Is there any hope at all for Locality?

[andrewkirk]

As I understand it, EPR proposed their entanglement thought experiment as a means of demonstrating that Quantum Mechanics was incomplete, and hence that the Copenhagen interpretation (which says that the wave function is a complete description of the state of a system) was wrong. They postulated the existence of hidden variables as a way of 'completing' the theory. Here 'hidden' just means 'not in any way reflected in the wave function'.

Bell proved that any extension of QM that uses hidden variables will predict correlations for measurements of entangled particles that differ from what QM predicts, if the principle of locality is to be maintained.

Aspect et al showed, subject to various minor loopholes on which most people seem to place not much reliance, that experimentally observed correlations follow the QM predictions rather than those predicted by a hidden variable theory that preserves locality.

From this we inductively conclude that there is no valid hidden variable theory that preserves locality.

Various presentations of this topic suggest that the tests of Bell's theorem have shown that we cannot maintain both locality and something else, where that something else is variously described as realism, counterfactual definiteness, or other similarly vague-seeming terms. This seems consistent with EPR's and Bell's original ideas, which were to challenge or defend the Copenhagen interpretation that a particle does not have a definite position and momentum unless it is in an eigenstate of one of the two operators.

But I can't see how even accepting that (ie accepting non-realism or non-counterfactual definiteness) allows us to still believe in locality in the face of the Bell theorem and the subsequent experiments. The correlations in Bell's theorem imply that Alice measuring spin along a certain axis has an instantaneous effect on the probability distribution of the results of Bob's measurement. So retreating into the indeterminacy of the Copenhagen interpretation does not appear to have allowed us to preserve locality since an instantaneous effect has occurred across a spacelike interval.

I realize that this is a hand-wave rather than a mathematical proof, but I find myself unable to imagine what sort of a theory (extension of QM) or interpretation could remain consistent with the Bell results while still preserving locality.

I would be grateful for any light that contributors are able to shed on my fog of puzzlement.

 

[bhobba]

But I can't see how even accepting that (ie accepting non-realism or non-counterfactual definiteness) allows us to still believe in locality in the face of the Bell theorem and the subsequent experiments.

It depends on what you mean by locality. If you mean strange correlations can occur instantaneously then yes locality is dethroned. But that is not what is generally meant by locality which is the ability to actually send information. You can't use QM correlations to do that so locality is saved.

Thanks
Bill

 

[Nugatory]

The correlations in Bell's theorem imply that Alice measuring spin along a certain axis has an instantaneous effect on the probability distribution of the results of Bob's measurement. So retreating into the indeterminacy of the Copenhagen interpretation does not appear to have allowed us to preserve locality since an instantaneous effect has occurred across a spacelike interval.

Superdeterminism gives us the correlations without the instantaneous effect. However...

If you feel that accepting superdeterminism is even less palatable than accepting these instantaneous effects, you will have plenty of company.

 

[Demystifier]

Alternatives to quantum nonlocality:
https://www.physicsforums.com/blog.php?b=3622

 

[Maui]

Alternatives to quantum nonlocality:
https://www.physicsforums.com/blog.php?b=3622

- many worlds - objective reality exists and is "local", but not in the 3-space (Everett, Deutsch, Tegmark, ...)

I think 'objective reality' requires causality and it seems the MWI has no explanation for the causal connections encountered on a daily basis between macroscopic objects. They are supposed to be emergent in the MWI, right?

 

[akhmeteli]

As I understand it, EPR proposed their entanglement thought experiment as a means of demonstrating that Quantum Mechanics was incomplete, and hence that the Copenhagen interpretation (which says that the wave function is a complete description of the state of a system) was wrong. They postulated the existence of hidden variables as a way of 'completing' the theory. Here 'hidden' just means 'not in any way reflected in the wave function'.

Bell proved that any extension of QM that uses hidden variables will predict correlations for measurements of entangled particles that differ from what QM predicts, if the principle of locality is to be maintained.

Aspect et al showed, subject to various minor loopholes on which most people seem to place not much reliance, that experimentally observed correlations follow the QM predictions rather than those predicted by a hidden variable theory that preserves locality.

From this we inductively conclude that there is no valid hidden variable theory that preserves locality.

Various presentations of this topic suggest that the tests of Bell's theorem have shown that we cannot maintain both locality and something else, where that something else is variously described as realism, counterfactual definiteness, or other similarly vague-seeming terms. This seems consistent with EPR's and Bell's original ideas, which were to challenge or defend the Copenhagen interpretation that a particle does not have a definite position and momentum unless it is in an eigenstate of one of the two operators.

