Undergrad What were Newton's thoughts on non-locality?

[stevendaryl]

If this is true, then it is obviously very easy for Alice to send a message to Bob FTL. At a pre-arranged time, Alice does measurement A or B on a set of particles which affect Bob's statistics. Bob then (a short time later) does his measurements and his statistics tell him whether Alice did measurement A or B. That is then a message from Alice to Bob FTL.

But @Derek P was not claiming that Alice could send information about her measurement choice to Bob. He was claiming that information about the combination measurement and result affected Bob.

Alice's measurement and result is a pair $(\alpha, A)$ where $\alpha$ is her orientation choice, and $A$ is her result, $\pm 1$.

The relevant question is not: "Can Bob learn something about $\alpha$?" For Derek's claim, the relevant question is: "Can Bob learn something about the pair $(\alpha, A)$?" The answer is certainly "yes". If Bob measures the spin of his particle along the z-axis, and gets result +1, then he knows afterward that $(\alpha, A) \neq (\hat{z}, +1)$. He didn't know that, previously. So he learns something about the combination of Alice's measurement + result. Which is what Derek was talking about.

Learning something about a pair of variables does not imply that you've learned anything about either variable, separately.

 

[PeroK]

But @Derek P was not claiming that Alice could send information about her measurement choice to Bob. He was claiming that information about the combination measurement and result affected Bob.

Alice's measurement and result is a pair $(\alpha, A)$ where $\alpha$ is her orientation choice, and $A$ is her result, $\pm 1$.

The relevant question is not: "Can Bob learn something about $\alpha$?" For Derek's claim, the relevant question is: "Can Bob learn something about the pair $(\alpha, A)$?" The answer is certainly "yes". If Bob measures the spin of his particle along the z-axis, and gets result +1, then he knows afterward that $(\alpha, A) \neq (\hat{z}, +1)$. He didn't know that, previously. So he learns something about the combination of Alice's measurement + result. Which is what Derek was talking about.

Learning something about a pair of variables does not imply that you've learned anything about either variable, separately.

That is correlation. Not "cause and effect", as is being claimed.

The results are correlated, but the statistics on one particle are not influenced by the choice of measurement on the other. Bob has no way to tell, without communication from Alice, a) whether she has measured anything or b) what she has chosen to measure.

I don't believe @Derek P agrees with this last statement.

 

[A. Neumaier]

then he knows afterward that

Only if Alice actually measured something. If she instead took a nap, or if her detector failed because of a power outage, Bob concluded something wrongly.

Bob gets conditional information only, of the kind: ''Should Alice have measured $\alpha=\hat z$ then her result was $-1$.'' Because Bob doesn't know whether the hypothesis holds, he knows nothing. Having about tomorrow's whether the conditional information that ''Should there be no clouds it will not rain'' tells in fact nothing useful about the weather tomorrow, unless we have information about tomorrows clouds.

In any case, whatever statistics from data collected by Bob can be made (by Bob or Charles) before Alice's choices or results become available to them will be completely unaffected by the behavior of Alice and her detector. Thus there are no causality violations, in contradiction to the claim of @Derek P:

No the bad thing is non-local causality. You cannot avoid something from Alice getting to Bob FTL, whether you call it information or not.

This something is called ''conditional information''. But nothing in relativity forbids conditional information to be passed faster than light. For example, we know lots of conditional information about what can or cannot happen inside black holes although no information can flow out from there. Conditional information is what we can get from theory independent of observation, but theoretical conclusions apply instantaneously and have no speed limit.

Causality only demands that information flow is limited by the speed of light. Thus causality is not violated in Bell-type experiments.

 

[Derek P]

This something is called ''conditional information''. But nothing in relativity forbids conditional information to be passed faster than light. For example, we know lots of conditional information about what can or cannot happen inside black holes although no information can flow out from there. Conditional information is what we can get from theory independent of observation, but theoretical conclusions apply instantaneously and have no speed limit.
Causality only demands that information flow is limited by the speed of light. Thus causality is not violated in Bell-type experiments.

