Quantum Mechanics without Measurement

[stevendaryl]

I recommend the following paper by Robert B. Griffiths on developing the theory of quantum mechanics without giving a special role to measurements:

http://arxiv.org/pdf/quant-ph/0612065v1.pdf

In my opinion, it does not answer all the questions about locality and realism that come up in discussions about interpretations of quantum mechanics. But what I like about it is that it removes the special role that measurement plays in some formulations of quantum mechanics, and eliminates the need for wave function collapse.

Why was I specifically Googling for a formulation of quantum mechanics without measurements? Measurement is fundamental to some ways of presenting quantum mechanics. There is the "collapse interpretion" (which I think is due to Von Neumann) in which systems evolve deterministically according to Schrodinger's equation between measurements, but then the act of measurement causes a discontinuous, nondeterministic "collapse" of the wavefunction into an eigenstate of whatever observable was being measured. There are other interpretations that don't introduce collapse, but do make measurements the fundamental ingredient in the interpretation of quantum mechanics. For example, in the paper by Lucien Hardy
http://arxiv.org/pdf/quant-ph/0101012v4.pdf

The state associated with a particular preparation is defined to be (that thing represented by) any mathematical object that can be used to determine the probability associated with the outcomes of any measurement that may be performed on a system prepared by the given preparation.

Some people think that such an emphasis on measurement is appropriate, since physics is an empirical science, and empirical science is founded on measurements, experiments, observations, etc. However, I find it very unsatisfactory for measurement to play a key role in the formulation a of fundamental theory because measurements are not fundamental. A measuring device is, after all, a physical object, presumably governed by the same physical laws that govern atoms and molecules and light and gravity. What makes a particular physical object suitable to be considered a "measuring device" is pretty complicated:

• There must be an interaction between the system being measured and states of the measuring device.
• The measuring device must act as an "amplifier", so that microscopic properties of the system being measured can trigger macroscopic changes in the state of the device.
• The measuring device must have states that are sufficiently "orderly" to interpret easily. Either, there must be a number of discrete states in the measuring device that are observably different, or else there must be a continuous sets of states that can readily be interpreted as a linear scale.
• The act of measurement should result in a "record", an irreversible change that can be reliably checked later.

My objection to using measurements as primitive terms in formulations of quantum mechanics is that measurements are anything but primitive. You have to use physics to design objects that can act as measuring devices, but the measuring devices have to already exist before you can give any interpretation to the physics. This is circular. Of course, it's not really that bad, because of the fact that we know that classical physics works approximately for macroscopic objects. So we can use classical physics to design a "first cut" at measuring devices, and then use the knowledge of quantum mechanics that we get from those devices to make improved devices, and so bootstrap our way to a self-consistent notion of physics and measuring devices.

But it seems very messy. What I would prefer is a formulation of quantum mechanics that is about what happens in the world of particles and fields, and then use that theory to derive what makes a good measurement device in a noncircular way. I think that's the approach that Griffiths takes.

 

[bhobba]

Yes Decoherent Histories is a nice interpretation that avoids many of the issues with other formulations. In a sense it is Many Worlds without the Many Worlds.

But it comes at a cost - it complicates things IMHO unnecessarily, and to some extent, with its use of frameworks, is really defining your way out of problems.

Still many proponents call it Copenhagen done right:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.html

Lubos is correct IMHO - it removes a slight blemish with Copenhagen. Personally though I prefer the Statistical interpretation including decoherence - it seem's a bit cleaner to me.

Thanks
Bill

 

[Demystifier]

In my opinion, it does not answer all the questions about locality and realism that come up in discussions about interpretations of quantum mechanics.

This, indeed, is the main problem with the Griffiths interpretation. To avoid EPR "paradox" and consequences of the Bell theorem, Griffiths proposes to abandon the rules of classical LOGIC, replacing them with a kind of quantum logic:
http://lanl.arxiv.org/abs/1105.3932
http://lanl.arxiv.org/abs/1110.0974
Most physicists, mathematicians, and even logicians, find it very unattractive.

In particular, let me quote from http://www.scholarpedia.org/article/Bell's_theorem
"Thus, in CH [Consistent Histories], a "quantum measurement" is really supposed to be a measurement, simply revealing the pre-existing value of the measured observable; it is not the interaction with the apparatus that creates the observed value. That sounds a lot like a non-contextual hidden variables theory, which, as we now know, must lead to inconsistencies with the quantum predictions. ... The proponents of CH ... have imposed a rule which says essentially that arguments involving probabilities for several histories, not all of which belong to the same decoherent family, are forbidden. ... By forbidding the reasoning used to prove inequality (1), the aforementioned rule of CH prevents us from arriving at the contradiction. But a physical theory is not simply a game for which one can impose arbitrary rules about what reasonings are permitted for the propositions of the theory; if a physical theory implies both P and Q then the logical consequences of both P and Q will hold in a world governed by that theory and there is nothing that the proponents of the theory can do to prevent that. One might try to find an actual objection against the reasoning leading to inequality (1), but one cannot simply state as a "rule" that the reasoning is forbidden. ... We suspect that the proponents of CH would object to the proof of inequality (1) (within CH) by claiming that one cannot assume that all the random variables Zαi are defined over the same probability space because on each run of the experiment the value of only one among the Zα1 and the value of only one among the Zα2 is going to be observed. But if the experiments merely reveal pre-existing values then, on each run of the experiment, all the variables Zαi have a well-defined value (which may or may not turn out to be observed). ... The objection against the possibility of modeling the Zαi as random variables on the same probability space is effective only when one takes their values to be created by the experiments ... But reinterpreted in terms of values being created by experiment, CH would be pointless — it would just be orthodox quantum theory."

