Determinism, realism, hidden variables

[DrChinese]

I'd use a classical analogy - the outcome of tossing a coin is not usually observer-dependent because typically two observers look at the coin from the same side. But if a coin were spun and made to come to rest in a vertical plane between two observers, they would see opposite faces. Does that mean the observed outcome is observer-dependent? I'd say yes it does. But does that mean reality is observer-dependent? Surely not! To make such a claim you would have to equate reality with the observed outcome. Why would anyone do that knowing the nature of coins? So why do they do it knowing the nature of quantum superposition?

Precisely because the quantum world is not the classical world. There are an infinite number of choices of how the observers measure the quantum coins. By Bell, we know that the observations cannot be locally predetermined as in the classical case (and as EPR expected). So there is plenty of reason to reject classical realism. Or locality if you prefer.

I do not believe in observer independence (objective realism) regardless. There is no meaning to counterfactual measurements, a view I believe most Bohmians share. That is a rejection of the EPR viewpoint regarding elements of reality.

 

[dlgoff]

I do not believe in observer independence (objective realism) regardless.

Not to be speculative, but could there be some sort of mathematical step function where this could be possible for some quantum states? Thinking of Wojciech H. Zurek's pointer states here.

 

[naima]

implicitly. $\lambda$ represents any facts about the intersection of the backwards lightcones of the two measurement events.

You can say that it is implicit if somewhere else Bell wrote it explicitly.
Where?

 

[Derek Potter]

I do not believe in observer independence (objective realism) regardless.

Yes, well that's the point, isn't it? You do not "believe in" objective realism. But you cannot justify that non-belief from Bell. It is perfectly possible to construct a theory which asserts an observer-independent reality but predicts observer-dependent observations of the quantum kind. You don't have to look very far to find one.

 

[naima]

It is perfectly possible to construct a theory which asserts an observer-independent reality

Is it what you "believe"? how would you write this reality mathematically? equality, inequality, with another relation?

 

[stevendaryl]

You can say that it is implicit if somewhere else Bell wrote it explicitly.
Where?

In "Speakable and Unspeakable in Quantum Mechanics", Bell has an essay called "Theory of Local Beables", where he expands on the idea.

 

[Markus Hanke]

To be complete, I would think you would need to have a unified theory that describes measurement as a special case of an interaction, and the fact that it always results in an eigenvalue should be derivable.

Does the act of "measurement" not produce an entanglement relationship between aspects of the system, and the measurement apparatus ? Shouldn't this count as an "interaction" ?

 

[naima]

In "Speakable and Unspeakable in Quantum Mechanics", Bell has an essay called "Theory of Local Beables", where he expands on the idea.

And i will have to spend
45 dollars on Amazon to verify what you said.

 

[Jilang]

Here it is
http://cds.cern.ch/record/980036/files/197508125.pdf

 

[naima]

Thank you for the link

 

[Derek Potter]

Is it what you "believe"? how would you write this reality mathematically? equality, inequality, with another relation?

Sure I believe that it is possible. That's why I said it.

I have no idea why you would want to write it mathematically. An entity is postulated without mentioning observers. Observers are defined, not postulated. Observer-dependent phenomena are derived. This is done without invoking the fact that observers are not postulated.

But let's assume we write something like
reality(observer_1) = reality(observer_2)
Bearing in mind that the theory does not invoke this statement, where does that get you?

 

[naima]

I see that in the Bell's paper about beables, he uses the words light cones.
He also uses the Bell's relation about local hidden variables where the speed of light is absent.
Is there in his proof something about ftl signal? The Ockham razor principle tells us that it is not necessary to invoke light speed.

 

[Derek Potter]

Is there in his proof something about ftl signal? The Ockham razor principle tells us that it is not necessary to invoke light speed.

Yeah, you can put one of the systems in a perfect box after Schroedinger has finished tormenting his cat in it.
(Every experiment needs a cat.)

 

[Derek Potter]

Does the act of "measurement" not produce an entanglement relationship between aspects of the system, and the measurement apparatus ? Shouldn't this count as an "interaction" ?

