Quantum Mechanics without Measurement

[DevilsAvocado]

It's just the classical world.

Definition please, where is the cut?

 

[craigi]

Definition please, where is the cut?

It's everything that you don't find in a superposition of states. It that controversial?

 

[atyy]

The environment is within the universe already. It's just the classical world.

Quantum systems within the universe lose coherence though interaction with the classical world.

How can there be a classical world in CH? If it is a fundamental concept then the measurement problem is not solved. If it is not fundamental, how does the classical world emerge in CH?

 

[craigi]

How can there be a classical world in CH? If it is a fundamental concept then the measurement problem is not solved. If it is not fundamental, how does the classical world emerge in CH?

It's not a fundamental concept in CH. It emerges through the process of decoherence.

This is in the literature, right?

I'm not, by any means an authorative source on CH, I'm just trying to understand it, like yourselves. It's probably much better to look this stuff up, than ask me. I'm concerned that I'm going to end up misleading you, if I haven't already.

 

[DevilsAvocado]

It's everything that you don't find in a superposition of states.

You mean like a measurement apparatus?

I could be wrong, but to my understanding every electron in every atom that makes the measurement apparatus, is in a superposition. So where is the cut then?

I want an exact number, they usually work best in scientific formulations.

 

[bhobba]

The environment is within the universe already. It's just the classical world. Quantum systems within the universe lose coherence though interaction with the classical world.

Errr.

Not quite.

The environment is a quantum system with a large degree of freedom another quantum system interacts and becomes entangled with. By the process of tracing over that environment, and statistical averaging over that large degree of freedom (eg you have a large number of photons with uncorrelated phase), coherence is lost and the classical everyday world APPARENTLY emerges.

Thanks
Bill

 

[craigi]

Errr.

Not quite.

The environment is a quantum system with a large degree of freedom another quantum system interacts and becomes entangled with. By the process of tracing over that environment, and statistical averaging over that large degree of freedom (eg you have a large number of photons with uncorrelated phase), coherence is lost and the classical everyday world APPARENTLY emerges.

Thanks
Bill

Agreed, but help me out here. How is what I said wrong?

 

[atyy]

@craigi: Let me go and read more about decoherence in CH.

@stevendaryl: If we agree that at a fundamental level with no observers all frameworks occur but don't interact, such that for anyone universe we can ignore all frameworks except one, then don't we have a problem? The problem is that a single framework is just a classical stochastic process, and since this is at the fundamental level we can consider one history to be real. Thus we have a classical deterministic process. So we have classical reality. How can one get quantum mechanics from classical reality, unless one has a nonlocal hidden variables model?

 

[craigi]

If we agree that at a fundamental level with no observers all frameworks occur but don't interact, such that for anyone universe we can ignore all frameworks except one, then don't we have a problem? The problem is that a single framework is just a classical stochastic process, and since this is at the fundamental level we can consider one history to be real. Thus we have a classical deterministic process. So we have classical reality. How can one get quantum mechanics from classical reality, unless one has a nonlocal hidden variables model?

You're misinterpreting this. I think you should follow through this:

http://en.wikipedia.org/wiki/Consistent_histories]However,[/PLAIN] Griffiths[4] holds the opinion that asking the question of which set of histories will "actually occur" is a misinterpretation of the theory; histories are a tool for description of reality, not separate alternate realities.

 

[kith]

If we agree that at a fundamental level with no observers all frameworks occur but don't interact, such that for anyone universe we can ignore all frameworks except one, then don't we have a problem? The problem is that a single framework is just a classical stochastic process, and since this is at the fundamental level we can consider one history to be real. Thus we have a classical deterministic process. So we have classical reality.

Regardless of the exact meaning of "classical reality" such a notion surely includes simultaneous sharp values for all observables. Histories in CH don't have this.

Also your use of terminology seems odd to me. What does it even mean for different frameworks -which are different ways of talking about what happens in the system- to "occur" or to "interact"?

 

[DevilsAvocado]

OK let's leave out the negative probabilities then. Working through the example in the link you could consider that each of the eight scenarios are equally likely for the particle up until the point it's measured. At that point scenarios (1) and (8) are wiped out by the process of measurement as they can never be measured with that result. The probability of measuring a coincidence would then be 6x.333/8. Which is 0.25.