 

[Jilang]

This, indeed, is the main problem with the Griffiths interpretation.

In particular, let me quote from http://www.scholarpedia.org/article/Bell's_theorem
"Thus, in CH [Consistent Histories], a "quantum measurement" is really supposed to be a measurement, simply revealing the pre-existing value of the measured observable; it is not the interaction with the apparatus that creates the observed value. That sounds a lot like a non-contextual hidden variables theory, which, as we now know, must lead to inconsistencies with the quantum predictions. ...

I was particularly taken with page 13 of Stevendaryl's link. I was pretty confident that the situation at t2 would be as described, but at t1 I did a double take and had to read it a few times! Basically it says that the spin must be a certain value just before the particle enters the magnetic field of the Stern Gerlach experiment in order for everything to be consistent. However it does NOT claim that the spin is fixed at t0 (I.e. When it is emitted). That sounds not so much like a hidden variable, but more like a random variable, becoming crystallised out on entering the field.

 

[Jilang]

Yes Decoherent Histories is a nice interpretation that avoids many of the issues with other formulations. In a sense it is Many Worlds without the Many Worlds.

But it comes at a cost -

It would appear that the real cost which Griffiths talks about is that in consistent histories the time development of a quantum system is a random process, one is which the future and past states are not determined by the present state, but only related to it by certain probabilities.

 

[Demystifier]

Jilang, you are right that Griffiths interpretation is a probabilistic interpretation, and not a deterministic one. However, I wouldn't call it a cost. Furthermore, being fundamentally probabilistic does not mean that it is not about hidden variables. Namely, hidden variables do not necessarily need to be deterministic. Hidden variables just mean that the system's properties (which may be measured if one wishes to) exist even if one does not measure them.

The problem is that Griffiths wants to avoid the Bell theorem, according to which hidden variables (not necessarily deterministic) must necessarily be nonlocal. He avoids Bell theorem not by rejecting assumptions of the Bell theorem, but by rejecting classical LOGIC leading from the assumptions to the theorem.

Indeed, any logical conclusion may be avoided by rejecting the rules of logic. This technique, for instance, is often used by politicians. But should we allow it in science? I don't think so.

 

[Jilang]

Perhaps not a cost, but as Griffiths says "all of this at what price?". Not only giving up determinism and ordinary propositional logic, but also the quantum logic proposed by Birkhoff and Von Neumann. Seems expensive! Still I'm blown away.

 

[EskWIRED]

He avoids Bell theorem not by rejecting assumptions of the Bell theorem, but by rejecting classical LOGIC leading from the assumptions to the theorem.

Which rules of logic are rejected by him?

 

[Demystifier]

Which rules of logic are rejected by him?

Essentially, the following rule is rejected:
(A is true) & (B is true) --> (A & B) is true

His argument is the following: A is true in one framework, B is true in another framework, but you cannot combine statements from different frameworks. There is no single framework in which both A and B are true.

His concept of "framework" itself remains somewhat vague, but let me present my own idea of what that might mean:
"Madonna is not a good singer" is true in my framework, "Madonna is a good singer" is true in somebody else's framework with a different taste for music, but there is no person in the world in whose framework "Madonna both is and isn't a good singer".

However, such a view of "framework" attributes an important role to subjective observers, which is not what Griffiths does. Therefore the "framework" is his interpretation must be something else, but it's difficult to tell what.

 

[bhobba]

His concept of "framework" itself remains somewhat vague

Yea - it kinda reminds me of defining your way out of problems, and that its a bit vague - so much the better.

But then again exactly what an observation is in Copenhagen is a bit vague as well.

When people press me about that one its really horrid I have to get so handwavey.

Thanks
Bill

 

[martinbn]

I am not sure but I think that the word "logic" is used in two different ways. One as the rules we use to make conclusions and another as the algebra of certain propositions. The examples of phase spaces in classical and quantum mechanics seems to show that. If you consider a set and a family of subsets you can define "negation" (compliment), "and" (intersection) and "or" (union) and have the logic of subsets. Similarly for the subspaces of a Hilbert space "negation" (orthogonal compliment) and so on. The two logics are obviously different in the second you do not have the distributive property. But the logic by which you would go and prove statements in either situation is the same. A mathematician proving theorems in the first case, who decides to prove theorems in the second is not abandoning logic.

 

[stevendaryl]

Unless I'm missing something, the logic and probability associated with decoherent histories seems to be exactly analogous to the logic and probability associated with a single moment in time. I guess a single moment in time would be a degenerate case of a history, but I would like to look at that case because it's particularly simple to analyze.

With a single moment in time, we have the following collection of "atomic" statements (in the sense of "indivisible", not having anything to do with nuclei):

For every observable \mathcal{O}_i corresponding to a Hermitian operator \hat{O}_i and for every eigenvalue \lambda of that operator, there is a corresponding atomic statement: "\mathcal{O}_i has value \lambda". In the usual way, every statement corresponds to a projection operator P^i_\lambda, which projects an arbitrary state onto the subspace in which operator \hat{O}_i has eigenvalue \lambda.