Steven was talking about the "standard" way QM is presented. The standard approach just asserts observation of eigenvalues. What you describe is measurement theory and may account for eigenvalues. Certainly this is why Steven mentioned MWI which definitely claims to account for them as well as everything else that people find strange. Or not.

 

[stevendaryl]

I see that in the Bell's paper about beables, he uses the words light cones.
He also uses the Bell's relation about local hidden variables where the speed of light is absent. Is there in his proof something about ftl signal? The Ockham razor principle tells us that it is not necessary to invoke light speed.

In EPR, there are the following relevant events:

1. $e_1$: A pair of particles is created at one location.
2. $e_2$: Alice chooses her detector settings.
3. $e_3$: Alice measures the spin of one of the particles.
4. $e_4$: Bob chooses his detector settings.
5. $e_5$: Bob measures the spin of the other particle.

Bell's assumption is that a measurement result can depend only on facts about the causal past of that measurement. So he assumes that Bob's result at $e_5$ cannot depend on anything that happens at $e_2$ or $e_3$, and that Alice's result at $e_3$ cannot depend on anything that happens at $e_4$ or $e_5$. In terms of light cones, Bell is assuming that

• $e_2$ and $e_3$ are not in the backward lightcone of $e_5$
• $e_4$ and $e_5$ are not in the backward lightcone of $e_3$

If those assumptions do not hold, then Bell's proof is invalid. It's easy to come up with a classical (non-quantum) model that can explain the EPR correlations in that case.

Ockham's razor is not relevant here, because Bell is not trying to explain anything. He's trying to prove that no explanation (of a certain type) is possible.

 

[naima]

I see that in the Bell's paper about beables, he uses the words light cones.
He also uses the Bell's relation about local hidden variables where the speed of light is absent.
Is there in his proof something about ftl signal? The Ockham razor principle tells us that it is not necessary to invoke light speed.

And it is what is done in the Bertlmann's socks paper (written later)
You say that
"Bell's assumption is that a measurement result can depend only on facts about the causal past of that measurement."
Where it is needed in the derivation of the inequality (1984 paper)?

 

[stevendaryl]

You say that
"Bell's assumption is that a measurement result can depend only on facts about the causal past of that measurement."
Where it is needed in the derivation of the inequality (1984 paper)?

It's clear that Bell's theorem is false without the assumption about lightcones.

Let $P(A, B | \alpha, \beta, \lambda) =$ the probability that Alice gets result $A$ and Bob gets result $B$, given that Alice chooses detector setting $\alpha$, Bob chooses detector setting $\beta$, and that $\lambda$ is some unknown parameter shared by both particles. We can write, in perfect generality:

$P(A, B | \alpha, \beta, \lambda) = P_A(A | \alpha, \beta, \lambda) P_B(B| A, \alpha, \beta, \lambda)$

where $P_A(A | \alpha, \beta, \lambda) =$ the probability that Alice gets result $A$, given $\alpha$, $\beta$, and $\lambda$, and $P_B(B | A, \alpha, \beta, \lambda) =$ the probability that Bob gets result $B$, given $A, \alpha$, $\beta$, and $\lambda$.

Now, Bell assumes the following:

1. $P_A(A | \alpha, \beta, \lambda) = P_A(A | \alpha, \lambda)$ (Alice's result cannot depend on Bob's setting)
2. $P_B(B | A, \alpha, \beta, \lambda) = P_B(B | \beta, \lambda)$ (Bob's result cannot depend on Alice's setting, or Alice's result)

These two assumptions imply the following form for $P(A,B|\alpha, \beta)$:

$P(A,B|\alpha, \beta) = \sum_\lambda P_{hv} (\lambda) P_A(A |\alpha, \lambda) P_B(B|\beta, \lambda)$

The result predicted by quantum mechanics for the twin-pair, spin-1/2, anti-correlated EPR experiment is:

• There are 2 possible results for each measurement: $A =$ spin-up or spin-down, $B =$ spin-up or spin-down.
  