That doesn't work. It's quite easy to see if we use a binary representation in "Bell's ABC":
(and excludes decimal 0 & 7 because this will never ever work)

From this picture we see two groups that are XOR mirrored, i.e. 001 XOR 111 = 110 (or decimal 1 XOR 7 = 6). This means the "Yellow Group" above is an inverted mirror of the "Purple Group", regarding combinations and "hits".

To get a value like 25% we need one "hit" (i.e. same binary value) and three "misses" (i.e. different binary value). Naturally we must make four runs to get a value like 25%, and since we don't know the settings in advance, these four combinations must be able to handle all three AB, AC & BC settings.

Let's start by picking the first three in order, i.e. decimal 1 to 3. Immediately we see that there are no problems in the "Yellow Group", it's safe regarding all possible combinations, i.e. one "hit" and two "misses" for all three AB, AC & BC settings.

So let's pick the forth combination.

Now problems start. We know we can't pick another value from the "Yellow Group", since we are then guaranteed to get doublets on "hits" (2/4 = 50%). And we know that the "Purple Group" is an inverted mirror regarding combinations, and that it doesn't matter if it's 11 or 00, both are "hits".

Not looking good...

Let's check to be sure: Our fourth combination, decimal 4, fail for setting BC with "hits" in both 3 & 4.

Let's try decimal 5 as our fourth combination: This fails as well, but now for setting AC with "hits" in both 2 & 5.

Let's try decimal 6 as our fourth combination: This fails as well, but now for setting AB with "hits" in both 1 & 6.

No options left = impossible!


(I believe you could make a gifted 10-yearold understand this quite simple logic, and this makes it even more astonishing that a physics professor doesn't...)

 

[DevilsAvocado]

Regardless of the exact meaning of "classical reality" such a notion surely includes simultaneous sharp values for all observables. Histories in CH don't have this.

Well, if you do not have anything there from the beginning – including functions, "Little Green Men", or whatever – your interpretation is non-realistic. Period.

And I do hope that you understand, from my previous post, that anything preexisting in EPR-Bell experiments, can't survive empirical outcomes without non-locality.

It doesn't matter if you call it "almost real" or whatever, since you only provides words, it will only be words without any scientific meaning.

This would perhaps be okay for a "normal interpretation" – that does not contradict QM – but in this case it's very inappropriate.

 

[kith]

Well, if you do not have anything there from the beginning – including functions, "Little Green Men", or whatever – your interpretation is non-realistic. Period.

And I do hope that you understand, from my previous post, that anything preexisting in EPR-Bell experiments, can't survive empirical outcomes without non-locality.

I don't agree with what you wrote but on the other hand I don't claim that CH is realistic or local in the first place. I don't see a problem with CH being non-realistic and non-local because its main goal is to not use special physics to describe the measurement process while sticking as close to the Copenhagen approach as possible. Some people think that CH essentially is Copenhagen.

 

[craigi]

Well, if you do not have anything there from the beginning – including functions, "Little Green Men", or whatever – your interpretation is non-realistic. Period.

And I do hope that you understand, from my previous post, that anything preexisting in EPR-Bell experiments, can't survive empirical outcomes without non-locality.

It doesn't matter if you call it "almost real" or whatever, since you only provides words, it will only be words without any scientific meaning.

This would perhaps be okay for a "normal interpretation" – that does not contradict QM – but in this case it's very inappropriate.

"anything"?

but we know the wavefunction to be defined "there" in local, but non-realistic interpretations. I'm not being pedantic here. I think it's important to distinguish between what can and can't be in this "anything", in order to understand the concept of local realism.

Local realism and the Bell tests aren't concerned with pre-existing "anything". They're concerned with objective pre-existing values for measurable quantities.

 

[DevilsAvocado]

I don't agree with what you wrote but on the other hand I don't claim that CH is realistic or local in the first place. I don't see a problem with CH being non-realistic and non-local

And this is absolutely 100% okay, no problem!

Much more troublesome are statements like this [my bolding]:

http://arxiv.org/abs/0908.2914]The[/PLAIN] analysis in this paper implies that claims that quantum theory violates “local realism” are misleading.

http://quantum.phys.cmu.edu/CHS/quest.html]How[/PLAIN] is the EPR paradox handled in consistent histories?

