Determinism, realism, hidden variables

[Jilang]

I think it's possible that that idea, when fleshed out, would lead to something like Many-Worlds or Consistent Histories. Not that those are completely free of conceptual problems, either.

I haven't encountered any formulation that considers wavefunctions for different observers or how they transform from one to another. I would be very interested in any links that may shed light on this subject, as I agree that they are subjective animals.

 

[Paul Colby]

The problem with this is the EPR criterion of reality. The measurement in the same direction by Bob predicts, with certainty, the result of the measurement by Alice. In dBB theory, where faster than light causal influences exist, this is unproblematic, but in any Einstein-causal theory you have a problem explaining this with a "cooperative deal" with the measurement device of Alice.

I'm kind of a luddite. For example the fact that the speed of light is constant in every frame makes no sense "intuitively" but I accept it as actual fact for all the reasons we know and love and move on. Question, what's missing from QM that people don't feel comfortable with once the basic rules are accepted?

The entire EPR elements of reality stuff is clearly broken right from the get go by the basic rules. A given spin eigenstate may always be found in a different one simply by measuring along another axis. Clearly the whole "spin has a value" thing is pretty strongly depends on the measurement performed as a matter of basic principle. So I ask, what in QM need interpretation? Looks complete to me.

 

[eltodesukane]

<It gives rules how to compute probabilities, but explains nothing.>
<But what if those probabilistic rules are the explanation ? What if the universe actually does play dice ?>
-- In the blockworld view of reality, spacetime exits as a block, all of space and all of time within it.
To us, the transition from present time to future time may appear deterministic or probabilistic.
But from the blockworld point of view it doesn`t matter. The whole of spacetime is there, fixed, immutable, unchanging.

 

[Paul Colby]

<It gives rules how to compute probabilities, but explains nothing.>

Can you define "explain" in this context? The fact that a system may be assigned a state vector is fundamental, just like c being a constant. Can one be expected to explain constancy of c without falling back on observation or theory based on such?

 

[Derek Potter]

There is another problem, which is the sense in which anything at all happens in MWI. I can't remember the exact argument showing why this is problem, but it might be something like this: if you have the wave function of the whole universe then (at least nonrelativistically), you can write it as a superposition of energy eigenstates. Because wave function evolution is linear, you can treat each eigenstate as a separate universe that doesn't interact with any of the others. But an energy eigenstate is essentially a static world--the only time evolution is just an overall phase.

In the energy basis each world is stationary but in any other basis a world is a superposition of those energy states so they will interfere (or beat) and stuff will happen. I think this highlights the fact that in MWI, the basis is essentially arbitrary: you don't have just one set of worlds, you have many alternative sets. I don't see the problem with MWI saying that in some bases the worlds are static, in many bases the worlds are chaotic meaningless monsters, but in a few the worlds are quite like this one(s). What am I missing?

 

[Ilja]

.
We do? Would that be that deeply suspect category of interpretation in which... I can hardly bring myself to say this... in which, gulp, there are no *proper* mixtures? :)

? I don't understand what you mean. Mixtures, proper or improper, who cares?

I'm kind of a luddite. For example the fact that the speed of light is constant in every frame makes no sense "intuitively" but I accept it as actual fact for all the reasons we know and love and move on. Question, what's missing from QM that people don't feel comfortable with once the basic rules are accepted?

The entire EPR elements of reality stuff is clearly broken right from the get go by the basic rules. A given spin eigenstate may always be found in a different one simply by measuring along another axis. Clearly the whole "spin has a value" thing is pretty strongly depends on the measurement performed as a matter of basic principle. So I ask, what in QM need interpretation? Looks complete to me.

For me, the Poincare group is simply the symmetry group of the wave equation. It contains some strange transformations which mix up space and time, but that's an accidental symmetry, that's all.

Instead, the EPR criterion of reality is a simple and reasonable criterion. Usually such simple principles do not give very much, but combined with the fundamental variant of Lorentz symmetry, which leads to Einstein causality, it gives some non-trivial predictions which appear to be false. Bad luck for the idea that relativistic symmetry is fundamental - an idea which is, anyway, quite artificial.