The required information is unconditional - namely Alice's actual setting and Alice's actual result.

 

[Derek P]

In any case, whatever statistics from data collected by Bob can be made (by Bob or Charles) before Alice's choices or results become available to them will be completely unaffected by the behavior of Alice and her detector. Thus there are no causality violations, in contradiction to the claim of @Derek P:

Well that is highly ambiguous. If you are saying that the events CANNOT be affected because of relativity, causality etc then of course I would agree. But in a well-designed EPR experiment the observations ARE affected.

 

[A. Neumaier]

The required information is unconditional - namely Alice's actual setting and Alice's actual result.

None of this information is available to Bob, hence he cannot use the conditional information available to him, hence there is no causality problem.

The conditional information and the correlations become actual only when someone has access to the actual data resolving the condition.

But in a well-designed EPR experiment the observations ARE affected.

No, the observations are simply correlated - you are postulating in addition a notion of being affected which does not exist.

One cannot say that Alice's actions and observations cause (or affect) Bob's observations to be correlated. This is due to the Lorentz invariance of all relativistic arguments. There are always Lorentz frames in which Alice acts later than Bob observes, and others in which Bob acts later than Alice. So who can be said to cause (or affect) what?

Causality is simply inapplicable to an analysis of correlations at spacelike distances because any meaningful use of this notion depends on a notion of before and after, which doesn't exist in this case.

 

[Demystifier]

The point I wanted to make is that Bell's theorem is not about quantum mechanics, but about classical assumptions regarding intuition and rules.

I agree that Bell's theorem is not about QM. But I disagree that it is about classical physics. His theorem does not assume classical physics. His theorem assumes locality and standard probability theory. The standard probability theory is a branch of mathematics and as such it does not depend on physics. The standard probability theory is just a part of the standard scientific method [E.T. Jaynes, Probability Theory The Logic of Science, Cambridge University Press, 2003]. In other words, the Bell theorem says that assumptions of (i) locality and (ii) standard scientific method are in contradiction with QM. Since QM is in agreement with observations, it follows that either (i) locality or (ii) standard scientific method (or both) is wrong.

Those who insist that QM is local actually deny the standard scientific method. For instance, one of the principles of the scientific method is the Reichenbach's common cause principle: a correlation between events A and B indicates either that A causes B, or that B causes A, or that A and B have a common cause (which Bell denotes by $\lambda$). Those who insist that QM is local usually deny the Reichenbach's common cause principle.

 

[A. Neumaier]

I disagree that it is about classical physics.

Classical physics is implied not in the formal theorem but in its application to the experiments. To apply it to the latter and construct an apparent paradox, one argues that all observables have sharp values, and that the particle travel like classical point particles along straight paths, with finite velocity $c$, etc.

All this is justified only by invoking the principles of classical physics.

Reichenbach's common cause principle: a correlation between events A and B indicates either that A causes B, or that B causes A, or that A and B have a common cause. Those who insist that QM is local often deny the Reichenbach's common cause principle.

Reichenbach's principle is not a fundamental physical law, but a principle with only limited applicability. It is based on classical, deterministic and nonrelativistic reasoning.

It assumes determinism, since in a stochastic process, all noise is uncaused, without a common cause.

It assumes a linearly ordered view of time, hence nonrelativistic physics. Nothing in the formalism of classical relativity forbids uncaused spacelike correlations to exist. For example, one can assume a constant (hence maximally correlated) values of a classical field and its time derivative at $t=0$ and finds a unique solution of the d'Alembert equations, fully consistent with the principles of relativity.

Thus it is completely inapplicable to the discussion of quantum probabilities, or relativistic issues.

 

[Derek P]

None of this information is available to Bob, hence he cannot use the conditional information available to him, hence there is no causality problem.

The conditional information and the correlations become actual only when someone has access to the actual data resolving the condition.

The way you defined conditional information, it was available to Bob even before the experiment. The correlations may only be known when someone has access to both sets of data, but the Alice's and Bob's outcomes are known to themselves at the moment of observation.

