Determinism, realism, hidden variables

[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.

 

[Demystifier]

But then if A and B are spacelike, how can A cause anything at B?

E.g. by not being described by a hyperbolic partial differential equation. Then what equation is relevant? Nobody knows for sure, but one well known possibility is the equations of Bohmian mechanics. They are non-local, in a sense similar to equations of non-relativistic Newtonian gravity.

 

[martinbn]

E.g. by not being described by a hyperbolic partial differential equation. Then what equation is relevant? Nobody knows for sure, but one well known possibility is the equations of Bohmian mechanics. They are non-local, in a sense similar to equations of non-relativistic Newtonian gravity.

Yes, that's a possibility. But that would be signaling with infinite speed (or at least with no bounded speed). So why would that be called [insert adjective]-locality?

That's is still my confusion. The distinction between signal locality and Bell locality. It seems that better words would be simply locality and non-locality. Yet, it seems that there is some kind of Freudian distinction between non-locality and Bell-locality. Where the second one has some kind of causal relation ( things at A affect those at B) but it is done without any local interaction (which is what I thought signaling means).

 

[Derek Potter]

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.

And Bell proved that if you simulate spacelike separation, what you describe cannot be achieved.

 

[martinbn]

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.

Sure, but neither affects the other i.e. neither causes the other to flash a certain colour.

 

[Derek Potter]

Sure, but neither affects the other i.e. neither causes the other to flash a certain colour.

And there can be no common cause if spacelike separation is present or simulated.

 

[Ilja]

Well, you say, Bell non-local experiments are evidence for non-local cause. Bell non-locality is not an interaction in the same sense as passing a signal. It's not a non-local interaction in this sense. It's more like precognition.

The point is a different one.

In Bell's theorem, we have a 100% correlation and exclude, via the violation of Bell's inequality, that it may be explained by a common cause in the past. $C\to A$ and $C\to B$. This leaves two explanations: $A\to B$ and $B\to A$. Above would violate Einstein causality.

But any correlation which has two such explanations cannot be used to send information, nor from A to B, nor from B to A, because this would be in contradiction with one of the two remaining explanations.

So, it is our situation, our imperfect knowledge, which makes the difference. We don't know which explanation is the correct one. One may be the correct one. And there may be, on the unknown, fundamental level, as well a usual signal, with some finite speed, simply a larger one than c, nothing more "nonlocal" than our existing theories.

 

[martinbn]

And there can be no common cause if spacelike separation is present or simulated.

Yes, but you state that they can affect each other in some other way without sending signals.

 

[stevendaryl]

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?

The difference has to do with what variables governing a situation are visible, and what variables are controllable. For Alice to signal Bob, it must be the case that variables that are controllable by Alice can affect variables that are visible to Bob. You can have effects without signals if the variables controllable by Alice only affect variables that are not visible to Bob.

Let me illustrate this with an EPR-inspired example:

We have a pair of devices, one belonging to Alice and one belonging to Bob, each with the following features:

• It has a dial that can be set to any value between 0 and $2 \pi$.
• It has an internal memory that can store a real number between 0 and 1. Initially, the value is 1/2.
  
• It has a light bulb that can either be on or off.
• It has a button that can be pressed.

Let $P_A$ be the internal value for Alice's device, and let $P_B$ be the internal value for Bob's device, and let $\alpha$ be the dial setting for Alice's device, and let $\beta$ be the dial setting for Bob's device. When Alice pushes the button on her device,

• With probability $P_A$, her light comes on, and Bob's device's internal variable is set to $f(\alpha, \beta)$.
• With probability $1 - P_A$, her light goes off, and Bob's device's internal variable is set to $1 - f(\alpha, \beta)$

When Bob pushes his button,

• With probability $P_B$, his light comes on, and Alice's device's internal variable is set to $f(\alpha, \beta)$.
• With probability $1 - P_B$, his light goes off, and Alice's device's internal variable is set to $1 - f(\alpha, \beta)$

So in this set-up, Alice pushing the button affects Bob's device: it causes the internal variable to change values. But she cannot control what value it changes to. The only thing that Alice controls is her setting $\alpha$, and the only things that are visible to Bob are his own setting and the light bulb state. Based just on what's visible, Bob cannot deduce anything about Alice's setting, so it's not possible for Alice to signal to Bob.