 

[Paul Colby]

Instead, the EPR criterion of reality is a simple and reasonable criterion.

Yet in rather direct conflict with the rules of QM. For me this suggest I can live without it and move on.

 

[Derek Potter]

? I don't understand what you mean. Mixtures, proper or improper, who cares?

Some of us do.

And thanks for reminding me why I don't hang around PF much these days.

 

[Ilja]

Yet in rather direct conflict with the rules of QM. For me this suggest I can live without it and move on.

Which conflict? There is none, there are EPR-realistic interpretations of QM.

 

[Paul Colby]

Which conflict? There is none, there are EPR-realistic interpretations of QM.

So, if I measure an eigenstate of A and get with certainty a value of, $\alpha$, then $\alpha$ has a element of reality? Okay, so what. They made up a definition. It doesn't then follow this definition is in anyway a useful one. In fact conceptually it's harmful because it's pretty clear it isn't one that is helpful in understanding QM or the way the world is observed to work. Since QM works fine without the EPR reality criterion, why include it? Does including it help one understand the three way correlations found in a GHZ type experiment? I think not.

 

[Ilja]

You think it is pretty clear that the EPR criterion isn't helpful? I think that, instead, it is extremely helpful.

What is the way science makes progress? By falsifying wrong theories. Here, the EPR criterion was extremely helpful, because it has allowed us to falsify a whole class of theories - theories where relativistic symmetry is fundamental. I think it is extremely important that this class of theories has been falsified, because it has obtained in modern physics a status which no physical hypothesis deserves at all - that of a quasi-religious dogma.

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

This is what one has to reject if one wants to save the thesis that relativistic symmetry is fundamental. I think that to reject this criterion can be classified in a very natural way as denial of reality.

 

[Markus Hanke]

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

This basically boils down to asking a "Yes-No" question - does a particular measurement on a given preparation yield a specified value, or not ? The problem I see with this is that you have to disturb the system in order to answer this question; if you don't perform a measurement, you will not know if the answer is yes or no. In fact, there is no a priori reason to assume that, prior to measurement, it is even meaningful to say that it must be either yes or no, since the state of the system is fundamentally linked to the measurement process.

 

[Markus Hanke]

Some further reading on these subjects led me across this interpretation of QT :

http://plato.stanford.edu/entries/qm-relational/

This is ticking a lot of boxes for me, and is definitely a very interesting way to look at the theory, as at first glance it seems to eliminate some of the conceptual issues. Is anyone here familiar with the relational interpretation - in particular, what are its problems/criticisms ? Is there anything I am not aware of that immediately kills this as a valid interpretation, or is it considered potentially viable ?

 

[Demystifier]

Some further reading on these subjects led me across this interpretation of QT :

http://plato.stanford.edu/entries/qm-relational/

This is ticking a lot of boxes for me, and is definitely a very interesting way to look at the theory, as at first glance it seems to eliminate some of the conceptual issues. Is anyone here familiar with the relational interpretation - in particular, what are its problems/criticisms ? Is there anything I am not aware of that immediately kills this as a valid interpretation, or is it considered potentially viable ?

Here is a critique. According to relational interpretation, it does not make sense to say that something (call it A) exists. It only makes sense that something exists relative to something else (say B). But what about (A and B) together? Does the entity (A and B) exists by itself, or does it only exist relative to something else (say C). If (A and B) exists by itself, then it contradicts the relational interpretation. If it exists only relative to C, then what about the existence of (A and B and C)? Or (A and B and C and D)? In this way you either must violate relational interpretation at some point, or introduce an infinite regress. Both options are problematic.

If this is too abstract, here is an explicit example.
- Do you exist by yourself? Or do you only exist relative to the screen you are watching right now?
- Do (you and screen) exist by themselves? Or do (you and screen) only exist relative to the computer wired with the screen?
- Do (you and screen and computer) exist by themselves? Or do (you and screen and computer) only exist relative to internet to which the computer is connected?
- Etc, etc ...
...
- Does the whole Universe exists by itself? Or does it only exist relative to, well, God?

In short, the relational interpretation leads to an infinite regress not much different from the von Neumann infinite regress. Von Neumann cut the regress by introducing a collapse associated with consciousness. But adherents of relational interpretation do not want to deal with consciousness in any explicit way, and they have no idea how to cut the regress.

