Quantum Mechanics without Measurement

[stevendaryl]

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?

I think that's correct. As I said in another post, reasoning about macroscopic objects using the apparatus of quantum mechanics is very difficult, because you can't really write down a wave function for the object. So there is a certain amount of handwaving involved, and it's never clear (to me, anyway) whether whatever conclusions we draw are artifacts of the handwaving or are real implications of QM.

 

[kith]

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.

Isn't the conncection to physics that although we can easily predict what happens using the second family, we cannot build the corresponding measurement devices because the fundamental interactions between the device and the system will decohere the macroscopic superposition eigenstates very quickly? Or put differently: We will always have the ambiguity of multiple histories from this family because we never end up in eigenstates.

 

[stevendaryl]

Isn't the conncection to physics that although we can easily predict what happens using the second family, we cannot build the corresponding measurement devices because the fundamental interactions between the device and the system will decohere the macroscopic superposition eigenstates very quickly? Or put differently: We will always have the ambiguity of multiple histories from this family because we never end up in eigenstates.

I'm on shaky grounds here, but that sounds right. And philosophical, I find it to be an improvement over Copenhagen, in that, as I said, the assumption that measuring devices always have definite macroscopic states is a practical, subjective choice, rather than there being something magical about the measurement process. In the end, you probably get the same quantitative predictions either way, so maybe it's a matter of taste.

 

[craigi]

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.

Try chapter 12 here:
http://www.siue.edu/~evailat/

I can't vouch for this but it does seem to cover it.

I'm sure Griffiths must have published his own treatment of the problem, though.

 

[stevendaryl]

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

I once worked out for myself a way to "explain" EPR results using negative probabilities. I may have already posted about it, but it's short enough that I can reproduce it here.

Let's simplify the problem of EPR by considering only 3 possible axes for spin measurements:

\hat{a} = the x-direction
\hat{b} = 120 degrees counterclockwise from the x-direction, in the x-y plane.
\hat{c} = 120 degrees clockwise from the x-direction, in the x-y plane.

We have two experimenters, Alice and Bob. Repeatedly we generate a twin pair, and have Alice measure the spin of one along one of the axes, and have Bob measure the spin of the other along one of the axes.

Let i range over \{ \hat{a}, \hat{b}, \hat{c} \}.
Let X range over { Alice, Bob }
Let P_X(i) be the probability that experimenter X measures spin-up along direction i.
Let P(i, j) be the probability that Alice measures spin-up along axis i and Bob measures spin-up along axis j. The predictions of QM are:

1. P_X(i) = 1/2
2. P(i,j) = 3/8 if i \neq j
3. P(i, i) = 0

One approach for a hidden-variables explanation would be this:

• Associated with each twin-pair is a hidden variable \lambda which can take on 8 possible values: \lambda_{\{\}}, \lambda_{\{a\}}, \lambda_{\{b\}}, \lambda_{\{c\}}, \lambda_{\{a, b\}}, \lambda_{\{a, c\}}, \lambda_{\{b, c\}}, \lambda_{\{a, b, c\}}
• The probability of getting \lambda_x is p_x (where x ranges over all subsets of \{ a, b, c \}.)
• If the variable has value \lambda_x, then Alice will get spin-up along any of the directions in the set x, and will get spin-down along any other direction.
• If the variable has value \lambda_x, then Bob will get spin-down along any of the directions in the set x, and will get spin-upalong any other direction (the opposite of Alice).

So if you assume symmetry among the three axis, then it's easy to work out what the probabilities must be to reproduce the predictions of QM. They turn out to be:

p_{\{\}} = p_{\{a, b, c\}} = -1/16
p_{\{a\}} = p_{\{b\}} = p_{\{c\}} = p_{\{a, b\}} = p_{\{a, c\}} = p_{\{b, c\}} = 3/16

So the probability that Alice gets spin-up along direction \hat{a} is:

p_{\{a\}} + p_{\{a, b\}} + p_{\{a, c\}} + p_{\{a, b, c\}} = 3/16 + 3/16 +3/16 - 1/16 = 1/2

The probability that Alice gets spin-up along direction \hat{a} and Bob gets spin-up along direction \hat{b} is:

p_{\{a\}} + p_{\{a, c\}} = 3/16 + 3/16 - 1/16 = 3/8

So if we knew what a negative probability meant, then this would be a local hidden-variables model that reproduces the EPR results.