The distinction between "affecting" and "signaling" depends on some variables being "hidden"---not visible or directly controllable.

 

[Derek Potter]

Yes, but you state that they can affect each other in some other way without sending signals.

I didn't say quite that. I said that even if they affect each other (Bell non-locality) - perhaps by sending something that we can't control - it doesn't automatically mean we can send signals (signal non-locality).

 

[Derek Potter]

the two remaining explanations

Do you mean non-causality and non-definiteness etc?

 

[Paul Colby]

In Bell's theorem, we have a 100% correlation and exclude, via the violation of Bell's inequality, that it may be explained by a common cause in the past. C→AC→AC\to A and C→BC→BC\to B. This leaves two explanations: A→BA→B A\to B and B→AB→AB\to A. Above would violate Einstein causality.

Thanks for the clarity. I really haven't invested enough time becoming familiar with these concepts. So, one may construct purely classical examples for which $A\rightarrow B$ and $\rightarrow A$ isn't a violation and isn't a mystery. From my perspective the issues aren't in some apparent non-local "cause" since the quantum and classical examples are no different in regard to correlations of space-like separated measurements. The conceptual problems arrises because one or more components of QT are taken as what Bell referred to as beables which they clear are not. These problems are cooked into QM from the get go and are very likely have no classical resolution.

 

[Simon Phoenix]

In a probably misguided attempt to cut through all the philosophical and technical jargon I tend to try to look at these issues in rather simple terms.

In essence I think it would be a very strange theory of physics in which the results (statistics) of an experiment 'here' were affected by the settings of measurement devices 'there' - irrespective of whether here and there were spacelike separated. I do not really care whether this is technically known as 'Bell locality' or 'Einstein locality' or the locality dreamt up by my Aunt Doris.

Given that entanglement is a pretty ubiquitous phenomenon in QM (pretty much every interaction of 2 quantum systems leads to entanglement) then we can imagine hundreds, if not thousands, of different measurements, experiments and measurement devices that we could employ to demonstrate entanglement via a violation of some suitable 'Bell' inequality.

Are we to require a theory of physics in which every single possible variant of measurement and measurement device had this property that settings 'there' affect results 'here'? How do our devices and systems here even 'know' about what's happening 'there'? Is there some mystical field or potential that (in effect) transmits this information in the same kind of way for every conceivable experimental test or measurement device? Whether this (in effect) information transfer is happening slower or faster than light speed, I think that's stretching credulity a little too far for my tastes.

So, in a nutshell, we can have a theory in which we have so-called hidden variables that possesses this 'realistic' character we're used to from the variables of classical physics - but in order to make it work we have to have something that, in effect, transfers information about device settings from 'there' to 'here'. My own personal view is that the violation of 'locality' in the sense I've outlined above is a much weirder thing than the violation of 'realism'.

The dBB theory is such a theory - personally I find it weirder than QM with its complex guiding potential and non-local character. But as I guess after dicking about with a ton of unwieldy equations it gives the same answers as plain old vanilla QM then dispensing with 'realism' or 'locality' in one's metaphysical view of nature is largely a matter of personal preference.

 

[LaserMind]

I ask a question: could I write a program that simulates two pixels as entangled?

The pixels themselves have no influence on each other. All the influence is done behind the scenes by simple code.

Does that contradict Bells somehow?

 

[DrChinese]

I ask a question: could I write a program that simulates two pixels as entangled?

The pixels themselves have no influence on each other. All the influence is done behind the scenes by simple code.

You can write a program that simulates Bell for the so-called "perfect" correlations. But not for correlations at all angles. The cos^2(theta) rule can't be simulated for all pairings for randomized settings of measurements by Alice and Bob. Specifically, for Alice and Bob randomly (and independently) selecting as their measurement angles 0, 120 and 240 degrees: you will end up with wrong percentages as N gets larger. With a computer simulation, that is.

 

[Paul Colby]

I ask a question: could I write a program that simulates two pixels as entangled?

If your pixel observables commute you can.

 

[Derek Potter]

I ask a question: could I write a program that simulates two pixels as entangled?
The pixels themselves have no influence on each other. All the influence is done behind the scenes by simple code.
Does that contradict Bells somehow?