 

[Markus Hanke]

In short, the relational interpretation leads to an infinite regress not much different from the von Neumann infinite regress.

Very interesting point, thank you. A fascinating problem indeed. It reminds me a little of the concept of "motion" in relativity - it makes no sense to talk about the motion of A, unless one has a reference point B with respect to which the motion happens. Motion is quite simply not an intrinsic property that can be measured in isolation. But what about B ? Does it move, and if so, with respect to what ? And how about the A-B system ? And so on. One could also conceptualise an infinite regress. We get around this by choosing a specific reference coordinate system ( which is arbitrary ) with an origin, so that we can express relationships between events ( which are not intrinsic to the objects themselves ), and we formulate the laws of physics such that their form does not explicitly depend on our choice of coordinates. We all know that this works well and does not lead to pesky infinities ( so far as motion is concerned ). By analogy, perhaps there is also a way to get around the infinite regress in RQM, I don't know.

By I do get your point about the regress, and I do agree that it seems to be a problem. It's still an interesting interpretation of QT, though.

 

[Derek Potter]

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

This is what one has to reject if one wants to save the thesis that relativistic symmetry is fundamental. I think that to reject this criterion can be classified in a very natural way as denial of reality.

So what happens to relativistic symmetry in MWI? One may predict that a succession of observations will show a persistent value in each world. But this is repeated with different values in every world. I don't think the Einstein criterion actually addresses relative realities or superpositions that involve the observer, does it? So I'm wondering whether MWI manages to keep relativistic symmetry by saying that the values are real in each world?

 

[Derek Potter]

Here is a critique. According to relational interpretation, it does not make sense to say that something (call it A) exists. It only makes sense that something exists relative to something else (say B). But what about (A and B) together? Does the entity (A and B) exists by itself, or does it only exist relative to something else (say C). If (A and B) exists by itself, then it contradicts the relational interpretation. If it exists only relative to C, then what about the existence of (A and B and C)? Or (A and B and C and D)? In this way you either must violate relational interpretation at some point, or introduce an infinite regress. Both options are problematic.

Why an infinite regress? Why not a self-consistent set of relations?
I mean something like this: A, B, C etc form a set. If x and y are members then x and y is a member. Existence is defined as the relation between any two (or more?) members.

This sounds incredibly similar to MWI. MWI was born out of explicitly considering entanglements and then you get exactly (?) what you describe apart from states taking the place of "things that exist". Why does relative existence pose any more problem than relative states?

 

[Heinera]

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

This basically boils down to asking a "Yes-No" question - does a particular measurement on a given preparation yield a specified value, or not ? The problem I see with this is that you have to disturb the system in order to answer this question; if you don't perform a measurement, you will not know if the answer is yes or no. In fact, there is no a priori reason to assume that, prior to measurement, it is even meaningful to say that it must be either yes or no, since the state of the system is fundamentally linked to the measurement process.

I think what EPR means with that sentence is that you can make a prediction without disturbing the system. Veryfying that prediction by a later observation would of course disturb the system.

E.g., by a measurement at Alice we can make a prediction about Bob's result, where Bob's part of the experiment is regarded as an isolated system due to space-like separation.

 

[Paul Colby]

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

This is what one has to reject if one wants to save the thesis that relativistic symmetry is fundamental. I think that to reject this criterion can be classified in a very natural way as denial of reality.

Well, by this criterion if the spin component along the z-axis is an "element of reality" for a given system then, by the same criterion, the spin component along a direction 0.0001 (or any finite number of) degrees off the z-axis is no longer "real" in the same sense. We would have to accept reality becoming discontinuous. We could also assume, as I would prefer, the EPR reality criterion is silly in a quantum mechanical context. I have little trouble rejecting "elements of reality" given the overwhelming evidence for QM being the way of the world.

 

[stevendaryl]

Well, by this criterion if the spin component along the z-axis is an "element of reality" for a given system then, by the same criterion, the spin component along a direction 0.0001 (or any finite number of) degrees off the z-axis is no longer "real" in the same sense.