 

[atyy]

I'm not sure this is related to the negative probabilities above, but thought I'd mention it. There is a standard object in quantum mechanics, called the Wigner function, which is considered the closest thing to a joint probability distribution over canonical variables like position and momentum. As with a classical probability distribution, integrating over momentum gives a classical position distribution, and integrating over position gives a classical momentum distribution. For a free particle or harmonic oscillator, the Wigner function evolves as a classical probability distribution. In general the Wigner function itself has negative parts, which prevents it from being interpreted as a classical probability distribution, but when it is entirely positive, such as for a Gaussian wavefunction, I believe it is ok to assign trajectories to quantum particles.

 

[atyy]

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.

Yes. For example, many-worlds evades the Bell theorem because the Bell theorem assumes that each measurement has only one outcome, but in many-worlds all outcomes appear. Incidentally, Wallace seems to say the state vector in many-worlds is nonlocal. At any rate, it seems clear in many-worlds why the Bell theorem is evaded. The question is whether in CH the requirement of consistency is enough to evade the Bell theorem, or whether something more is required. What exactly is the means by which CH evades the Bell theorem, if it does?

 

[Jilang]

Yes, it's related as it is a quasiprobaility distribution (nice term that!) These can relax some of the axioms of standard probability, like the first axiom, and allow negative probabilities.
http://en.wikipedia.org/wiki/Quasiprobability_distribution

 

[atyy]

http://arxiv.org/abs/1201.0255
Quantum Counterfactuals and Locality
Robert B. Griffiths
Found. Phys. 42 (2012) pp. 674-684

"Stapp asserts that the validity of a certain counterfactual statement, SR in Sec. 4 below, referring to the properties of a particular particle, depends upon the choice of which measurement is made on a different particle at a spatially distant location. ... It will be argued that, on the contrary, the possibility of deriving the counterfactual SR depends on the point of view or perspective that is adopted—specifically on the framework as that term is employed in CQT—when analyzing the quantum system, and this dependence makes it impossible to construct a sound argument for nonlocality, contrary to Stapp’s claim."

"Our major disagreement is over the conclusions which can be drawn from these analyses. Stapp believes that because he has identified a framework which properly corresponds to his earlier argument for nonlocal influences, and in this framework the ability to deduce SR is linked to which measurement is carried out on particle a, this demonstrates a nonlocal influence on particle b. I disagree, because there exist alternative frameworks in which there is no such link between measurement choices on a and the derivation of SR for b."

So CH is nonlocal in some frameworks?

 

[atyy]

http://arxiv.org/abs/0908.2914
Quantum Locality
Robert B. Griffiths
(Submitted on 20 Aug 2009 (v1), last revised 13 Dec 2010 (this version, v2))
Foundations of Physics, Vol. 41, pp. 705-733 (2011)

"It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply classical concepts and introduce probabilities in a manner inconsistent with the Hilbert space structure of standard quantum mechanics. Instead, Einstein locality is a valid quantum principle: objective properties of individual quantum systems do not change when something is done to another noninteracting system. There is no reason to suspect any conflict between quantum theory and special relativity."

"Many errors contain a grain of truth, and this is true of the mysterious nonlocal quantum influences. Quantum mechanics does deal with states which are nonlocal in a way that lacks any precise classical counterpart."

"The analysis in this paper implies that claims that quantum theory violates “local realism” are misleading."

!

 

[bhobba]

I'm sure Griffiths must have published his own treatment of the problem, though.

He has:
"Correlations in separated quantum systems: a consistent history analysis of the EPR problem," Am. J. Phys. 55 (1987).

Its also in his book, Consistent Quantum Theory which I have a copy of - see Chapters 23 and 24.

It not only explains his interpretation, but is a good resource about the interpretive issues with QM in general.

Thanks
Bill

 

[morrobay]

He has:
"Correlations in separated quantum systems: a consistent history analysis of the EPR problem," Am. J. Phys. 55 (1987).

Its also in his book, Consistent Quantum Theory which I have a copy of - see Chapters 23 and 24.

It not only explains his interpretation, but is a good resource about the interpretive issues with QM in general.

Thanks
Bill

Given that consistent histories can be used to describe how a particle interacts with a measuring apparatus
and that randomness of A1 A2 can arise during measurement process, no joint probability distribution. Does Griffiths anywhere have a local non realistic ( non counterfactual definiteness) explanation/model for violations of Bell inequalities ?

 

[bhobba]

Does Griffiths anywhere have a local non realistic ( non counterfactual definiteness) explanation/model for violations of Bell inequalities ?

