just consider it, stuff that does not happen.

All of the interpretations throw out stuff they don't like in favour of stuff that they do, but none of these things are tangible physical things, purely concepts that we use to try make sense of them.

 

[DevilsAvocado]

In everything I have read from him, Griffiths says that it doesn't make sense to search for hidden variable theories because Bell's theorem tells us that they are ugly. This is simply the mainstream view.

Agreed, a lot of things don't make sense. Regarding ugly HV, I think that is something you have to confront Demystifier, or maybe atyy with, personally I'm agnostic.

I don't know what he says about the definition of the terms "locality" and "realism", but this is just a semantic sidenote and really not the core issue of this thread.

Okay, "semantic sidenote" is fine by me, with the reservation that if an interpretation can't handle Bell's theorem it's basically dead, and if I'm not mistaken, that's also what stevendaryl said last time he posted.

 

[stevendaryl]

I'm not sure what it about Griffiths' interpretation that's bugging you so much, but none of the interpretations prove any new physics. That is not their purpose. Their goal is epistemological rather than ontological. Some, including myself, believe that they could something of ontological value, but this hasn't happened yet.

But I think the Devil's Avocado wants (and I couldn't find it by googling) is a demonstration of how CH works by applying it to the EPR problem. What are the possible sets of consistent histories, and what would be an example of an inconsistent set?

It's a little complicated to see how to apply the technical definition, because the notion of "consistency" involves time evolution of projection operators. But once you involve macroscopic objects like measuring devices, we don't have a comprehensible expression for the time evolution (because it involves an ungodly number of particles).

Let me just think out loud:

My guess would be that a (simplified, approximate) history would have 6 elements:

1. Alice's detector orientation. (\theta_A)
2. Bob's detector orientation. (\theta_B)
3. A spin state for Alice's particle immediately before detection. (\sigma_A)
4. A spin state for Bob's particle immediately before detection. (\sigma_B)
5. Alice's result (spin up or spin down) (R_A)
6. Bob's result (spin up or spin down) (R_B)

So a history is a vector of six elements:
\langle \theta_A, \theta_B, \sigma_A, \sigma_B, R_A, R_B \rangle

To apply Griffiths' approach, we need to first figure out which collections of 6-tuples are consistent. What I think is true is that any macroscopic state information is consistent, in Griffiths' sense (although it might have probability zero). So whatever rules for consistent histories should only affect the unobservable state information (the particle spins).

 

[DevilsAvocado]

But I think the Devil's Avocado wants (and I couldn't find it by googling) is a demonstration of how CH works by applying it to the EPR problem. What are the possible sets of consistent histories, and what would be an example of an inconsistent set?

Thanks a lot Steven, finally! :thumbs:

I'll study your explanation and get back.

 

[kith]

I have now read Griffiths' paper and I am not sure what to think of it.

Firstly, my previous notion of one histroy being the "right" one isn't what he has in mind (he explicitly acknowledges different, mutually exclusive histories to be equally valid in the middle of section VI). So the catch phrase "Many worlds without the many worlds" doesn't seem appropriate to me.

Now what does he do? In section V, he uses a toy model to analyze the measurement process. This analysis seems conceptually not very different from what Ballentine or a MWI person would do.

In section VI, he introduces his families of histories to explore which assumptions about properties before performing a measurement can be combined consistently. A history is a succession of statements about the system, while a family of histories is a set of possible histories. Although within one family, the realized outcome of an experiment may be only compatible with one history, different views about the possible intermediate states corresponding to different families are possible. As mentioned above, he thinks that all of these families / points of view about intermediate states should be considered equally valid or "real". Therefore, CH seems more lika a meta interpretation to me.

Now what I don't understand is the relevance of the existence of more than one family of histories to the measurement problem. For example, his analysis of the measurment process takes place before he even introduces them.

 

[stevendaryl]

Thanks a lot Steven, finally! :thumbs:

I'll study your explanation and get back.

I haven't explained anything. I was trying to publicly work out what the CH description of EPR might look like. I'm not finished, because I'm stuck on figuring out which collections of histories are "consistent" in Griffiths' sense.