If \mathcal{C} = \{ \mathcal{O}_1, \mathcal{O}_2, \ldots \} is a collection of observables corresponding to mutually commuting operators, then we can do ordinary logic and probability in reasoning about all the atomic statements involving observables in \mathcal{C}.

Fix an initial state |\Psi\rangle, then

The probability that \mathcal{O}_i has value \lambda is given by the expression \langle \Psi|P^i_\lambda|\Psi\rangle
​

(with an easy generalization to mixed states). Then it's easy enough to define "not", "and" and "or" in terms of these atomic statements, and we can compute probabilities for compound statements and we can compute conditional probabilities, etc.

So all of this is exactly like classical logic. The difference is that there are statements that are not expressible in terms of the atomic statements of \mathcal{C}, namely statements involving observables corresponding to noncommuting operators.

So that's the difference with classical logic: We choose a set \mathcal{C}, and then we can use classical logic, but we can't use classical logic to reason about the collection of all statements, just the statements associated with \mathcal{C}.

It seems to me that the decoherent histories approach just changes the focus from statements about a single moment to statements about the entire history. But the relationship with logic and probability is the same: You can reason using logic and probability, but only about a suitably compatible collection of statements.

 

[Jilang]

Is this the same as saying that incompatible observables cannot share the same probability space? I think I read that somewhere but I might have got hold of the wrong end of the stick!

 

[stevendaryl]

Is this the same as saying that incompatible observables cannot share the same probability space? I think I read that somewhere but I might have got hold of the wrong end of the stick!

I had heard that phrase, as well, but I didn't really know what it meant.

 

[Jilang]

But It looks like that's exactly what you said in your post #12 or are you pulling my leg?

If the concept of a framework seemed sort of vague should we think of it a probability space instead?

 

[stevendaryl]

But It looks like that's exactly what you said in your post #12 or are you pulling my leg?

If the concept of a framework seemed sort of vague should we think of it a probability space instead?

Well, the time that I had read that phrase, I thought that the author was saying that there was something wrong with Bell's theorem, because Bell erroneously assumed that the hidden variables are defined on the same probability space. If my discussion is what was meant, then it's not that Bell made an error. This kind of "logic" isn't hidden-variables in the sense of Bell.

 

[Jilang]

Isn't Bells inequality just a consequence of set theory where 3 attributes A,B and C are all compatible. E.g. The number of girls over 5 foot 5 with brown hair etc? Don't we need observables to be compatible to make a statement like ( A and B ) to have any logical meaning? Perhaps I'm missing something important.

 

[stevendaryl]

Isn't Bells inequality just a consequence of set theory where 3 attributes A,B and C are all compatible. E.g. The number of girls over 5 foot 5 with brown hair etc? Don't we need observables to be compatible to make a statement like ( A and B ) to have any logical meaning? Perhaps I'm missing something important.

Well, yeah, that's what the "quantum logic" says. Classical logic, however, says that "A and B" is always meaningful, provided that A is meaningful and B is meaningful.

 

[Demystifier]

Let me try to explain all this in terms of everyday-life concepts.

Except being an excellent physicists, Feynman is also known for being a good lover. (That can also be said for Schrodinger, but let us stick with Feynman.)

So, we can say that Feynman is a good physicist, and we can also say that Feynman is a good lover.
But can we say that Feynman is a good scientist and a good lover?

From the experimental point of view, no one ever seen Feynman to be a good physicist and a good lover at the same time. Under some conditions Feynman behaves as a good physicist, while under other conditions he behaves as a good lover. You don't need to know much about psychology to understand that there are no conditions under which he will show his physicist and lover abilities at the same time. So whether he behaves as a good physicist or a good lover depends on the CONTEXT. Feynman (just like any other human being) is - contextual.

Needles to say, this psychological contextuality is very much analogous to quantum contextuality.

All this is common sense, but we still didn't answer our first question: Can we say that Feynman is a good physicist and a good lover?

Most people don't see any problem with saying that. Yet, someone thinking about it in the same way as Griffiths thinks about quantum phenomena would conclude that it is not consistent to say that. He would explain that "being a good physicist" and "being a good lover" belongs to different frameworks, and that one should not combine statements from different frameworks.

So, would you agree with someone who tells you that it is inconsistent to say that "Feynman is a good physicist and a good lover"? If you would, then you might also like the Griffiths interpretation of quantum mechanics. If you wouldn't, then Griffiths interpretation of quantum mechanics is not something you might like.

All that is nice, but for me the real scientific issue is the following. Suppose you are a psychologist who wants to explain WHY Feynman never shows his physicist and lover abbilities at the same time. And suppose that someone tells you that this is BECAUSE those two properties belong to different frameworks, so that it is not logically consistent to SAY that he is a good physicist and a good lover. As a psychologist, would you be satisfied with such an explanation? I certainly wouldn't.

For the same reason, as a physicist, I am not satisfied with the Griffiths interpretation of quantum phenomena. The Griffiths interpretation constrains the language of talking about quantum phenomena, but for me it doesn't explain anything at the scientific level.

P.S.
If you liked the explanation of quantum mechanics above in terms of common-sense psychology, then see also
https://www.physicsforums.com/blog.php?b=9
https://www.physicsforums.com/blog.php?b=7

 

[stevendaryl]

Let me try to explain all this in terms of everyday-life concepts.

Except being an excellent physicists, Feynman is also known for being a good lover. (That can also be said for Schrodinger, but let us stick with Feynman.)