Einstein, Podolsky, and Rosen (EPR) in a celebrated paper [2] showed that by measuring the property of some system A located far away from another system B one can, under suitable conditions, infer something about the system B. By itself the possibility of such an indirect measurement is not at all surprising, as one can see from the following example. Colored slips of paper, one red and one green, are placed in two opaque envelopes, which are then mailed to scientists in Atlanta and Boston. The scientist who opens the envelope in Atlanta and finds a red slip of paper can immediately infer, given the experimental protocol, the color of the slip of paper contained in the envelope in Boston, whether or not it has already been opened. There is nothing peculiar going on, and in particular there is no mysterious influence of one "measurement" on the other slip of paper. The quantum mechanical situation considered by EPR is more complicated than indicated by this example in that one has the possibility of measuring more than one property of system A and also considering more than one property of system B. However, when one does a proper analysis [3], the conclusion is just the same as in the "classical" case of the colored slips of paper.

This last sentence is not only terribly wrong, but extremely ill-informed, since it completely neglects everything discovered since 1935. Misleading is an understatement.

I can provide more "insinuation quotes", but I think you get the picture.
This kind of "vague claims", without a single shred of evidence, is definitely not okay.

 

[DevilsAvocado]

but we know the wavefunction to be defined "there" in local, but non-realistic interpretations.

Yes, there are different interpretations on the wavefunction as ontic vs. epistemic. However for any ontic wavefunction you will need non-locality, to make it all work.

Local realism and the Bell tests aren't concerned with pre-existing "anything". They're concerned with objective pre-existing values for measurable quantities.

True, but I thought it would be kind of 'obvious', or else; how do you define subjective pre-existing values??

 

[craigi]

True, but I thought it would be kind of 'obvious', or else; how do you define subjective pre-existing values??

Cool. Just wanted to make sure that you weren't taking non-locality too far. Subjective, would be different for different for different observers.

Yes, there are different interpretations on the wavefunction as ontic vs. epistemic. However for any ontic wavefunction you will need non-locality, to make it all work.

That may be true of dBB and VN, but are you sure that's true of all interpretations? What about the MWI and Cosmological Interpretation?

 

[DevilsAvocado]

Subjective, would be different for different for different observers.

Do you really claim that if Alice is looking at the Moon it's a sphere, and when Bob is doing the same it is a cube, and both should be regarded equally real, and this should be understood as a more "natural" and "classical" version of QM, that pays a "lesser price" than non-locality??

... this is getting weirder and weirder ...

What about the MWI and Cosmological Interpretation?

Same thing, very few would accept gazillion universes as classical local realism, and most regard it as a much higher price than non-locality.

At least one of these three options has to be abandoned to be compatible with QM theory & experiments:

• Locality
• Realism
• Free will*

*I.e. give up our freedom to choose (random) settings, which would conduce to Superdeterminism.

Or, you could create an interpretation that throws unwarranted data out of our observable universe to be gone forever, however classical local realism is a dead parrot in all cases. There's always a price to pay – make your pick.

 

[bhobba]

Some people[/url] think that CH essentially is Copenhagen.

What I think is really meant is Copenhagen done right - in fact Griffiths says exactly that.

It fixes up a few blemishes in Copenhagen such as exactly what is an observation by doing away with them and replacing it with the idea of a history which is rigorously defined by projections.

As I have mentioned a number of times to me its more complicated than necessary to achieve that goal.

Thanks
Bill

 

[Demystifier]

That may be true of dBB and VN, but are you sure that's true of all interpretations? What about the MWI and Cosmological Interpretation?

MWI is local, but not in the usual 3 or 4 dimensional space. It is local in an abstract higher dimensional configuration or Hilbert space. But it does not make MWI better than dBB, because in this higher dimensional configuration space, dBB is local too.

In the usual 3 or 4 dimensional space, MWI is neither local nor non-local, because in this space MWI does not even exist.

 

[stevendaryl]

MWI is local, but not in the usual 3 or 4 dimensional space. It is local in an abstract higher dimensional configuration or Hilbert space. But it does not make MWI better than dBB, because in this higher dimensional configuration space, dBB is local too.

In the usual 3 or 4 dimensional space, MWI is neither local nor non-local, because in this space MWI does not even exist.

But dBB exists as a nonlocal 3-dimensional theory. The many-particle wave function \Psi happens to be a function on configuration space, but as far as dBB is concerned, it's just a mathematical object that you compute from initial conditions. Then you use this mathematical object to predict the motion of particles in ordinary 3D space. So it ends up being a (strange) 3D theory.