Obviously you could simulate entanglement. Just use the formulae that Dr Chinese has posted.

However it would not and cannot contradict Bell if you properly simulate the spacelike separation and fulfil the conditions stipulated in Bell's theorem.

Note that "behind the scenes" pretty well gives the game away. You would be using non-local variables. If you avoided that and kept everything else correct you would not be able to create the required correlations. A theorem is a theorem.

For a suggested protocol that avoids information leaking from one data set to another, try the Quantum Randi Challenge. https://arxiv.org/abs/1207.5294

 

[LaserMind]

Obviously you could simulate entanglement. Just use the formulae that Dr Chinese has posted.

However it would not and cannot contradict Bell if you properly simulate the spacelike separation and fulfil the conditions stipulated in Bell's theorem.

Note that "behind the scenes" pretty well gives the game away. You would be using non-local variables. If you avoided that and kept everything else correct you would not be able to create the required correlations. A theorem is a theorem.

For a suggested protocol that avoids information leaking from one data set to another, try the Quantum Randi Challenge. https://arxiv.org/abs/1207.5294

I am thinking about using spots on a computer screen to simulate entanglement of particles in space. Could I do it or would it contradict Bells?
It would have a button that when clicked then pairs of spots would reveal their correlated states (I would
random number generator to set the color of one particle (spot) exactly when its clicked and its partner's
from one color's code to give the other color).

If I can do that without disobeying some law then isn't it a pretty good simulation of what we have in real life?

 

[DrChinese]

I am thinking about using spots on a computer screen to simulate entanglement of particles in space. Could I do it or would it contradict Bells?
It would have a button that when clicked then pairs of spots would reveal their correlated states (I would
random number generator to set the color of one particle (spot) exactly when its clicked and its partner's
from one color's code to give the other color).

If I can do that without disobeying some law then isn't it a pretty good simulation of what we have in real life?

First, you should really start a new thread to discuss simulating entanglement via code.

Second, there are a number of past threads on this subject too.

Third, you should thoroughly understand the issues involved BEFORE you further take up anyone's time. There is no problem with measurements at the same angle (assuming you use spin or polarization as an observable). It is other angles that have a problem, and you are apparently unaware of the QM rules there.

Actually, I guess I have the order of the above exactly reversed.

 

[Derek Potter]

I am thinking about using spots on a computer screen to simulate entanglement of particles in space. Could I do it or would it contradict Bells?
It would have a button that when clicked then pairs of spots would reveal their correlated states (I would
random number generator to set the color of one particle (spot) exactly when its clicked and its partner's
from one color's code to give the other color).
If I can do that without disobeying some law then isn't it a pretty good simulation of what we have in real life?

But that is not what entanglement means. It's a lot more complicated than just a correlation. See Dr Chinese's earlier post. And even the Alice and Bob scenario where there is perfect anti-correlation only occurs if they chose their detector orientations to be the same. You don't even have anything corresponding to their detector angles. And even that perfect correlation doesn't illustrate entanglement because it doesn't violate Bell's inequality - you can explain it with a contrived classical explanation. Only when you have the whole lot can you claim to be simulating entanglement. And you won't be able to do that without having some behind the scenes non-locality. In other words you'll be able to simulate quantum results only by cheating on the conditions.

 

[Ilja]

Do you mean non-causality and non-definiteness etc?

No, as described after the : sign, a direct causal influence $A\to B$, or, alternatively, $B\to A$.

Counterfactual definiteness is not an assumption, but derived from the EPR argument. And to reject causality is not an explanation, it means to reject the very idea to search for explanations. Without causality we are back to astrology. (Not exactly, even astrologers have searched for explanations).

 

[DrChinese]

Counterfactual definiteness is not an assumption, but derived from the EPR argument.

This is not a fair statement. CFD is derived by EPR ONLY by in turn making assumptions. Specifically, they assume that all elements of reality (per their definition) are simultaneously real. That rules out CFD per se.

 

[Ilja]

This is not a fair statement. CFD is derived by EPR ONLY by in turn making assumptions. Specifically, they assume that all elements of reality (per their definition) are simultaneously real. That rules out CFD per se.

I don't understand.

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.

Given the Bell state and Einstein causality, we can do this for all directions. Choose the direction, measure, compare, see the 100% correlation. Fine. Thus, the results are real, predefined, for all directions. This is how the EPR criterion is formulated: "we can", not "we do".