I don't see it that way, at all. The claim is not that something is only real if it allows predictions with certainty, only that if something allows predictions with certainty, then it is real.

It's hard for me to understand what it means to reject the EPR notion of reality. If Alice knows ahead of time what Bob's measurement result will be, then is that a physical, objective fact about Bob and his particle? How can it not be? (Well, I can think of a couple of ways, but I'll get to those in a while...)

Or let's take a different tack: Suppose Alice is "preparing" positrons for Bob by passing them through a filter that only allows those particles with spin-up in the z-direction to get to Bob. Then Bob is faced with positrons that are in the spin-state |U\rangle. Is that a physical, objective fact about Bob's positrons, or not? If not, what kind of information is it?

...

Oh, two ways in which the EPR notion of reality might be false are: (1) If Alice and her detector affects Bob's result, then the knowledge that Bob will definitely measure spin-down (or whatever) is a fact about Alice, not (exclusively) a fact about Bob. (2) In Many-Worlds, Alice measuring spin-up doesn't say anything about what Bob will measure, because Bob will measure both outcomes in any case.

 

[Demystifier]

I mean something like this: A, B, C etc form a set. If x and y are members then x and y is a member. Existence is defined as the relation between any two (or more?) members.

I don't get it. How are x and y related to A, B and C?

This sounds incredibly similar to MWI. MWI was born out of explicitly considering entanglements and then you get exactly (?) what you describe apart from states taking the place of "things that exist". Why does relative existence pose any more problem than relative states?

That does sound similar to relative states, but not to MWI. Relative states is not the same as MWI. MWI is the Wheeler's reinterpretation of the Everett's relative states.

 

[Demystifier]

Very interesting point, thank you. A fascinating problem indeed. It reminds me a little of the concept of "motion" in relativity - it makes no sense to talk about the motion of A, unless one has a reference point B with respect to which the motion happens. Motion is quite simply not an intrinsic property that can be measured in isolation. But what about B ? Does it move, and if so, with respect to what ? And how about the A-B system ? And so on. One could also conceptualise an infinite regress. We get around this by choosing a specific reference coordinate system ( which is arbitrary ) with an origin, so that we can express relationships between events ( which are not intrinsic to the objects themselves ), and we formulate the laws of physics such that their form does not explicitly depend on our choice of coordinates. We all know that this works well and does not lead to pesky infinities ( so far as motion is concerned ). By analogy, perhaps there is also a way to get around the infinite regress in RQM, I don't know.

Interesting analogy, but there is one big difference. The property of being in motion is not a prerequisite for having other properties. The property of existing is. For how can something have any properties if it doesn't even exist? In other words, existence is elementary and motion is not. A non-elementary thing my be relative, but an elementary thing should be absolute.

OK, now it's definitely philosophy and not physics. But that's another reason for not taking relational QM seriously. Of course, all interpretations are somewhat philosophical, but relational interpretation seems to be much more philosophical than other interpretations.

 

[Paul Colby]

Is that a physical, objective fact about Bob's positrons, or not?

The terms "physical" and "objective" are being used here for their emotional content. It's like if one can label a fact "subjective" it is somehow less worthy of correctness. I'm of the opinion that additional terms like these are used to hide the "mind's eye" in. All experience to date shows that assigning a numerical value (rather than a QM state) to the positron is not a fruitful way of viewing the world.

 

[harrylin]

Well, by this criterion if the spin component along the z-axis is an "element of reality" for a given system then, by the same criterion, the spin component along a direction 0.0001 (or any finite number of) degrees off the z-axis is no longer "real" in the same sense. We would have to accept reality becoming discontinuous. We could also assume, as I would prefer, the EPR reality criterion is silly in a quantum mechanical context. I have little trouble rejecting "elements of reality" given the overwhelming evidence for QM being the way of the world.

A measured spin "component" is definitely the outcome of disturbing the system. It's therefore doubtful to consider that as an "element of reality" of the the undisturbed system, as intended by EPR and understood by Bell. There was only assumed to be an element of reality that corresponds to it.
Coincidentally, I read yesterday that a measured spin component is certainly not an "element of reality" of the electrons in the DBB interpretation - once more, http://arxiv.org/abs/1305.1280 "The Pilot-Wave Perspective on Spin" -Norsen

 

[Ilja]

So what happens to relativistic symmetry in MWI?