 

[stevendaryl]

Now what I don't understand is the relevance of the existence of more than one family of histories to the measurement problem. For example, his analysis of the measurement process takes place before he even introduces them.

The way I understand it is that we choose to use a family of histories in which macroscopic objects (e.g., measuring devices) have definite macroscopic states. But one could instead choose a different family of histories, where macroscopic objects are in macroscopic superpositions. The latter family would be pretty much useless for our purposes, but would be perfectly fine as far as the Rules of Quantum Mechanics (and the CH interpretation) are concerned. So CH makes it a matter of usefulness that we treat measuring devices specially--it's a choice on our part, rather than being forced on us by the physics. So to me it seems very much like Copenhagen, except that the "wave function collapse caused by measurement" is no longer considered a physical effect, but is instead an artifact of what we choose to analyze.

I think that in some ways, CH is like Copenhagen, and in other ways, it's like MWI, although there are two completely different notions of "alternatives" considered at the same time. Within a particular family of histories, there are alternative histories. So that's one notion of alternative, and it's the one that people normally think of when they think of many worlds. But there is a second kind of alternative, which is the choice of which family to look at.

 

[DevilsAvocado]

Here's a first note that maybe could help you to get further:

My guess would be that a (simplified, approximate) history would have 6 elements:

1. Alice's detector orientation. (\theta_A)
2. Bob's detector orientation. (\theta_B)
3. A spin state for Alice's particle immediately before detection. (\sigma_A)
4. A spin state for Bob's particle immediately before detection. (\sigma_B)
5. Alice's result (spin up or spin down) (R_A)
6. Bob's result (spin up or spin down) (R_B)

So a history is a vector of six elements:
\langle \theta_A, \theta_B, \sigma_A, \sigma_B, R_A, R_B \rangle

If you have definite spin in 3 & 4, everything I know tells me that the only way to handle 5 & 6 is by non-locality, since what settles the level of correlations in 5 & 6 is the relative angle between 1 & 2.

 

[DevilsAvocado]

I haven't explained anything. I was trying to publicly work out what the CH description of EPR might look like. I'm not finished, because I'm stuck on figuring out which collections of histories are "consistent" in Griffiths' sense.

It's okay, your post is definitely a progress compared to what we (including myself) have produced in this thread lately.

 

[atyy]

That's not what he says in your quote. He says if we want to construct a hidden variables theory, Bell tells us that we have to embrace either non-locality or backwards causation. His "solution" is simple: like Bohr, he doesn't want to construct a hidden variables theory in the first place. So what he rejects is EPR realism. Calling his theory realistic may be sensible from another point of view but this is certainly not EPR realism which is what Bell's theorem is about.

/edit: I also wrote a statement about locality here but actually, I think this should be discussed in an own thread.

But is it true that not having hidden variables is enough to make quantum mechanics local? Gisin http://arxiv.org/abs/0901.4255 (Eq 2) argues that the wave function itself can be the "hidden variable", but a nonlocal one. Laloe http://arxiv.org/abs/quant-ph/0209123 (p50) says it is still unsettled whether quantum mechanics is itself local.

 

[kith]

The way I understand it is that we choose to use a family of histories in which macroscopic objects (e.g., measuring devices) have definite macroscopic states. But one could instead choose a different family of histories, where macroscopic objects are in macroscopic superpositions.

Let me check if I get you right: In order to describe measurements, we use a family with an observable whose eigenstates are product states of system+apparatus. It would be equally valid to use another family with an observable which is incompatible with the first one. Such an observable could have entangled states of system+apparatus as eigenstates. In the second family, a measurement wouldn't yield a definite state but a state with different probabilities for macroscopic superpositions. Do you agree with this so far?

 

[kith]

But is it true that not having hidden variables is enough to make quantum mechanics local? Gisin http://arxiv.org/abs/0901.4255 (Eq 2) argues that the wave function itself can be the "hidden variable", but a nonlocal one. Laloe http://arxiv.org/abs/quant-ph/0209123 (p50) says it is still unsettled whether quantum mechanics is itself local.

I don't really have an informed opinion on this. QM without simultaneous hidden variables still allows for different ontologies and I think it depends mostly on them whether we say it is local or not.