So, we can say that Feynman is a good physicist, and we can also say that Feynman is a good lover.
But can we say that Feynman is a good scientist and a good lover? ...

I sort of get the analogy. However, in the case of Feynman, we could bring the framework into the question, for example:

"If we were speaking from within the framework of physics, would you say that Feynman was a good physicist?"

"If we were speaking from within the framework of lovemaking, would you say that Feynman was a good lover?"

So it's possible that both of these questions can have the answer "yes" simultaneously. Feynman can't demonstrate the truth of both of these at the same time, because the demonstration of one requires a setting that is incompatible with the demonstration of the other. But it still makes sense to ask if both are true simultaneously.

This is sort of like "contrafactual definiteness" in discussions of Bell's inequality. Measuring the spin of an electron in the x-direction is incompatible with measuring the spin in the z-direction. So we can't, with a single experiment, know the answer to the questions:

"Is the electron spin-up in the z-direction?"
"Is the electron spin-up in the x-direction?"

However, you could make the questions into hypotheticals as follows:

"If I were to measure the z-component of spin, would I get spin-up?"
"If I were to measure the x-component of spin, would I get spin-up?"

By analogy with the Feynman case, one might think that it makes sense to ask the two questions simultaneously, even if there is no way to determine the answers (by a single experiment). You might think that a question whose answer cannot be know might as well be meaningless. But that's not exactly true, because people can do case-based analysis. For example, in logic, you can reason

• If A is true, then B is true.
• If A is false, then C is true.
• Therefore, B or C must be true.

The violation of Bell's inequality in EPR type experiments shows, in a sense, that certain conjunctions whose truth values are unknown cannot consistently be given a truth value. It's not just that we can't know or demonstrate the truth of the conjunction, but that it really doesn't have a consistent truth value.

 

[stevendaryl]

There's unfortunately a tendency to take a particular way of explaining quantum weirdness and assuming that it's the heart of quantum mechanics. Then you can find nonquantum analogies, and feel comforted (or disappointed, depending on your personality) that things aren't really so weird, after all.

The one that people latched onto from the very beginning was Heisenberg's "disturbance" interpretation of his uncertainty principle. To try to measure position of a tiny particle very precisely, you have to "see" it with a very small-wavelength light ray. But since light carries momentum as well, this changes the trajectory of the electron in an uncontrolled way. So no experiment can precisely determine the position and momenta of a particle. Similarly, measuring the z-component of an electron's spin invariably changes the x-component of spin in an uncontrollable way. So you think of the uncertainty principle in terms of the existence of incompatible properties where the set-up to measure one necessarily prevents you from measuring the other.

But the genius of the EPR experiment is that it gets around this problem. If you have two particles that have opposite spins, then you can measure the z-component of spin for one particle, and measure the x-component of spin for the other particle. Since the spins are correlated perfectly, this allows us to know the spins in the x-direction and z-direction simultaneously. But quantum mechanics doesn't allow us to make that conclusion (which would be perfectly justified from the point of view of classical probability and logic).

 

[craigi]

This has got me thinking. Is anyone working on a meta-interpretation? By this, I essentially mean a single mathematical expression of all possible interpretations of quantum physics.

What we have at the moment are many interpretations that select aspects of classicality to lock down and allow those remaining to have non-classical features in a hypothetical world, but conververgence in observable cases. It seems that it should, in theory at least, be possible to express this combination of features in a mathematical form. I'm going to go as far as suggesting that we should be able to derive such an expression.

I'm going to make a wild conjecture here, but imagine if such a meta-interpretation provided a hint on how to unite gravity with QM. Can anyone demonstrate that such a hint couldn't exist?

 

[martinbn]

I don't think the Feynman example is very good. I think you need to add a moment of time. Say, "F. is going to be a good physicist tomorrow at 5pm" is meaningful. So is "F. is going to be a good lover tomorrow at 5pm". But when you connect them with an "and" to form "F. is going to be a good physicist tomorrow at 5pm and F. is going to be a good lover tomorrow at 5pm" you get a meaningless statement.

 

[Demystifier]

I sort of get the analogy. However, in the case of Feynman, we could bring the framework into the question, for example:

"If we were speaking from within the framework of physics, would you say that Feynman was a good physicist?"

"If we were speaking from within the framework of lovemaking, would you say that Feynman was a good lover?"

So it's possible that both of these questions can have the answer "yes" simultaneously. Feynman can't demonstrate the truth of both of these at the same time, because the demonstration of one requires a setting that is incompatible with the demonstration of the other. But it still makes sense to ask if both are true simultaneously.

This is sort of like "contrafactual definiteness" in discussions of Bell's inequality. Measuring the spin of an electron in the x-direction is incompatible with measuring the spin in the z-direction. So we can't, with a single experiment, know the answer to the questions:

"Is the electron spin-up in the z-direction?"
"Is the electron spin-up in the x-direction?"

However, you could make the questions into hypotheticals as follows:

"If I were to measure the z-component of spin, would I get spin-up?"
"If I were to measure the x-component of spin, would I get spin-up?"

By analogy with the Feynman case, one might think that it makes sense to ask the two questions simultaneously, even if there is no way to determine the answers (by a single experiment). You might think that a question whose answer cannot be know might as well be meaningless. But that's not exactly true, because people can do case-based analysis. For example, in logic, you can reason

• If A is true, then B is true.
• If A is false, then C is true.
• Therefore, B or C must be true.