There are, clearly, additional assumptions: Einstein causality does not follow from the EPR criterion, and the quantum statistics of the Bell state are assumed too. But this is nonetheless the EPR argument.

 

[DrChinese]

Giving up realism means giving up any idea of explanation completely. There is no longer any reality outside, all this is a dream or fantasy or so. There would be no point of doing science, if not for the purpose of studying objective reality.

This is not a description of non-realism. It is a gross distortion and ignores much which has been written on the subject.

 

[DrChinese]

I don't understand. ... Given the Bell state and Einstein causality, we can do this for all directions. Choose the direction, measure, compare, see the 100% correlation. Fine. Thus, the results are real, predefined, for all directions.

That leap is by assumption. EPR simply rejects any other viewpoint as unreasonable. As obviously you do. Nonetheless, it is circular reasoning to assume CFD and then say you have proved it. See the last 2 paragraphs of EPR.

 

[stevendaryl]

This is not a fair statement. CFD is derived by EPR ONLY by in turn making assumptions. Specifically, they assume that all elements of reality (per their definition) are simultaneously real. That rules out CFD per se.

I'm not sure what you mean by that. The way that I see it is that E, P, and R were assuming a particular sort of theory, whereby the results of an experiment depend only on local facts. So, as Bell formulated this, that means that Alice's result depends only on facts about her device and facts about her particle, and similarly for Bob. This implies Bell's assumed form for the joint probability distribution:

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

where $A$ represent's Alice's result (assumed to be a boolean), $B$ represents Bob's result, $\alpha$ represents facts about Alice's detector, $\beta$ represents facts about Bob's detector, and $\lambda$ represents facts about the twin pair creation event.

This form seems at first to allow for the possibility that the results are nondeterministic. But if you impose perfect anti-correlations, then that implies:

$P(A|\alpha, \lambda) P(B|\alpha, \lambda) = 0$ (It is impossible for them to both get spin-up with the same detector settings.)
$(1-P(A|\alpha, \lambda))(1 - P(B|\alpha, \lambda)) = 0$ (It is also impossible for them to both get spin-down)

These two facts imply that $P(A|\alpha, \lambda) =$ 0 or 1 and $P(B|\beta, \lambda) =$ 0 or 1.

So Bell's factorizability assumption implies that the outcomes are deterministic functions of $\lambda$ and the detector settings, which implies contrafactual definiteness (in the sense that the assumed model implies that there is a definite answer to the question: What would Bob's result have been if he chose a different detector setting?)

 

[Ilja]

That leap is by assumption. EPR simply rejects any other viewpoint as unreasonable. As obviously you do. Nonetheless, it is circular reasoning to assume CFD and then say you have proved it. See the last 2 paragraphs of EPR.

It is certainly nothing circular here, because the EPR criterion is clearly different from CFD. In particular, there are EPR-realistic interpretations of QT like dBB theory, but CFD does not hold in dBB. So CFD is clearly a stronger assumption.

Of course, other viewpoints are possible. But rejecting the EPR criterion means simply rejecting reality and may be classified as mysticism.

 

[DrChinese]

I'm not sure what you mean by that. ...

So Bell's factorizability assumption implies that the outcomes are deterministic functions of $\lambda$ and the detector settings, which implies contrafactual definiteness (in the sense that the assumed model implies that there is a definite answer to the question: What would Bob's result have been if he chose a different detector setting?)

I am talking about Ilja's (incorrect) statement that EPR "proves" CFD. Bell essentially (and usefully) makes it an assumption (along with locality) and shows that those 2 assumptions (together) do not fit with QM. So one or both must be wrong.

EPR says: "One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this."

Clearly, CFD is inconsistent with the more restrictive requirement. EPR takes the less restrictive view (assuming CFD) and then concludes any other perspective is unreasonable. Well, that places a lot of physicists in the unreasonable camp. Who really thinks that particles have simultaneously well defined P and Q?

 

[DrChinese]

It is certainly nothing circular here, because the EPR criterion is clearly different from CFD.

Not in any way I can see. And if you were correct, every physicist would be a Bohmian.

 

[PeterDonis]

Thread closed for moderation.

Edit: The thread appears to have run its course and will remain closed.