But I can't see how even accepting that (ie accepting non-realism or non-counterfactual definiteness) allows us to still believe in locality in the face of the Bell theorem and the subsequent experiments. The correlations in Bell's theorem imply that Alice measuring spin along a certain axis has an instantaneous effect on the probability distribution of the results of Bob's measurement. So retreating into the indeterminacy of the Copenhagen interpretation does not appear to have allowed us to preserve locality since an instantaneous effect has occurred across a spacelike interval.

I realize that this is a hand-wave rather than a mathematical proof, but I find myself unable to imagine what sort of a theory (extension of QM) or interpretation could remain consistent with the Bell results while still preserving locality.

I would be grateful for any light that contributors are able to shed on my fog of puzzlement.

This post https://www.physicsforums.com/showpost.php?p=4371341&postcount=1 (and the long thread quoted there) may be irrelevant to the questions in your post (as it takes the loopholes seriously), but is clearly relevant to the title of your post.

 

[meBigGuy]

http://www.science20.com/hammock_physicist/einstein_got_it_wrong_can_you_do_better-85544
I like this entanglement analogy. Gives a much clearer idea of what entanglement is(n't). God is Frugal.
Don't let the title put you off.

Maybe others don't think so highly of this analogy. I'm interested in opinions.

 

[bhobba]

I think 'objective reality' requires causality and it seems the MWI has no explanation for the causal connections encountered on a daily basis between macroscopic objects. They are supposed to be emergent in the MWI, right?

Errrr - since MWI is completely deterministic and causal why you would say that I have zero idea.

The issue with MWI is, and always has been, how do you get probabilities from a totally deterministic theory. One can assume the experience of measurement is probabilistic and use Gleason's Theorem or some other means but unless you can derive it from the universal quantum state it assumes the theory is blemished - not incorrect or disproven - but blemished.

Then of course you have this extremely extravagant exponential increase in the number of worlds that simply sounds - well weird.

However in many other ways it is beautiful, really beautiful.

Thanks
Bill

 

[bhobba]

Maybe others don't think so highly of this analogy. I'm interested in opinions.

Read the link.

Interesting conclusion:
'The inevitable conclusion is that if there is a more fundamental truth from which the known laws of quantum physics are emergent, this more fundamental truth must be at least as weird as quantum theory. More in particular, a classical physics theory capable of explaining all of quantum physics - Einstein's hope - can not exist.'

Errrrr. Not so fast Obi Wan.

It depends on what you mean by 'weird'. If you mean a theory that conforms to Einsten's view of the world then the jury is out - that may or may not be possible. Einstein was well aware of the problems EPR posed - he was one of the authors after all. GR is weird - but Einstein invented that. It is not mere weirdness that is the issue - it is Einsteins view of the world - namely being real, objective, independent of observation and deterministic. There may be a reality from which QM emerges that is like that - or not - no one knows.

However if history is any guide there is probably a surprise or two along the way of investigating it.

Thanks
Bill

 

[meBigGuy]

Don't get hung up on weird. if quantum mechanics is quantum-weird, then whatever underlies it must be quantum-weird too. But classical physics can't ever contain the "quantum weirdness", not that it doesn't have classical-weirdness of its own. But, whether or not one agrees with that shouldn't take away from the mental exercise.

For me it the article was more about the sentence before it:

"These spooky effects force us to answer the question 'does something exist if we can not know anything about it?' with a resounding 'no'. What can not be observed does not exist. This is not a crazy philosophical thought, but a hard experimental fact."
That is the source of my "God is Frugal" conclusion.

But, with respect to the analogy itself, did you see it as a meaningful mental exercise that illustrates a subtlety behind the reality of entanglement?

 

[bhobba]

Don't get hung up on weird. if quantum mechanics is quantum-weird, then whatever underlies it must be quantum-weird too.

That does not follow. Eg Primary State Diffusion derives QM from an underlying sub quantum world that is quite classical. Of course there will be departures from QM in the sub quantum world that it applies to, like there is departures from classical physics in the Quantum domain. As Bohr said to Einstein - stop telling God what to do. Same here - stop telling nature how to behave.

But, with respect to the analogy itself, did you see it as a meaningful mental exercise that illustrates a subtlety behind the reality of entanglement?

No

Thanks
Bill

 

[mfb]

What can not be observed does not exist.

I disagree with that very general looking concept.

What happened to the matter we see as cosmic microwave background today? It is beyond our event horizon, we cannot observe how it looks today. Do you think the matter just vanished magically? I do not think so. It is way more natural to assume that it still exists, and formed galaxies just as matter around us did.

Occam's razor: it is easier to assume galaxies outside our observable universe exist, as this gives an easier description of the universe - a universe where galaxies do not vanish magically.
The same can happen in QM.