The violation of Bell's inequality in EPR type experiments shows, in a sense, that certain conjunctions whose truth values are unknown cannot consistently be given a truth value. It's not just that we can't know or demonstrate the truth of the conjunction, but that it really doesn't have a consistent truth value.

I agree with everything you say above. But in your opinion, what (if anything) does it tell us about the Griffiths interpretation?

 

[Demystifier]

But when you connect them with an "and" to form "F. is going to be a good physicist tomorrow at 5pm and F. is going to be a good lover tomorrow at 5pm" you get a meaningless statement.

Fine. But suppose you want to EXPLAIN why F. (or anybody else) is never a physicist and a good lover at the same time. Would you count the assertion above (that it is meaningless) as an explanation?

 

[stevendaryl]

I don't think the Feynman example is very good. I think you need to add a moment of time. Say, "F. is going to be a good physicist tomorrow at 5pm" is meaningful. So is "F. is going to be a good lover tomorrow at 5pm". But when you connect them with an "and" to form "F. is going to be a good physicist tomorrow at 5pm and F. is going to be a good lover tomorrow at 5pm" you get a meaningless statement.

Maybe. Except that you can imagine letting Feynman do a coin toss at the last minute to do physics or to make love. Then before the coin toss, it is certainly meaningful to say "If the result is heads, then Feynman will be a good physicist." and it is meaningful to say "If the result is tails, then Feynman will be a good lover." I don't see any reason for the conjunction to be meaningless. They could both be true. Presumably, a detailed theory of what makes a good physicist or a good lover would be able to say whether the statement "If the result is heads, then Feynman will be a good physicist" is true before actually tossing the coin.

 

[stevendaryl]

I agree with everything you say above. But in your opinion, what (if anything) does it tell us about the Griffiths interpretation?

Only that Griffiths' approach seems to be the same kind of abandonment of classical logic for histories that quantum logic is for properties at a single moment. He's able to recover classical logic only by restricting statements to a collection of "compatible" statements.

 

[atyy]

Fine. But suppose you want to EXPLAIN why F. (or anybody else) is never a physicist and a good lover at the same time. Would you count the assertion above (that it is meaningless) as an explanation?

But maybe that is not the right criticism of CH. When they say "Copenhagen done right", I assume they mean the possibility that quantum mechanics is truly weird and there cannot be hidden variables (let's say QM and Lorentz invariance are exact, so that dBB is ugly; and also there is no arrow of time, so many-worlds is also ugly). Then doesn't CH solve the measurement problem within an unrealistic framework?

(I guess your answer is "no", because there is no single framework in CH?)

 

[Demystifier]

Only that Griffiths' approach seems to be the same kind of abandonment of classical logic for histories that quantum logic is for properties at a single moment. He's able to recover classical logic only by restricting statements to a collection of "compatible" statements.

Fine. But in your opinion, does the physicist/lover complementarity can help us to better understand the Griffiths approach? And if it does, would you say that it increaes or decreses the value of his approach?

 

[Demystifier]

But maybe that is not the right criticism of CH. When they say "Copenhagen done right", I assume they mean the possibility that quantum mechanics is truly weird and there cannot be hidden variables (let's say QM and Lorentz invariance are exact, so that dBB is ugly; and also there is no arrow of time, so many-worlds is also ugly). Then doesn't CH solve the measurement problem within an unrealistic framework?

(I guess your answer is "no", because there is no single framework in CH?)

My answer is indeed "no", but for a different reason. If I cannot solve a problem by other means, then accepting it's weirdness will not resolve the problem either. At best it may make me stop thinking about the problem, which perhaps is not bad at all, but just because I stopped thinking about the problem doesn't mean I have solved it.

 

[Jilang]

Fine. But suppose you want to EXPLAIN why F. (or anybody else) is never a physicist and a good lover at the same time. Would you count the assertion above (that it is meaningless) as an explanation?

No, I wouldn't. F. being a classical dude can exist in an eigenstate of being a good lover and a good physicist at the same time. Whenever you measure each attribute you will get a consistent result which ever order to measure them in and how many times (within reason!). Hence it is not meaningless to say he is both at the same time. They are not mutually incompatible.

However if the spin of a spin 1/2 particle with S^2 = s(s+1)} has a component 1/2 along the z axis it cannot also have a component of 1/2 along the x-axis at the same time. The geometry of a triangle would say that the most it can be would be 1/√2 so the eigenstates are mutually incompatible.

 

[atyy]

My answer is indeed "no", but for a different reason. If I cannot solve a problem by other means, then accepting it's weirdness will not resolve the problem either. At best it may make me stop thinking about the problem, which perhaps is not bad at all, but just because I stopped thinking about the problem doesn't mean I have solved it.

If Bell's theorems are correct, and if the inequalities can be shown to be violated, then we are left with nonlocal realism or local nonrealism or superdeterminism or variables over which a probability distribution does not exist. dBB solves the measurement problem in nonlocal realism. Would you accept CH as a solution to the question of what local nonrealism might be in a way that solves the measurement problem (eg. solipsism is local nonrealism, but it has a measurement problem)?