The thing that's a little weird (I should say, one of the many things that are a little weird) about dBB is that the wave function is not uniquely determined by conditions in the "real" world. Schrodinger's equation determines how the wave function evolves, given its value at t=0, but doesn't say what the value at t=0 is. I guess you could do something like Bayesian analysis to figure out, retroactively, what the most likely starting wave function was.

 

[craigi]

Do you really claim that if Alice is looking at the Moon it's a sphere, and when Bob is doing the same it is a cube, and both should be regarded equally real, and this should be understood as a more "natural" and "classical" version of QM, that pays a "lesser price" than non-locality??

I don't make any such claim, because I'm not supporting or opposing any particular interpretation. Certainly, under the Cosmological Interpretation, a Bob looking at a cubic moon, if possible, which we should imagine that it is, does exist. Though we'd expect it to be highly improbable. Does that make probable scenarios "more real" than improbable ones? Well that really depends what you mean by "more real", but we should be careful not to use it as a term to support prejudices. Without a doubt, we've all experienced improbable situations, that we wouldn't consider to be "not real".

Same thing, very few would accept gazillion universes as classical local realism, and most regard it as a much higher price than non-locality.

At least one of these three options has to be abandoned to be compatible with QM theory & experiments:

• Locality
• Realism
• Free will*

*I.e. give up our freedom to choose (random) settings, which would conduce to Superdeterminism.

I'd wouldn't say that you even need superdeterminsm to doubt free will, but I understand your point.

Personally, I don't have a favourite pair from that list, but for me, it's the most fascinating thing in physics that removing anyone of the three can result in mathematially equivalent descriptions of nature.

Where do you feel that Popper's Experiment fits into all of this?

 

[stevendaryl]

I don't make any such claim, because I'm not supporting or opposing any particular interpretation. Certainly, under the Cosmological Interpretation, a Bob looking at a cubic moon, if possible, which we should imagine that it is, does exist. Though we'd expect it to be highly improbable. Does that make probable scenarios "more real" than improbable ones? Well that really depends what you mean by "more real", but we should be careful not to use it as a term to support prejudices. Without a doubt, we've all experienced improbable situations, that we wouldn't consider to be "not real".

I'd wouldn't say that you even need superdeterminsm to doubt free will, but I understand your point.

Personally, I don't have a favourite pair from that list, but for me, it's the most fascinating thing in physics that removing anyone of the three can result in mathematially equivelent descriptions of nature.

To me, what's fascinating about quantum mechanics is that it is simultaneously so weird, and yet our everyday experience is so classical. This is the sense in which Copenhagen was right. It doesn't actually make sense, as a coherent interpretation of quantum mechanics, but it does summarize how quantum mechanics works, pragmatically. The microscopic realm is, for almost all practical purposes, just a mathematical fiction used to compute macroscopic probabilities, but then macroscopic facts seem very classical: No superpositions of any macroscopic objects, no macroscopic nonlocality (in the sense that macroscopic actions here have a causal effect on macroscopic facts far away). So that's why there is no consensus about interpretations of quantum mechanics, and no urgency to come to a consensus: the Copenhagen/shut-and-calculate interpretation works too well. It's more of an intellectual/philosophical mystery than it is a physics problem.

Of course, I'm drawn to it because my only interest in physics these days (not being a physicist for a living) is as an intellectual puzzle.

 

[DevilsAvocado]

I don't make any such claim, because I'm not supporting or opposing any particular interpretation. Certainly, under the Cosmological Interpretation, a Bob looking at a cubic moon, if possible, which we should imagine that it is, does exist. Though we'd expect it to be highly improbable. Does that make probable scenarios "more real" than improbable ones? Well that really depends what you mean by "more real", but we should be careful not to use it as a term to support prejudices. Without a doubt, we've all experienced improbable situations, that we wouldn't consider to be "not real".

I don't know enough about the Cosmological interpretation to tell how Max Tegmark solves outcomes from EPR-Bell experiments, but if Bob is looking at a cubic moon which Alice has determined as a sphere – this would be the end of science.

The only way to verify the accuracy of a scientific theory is by repeatable experiments, and if everyone gets their own "personal outcome" – no scientific theory could ever be experimentally verified.

As I understand "subjective realism" in CH, there is a 'superposition' of pre-existing values, which will be determined/finalized at measurement (as in the description of the colored slips of paper in envelopes).