 

[meBigGuy]

@mfb, did you read the article?
BTW, The word "observation" has nothing to do with whether something is observable by you or I, but rather whether it interacts.

@bhobba
We're going on about semantics. Whatever ultimately underlies QM must explain, and encompass, quantum-weird, you feel it can do that without being just as weird. OK. I'll accept that.
Could you elaborate on your "no" answer?

 

[mfb]

@mfb, did you read the article?

No, and as I posted I just think the quoted statement is (or looks) too general.

BTW, The word "observation" has nothing to do with whether something is observable by you or I, but rather whether it interacts.

Those galaxies do not interact with us any more.

 

[bhobba]

Could you elaborate on your "no" answer?

Exactly what analogy are you referring to? The socks thought experiment? That's a thought experiment not an analogy. Aside from that all I got from the article was this idea that Einstein was wrong. He wasn't - there may indeed be an underlying reality from which QM emerges that conforms to his intuition.

Thanks
Bill

 

[Nugatory]

[Quoting Johannes Koelman]

"These spooky effects force us to answer the question 'does something exist if we can not know anything about it?' with a resounding 'no'. What can not be observed does not exist. This is not a crazy philosophical thought, but a hard experimental fact."

As with most claims about experimental support for interpretational positions, there's some overreach going on. A weaker but more defensible statement would be:

These spooky effects allow me to answer the question 'does something exist if we can not know anything about it?' with a resounding 'no'. What can not be observed does not exist. This is not a crazy philosophical thought, but a reasonable position suggested by hard experimental fact.

 

[the_pulp]

Here is a chance for locality. See page 37 of:

New Insights on Time-Symmetry in Quantum Mechanics, Yakir Aharonov and Jeff Tollaksen



"...Traditionally, it was believed that “contextuality” was very closely related
to “kinematic-nonlocality.” Typically, kinematic-nonlocality refers to correlations,
such as eq. 1.1, that violate Bell’s-inequality with the consequence that
QM cannot be replaced with a local realistic model. Similarly, contextuality
refers to the impossibility of replacing QM with a noncontextual realistic theory.
Applying this now to the relativistic-paradox (§1.1), we see that Lorentz
covariance in the state-description can be preserved in TSQM [9] because the
post-selected vector A
z = +1 propagates all the way back to the initial preparation
of an EPR state,..."

I really love this interpretation, perhaps for my ignorance, but it seems to solve apparent "non-locality" and apparent "Time Asymmetry".

 

[stevendaryl]

http://www.science20.com/hammock_physicist/einstein_got_it_wrong_can_you_do_better-85544
I like this entanglement analogy. Gives a much clearer idea of what entanglement is(n't). God is Frugal.
Don't let the title put you off.

Maybe others don't think so highly of this analogy. I'm interested in opinions.

The story of Albert's socks is pretty long-winded and takes forever to get to the point, but I agree that the situation described is very analogous to weird quantum correlations. In particular, you have correlations that cannot be explained in terms of a locally realistic model, but can easily be explained using nonlocal interactions, or using superdeterminism.

I'd like to see the details of the argument that the sock drawer can be "implemented" using entangled pairs.

 

[stevendaryl]

Alternatives to quantum nonlocality:
https://www.physicsforums.com/blog.php?b=3622

It's a nice list except for the inclusion of Joy Christian's approach. That is nonsense, in my opinion.

 

[stevendaryl]

Errrr - since MWI is completely deterministic and causal why you would say that I have zero idea.

The issue with MWI is, and always has been, how do you get probabilities from a totally deterministic theory. One can assume the experience of measurement is probabilistic and use Gleason's Theorem or some other means but unless you can derive it from the universal quantum state it assumes the theory is blemished - not incorrect or disproven - but blemished.

Then of course you have this extremely extravagant exponential increase in the number of worlds that simply sounds - well weird.

However in many other ways it is beautiful, really beautiful.

Thanks
Bill

Well, in MWI, I don't think it's really meaningful to talk about the number of worlds increasing. There's only the wave function, and it's a single thing. The many-worlds are just ways of splitting up that single object.

An objection that I sort of have sympathy for is the business about justifying the Born rule in MWI. On the one hand, that seems pretty crucial, because without the Born rule, quantum mechanics makes basically no predictions at all. (Well, that's not completely true. There are circumstances where QM gives a 0% or 100% probability for something, and we can make sense of those without worrying too much about the meaning of probability.) On the other hand, what could it mean to justify the Born rule?

I guess going further would be leaving physics and venturing into philosophy, but there is something philosophically puzzling about probabilistic theories. If someone claims that a coin has a 50/50 chance of landing heads-up, you can test that claim by flipping the coin many times and counting how many times it ends up heads. But this kind of test assumes a numerical equivalence: The probability for a single throw = The relative frequency for many throws. But how is that justified? It's certainly possible to flip a coin 1000 times and get "heads" every time. But we assume that that's an unlikely enough occurrence that we can ignore it. But what does "unlikely" mean, here, physically?