 

[martinbn]

Maybe. Except that you can imagine letting Feynman do a coin toss at the last minute to do physics or to make love. Then before the coin toss, it is certainly meaningful to say "If the result is heads, then Feynman will be a good physicist." and it is meaningful to say "If the result is tails, then Feynman will be a good lover." I don't see any reason for the conjunction to be meaningless. They could both be true. Presumably, a detailed theory of what makes a good physicist or a good lover would be able to say whether the statement "If the result is heads, then Feynman will be a good physicist" is true before actually tossing the coin.

So! There is not claim that all conjunctions are meaningless. But you have completely changed the experimental set up. This is a different scenario.

 

[martinbn]

Fine. But suppose you want to EXPLAIN why F. (or anybody else) is never a physicist and a good lover at the same time. Would you count the assertion above (that it is meaningless) as an explanation?

Yes, if it is a logical necessity it is a good explanation. But what is your point? If it is something is meaningless it is meaningless, saying the opposite cannot be a part of a good explanation.

 

[atyy]

Here are some of the criticisms of CH I've heard. Have these been resolved or are they non-problems?

1. Dowker and Kent say that it isn't obvious that there is any quasiclassical realm in CH. http://arxiv.org/abs/gr-qc/9412067

2. Laloe says that in CH there are consistent histories in which the cat is both dead and alive. http://arxiv.org/abs/quant-ph/0209123 (p88)

 

[Demystifier]

Yes, if it is a logical necessity it is a good explanation.

Yes, but CH is not a logical necessity. For instance, nonlocal hidden variables are logically not excluded.

But what is your point? If it is something is meaningless it is meaningless, saying the opposite cannot be a part of a good explanation.

Generaly, something can be meaningless only within a certain predefined rules of language. The CH interpretation proposes one such set of rules, and within this language some statements are meaningless. But they still have meaning outside of this language, i.e., in some other interpretation of quantum mechanics. So the real question is: Should we accept the rules of language proposed by CH? My point is that we shouldn't.

 

[Demystifier]

Would you accept CH as a solution to the question of what local nonrealism might be in a way that solves the measurement problem

No I wouldn't.

(eg. solipsism is local nonrealism, but it has a measurement problem)?

In an attempt to understand local nonrealism as a kind of solipsism WITHOUT a measurement problem, I have constructed my own model of solipsistic local hidden variables:
http://lanl.arxiv.org/abs/1112.2034 [Int. J. Quantum Inf. 10 (2012) 1241016]

 

[DevilsAvocado]

Some people think that such an emphasis on measurement is appropriate, since physics is an empirical science, and empirical science is founded on measurements, experiments, observations, etc. However, I find it very unsatisfactory for measurement to play a key role in the formulation a of fundamental theory because measurements are not fundamental.

I absolutely agree, and so do J. S. Bell in his last article – Against ‘Measurement’ (1990).

http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf]Here[/PLAIN] are some words which, however legitimate and necessary in application, have no place in a formulation with any pretension to physical precision: system, apparatus, environment, microscopic, macroscopic, reversible, irreversible, observable, information, measurement.

The concepts 'system', 'apparatus', 'environment', immediately imply an artificial division of the world, and an intention to neglect, or take only schematic account of, the interaction across the split. The notions of 'microscopic' and 'macroscopic' defy precise definition. So also do the notions of 'reversible' and 'irreversible'. Einstein said that it is theory which decides what is 'observable'. I think he was right – 'observation' is a complicated and theory-laden business. Then that notion should not appear in the formulation of fundamental theory. Information? Whose information? Information about what?

On this list of bad words from good books, the worst of all is 'measurement'. It must have a section to itself.

A measuring device is, after all, a physical object, presumably governed by the same physical laws that govern atoms and molecules and light and gravity. What makes a particular physical object suitable to be considered a "measuring device" is pretty complicated:

• There must be an interaction between the system being measured and states of the measuring device.
• The measuring device must act as an "amplifier", so that microscopic properties of the system being measured can trigger macroscopic changes in the state of the device.
• The measuring device must have states that are sufficiently "orderly" to interpret easily. Either, there must be a number of discrete states in the measuring device that are observably different, or else there must be a continuous sets of states that can readily be interpreted as a linear scale.
• The act of measurement should result in a "record", an irreversible change that can be reliably checked later.

Yes, and to be picky (and maybe make things worse), there are also quantum "measuring devices", for example a beamsplitter; where we do have an interaction and measurement of states, but no microscopic amplification or irreversibility (i.e. quantum measurements could easily be undone).

It seems that the root of the 'confusion' is the Schrödinger wavefunction vs. the Born rule |ψ|², which afaik is just a 'hack', without any rigorous mathematical 'explanation'. Bell seems to agree even on this point.

http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf]In[/PLAIN] the beginning, Schrodinger tried to interpret his wave- function as giving somehow the density of the stuff of which the world is made. He tried to think of an electron as represented by a wavepacket – a wavefunction appreciably different from zero only over a small region in space. The extension of that region he thought of as the actual size of the electron - his electron was a bit fuzzy. At first he thought that small wavepackets, evolving according to the Schrodinger equation, would remain small. But that was wrong. Wavepackets diffuse, and with the passage of time become indefinitely extended, according to the Schrodinger equation. But however far the wavefunction has extended, the reaction of a detector to an electron remains spotty. So Schrodinger's 'realistic' interpretation of his wavefunction did not survive.

Then came the Born interpretation. The wavefunction gives not the density of stuff, but gives rather (on squaring its modulus) the density of probability. Probability of what, exactly? Not of the electron being there, but of the electron being found there, if its position is 'measured'.