If this is correct, the truth is that it does not work all the way, even if it will 'solve' the problem of CFD, and this is why:

In all cases of EPR-Bell experiments where we have non-parallel settings, as in DrC's example with three settings separated by cos²(120°) = 25% correlation, it looks like you might get away with it at first sight, by having a 'superposition' of real pre-existing pending values of 1 or 0, which somehow get it right in the end.

But then you must explain how space-like separated Alice & Bob are 'synchronized' during four runs, to produce 25% correlated outcomes like this:

Alice [0, 1, 0, 1] 
Bob   [1, 0, 1, 1]

And besides this "little" problem, you also have to cover the fact the settings could be parallel, i.e. cos²(0°) = 100% correlation:

Alice [0, 1, 0, 1] 
Bob   [0, 1, 0, 1]

There is no classical explanation for this, whether there are "subjective pre-existing" values or not.

 

[DevilsAvocado]

No superpositions of any macroscopic objects,

It looks like Bohr will have some trouble surviving as quantum machines gets bigger and bigger...

https://www.youtube.com/watch?v=CJEn7Tan9do
http://www.youtube.com/embed/CJEn7Tan9do

 

[craigi]

I don't know enough about the Cosmological interpretation to tell how Max Tegmark solves outcomes from EPR-Bell experiments, but if Bob is looking at a cubic moon which Alice has determined as a sphere – this would be the end of science.

It's very unlikely, if possible at all, that they're going to meet each other under any interpretation. Even if they did, I doubt Alice would believe him

 

[DevilsAvocado]

It's very unlikely, if possible at all, that they're going to meet each other under any interpretation. Even if they did, I doubt Alice would believe him

That's true in MWI, but I'm not sure about Cosmological interpretation (and CH). Anyway, if Bob & Alice's forks can never meet – how can we talk about "subjective realism"? What we've got (in MWI) is "parallel realism".

Furthermore, I think this shows maybe the biggest weakness of MWI – there will be forks where the Moon is a cube. The question is; why don't we see any of these 'everything-that-can-happen-will-happen' peculiarities in our fork??

 

[craigi]

That's true in MWI, but I'm not sure about Cosmological interpretation (and CH). Anyway, if Bob & Alice's forks can never meet – how can we talk about "subjective realism"? What we've got (in MWI) is "parallel realism".

Furthermore, I think this shows maybe the biggest weakness of MWI – there will be forks where the Moon is a cube. The question is; why don't we see any of these 'everything-that-can-happen-will-happen' peculiarities in our fork??

Well we do see some weird stuff, but how weird do you want to get? How normal would it have to be before you'd say it was too normal? If the moon was a cube, you probably wouldn't see it as all that weird.

Because there's vastly more relatively normal possibilities than super weird ones, you're much more likely to get the relatively normal ones.

See the Principle of Mediocrity:
http://en.wikipedia.org/wiki/Mediocrity_principle

 

[atyy]

You're misinterpreting this. I think you should follow through this:

Regardless of the exact meaning of "classical reality" such a notion surely includes simultaneous sharp values for all observables. Histories in CH don't have this.

Also your use of terminology seems odd to me. What does it even mean for different frameworks -which are different ways of talking about what happens in the system- to "occur" or to "interact"?

It looks like Griffiths's CH http://arxiv.org/abs/1105.3932 and Gell-Mann and Hartle's DH http://arxiv.org/abs/1106.0767 are not the same. Griffiths's CH is that things are real if we reject that A is true, B is true means A is true and B is true, while Gell-Mann and Hartle's DH find that having multiple real histories that don't stitch together challenging for a notion of reality.

 

[kith]

Griffiths's CH is that things are real if we reject that A is true, B is true means A is true and B is true

This may be a subtIety but I don't agree. Contrary to von Neumann's quantum logic approach, Griffiths doesn't modify the laws of logic. He says that in order to talk consistently about probabilities, you must set up a sample space first. This defines the properties to which the probabilities are assigned.

It is not unusual that there are multiple ways to do this. Wikipedia uses the multiple properties of cards in a deck as an example. What is unusual is that these sample spaces can not always be combined in QM. This is because the Born rule tells us to use projectors to assign probabilities to properties. If we try to combine these properties, the probabilities may depend on the order we assign them because the projectors may be non-commuting. So combining properties doesn't always make sense. Independent of CH, I think this is a very simple and elegant way to see why naive realism isn't compatible with QM.