He only discusses his interpretation.

As I have said he believes his interpretation is realistic, but if it really is that is an open issue.

I like CH, but its not my favorite because I find it a bit more complex than I think necessary, with frameworks and what not. I simply assume after decoherence the improper mixed state is a proper one - easy as far as I am concerned without this baggage of frameworks, histories, blah, blah, blah.

I am the wrong person to ask about if an interpretation is non counterfactual etc. Terms like that to me is philosophical verbosity. I can't even remember without looking it up exactly what it means.

My view is much simpler. QM is basically the most reasonable general probability model for physical systems that allows continuous transformations or equivalently entanglement. Its entanglement with the environment and measurement apparatus that leads to observations - properties exist because of that, and systems don't actually have properties apart from that. So, just prior to observation outcomes are actualized via dechoerence - but before that - blah. Is that counterfactual definite - maybe, maybe not - I will let others judge. As I said I am not into that sort of thing.

Thanks
Bill

 

[DevilsAvocado]

"The analysis in this paper implies that claims that quantum theory violates “local realism” are misleading."

!

wow... just wow... if this is not refuting QM & Bell's theorem, then what is??

If he can't provide anything more than his own words of unverified ideas, without any form of mathematical/logical formulation, it looks like my first claim about a "preposterous word-salad" is rightfully justified indeed...

He's up against a whole world of professional and rigorous experiments, working flawlessly every time... what on Earth will this man say when Anton Zeilinger and Alain Aspect receive the Nobel Prize in Physics – the whole world is wrong and he is right, even if he can't prove it?

Gosh

 

[DevilsAvocado]

So if we knew what a negative probability meant, then this would be a local hidden-variables model that reproduces the EPR results.

I think that negative probabilities means that it is simply impossible to mimic this feature by any means of classical tools. LHV requires 'something' to be 'there' all the time, definitely. If the probability of 'something' to be 'there' is negative – it means it's not 'there', i.e. it's not definite.

DrC has a useful page that effectively proves the mathematical impossibility of LHV – it just doesn't work! (i.e. unless 'someone' wants to refute mathematics as well...)

http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm

 

[craigi]

He only discusses his interpretation.

As I have said he believes his interpretation is realistic, but if it really is that is an open issue.

I like CH, but its not my favorite because I find it a bit more complex than I think necessary, with frameworks and what not. I simply assume after decoherence the improper mixed state is a proper one - easy as far as I am concerned without this baggage of frameworks, histories, blah, blah, blah.

I am the wrong person to ask about if an interpretation is non counterfactual etc. Terms like that to me is philosophical verbosity. I can't even remember without looking it up exactly what it means.

My view is much simpler. QM is basically the most reasonable general probability model for physical systems that allows continuous transformations or equivalently entanglement. Its entanglement with the environment and measurement apparatus that leads to observations - properties exist because of that, and systems don't actually have properties apart from that. So, just prior to observation outcomes are actualized via dechoerence - but before that - blah. Is that counterfactual definite - maybe, maybe not - I will let others judge. As I said I am not into that sort of thing.

Thanks
Bill

CFD, is really dBB's realm. Particles with definite properties independent of measurement. Though in CH, measurement doesn't play a central role, it's not considered to be CFD. For most interpretations, this is one of the first things they throw out. dBB really wanted to retain that, so made concessions elsewhere.

 

[Jilang]

DrC has a useful page that effectively proves the mathematical impossibility of LHV – it just doesn't work! (i.e. unless 'someone' wants to refute mathematics as well...)

http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm

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.

 

[stevendaryl]

wow... just wow... if this is not refuting QM & Bell's theorem, then what is??

I don't know why you say that. He definitely is not refuting QM. The whole point is to give a more sound treatment of QM. He's definitely not refuting Bell' theorem. It's a theorem, after all. What he's doing is questioning the definition of "local realism". What should be the appropriate formal definition of an informal, intuitive idea is up for debate. In contrast, the experimental predictions of quantum mechanics and mathematical theorems are not up for debate (although their implications or meaning might be).

He's up against a whole world of professional and rigorous experiments, working flawlessly every time... what on Earth will this man say when Anton Zeilinger and Alain Aspect receive the Nobel Prize in Physics – the whole world is wrong and he is right, even if he can't prove it?
Gosh

He's not questioning any of that.

 

[craigi]

Apologies, if this is treading old ground, but earlier in this thread, some suggested that they found the idea of non-classical logic applied to quantum physics unsatisfactory. My question is that is this really something that is specific to CH?