Why this aversion to 'being' and insistence on 'finding'? The founding fathers were unable to form a clear picture of things on the remote atomic scale. They became very aware of the intervening apparatus, and of the need for a 'classical' base from which to intervene on the quantum system. And so the shifty split.

And the "shifty split" is still there; 24 years later, as Steven Weinberg explains.

[my bolding]

http://scitation.aip.org/content/aip/magazine/physicstoday/article/58/11/10.1063/1.2155755]Bohr’s[/PLAIN] version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?

Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus. The difficulty is not that quantum mechanics is probabilistic — that is something we apparently just have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.

Regarding Griffiths; the urge to 'eradicate' measurements altogether, I think has more to do with the problem that we do have empirical evidence (i.e. EPR-Bell experiments) that do not fit his consistent worldview – and the easiest thing to do is just to get rid of the whole enchilada, by some preposterous word-salad, that no one can take seriously.

And yet it moves -- Galileo Galilei​

Griffiths makes two disastrous mistakes:

1)

Bell's theorem is a no-go theorem, which put restrictions on the classical world, not quantum mechanics, and to try to solve this dilemma by 'modifications' on Hilbert space, quantum logic, etc, is just ridiculous. QM works – classical local realism don't!

We can forget everything about Bell's theorem and QM, and instead put "Barnum & Bailey Circus – The Greatest Show on Earth", in its place:

 Classical      |     Barnum & Bailey              |     Classical
----------------------------------------------------------------------------
 Source  -->    |     Entanglement Circus   -->    |     Measurement data 
----------------------------------------------------------------------------

Now, if we empirically have tested the Barnum & Bailey Circus for almost a hundred years, without finding one single error, we have to assume that this circus is not cheating, right?

And since the outcome is classical, we can inspect the results without any 'influences' from Barnum & Bailey, right?

Then, the only rational way is to check if we can replicate the 'trick' without Barnum & Bailey, and if we can't do this, then the only option left is modifications in our view on the classical part, even if it hurts, right?

Thus, it doesn't really matter what 'trick' Barnum & Bailey performs, because we have checked their business model for almost a hundred years, and Barnum & Bailey are true/compatible to all tests performed this far (which also means that this reputation can never be taken away from them, no matter what happens in the future), right?

Conclusion: We must modify our view* on the classical part in this show; this is the only way out, Griffiths is on the wrong path, leading to a dead end.

*I.e. "Barnum & Bailey" has the capability to perform a 'trick' that is empirical true, but impossible to replicate with only the tools available in the classical part.​

2)

Griffiths tries to put science on The Platonic Pedestal of Eternal, Ultimate and Consistent Truth – but he has already lost the game (obviously without even knowing it). Gödel's incompleteness theorem proves that any system that is sufficiently powerful cannot be both consistent and complete.

Thus, Griffiths is using logic – proven to be either inconsistent or incomplete – to prove physics consistent and complete.​

Result = Inconsistent Fairy Tales

 

[atyy]

No I wouldn't.

Why don't you consider CH to be a version of local nonrealism without a measurement problem?

In an attempt to understand local nonrealism as a kind of solipsism WITHOUT a measurement problem, I have constructed my own model of solipsistic local hidden variables:
http://lanl.arxiv.org/abs/1112.2034 [Int. J. Quantum Inf. 10 (2012) 1241016]

Yes, I think that works.

 

[DevilsAvocado]

This, indeed, is the main problem with the Griffiths interpretation. To avoid EPR "paradox" and consequences of the Bell theorem, Griffiths proposes to abandon the rules of classical LOGIC, replacing them with a kind of quantum logic:
http://lanl.arxiv.org/abs/1105.3932
http://lanl.arxiv.org/abs/1110.0974
Most physicists, mathematicians, and even logicians, find it very unattractive.

In particular, let me quote from http://www.scholarpedia.org/article/Bell's_theorem
"[...] By forbidding the reasoning used to prove inequality (1), the aforementioned rule of CH prevents us from arriving at the contradiction. But a physical theory is not simply a game for which one can impose arbitrary rules about what reasonings are permitted for the propositions of the theory;"

The problem is that Griffiths wants to avoid the Bell theorem, according to which hidden variables (not necessarily deterministic) must necessarily be nonlocal. He avoids Bell theorem not by rejecting assumptions of the Bell theorem, but by rejecting classical LOGIC leading from the assumptions to the theorem.

Indeed, any logical conclusion may be avoided by rejecting the rules of logic. This technique, for instance, is often used by politicians. But should we allow it in science? I don't think so.

Thank you very much for this Demystifier. In an earlier thread, I did find it necessary to defend Griffiths as not being a crackpot. After all, he is a Professor of Physics at Carnegie Mellon University.

But now, I'm not so sure about this...

 

[DevilsAvocado]

Except being an excellent physicists, Feynman is also known for being a good lover. (That can also be said for Schrodinger, but let us stick with Feynman.)

So, we can say that Feynman is a good physicist, and we can also say that Feynman is a good lover.
But can we say that Feynman is a good scientist and a good lover?

This could be hard to prove, however with Schrödinger the case is a little bit ambiguous... Schrödinger discovered quantum theory while hunkered down with a lover in a Swiss chalet... and when pressed to write about his creative life... he protested, saying that he felt the part his lovers played in it was crucial, but discretion would require him to leave that out.