So what Griffiths says is that your statement A is necessarily of the form "in framework X, the particle has the property Y" and there's no problem to talk about A AND B.

 

[atyy]

This may be a subtIety but I don't agree. Contrary to von Neumann's quantum logic approach, Griffiths doesn't modify the laws of logic. He says that in order to talk consistently about probabilities, you must set up a sample space first. This defines the properties to which the probabilities are assigned.

It is not unusual that there are multiple ways to do this. Wikipedia uses the multiple properties of cards in a deck as an example. What is unusual is that these sample spaces can not always be combined in QM. This is because the Born rule tells us to use projectors to assign probabilities to properties. If we try to combine these properties, the probabilities may depend on the order we assign them because the projectors may be non-commuting. So combining properties doesn't always make sense. Independent of CH, I think this is a very simple and elegant way to see why naive realism isn't compatible with QM.

So what Griffiths says is that your statement A is necessarily of the form "in framework X, the particle has the property Y" and there's no problem to talk about A AND B.

Yes, in framework X, it's just classical stochastic processes. So in each framework, one history is real, so let's say that statement A is true in framework X. However, all frameworks "exist simultaneously". So we also have that statement B is true in framework Y. Normal logic would say that it is then true to say A is true in framework X and B is true in framework Y. But apparently this is forbidden.

 

[craigi]

Yes, in framework X, it's just classical stochastic processes. So in each framework, one history is real, so let's say that statement is A is true in framework X. However, all frameworks "exist simultaneously". So we also have that statement B is true in framework Y. Normal logic would say that it is then true to say A is true in framework X and B is true in framework Y. But apparently this is forbidden.

A : Property X in Framework Y
B : Property X' in Framework Y'

Now we can talk of A and B. It's not forbidden by any particular rule, but there is no framework where this has physical meaning.

We sort of knew this all along under CI as soon as we encountered spin, but we were told to shut up if we asked too many questions.

The problem was without the clarification of CH, CI could be easily misinterpreted as saying a particle can't have Sx and Sz both equal to 1/2 at the same time, for instance. I'm sure many of us have said it, but it's not true and it's not false either.We can create classical analogs, by considering photographic projections, for instance:

A : The object is facing X in photograph Y
B : The object is facing X' in photograph Y'

 

[kith]

Yes, in framework X, it's just classical stochastic processes. So in each framework, one history is real, so let's say that statement A is true in framework X. However, all frameworks "exist simultaneously". So we also have that statement B is true in framework Y. Normal logic would say that it is then true to say A is true in framework X and B is true in framework Y. But apparently this is forbidden.

No, this should be a perfectly valid statement.

 

[atyy]

No, this should be a perfectly valid statement.

Then why is it said that the frameworks are in compatible and statements from them cannot be combined. What you are saying here is that they can be combined. To me if this is possible, aren't they just like different reference frames?

 

[bhobba]

Agreed, but help me out here. How is what I said wrong?

The environment is NOT just the classical world. Its entirely quantum.

Thanks
Bill

 

[kith]

Then why is it said that the frameworks are in compatible and statements from them cannot be combined.

They refer to statements from within frameworks and not to the kind of meta-statements we have made.

What you are saying here is that they can be combined. To me if this is possible, aren't they just like different reference frames?

In a way, yes.

 

[craigi]

The environment is NOT just the classical world. Its entirely quantum.

Thanks
Bill

I'm probably using non-standard definitions, because I see them as equivalent.

Is it right for me to consider the classical world as a degenerate case of the quantum world and the environment to exhibit exactly the same lack of coherence?

 

[atyy]

What you are saying here is that they can be combined. To me if this is possible, aren't they just like different reference frames?

In a way, yes.

So if in some sense, the frameworks are compatible, shouldn't there be an "invariant object" that is the true reality underlying them? In the analogy with reference frames, we cannot combine coordinate statements from different frames, but we can speak of the geometrical object which is coordinate-independent. Is there none here? Or could there be one that hasn't been discovered? (Actually, doesn't the Gell-mann and Hartle paper http://arxiv.org/abs/1106.0767 try to do that?)