I think we all notice something unsatisfactory when we first learn about it, but then we dismiss it without demanding an answer. If we consider a single spin half particle,

A: Sx = +1/2
B: Sx = -1/2
C: Sz = +1/2
D: Sz = -1/2

Classical logic would tell us that since,

C or D = 1

(A and C) or (A and D) = A

but we know that from the QM forumlation that the LHS is always false and that the RHS is sometimes true.

Does this not demonstrate that classical logic cannot be applied to QM without extra rules, independent of interpretation?

 

[stevendaryl]

I think that negative probabilities means that it is simply impossible to mimic this feature by any means of classical tools. LHV requires 'something' to be 'there' all the time, definitely. If the probability of 'something' to be 'there' is negative – it means it's not 'there', i.e. it's not definite.

Negative probability would not be "not there"--that would be "zero probability". The thing about negative probability is that since probabilities have to sum to one, if some probabilities are negative, then other probabilities have to add up to greater than one.

 

[stevendaryl]

Negative Probabilities

Here's a sketch of a way that negative probabilities can make some sense, which is sort of reminiscent of relativistic quantum mechanics.

Suppose you have a string running from left to right. Impose a coordinate system, with the x-axis going horizontally and the y-axis running vertically. If the shape of the string is random, then you could perhaps describe the situation by giving a probability distribution at each point of the x-axis: P(x,y) dy = the probability that the string runs through some point in the interval (x,y \pm dy). If the string is mostly horizontal, and the curves are not too wild, then you can expect that:

\int P(x,y) dy = 1

That is, if you pick a value for x, the string has to cross at some point, so the probability of it crossing must add up to one.

But now consider a wilder shape for the string, as shown in the picture below. As you can see, the string passes point A once, but passes point B 3 times, and passes point C 5 times. So we can no longer describe the random string using a probability distribution of the form P(x,y). However...

What is interesting about the pattern of crossings is that the number of crossings is odd (assuming that the far left-end of the string and far right-end of the string are fixed in place). That's because for every section where the string is running right-to-left, there must be a corresponding section where the string is running left-to-right. In the picture below, we color the left-to-right sections blue, and the right-to-left sections red. Then instead of a probability that adds up to 1, we have some kind of density function

D(x,y) dy

which can be either positive or negative. Positive density means that blue sections are more likely than red sections. Negative density means that red sections are more likely than blue sections. The constraint now is that

\int D(x,y) dy = 1

where D(x,y) counts the excess of blue sections over red sections.

I've toyed with the idea of a local hidden variables theory where instead of probabilities there were densities, which could be either positive or negative. I couldn't find any way to make sense of that for the EPR experiment, though.

 

[atyy]

Apologies, if this is treading old ground, but earlier in this thread, some suggested that they found the idea of non-classical logic applied to quantum physics unsatisfactory. My question is that is this really something that is specific to CH?

I think we all notice something unsatisfactory when we first learn about it, but then we dismiss it without demanding an answer. If we consider a single spin half particle,

A: Sx = +1/2
B: Sx = -1/2
C: Sz = +1/2
D: Sz = -1/2

Classical logic would tell us that since,

C or D = 1

(A and C) or (A and D) = A

but we know that from the QM forumlation that the LHS is always false and that the RHS is sometimes true.

Does this not demonstrate that classical logic cannot be applied to QM without extra rules, independent of interpretation?

Can't one say that since Sx and Sz cannot be simultaneously measured, (A and C) doesn't exist, so classical logic is fine? ie. Can one say that as long as one knows how to make a classical/quantum cut, and what a measurement is, then QM satisfies the rules of common sense?

 

[craigi]

Can't one say that since Sx and Sz cannot be simultaneously measured, (A and C) doesn't exist, so classical logic is fine? ie. Can one say that as long as one knows how to make a classical/quantum cut, and what a measurement is, then QM satisfies the rules of common sense?

Sure, but that is pretty much how CH works. I think there other ways to forbid classical logic here too. TTere's no way around it.

 

[stevendaryl]

Apologies, if this is treading old ground, but earlier in this thread, some suggested that they found the idea of non-classical logic applied to quantum physics unsatisfactory. My question is that is this really something that is specific to CH?

I think we all notice something unsatisfactory when we first learn about it, but then we dismiss it without demanding an answer. If we consider a single spin half particle,

A: Sx = +1/2
B: Sx = -1/2
C: Sz = +1/2
D: Sz = -1/2

Classical logic would tell us that since,

C or D = 1

(A and C) or (A and D) = A

but we know that from the QM forumlation that the LHS is always false and that the RHS is sometimes true.