It seems that ultimately what we're doing is defining a "normal world" to be one where relative frequencies are roughly equal to probabilities, and assuming that we live in a normal world. The further piece of information, that the set of "normal worlds" has measure 1, doesn't really add a lot to me, because the set having measure 1 doesn't mean that our world is in it. You can say that it means that it is likely that our world is in it, but once again, what does "likely" mean here?

What it boils down to, to me, is this: Treating events that have probability 0 as if they were impossible, is not actually justified, but it is a self-consistent way to reason. That's true with classical probabilities. MWI with the Born rule is in no worse shape. We can't justify the assumption that relative frequencies will approximately equal the probabilities given by the Born rule, but it is a self-consistent way to reason, and reasoning about probabilities without some such rule is impossible.

 

[audioloop]

I think 'objective reality' requires causality

not necesarily, in RBW there is no causality but there is objective reality.

 

[bhobba]

Treating events that have probability 0 as if they were impossible, is not actually justified, but it is a self-consistent way to reason.

Hmmmm. Thinking in terms of the Kolmogorov Axioms if you have an event space with elements of probability zero and you remove them you have just as legitimate an event space. This means its just as valid a model, but since they are no longer in the event space obviously can never occur. To me this means any reasonable modelling of an actual situation by probability means an event of probability zero can never occur.

In fact this is the way the frequentest probability interpretation is given meaning that is not circular via the law of large numbers. A very large number of trials will lead to a an event space with one element having probability infinitesimally close to one and all the other elements infinitesimally close to zero so can be ignored. This is the ensemble with the outcomes in proportion to the probability.

Of course this is for discreet event spaces - continuous spaces have their own subtlety associated with probability zero.

But we are really getting off track here - this is a general issue of probability theory not peculiar to QM and is best pursued in its own thread.

Thanks
Bill

 

[Maui]

not necesarily, in RBW there is no causality but there is objective reality.

Then what you call 'objective reality' is not fully objective. I have not seen to date a fully objective reality in agreement with the postulates of qm, except maybe the bohemian interpretation. An objective reality that is completely macroscopically causal cannot arise out of indeterminism or multiple possibilities(the MWI). If macroscopic causality is emergent or simply apparent, then objective reality isn't really objective. I am seeking a definition of the adjective 'objective' that both people on the street and Nobel prize winners would collectively agree to and people engaged in fundamental physics are much more flexible about reality than the general population.

 

[stevendaryl]

Hmmmm. Thinking in terms of the Kolmogorov Axioms if you have an event space with elements of probability zero and you remove them you have just as legitimate an event space. This means its just as valid a model, but since they are no longer in the event space obviously can never occur. To me this means any reasonable modelling of an actual situation by probability means an event of probability zero can never occur.

I don't see how it means that. As I said, it's self-consistent to ignore events of probability zero, but the conclusion that probability zero MEANS that it won't happen isn't justified.

The probability zero events that I'm talking about are events such as an infinite sequence of coin flips ending up all heads, or all tails, or otherwise violating the rule that relative frequencies be the same as probabilities. I guess you could say that no such sequence can occur, but there's another sense in which they are just as "likely" as any other sequence. Any particular sequence has probability zero, but SOME sequence has to occur.

In fact this is the way the frequentest probability interpretation is given meaning that is not circular via the law of large numbers.

It seems circular to me. The law of large numbers doesn't say that relative frequency approaches probability, it says that the set of sequences for which this doesn't happen has measure zero. Why does measure zero mean it doesn't happen? Any actual run has probability zero.

A very large number of trials will lead to a an event space with one element having probability infinitesimally close to one and all the other elements infinitesimally close to zero so can be ignored.

I agree--it CAN be ignored, in the sense that that is a consistent way to reason. I don't see that it's justified, it's an additional assumption, it seems to me.

But we are really getting off track here - this is a general issue of probability theory not peculiar to QM and is best pursued in its own thread.

I agree, but my point is that the complaint against MWI that it doesn't justify the Born is bordering on a philosophical complaint, rather than a physical one.

 

[audioloop]

Then what you call 'objective reality' is not fully objective. I have not seen to date a fully objective reality in agreement with the postulates of qm, except maybe the bohemian interpretation. An objective reality that is completely macroscopically causal cannot arise out of indeterminism or multiple possibilities(the MWI). If macroscopic causality is emergent or simply apparent, then objective reality isn't really objective. I am seeking a definition of the adjective 'objective' that both people on the street and Nobel prize winners would collectively agree to and people engaged in fundamental physics are much more flexible about reality than the general population.

objectivity does not require causality.

