Determinism, realism, hidden variables

[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.

 

[Derek Potter]

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?

My apologies, I overlooked that you are a science advisor.

"Exactly"? I hope you are using that term colloquially. It is no use asking me for a formal definition of anything.

Informally, it means that events at A can cause events at B even though it is impossible for external data to control A so that B receives the message. So A and B can, for instance, agree about a random variable. That's not signalling as C cannot control it and so cannot control the result on B.

 

[martinbn]

No, it would not be called signaling.

I see. But isn't this a non-standard use of terminology?

My apologies, I overlooked that you are a science advisor.

Sorry, I didn't mean to be patronizing.

"Exactly"? I hope you are using that term colloquially. It is no use asking me for a formal definition of anything.

Informally, it means that events at A can cause events at B even though it is impossible for external data to control A so that B receives the message. So A and B can, for instance, agree about a random variable. That's not signalling as C cannot control it and so cannot control the result on B.

That's how I understood the meaning of "affect". But then if A and B are spacelike, how can A cause anything at B?

 

[Demystifier]

I see. But isn't this a non-standard use of terminology?

Maybe, maybe not. For instance, wikipedia at
https://en.wikipedia.org/wiki/Signal_(electrical_engineering)
says:
"Definitions specific to sub-fields are common. For example, in information theory, a signal is a codified message, that is, the sequence of states in a communication channel that encodes a message."

It does not define "communication" and "message", but those words sound quite anthropomorphic to me.

 

[Derek Potter]

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

Humans don't have to be involved. The question is whether we could in principle send a message using A's effect on B. Humans are in effect a placeholder for a system which is the source of a message. so unless you postulate some way of controlling the radiation externally, there is no signalling. An alien race hurling planets into the star to create solar flares thereby communicating with a bug living on the comet would qualify as signalling.

This stuff is not very difficult (proof: I can understand it. QED) The only point in discussing it at all is to allay any concerns that entanglement might break relativity.

 

[LaserMind]

Think of entangled particles like two alternating flashing pixels on a screen.

Neither pixel has any information about its position yet when one is red the other is green and vica-versa.

They do not signal each other at all and have no knowledge of each other's state (color) yet their color-flashing behavior is perfectly correlated and instantaneous.