Please don't ask me anything about MWI. I'm unable to explain something about MWI using only decent language. It is simply inconsistent as an interpretation. Probabilities make sense only as a plausible expectation about what happens. If everything happens, it makes no sense at all.

I don't think the Einstein criterion actually addresses relative realities or superpositions that involve the observer, does it?

Of course, Einstein is a scientist, so ...

So I'm wondering whether MWI manages to keep relativistic symmetry by saying that the values are real in each world?

MWI rejects every argumentation once it does not like the results (that means, in particular, Bell's theorem) but on the other hand uses common sense postulates from the justification of Bayesian probability theory to justify the claim that they can somehow derive the Born rule. IMHO not more than an actual illustration how one can derive everything from a theory with contradictions.

 

[Ilja]

Well, by this criterion if the spin component along the z-axis is an "element of reality" for a given system then, by the same criterion, the spin component along a direction 0.0001 (or any finite number of) degrees off the z-axis is no longer "real" in the same sense. We would have to accept reality becoming discontinuous. We could also assume, as I would prefer, the EPR reality criterion is silly in a quantum mechanical context. I have little trouble rejecting "elements of reality" given the overwhelming evidence for QM being the way of the world.

To conclude from the EPR criterion of reality alone that some spin component is an element of reality is not possible. So, the problem does not exist. You have to add Einstein causality to derive something nontrivial about any spin. But once Einstein causality is not valid, no such problem arises.

 

[Paul Colby]

A measured spin "component" is definitely the outcome of disturbing the system. It's therefore doubtful to consider that as an "element of reality" of the the undisturbed system, as intended by EPR and understood by Bell

Help me out here. A system in an eigenstate of observable $A$ has this mythical "element of reality" prior to measurement but only if $A$ is an measurement is performed? Once performed, the system is disturbed yielding the eigenvalue $\alpha$ of $A$. I guess one must make an exception for an eigenstate and give the disturbance thing a pass? So, what exactly is the additional content associated with "element of reality"?

 

[Ilja]

A measured spin "component" is definitely the outcome of disturbing the system.It's therefore doubtful to consider that as an "element of reality" of the the undisturbed system, as intended by EPR and understood by Bell.
Coincidentally, I read yesterday that a measured spin component is certainly not an "element of reality" of the electrons in the DBB interpretation - once more, http://arxiv.org/abs/1305.1280 "The Pilot-Wave Perspective on Spin" -Norsen

The problem is that in the EPR-Bell experiment you have no possibility, if you believe in fundamental relativity or Einstein causality, to claim that a decision what to measure by Alice can distort the outcome measured by Bob.

In dBB, the decision of Alice immediately influences the measurement made by Bob. So the EPR criterion, indeed, gives nothing. But dBB is not an Einstein-causal interpretation of quantum theory. It is only realistic and causal.

 

[Markus Hanke]

Interesting analogy, but there is one big difference. The property of being in motion is not a prerequisite for having other properties. The property of existing is. For how can something have any properties if it doesn't even exist? In other words, existence is elementary and motion is not. A non-elementary thing my be relative, but an elementary thing should be absolute.

Good point
But then again, this immediately brings to mind a finding from QFT in curved space-time : different observers may measure different numbers of particles within the same spacetime, depending on the observer's state of motion. If that is the case, then in what sense can the existence of particles be considered "real" or "elementary" ? Perhaps the very notion of "particle" isn't as fundamental as we tacitly take it for.

But you are right, this is very philosophical and leads too far away from the topic of this thread, so let's not take this any further. It is just fascinating to ponder these questions !

 

[Derek Potter]

I don't get it. How are x and y related to A, B and C?

Oh sorry, I was trying to say too much at once. x and y are just general members. I changed to x and y because I thought it was clearer than sticking with A B and C which you had already used in specifice examples :)

That does sound similar to relative states, but not to MWI. Relative states is not the same as MWI. MWI is the Wheeler's reinterpretation of the Everett's relative states.

Well I totally agree with *that* distinction. Not many people make it.