 

[stevendaryl]

...my point is that the complaint against MWI that it doesn't justify the Born is bordering on a philosophical complaint, rather than a physical one.

In both classical probability and in Many-Worlds, you can just ASSUME, for any single collection of measure-zero 'possible worlds', that our actual world isn't in that collection. For practical purposes, you don't need to justify that assumption, as long as it's consistent to make it.

 

[audioloop]

but there is something philosophically puzzling about probabilistic theories. If someone claims that a coin has a 50/50 chance of landing heads-up, you can test that claim by flipping the coin many times and counting how many times it ends up heads. But this kind of test assumes a numerical equivalence: The probability for a single throw = The relative frequency for many throws. But how is that justified? It's certainly possible to flip a coin 1000 times and get "heads" every time. But we assume that that's an unlikely enough occurrence that we can ignore it. But what does "unlikely" mean, here, physically?

nice musing, going to the roots.------
"From the point of view of principles, I absolutely do not believe in a statistical basis for physics in the sense of quantum mechanics, despite the singular success of the formalism of which I am well aware. I do not believe such a theory can be made general relativistic. Aside from that, I consider the renunciation of the spatio-temporal setting for real events to be idealistic-spiritualistic. This epistemology-soaked orgy ought to come to an end. No doubt, however, you smile at me and think that, after all, many a young whore turns into an old praying sister, and many a young revolutionary becomes an old reactionary."
.-Albert Einstein.

 

[Maui]

objectivity does not require causality.

Can you elaborate what you mean by objectivity? Obviously you don't mean objects that exist in space and time and have their properties as we observe them because of their past interactions and transformations... but something else entirely.

 

[audioloop]

Can you elaborate what you mean by objectivity? Obviously you don't mean objects that exist in space and time and have their properties as we observe them because of their past interactions and transformations... but something else entirely.

objectivity is independence of existence.

nothing to do with "us"

as we observe them

irrelevant.

 

[Maui]

objectivity is independence of existence.




irrelevant.

I have no idea what you are saying but objectivity is the independence of measured values from the experimental setup. In the MWI, macro objects exist as parts of a giant wavefunction that splits into classical-like worlds. A classical-like world is different from a classical world where strict causality determines the properties of macro objects.

 

[stevendaryl]

I have no idea what you are saying but objectivity is the independence of measured values from the experimental setup. In the MWI, macro objects exist as parts of a giant wavefunction that splits into classical-like worlds. A classical-like world is different from a classical world where strict causality determines the properties of macro objects.

No, I wouldn't think that objectivity has anything to do with measurements. Objectivity is the existence of a unique external world that is independent of observers. In an objective model, a measurement is certainly revealing something pre-existing about the world, but there's no reason to assume that there is a one-to-one correspondence between what's true in the world and what we measure.

 

[audioloop]

Objectivity is the existence of a unique external world that is independent of observers.

Riiiiiiiiiight !

 

[Maui]

No, I wouldn't think that objectivity has anything to do with measurements. Objectivity is the existence of a unique external world that is independent of observers. In an objective model, a measurement is certainly revealing something pre-existing about the world, but there's no reason to assume that there is a one-to-one correspondence between what's true in the world and what we measure.

Then macro causality goes out the window which was my point from the beginning.

 

[Maui]

Riiiiiiiiiight !

I don't see your point but if it's about there being an outside reality that is different form what we observe (which is kind of obvious), there is some bad news for classical causality which can only exist in a purely classical setting and which can be found neither in experiment nor in theory.

What stevendaryl talks about is a classical-LIKE(or classically-consistent) world, not a classical world. In classical-like worlds macro causality would be secondary and emergent/apparent and when people usually say 'objective reality' they mean classical world, not classical-like world that comes about via decoherence + collapse/world splitting.

 

[meBigGuy]

@mfb Why would you assume it must interact with us? First tell me of something that exists that interacts (or will interact) with *NOTHING*, and how you know it exists. Then we can discuss that. Assuming anyone actually thinks *WE* must observe something for it to exist is a mis-interpretation of what is being said.

@Nugatory " This is not a crazy philosophical thought, but a reasonable position suggested by hard experimental fact." You will get no argument from me on that. Even with your edit, it is, to me, a profound concept.

@bhobba Don't be so difficult (is it intentional?). Ok, thought experiment. You are saying that the Albert's Socks thought experiment illustrated nothing worth thinking about. Your terse "No" answer indicates that you feel that it was not a meaningful mental exercise that illustrated a subtlety behind the reality of entanglement? I am nicely asking you to elaborate on that opinion.