Does this not demonstrate that classical logic cannot be applied to QM without extra rules, independent of interpretation?

I think that many people would say that the meaningful statement is not "The particle's spin in the z-direction is +1/2" but "When I measured the particle's spin in the z-direction, the result was +1/2". If you restrict the meaningful statements to observations and measurements, then classical logic applies.

But to me, that's exactly the same sort of modification of logic that CH is doing. So I guess I agree with you.

 

[craigi]

I think that many people would say that the meaningful statement is not "The particle's spin in the z-direction is +1/2" but "When I measured the particle's spin in the z-direction, the result was +1/2". If you restrict the meaningful statements to observations and measurements, then classical logic applies.

But to me, that's exactly the same sort of modification of logic that CH is doing. So I guess I agree with you.

So this restricts this logic, by sacrifcing CFD and giving the observer a causal role, which is the CI. I would suggest that when you say many people would say this, it's because the CI became ingrained in the teaching of QM for so long. I think if it weren't for that, it would seem at least as solipsistic as any other interpretation.

 

[atyy]

So this restricts this logic, by sacrifcing CFD and giving the observer a causal role, which is the CI. I would suggest that when you say many people would say this, it's because the CI became ingrained in the teaching of QM for so long. I think if it weren't for that, it would seem at least as solipsistic as any other interpretation.

CI is not solipsistic. The main correction to CI needed is the error in von Neumann's proof that hidden variables are impossible. With that, it's possible to take CI under the assumption that QM is incomplete. The nice thing is that CI has a common sense reality, because of the classical/quantum cut. Since QM is not a complete theory, there is no problem with needing a subjective observer. So CI sits at the centre of all interpretive possibilities, eg. dBB takes QM to be incomplete, but CH and many-worlds take it to be complete and nonreal or real.

 

[Maui]

So this restricts this logic, by sacrifcing CFD and giving the observer a causal role, which is the CI. I would suggest that when you say many people would say this, it's because the CI became ingrained in the teaching of QM for so long. I think if it weren't for that, it would seem at least as solipsistic as any other interpretation.

That which we call 'reality' is always brain generated(projected) and we know from SR and QM that reality is not classical. From neuroscience we know that brains can generate false impressions and memories of things that were not there(relevant to out viewpoint as opposed to someone suffering from schizophrenia). Given that knowledge already plays a part in certain areas of qm and reality is always experienced as classical, the role of the brain in the perception of the so called outside world should at least be examined. I wouldn't be astonished if it holds big surpizes on the nature of the fundamental particles(I would actually be truly astonished if one day it turns out that classicality is fundamental).
Yes, I know, there is a 100% agreement between observers about observations, but the observers themselves are of the same quantum nature and must rise to classicality in the same way as rocks, chairs, atoms and particle trajectories do. Weird indeed, but these are experimentally solid facts.

 

[atyy]

Does CH really solve the measurement problem? If the observer is included in the framework, who chooses the single framework?

 

[craigi]

Does CH really solve the measurement problem? If the observer is included in the framework, who chooses the single framework?

As in MWI, there is no measurement problem to solve in CH, so yes it does. The measurement problem is primairily a CI issue, though later interpretations such as Von Neumann, fall foul of it too. I think our dBB'ers and Ensemblers probably don't see a measurement problem either. Demystifier? Bill? Can you confirm?

I think that in CH everything in the classical environment, including the observer is part of a single framework and other frameworks occur in sufficiently isolated quantum systems. My terminology might be a bit off, but if I'm right this is where decoherence plays a big role.

 

[atyy]

As in MWI, there is no measurement problem to solve in CH, so yes it does. The measurement problem is primairily a CI issue, though later interpretations such as Von Neumann, fall foul of it too. I think our dBB'ers and Ensemblers probably don't see a measurement problem either. Demystifier? Bill? Can you confirm?

I think that in CH everything in the classical environment, including the observer is part of a single framework and other frameworks occur in sufficiently isolated quantum systems. My terminology might be a bit off, but if I'm right this is where decoherence plays a big role.

I agree that MWI and dBB have no measurement problem. The ensemble interpretation is just CI in density matrix language, and has a measurement problem because it has a classical/quantum cut.

Does CH really not have a measurement problem? If CH requires a single framework to be chosen, then who chooses the framework? Or must the observer lie outside, and choose the framework? Or do all frameworks occur?