• $P(A,B|\alpha, \beta) = \frac{1}{2} sin^2(\frac{\beta - \alpha}{2})$ (if $A = B$)
  
• $P(A,B|\alpha, \beta) = \frac{1}{2} cos^2(\frac{\beta - \alpha}{2})$ (if $A \neq B$)

Bell proved that it is impossible to find functions $P_{hv}, P_A, P_B$ that give those results. If you allow Bob's result to depend on Alice's setting and result, so that his probability has the form $P_B(B | A, \alpha, \beta, \lambda)$, then it is possible to find functions $P_{hv}, P_A, P_B$ that give those results. So Bell's proof depends on the fact that Bob's result is not influenced by Alice's setting or result.

 

[naima]

I liked your answer because it enables us to see what is really used.
$\beta$ does not appear in Alice's probability. It is true. But $\lambda$ has not to be a number. It may be a couple of numbers.
the first could be a property of something near Bob and the other the property of something near Alice.
The problem becomes the locality of $\lambda$

 

[Paul Colby]

What I don't like about Bell's argument as presented is the phrase "Bob's result" is set next to $P(B\vert \beta, \lambda)$ which is not really what I think Bob's result actually means. Alice could have perfect pre-knowledge of Bob's individual measurements (particle by particle) and Bob could still believe things are random.

 

[stevendaryl]

I liked your answer because it enables us to see what is really used.
$\beta$ does not appear in Alice's probability. It is true. But $\lambda$ has not to be a number. It may be a couple of numbers.
the first could be a property of something near Bob and the other the property of something near Alice.
The problem becomes the locality of $\lambda$

$\lambda$ is by definition something localized to the pair creation event. $\alpha$ represents properties that are local to Alice, and $\beta$ represents properties that are local to Bob.

 

[stevendaryl]

What I don't like about Bell's argument as presented is the phrase "Bob's result" is set next to $P(B\vert \beta, \lambda)$ which is not really what I think Bob's result actually means. Alice could have perfect pre-knowledge of Bob's individual measurements (particle by particle) and Bob could still believe things are random.

I don't understand what you mean. In what I wrote, $B$ is a variable that takes on two possible values: spin-up in whatever direction Bob chose, or spin-down in whatever direction Bob chose. $P(B | \beta, \lambda)$ is the assumed probability that Bob will get result $B$ given that he chose setting $\beta$ (the orientation of his detector) and the hidden variable has value $\lambda$.

I don't understand what the relevance of Alice's pre-knowledge is. If Alice has perfect knowledge about what Bob's result will be, that means, in terms of the model I gave, that:

$P_B(B | A, \alpha, \beta, \lambda) =$ 0 or 1.

Since Bob doesn't know the value of $A$ or $\lambda$, the relevant probabilities for him are:

$P_B(B | \alpha, \beta) = \sum_\lambda \sum_A P_{hv}(\lambda) P_A(A | \alpha, \beta, \lambda) P_B(B | A, \alpha, \beta, \lambda)$

Yes, it's possible for $P_B(B | \alpha, \beta) = \frac{1}{2}$ even though $P_B(B | A, \alpha, \beta, \lambda) =$ 0 or 1.

 

[Paul Colby]

I don't understand what you mean.

Sadly, this may hold for me as well. It appears possible for Alice and Bob to have multiple wave functions describing different states of knowledge about the two particles and have no contradictions (at least in my mind) between the two of them. I don't see that as being reflected in Bell's probability starting point though it may well be. It's also clear that Bell's stating point is not tenable from what's known about physics otherwise a $P_{hv}(\lambda)$ would exist. Well, I have to attend a wedding so duty calls.

 

[stevendaryl]

It's also clear that Bell's stating point is not tenable from what's known about physics otherwise a $P_{hv}(\lambda)$ would exist. Well, I have to attend a wedding so duty calls.

That's what Bell proved, that QM is not consistent with the sort of local theory that Einstein wanted. So you're agreeing with Bell, not disagreeing with him.

 

[stevendaryl]

Well, I have to attend a wedding so duty calls.

Have a good time, and best wishes to the happy couple.

 

[naima]

There are different kinds of locality, and people should distinguish them. The two most important kinds are signal locality and Bell locality.