 

[audioloop]

From this we inductively conclude that there is no valid theory that preserves locality.

or like says Gisin:Quantum Nonlocality: How Does Nature Do It?
http://www.alice.id.tue.nl/references/gisin-2009.pdf

"The quantum correlations are indeed coming from outside space-time in the sense that there is no story inside space-time that can describe them"

i prefer to say from other layer of reality/nature.
or Lorenzo:
Are quantum correlations genuinely quantum?
http://arxiv.org/abs/1205.0878

"It is shown that the probabilities for the spin singlet can be reproduced through classical resources, with no communication between the distant parties, by using merely shared (pseudo-)randomness"

 

[meBigGuy]

Objectivity is the existence of a unique external world that is independent of observers.

I am way out of my league here, so be forgiving. I'd like to pin down what is meant by "observers" in QM discussions. To me it infers any interaction within space/time. But that makes your above definition of objectivity somewhat empty since we established that (via Albert's socks) that there is no existence without observations (interactions within space/time). In light of that, is objectivity simply the existence of a unique external world that can be observed (and contains observers)?

 

[audioloop]

I am way out of my league here, so be forgiving. I'd like to pin down what is meant by "observers" in QM discussions. To me it infers any interaction within space/time. But that makes your above definition of objectivity somewhat empty since we established that (via Albert's socks) that there is no existence without observations (interactions within space/time). In light of that, is objectivity simply the existence of a unique external world that can be observed (and contains observers)?

independent of observers/interactions.

Reality is the state of things/objects as they actually exist.

 

[bhobba]

Don't be so difficult (is it intentional?). Ok, thought experiment. You are saying that the Albert's Socks thought experiment illustrated nothing worth thinking about. Your terse "No" answer indicates that you feel that it was not a meaningful mental exercise that illustrated a subtlety behind the reality of entanglement? I am nicely asking you to elaborate on that opinion.

Its not intentional. Its just in this sort of stuff needs precision of thought.

You asked:

But, with respect to the analogy itself, did you see it as a meaningful mental exercise that illustrates a subtlety behind the reality of entanglement?

Its simply a thought experiment illustrating some of the weirdness associated with QM. Entanglement is an interesting and subtle phenomena and as a mental exercise illustrating that its worthwhile. But its nothing beyond that.

Thanks
Bill

 

[stevendaryl]

I am way out of my league here, so be forgiving. I'd like to pin down what is meant by "observers" in QM discussions. To me it infers any interaction within space/time.

No, to me, an observer is something that can make notes about the world. Not every interaction is an observation.

To say that something is independent of observers just means that it exists whether or not there is anything conscious noting its existence. You know, a tree falling in a forest with no-one around.

 

[stevendaryl]

Are quantum correlations genuinely quantum?
http://arxiv.org/abs/1205.0878

"It is shown that the probabilities for the spin singlet can be reproduced through classical resources, with no communication between the distant parties, by using merely shared (pseudo-)randomness"

I'll take a look at that, but it seems to be claiming to have shown something that other people have shown to be impossible.

 

[bhobba]

I am way out of my league here, so be forgiving. I'd like to pin down what is meant by "observers" in QM discussions. To me it infers any interaction within space/time. But that makes your above definition of objectivity somewhat empty since we established that (via Albert's socks) that there is no existence without observations (interactions within space/time). In light of that, is objectivity simply the existence of a unique external world that can be observed (and contains observers)?

In QM an observer is any device, assumed to behave in a classical way, that registers something that occurred in the quantum domain. An example would be a particle detector. It clicks, flashes, or does something here in the classical macro world, when a subatomic particle is detected. In the standard Copenhagen interpretation the existence of such devices is assumed and a fundamental part of that interpretation. Some people get hung up on the usual meaning in everyday usage of observer as requiring a conscious observer and run into all sorts of semantic difficulties - that's another example of the precision of thought and expression required when dealing with this stuff I mentioned previously. I remember watching this movie What The Bleep Do We Know Anyway that was full of that sort of rubbish to the point it was embarrassing.

QM is a theory about observations on quantum systems - it is not a theory about what its doing, existing or anything like that when its not observed. The quantum state is simply a codification of the probabilities of the results of observations if you were to observe it. It tells you nothing other than that. Basically it is, at its fundamental level, a theory about systems interactions with other systems where those other systems change in some way that registers here in the commonsense, classical macro world. It changes nothing about that commonsense world out there - it exists independent of us, it is there when we are not looking and all the usual stuff we take for granted. QM in no way changed that.

The existence of a commonsense macro world is assumed but since everything is quantum this division is a blemish. What you want is a fully quantum theory of measurement. Great progress has been made along these lines (particularly in the area of decoherence) but some issues do remain - although what we do know have clarified a lot of things.