 

[craigi]

So if in some sense, the frameworks are compatible, shouldn't there be an "invariant object" that is the true reality underlying them? In the analogy with reference frames, we cannot combine coordinate statements from different frames, but we can speak of the geometrical object which is coordinate-independent. Is there none here? Or could there be one that hasn't been discovered? (Actually, doesn't the Gell-mann and Hartle paper http://arxiv.org/abs/1106.0767 try to do that?)

It would seem reasonable that there could be such an invariant object. In the photographic projection analog that I offered earlier, this would be the 3D world, where we can relate the different orientations.

I'm pretty sure that if we try to define such an invariant object for QM, we get what we refer to as the multiverse in certain interpretations, but CH doesn't go that far.

 

[kith]

So if in some sense, the frameworks are compatible, shouldn't there be an "invariant object" that is the true reality underlying them? In the analogy with reference frames, we cannot combine coordinate statements from different frames, but we can speak of the geometrical object which is coordinate-independent. Is there none here? Or could there be one that hasn't been discovered? (Actually, doesn't the Gell-mann and Hartle paper http://arxiv.org/abs/1106.0767 try to do that?)

The underlying object is the quantum system. The fact that we cannot describe "the real thing" in an unambigous way doesn't imply that it doesn't exist. The CH seems to be still kind of a minimal interpretation and the search for an unambigous description goes beyond it. In order to get it, I think you have to assume something more than CH does. Gell-Mann and Hartle for example talk about negative probabilities in the abstract of their paper (I haven't read it).

 

[atyy]

It would seem reasonable that there could be such an invariant object. In the photographic projection analog that I offered earlier, this would be the 3D world, where we can relate the different orientations.

I'm pretty sure that if we try to define such an invariant object for QM, we get what we refer to as the multiverse in certain interpretations, but CH doesn't go that far.

The underlying object is the quantum system. The fact that we cannot describe "the real thing" in an unambigous way doesn't imply that it doesn't exist. The CH seems to be still kind of a minimal interpretation and the search for an unambigous description goes beyond it. In order to get it, I think you have to assume something more than CH does. Gell-Mann and Hartle for example talk about negative probabilities in the abstract of their paper (I haven't read it).

Or could one say that the fact the the multiple frameworks are compatible in the sense that A is true in framework X and B is true in framework Y, imply the existence of this unknown object? What Gell-Mann and Hartle seem to be searching for does seem to match something like common sense reality, especially since if I include myself in the quantum system, I will be in all frameworks, and there is nothing outside to say in framework X or framework Y.

 

[craigi]

Or could one say that the fact the the multiple frameworks are compatible in the sense that A is true in framework X and B is true in framework Y, imply the existence of this unknown object?

That is a matter of taste.

We natually try apply the principle that the simplest explanation is the best, but some believe it's simpler to say it doesn't exist and some believe it's simpler to say that it does.

There is a new development though, which weakens the former argument somewhat. It's still controversial, but cosmologists increasingly believe that there may sufficient space, if not infinite space, beyond our cosmic horizon, for many duplicate universes, which realize all possibilities of the wavefunction. This field isn't purely theoretical either. There has been experimental verification of some predictions of this theory, though direct observation of another universe is impossible.

Possibly the most compelling thing about these interpretations is that we recover determinism is a very natural way.

CH isn't concerned with any of this though.

 

[stevendaryl]

A : Property X in Framework Y
B : Property X' in Framework Y'

Now we can talk of A and B. It's not forbidden by any particular rule, but there is no framework where this has physical meaning.

We sort of knew this all along under CI as soon as we encountered spin, but we were told to shut up if we asked too many questions.

The problem was without the clarification of CH, CI could be easily misinterpreted as saying a particle can't have Sx and Sz both equal to 1/2 at the same time, for instance. I'm sure many of us have said it, but it's not true and it's not false either.


We can create classical analogs, by considering photographic projections, for instance:

A : The object is facing X in photograph Y
B : The object is facing X' in photograph Y'

There is an easy resolution to that classical analogue, which is to say that both can be true simultaneously. The property is not "facing X", but "facing X in photograph Y". The same object can satisfy "facing X in photograph Y" and "facing X' in photograph Y'" at the same time.

The incompatibility of frameworks seems more extreme than that. It seems that you can't say: "X is true in framework F, and X' is true in framework F'" if F and F' are incompatible.

 

[craigi]

There is an easy resolution to that classical analogue, which is to say that both can be true simultaneously. The property is not "facing X", but "facing X in photograph Y". The same object can satisfy "facing X in photograph Y" and "facing X' in photograph Y'" at the same time.