Could you explain why Bell locality is not a signal locality? thanks

 

[Derek Potter]

Could you explain why Bell locality is not a signal locality? thanks

Let's see if anyone disagrees with this.

Bell locality means that A cannot affect B at spacelike separation.
Signal locality means that signals cannot be sent from A to B at spacelike separation.
Signalling has a precise meaning which is explained nicely in No-communication theorem

Obviously, Bell locality implies signal locality.
However signal locality does not imply Bell locality.

Signal locality is not invoked in the derivation of Bell's theorem. Neither does the theorem imply that signal locality is broken. The only reason for worrying about it is that if it were broken, both QM and special relativity would be broken too. So it is useful to make sure that when anyone talks about entanglement and non-locality, it means Bell non-locality.

 

[Demystifier]

Could you explain why Bell locality is not a signal locality? thanks

As Derek Potter said, it is possible to have signal locality without Bell locality.

 

[martinbn]

Bell locality means that A cannot affect B at spacelike separation.

This is not clear to me. What does it mean "to affect", given that there is no signaling? To me "to affect" means that A is the cause (or part of the cause) of B. If we exclude magic how does that work without signaling?

 

[DrAupo1]

Regardless of the experiments trying to prove subjective reality,versus objective reality,one thing seems to be overlooked:The internal mechanism by which we observe the results of any experiment.The human brain.There are processes within our brain that are not entirely understood,and some would argue are happening on a quantum level.I think we will never truly understand our own brain..if it were that simple,we would be too simple to comprehend it.We cannot be truly objective in our observations because we are imprisoned within our own subjective reality,thus all results,are perceived subjectively,even those that appear to be objective.The only way to observe total objective reality is to not exist in this dimension of space time.It is an intractable problem from our position.You cannot start by assuming that you do not exist.

 

[Derek Potter]

I'm guessing you didn't read the link I provided.
Signalling involves passing data from an external source to B via A. A making up random or uncontrollable data and sending it to B is therefore not signalling.

 

[martinbn]

I'm guessing you didn't read the link I provided.
Signalling involves passing data from an external source to B via A. A making up random or uncontrollable data and sending it to B is therefore not signalling.

I assume that was addressed to me. I did read and I am familiar with the theorem. But my questions is: what does it mean to affect if there is no signaling? The question is just about the terminology, to affect means what exactly?

 

[Derek Potter]

Regardless of the experiments trying to prove subjective reality,versus objective reality,one thing seems to be overlooked:The internal mechanism by which we observe the results of any experiment.The human brain.There are processes within our brain that are not entirely understood,and some would argue are happening on a quantum level.I think we will never truly understand our own brain..if it were that simple,we would be too simple to comprehend it.We cannot be truly subjective in our observations because we are imprisoned within our own subjective reality,thus all results,are
perceived subjectively,even those that appear to be objective.The only way to observe total objective reality is to not exist in this dimension of space time.It is an intractable problem from our position.You cannot start by assuming that you do not exist.

That is just metaphysical sophistry. The discussion here is about what actually happens - as verifiable in the laboratory. I could spend/waste days discussing thje objective/subjective boundary but a) it is quite unnecessary b) it is irrelevant to this topic and c) it would be against forum policy and would get the thread closed immediately by the mods.

 

[Demystifier]

This is not clear to me. What does it mean "to affect", given that there is no signaling? To me "to affect" means that A is the cause (or part of the cause) of B. If we exclude magic how does that work without signaling?

Signal is an affect controlled by a human. It is possible to have an affect which cannot be controlled by a human, in which case we have affect without signaling. See also
https://www.physicsforums.com/threa...ctual-definiteness.847628/page-2#post-5319182

 

[martinbn]

Signal is an affect controlled by a human. It is possible to have an affect which cannot be controlled by a human, in which case we have affect without signaling. See also
https://www.physicsforums.com/threa...ctual-definiteness.847628/page-2#post-5319182

A star emits light, which melts a comet. No humans involved, still there is signaling.

 

[Demystifier]

A star emits light, which melts a comet. No humans involved, still there is signaling.

No, it would not be called signaling.