Thanks
Bill

 

[stevendaryl]

I'll take a look at that, but it seems to be claiming to have shown something that other people have shown to be impossible.

The author is doing something kind of weird, it seems to me. In his model, (section 7.1) he's assuming that each experimenter's choice of detector setting is causally influenced by a random hidden variable shared by the experimenters.

 

[bhobba]

It seems circular to me. The law of large numbers doesn't say that relative frequency approaches probability, it says that the set of sequences for which this doesn't happen has measure zero. Why does measure zero mean it doesn't happen? Any actual run has probability zero.

I don't want to sidetrack this thread - this issue really needs a thread of its own. And if you decide to start one don't do it in the probability section of Physic's Forums because they work with mathematical probability which is fully described with zero problems by the Kolmogorov axioms without the nasty subtleties of actually applying it.

However I want to simply add your view is fairly common but does leave me scratching my head. Books like Fellers - Introduction To Probability completely avoid circularity by starting from the Kolmogorov axioms and via the Law of Large numbers derived rigorously from those axioms connects it to the frequency interpretation with no circularity. The Law of Large Numbers says as the number of trials increases the proportion of outcomes being the same as the probability approaches 1 - using some definition of convergence such as convergence in probability. Now the assumption is since it converges to it a sufficiently large number exists that for all practical purposes is the same ie is one. There is no circularity - simply a standard assumption made in applied math all the time.

Thanks
Bill

 

[bhobba]

No, to me, an observer is something that can make notes about the world. Not every interaction is an observation.

To say that something is independent of observers just means that it exists whether or not there is anything conscious noting its existence. You know, a tree falling in a forest with no-one around.

Good way of expressing it - must keep it in mind.

And indeed the standard Copenhagen interpretation assumes the existence of a world out there just like that eg trees falling in a forest make a sound regardless of if there is anyone there to hear it.

Thanks
Bill

 

[stevendaryl]

The Law of Large Numbers says as the number of trials increases the proportion of outcomes being the same as the probability approaches 1 - using some definition of convergence such as convergence in probability. Now the assumption is since it converges to it a sufficiently large number exists that for all practical purposes is the same ie is one. There is no circularity - simply a standard assumption made in applied math all the time.

I guess we would need to state explicitly what is being claimed in order to say whether it's circular or not. Certainly the proof of the law of large numbers isn't circular. It's a proof from the axioms of probability. But what I'm saying is that the law of large numbers by itself doesn't imply that one must treat probability 0 events as impossible.

Let's define for a sequence of coin flips:

F_n = \dfrac{H_n}{n}

where H_n is the number of heads in the first n coin flips.

To say that F_n \rightarrow \frac{1}{2} is to say that:

For every \epsilon > 0, there is a number \hat{n} such that for all n > \hat{n}, |F_n - \frac{1}{2}| < \epsilon. That's true for some sequences of coin flips, and false for other sequences of coin flips.

What the weak law of large numbers says is that the probability that |F_n - \frac{1}{2}| < \epsilon goes to 1 as n \rightarrow \infty

But the issue is whether probability 1 means "certain" and probability 0 means "impossible". The weak law of large numbers by itself doesn't say that.

The strong law of large numbers states that

The strong law of large numbers states that the sample average converges almost surely to the expected value.

But the meaning of "almost surely" is "true for all sequences except for a set of measure 0". Once again, the issue is why does having a set of measure 0 mean "impossible"?

The nice thing about probability zero is that it's consistent to treat any finite (or countable) set of probability zero events as if they were impossible. So it's a consistent way to reason. This is in contrast with an assumption saying "I'm going to ignore events that have only a 1% chance of happening." That's actually not a consistent way to reason, because if you wait long enough, events of probability 1/100 will happen.

 

[bhobba]

But what I'm saying is that the law of large numbers by itself doesn't imply that one must treat probability 0 events as impossible.

But the meaning of "almost surely" is "true for all sequences except for a set of measure 0". Once again, the issue is why does having a set of measure 0 mean "impossible"?

OK. I think I see where you are coming from. In applying the Kolmogorov Axioms they do not force you to associate a probability of zero with an event not in the event space and hence impossible. Its a reasonable assumption we make since its just as consistent with it in the event space as not in it. Welcome to applied math. But why anyone would want to make an issue it of it is beyond me. I used to get worked up about this kind of stuff a bit during my ubdergrad days but my teachers eventually cured me of it by pointing out the morass you end up in otherwise. I see a lot of that sort of thing with people discussing QM - you want to scream - why look at it that way and make things harder for yourself. Sometimes you get the distinct impression they take a perverse delight in it.