This opens a possibility for Schrödinger actually 'multitasking' in the Swiss chalet...

Seriously, everything that does not happen simultaneously cannot be proven true?? What a joke...

 

[Maui]

Quantum Mechanics without Measurement

also known as 'superposition'

 

[stevendaryl]

So! There is not claim that all conjunctions are meaningless. But you have completely changed the experimental set up. This is a different scenario.

I don't think so. The Feynman is precisely understood in terms of "hidden variables". Even though you have to make a choice whether to test his lover ability or his physics ability, we an assume that both abilities exist in him at the same time, although we can't demonstrate this.

So there is no contradiction that arises from assuming "hidden variables" in the Feynman case, while in the quantum mechanics it leads to a contradiction (or to a violation of something else important, such as locality).

 

[stevendaryl]

Thank you very much for this Demystifier. In an earlier thread, I did find it necessary to defend Griffiths as not being a crackpot. After all, he is a Professor of Physics at Carnegie Mellon University.

But now, I'm not so sure about this...

He is definitely not crackpot. You can disagree about whether he has solved the conceptual problems of quantum mechanics through his approach without saying he's a crackpot.

 

[stevendaryl]

also known as 'superposition'

No, I wouldn't say that that's very accurate.

 

[atyy]

Thank you very much for this Demystifier. In an earlier thread, I did find it necessary to defend Griffiths as not being a crackpot. After all, he is a Professor of Physics at Carnegie Mellon University.

But now, I'm not so sure about this...

If Griffiths has made a mistake, where could it be? On the one hand, CH is not a realistic theory, so it seems that it could escape the Bell theorem.

In http://quantum.phys.cmu.edu/CQT/chaps/cqt24.pdf (p289) he writes that "Thus the point at which the derivation of (24.10) begins to deviate from quantum principles is in the assumption that a function $\alpha(w_{a}, \lambda )$ exists for different directions $w_{a}$."

Well, so far I think what he says is ok, since Bell's point is indeed that these exist only if local realism holds, and quantum mechanics is not a local realistic theory.

Then he says "The claim is sometimes made that quantum theory must be nonlocal simply because its predictions violate (24.10). But this is not correct. First, what follows logically from the violation of this inequality is that hidden variable theories, if they are to agree with quantum theory, must be nonlocal or embody some other peculiarity. But hidden variable theories by definition employ a different mathematical structure from (or in addition to) the quantum Hilbert space, so this tells us nothing about standard quantum mechanics."

This seems fishy, because http://arxiv.org/abs/0901.4255 argues that the Bell theorem is compatible with quantum mechanics, since the wave function itself can serve as the hidden variable. It is simply that if one accepts "realism", then the wave function is nonlocal. So I don't think the Bell inequality is incompatible with quantum mechanics. Perhaps it is here that Griffiths has made a mistake.

Nonetheless, in the broader sense, it seems that Griffiths could be right, and CH could be local since it does seem to reject realism (ie. Griffiths's definition of "realism" is not common sense realism). Hohenberg's introduction to CH http://arxiv.org/abs/0909.2359, for example, says CH is not realistic theory - which given how some versions of Copenhagen don't favour realism - CH could I think be argued to be Copenhagen done right.

But exactly how is locality retained in CH? Hohenberg says it's because there is no single framework in CH in which Eq 11 http://arxiv.org/abs/0909.2359 is satisfied. Can that be the explanation? It seems it is not satisfied in the orthodox shut-up-and-calculate Copenhagenish view, but that doesn't make shut-up-and-calculate local. So is the explanation instead that P(A,B,a,b), where a and b range over non-commuting observables does not exist in any single framework?

What I'm asking is: in CH is the Bell inequality violated in any single framework?

 

[Maui]

No, I wouldn't say that that's very accurate.

It's accurate. There are many ways to define 'measurement'.

 

[stevendaryl]

It's accurate. There are many ways to define 'measurement'.

But "superposition" certainly doesn't mean the same thing as "Quantum Mechanics without Measurement".

 

[stevendaryl]

Regarding Griffiths; the urge to 'eradicate' measurements altogether, I think has more to do with the problem that we do have empirical evidence (i.e. EPR-Bell experiments) that do not fit his consistent worldview – and the easiest thing to do is just to get rid of the whole enchilada, by some preposterous word-salad, that no one can take seriously.

I think that is way too harsh. I don't see it that way at all. As someone else said, I see it as a way of doing Copenhagen without making measurement devices primary to the formulation. Instead, it makes histories of observables primary. That is a little bit of an improvement, because observables do have a definite definition within the framework of quantum mechanics, which is not true of "measurement".

I think that there is a sense in which what is being done is just systematizing the practice of quantum mechanics, which is basically Copenhagen, with as few non-physical, fuzzy elements as possible.

 

[stevendaryl]

I think has more to do with the problem that we do have empirical evidence (i.e. EPR-Bell experiments) that do not fit his consistent worldview.

I don't know why you say that EPR "doesn't fit in his worldview". EPR experiments can perfectly well be analyzed from the point of view of consistent histories. All the possible outcomes of an EPR experiment form "consistent histories", and the consistent histories approach would allow you to compute the probabilities of those outcomes. At least, I would assume that to be the case---if it's not, then I agree with you that consistent histories is complete garbage.

Let me do some Googling to see if there is a good analysis of EPR from the point of view of consistent histories. I would think that would be the very first thing that would be tried with any new foundation for quantum mechanics.