The incompatibility of frameworks seems more extreme than that. It seems that you can't say: "X is true in framework F, and X' is true in framework F'" if F and F' are incompatible.

I think you can say it, but no inferences can be drawn from it.

In the classical case we can construct a higher dimensional space where it does have meaning, but is this not also true in the quantum case?

To borrow terminology from other interpretations, are we not effectively saying, that the electron has Sx = 1/2 in one universe AND Sz = 1/2 in another universe, for example?

That all sounds fine, but obviously we're not going to be able to draw any conclusions from that.

 

[atyy]

The incompatibility of frameworks seems more extreme than that. It seems that you can't say: "X is true in framework F, and X' is true in framework F'" if F and F' are incompatible.

That's what I thought too, but craigi (#182) and kith (#183) indicate above that it is possible.

 

[stevendaryl]

I think you can say it, but it has no meaning and no inferences can be drawn from it.

In the classical case we can construct a higher dimensional space where it does have meaning, but is this not also true in the quantum case?

No, in the quantum case there is no higher dimensional framework that can make sense of all of the frameworks simultaneously.

A framework consists of a sequence of times, and a choice of an observable at each time. A history for a framework consists of an assignment of a value to each observable at each time in the framework.

Within a framework, classical logic and classical probability hold, which means that you can reason as if probability is just due to ignorance. So you can pretend that "The particle has spin-up along the x-axis at time t" is a meaningful statement, either true or false, but you don't know which.

So within each framework, you can reason as if there is a single "real" history, while the other histories aren't real. So if it's possible for each framework to have a "real" history, why isn't it possible to assume that there is a "master history" that chooses one history to be real out of each framework? If there were such a master history, it would allow one to say, for every possible observable and for every possible time, what the value of that variable is at that time.

This would be sort of like dBB on steroids. dBB has definite (though unknown) values for particle positions at every moment in time, but it does not treat other observables in an egalitarian manner.

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.

But then what would prevent us from asking a question along the lines of:
"What is the probability that the particle has spin-up along the x-axis and spin-up along the y-axis at time t=0?" One way of interpreting Bell's theorem is that there is no consistent probability that we can assign to conjunctions of statements involving incompatible observables.

One way out (described by the late mathematical physicist Pitowsky, which I read about in Stanley Gudder's book on quantum probability) is to assume nonmeasurable sets. It's a mathematical curiosity that it is possible to come up with a set of reals for which there is no consistent way to assign a probability that a random real is in that set. That doesn't mean that the set doesn't exist. It doesn't mean that it's impossible to pick a random real in that set, it just means that there is no way to compute a probability for such an event.

 

[stevendaryl]

That's what I thought too, but craigi (#182) and kith (#183) indicate above that it is possible.

I don't agree. Remember, a framework is nothing more than a choice of which observables and which moments in time to talk about. So suppose framework F has observable O1 at time t1, observable O2 at time t2, etc. Framework F' has observable O1' at time t1', O2' at time t2', etc.

Then saying "X is true in framework F" is a statement of the form
"O1 has value X1 at time t1, O2 has value X2 at time t2, ..."

Saying "X' is true in framework F'" is similarly a statement of the form
"O1' has value X1' at time t1', O2' has value X2' at time t2', ..."

So the conjunction "X is true in framework F and X' is true in framework F'" just amounts to saying:
"O1 has value X1 at time t1, O1' has value X1' at time t1', O2 has value X2 at time t2, O2' has value X2' at time t2' ..."

So I don't see the difference between the meta statement and the corresponding conjunction of ordinary statements.

 

[atyy]

Nonmeasurable sets are also a potential way to evade Bell's theorem. strangerep has mentioned that on PF before. But I don't know if there are any successful constructions using that potential out.

 

[kith]

Then saying "X is true in framework F" is a statement of the form
"O1 has value X1 at time t1, O2 has value X2 at time t2, ..."

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.

 

[atyy]

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.

Does this still make sense if the observer is included in the system, so that the observer is in all frameworks? Griffiths's version seems to make sense if the observer lies outside the system, but does it still make sense if the frameworks encompass everything? If the observer is in the system, who is doing the choosing of the framework that is real?

Could this be the reason for differences bewteen the Griffiths and Gell-Mann/Hartle versions of CH?