As you correctly point out the difference between the strong law and weak law of large numbers is the type of convergence - weak is convergence in probability - strong is almost assuredly. But from an applied viewpoint is not really relevant - the simple assumption is we can find a n large enough that is so close to one for all practical purposes it can be taken as one. Its the same sort of thing you see with instantaneous velocity - that's impossible as well but times so short exist it's the same for all practical purposes. People seem to accept that but for some reason not for probability - don't quite know why.

So to me the issue in applying probability is not one of circularity - its simply one of reasonable assumptions like we do in many areas of applied math.

I am ignoring issues with zero probability in continuous and infinite event spaces which is a whole new can of worms

Thanks
Bill

 

[stevendaryl]

OK. I think I see where you are coming from. In applying the Kolmogorov Axioms they do not force you to associate a probability of zero with an event not in the event space and hence impossible. Its a reasonable assumption we make since its just as consistent with it in the event space as not in it. Welcome to applied math. But why anyone would want to make an issue it of it is beyond me.

I'm not making an issue about anyone ASSUMING probability zero events never happen. I'm making an issue about the claim that that's somehow provably true. It's not. So in complaining about MWI that it doesn't justify the Born interpretation, my reaction is: what would it even mean to justify it?

There's a thought-experiment that sort-of relates to MWI. Imagine a world that is completely deterministic except for coin flips, and as far as anyone knows, there is no way to predict what the result will be. Let's assume that the way it works is that whenever anyone begins a coin flip, God stops time and makes two copies of the world, in the exact same state. In one of the copies, he let's the coin flip yield "heads" and in the other copy, he let's it yield "tails".

This metaphysics is completely deterministic, like MWI. But for people living in one of the copies of the world, it will appear that coin flips are non-deterministic. Are those people justified in assuming that a coin flip has probability \frac{1}{2} of resulting in "heads"? I think they would be. But is that probability derivable from the metaphysics?

But suppose instead of God making two copies, with one copy having result "heads" and the other copy having the result "tails", he makes three copies, two having result "heads" and only one having the result "tails"? Does that change the probability?

On the one hand, you could say that in this new metaphysics, a coin has a \frac{2}{3} chance of resulting in "heads" and a \frac{1}{3} chance of resulting in "tails". On the other hand, to the people living in one of the copies, it can't possibly make any difference what happens in a world that isn't their world. If they were previously justified in assuming "heads" has a probability of \frac{1}{2}, it is certainly permitted for them to continue to make that assumption.

I used to get worked up about this kind of stuff a bit during my ubdergrad days but my teachers eventually cured me of it by pointing out the morass you end up in otherwise.

I have no problems with people just saying: I'm not going to get into it, I'm going to assume X, to make things simpler. But I do have problems with people failing to realize that X is an assumption, not a necessary truth, and that reasonable people could make a different assumption.

I see a lot of that sort of thing with people discussing QM - you want to scream - why look at it that way and make things harder for yourself. Sometimes you get the distinct impression they take a perverse delight in it.

It's called trying to understand. People understand things by looking at them from lots of different angles.

As you correctly point out the difference between the strong law and weak law of large numbers is the type of convergence - weak is convergence in probability - strong is almost assuredly. But from an applied viewpoint is not really relevant - the simple assumption is we can find a n large enough that is so close to one for all practical purposes it can be taken as one. Its the same sort of thing you see with instantaneous velocity - that's impossible as well but times so short exist it's the same for all practical purposes. People seem to accept that but for some reason not for probability - don't quite know why.

As I said, I don't have any problem with making the assumption that relative frequencies approach probabilities. I just want it to be clear that it's an assumption, not a necessary truth. It simplifies our reasoning to make it (in some cases, we can't do much reasoning at all without it, or something similar). But to me, it strongly suggests Bayesianism. Probabilities are, at least partially, subjective.

 

[mfb]

@mfb Why would you assume it must interact with us?

I don't assume that. On the contrary, my point is that this is not a useful requirement for the existence of objects.

First tell me of something that exists that interacts (or will interact) with *NOTHING*, and how you know it exists.

How is that related to the discussion?

Assuming anyone actually thinks *WE* must observe something for it to exist is a mis-interpretation of what is being said.

I heard exactly that argument so many times...

 

[morrobay]

For locality with probability and statistics see:www.arxiv.org/pdf/quant-ph/0007005v2.pdf
For locality with geometric explanation see: www.iisc.ernet.in/currsci/jul252000/UNNIKRISHNAN.pdf
Regarding the inequality spin violations , I would like to hear from the particle physicists on whether
there is an explanation in terms of the spin changes of the particle from its interaction with the
detectors magnetic field. Sometimes it seems like non-locality is a sacred cow.