{quote]No, the observations are simply correlated - you are postulating in addition a notion of being affected which does not exist.[/quote]
I don't think I'm posulating anything. A is set up freely, no common cause with B. B depends on A. Therefore A causes B. What is the alternative?

One cannot say that Alice's actions and observations cause (or affect) Bob's observations to be correlated. This is due to the Lorentz invariance of all relativistic arguments. There are always Lorentz frames in which Alice acts later than Bob observes, and others in which Bob acts later than Alice. So who can be said to cause (or affect) what?.

Both. Which is absurd. Which is precisely why the paradigm used here must be faulty.

But in any case, the same experiments can be done under timelike separation. You can't then rule out the loophole of secret collusion between the particles but you have unambiguous causality violation, under the same paradigm.

 

[Derek P]

I agree that Bell's theorem is not about QM. But I disagree that it is about classical physics. His theorem does not assume classical physics. His theorem assumes locality and standard probability theory. The standard probability theory is a branch of mathematics and as such it does not depend on physics. The standard probability theory is just a part of the standard scientific method [E.T. Jaynes, Probability Theory The Logic of Science, Cambridge University Press, 2003]. In other words, the Bell theorem says that assumptions of (i) locality and (ii) standard scientific method are in contradiction with QM. Since QM is in agreement with observations, it follows that either (i) locality or (ii) standard scientific method (or both) is wrong.

Those who insist that QM is local actually deny the standard scientific method. For instance, one of the principles of the scientific method is the Reichenbach's common cause principle: a correlation between events A and B indicates either that A causes B, or that B causes A, or that A and B have a common cause (which Bell denotes by $\lambda$). Those who insist that QM is local usually deny the Reichenbach's common cause principle.

Or they point out that probability theory as applied to observations requires a map between the countable events and the observations. Classically the map is one-to-one. The quantum map is different and, with a good theory of measurement, it is quite sufficient to decompose the complete state into superposed separable (local) states. Whether Many Worlds is local or not thus depends on the precise meaning of local - the word was not designed to cope with superposition. Anything other interpretation, though...!

 

[DrChinese]

... For instance, one of the principles of the scientific method is the Reichenbach's common cause principle: a correlation between events A and B indicates either that i) A causes B, or that ii) B causes A, or that iii) A and B have a common cause (which Bell denotes by $\lambda$). Those who insist that QM is local usually deny the Reichenbach's common cause principle.

Referencing this experiment by Hensen et al, 2015: https://arxiv.org/abs/1508.05949

A Bell test is performed on between distant entangled electron spins. They are entangled via swapping, so the measured particles have no local connection to each other. Therefore there is no (prior, local) common cause, leaving just the first 2 options..

If A causes B, or B causes A, then that must occur non-locally. Or we deny Reichenbach's common cause principle as suggested. Or we could modify it to remove the implied requirement that a cause precede the effect.

 

[rubi]

The standard probability theory is a branch of mathematics and as such it does not depend on physics. The standard probability theory is just a part of the standard scientific method [E.T. Jaynes, Probability Theory The Logic of Science, Cambridge University Press, 2003]. In other words, the Bell theorem says that assumptions of (i) locality and (ii) standard scientific method are in contradiction with QM. Since QM is in agreement with observations, it follows that either (i) locality or (ii) standard scientific method (or both) is wrong.

That's not correct. There is no strictly defined "scientific method". Science does not depend on particular mathematical theories. They may be applicable in certain situations, but they needn't be applicable in principle. Science is not dogmatic in any way.

Those who insist that QM is local actually deny the standard scientific method. For instance, one of the principles of the scientific method is the Reichenbach's common cause principle: a correlation between events A and B indicates either that A causes B, or that B causes A, or that A and B have a common cause (which Bell denotes by $\lambda$). Those who insist that QM is local usually deny the Reichenbach's common cause principle.

Reichenbach's common cause principle is not a principle of the scientific method. On the contrary, probabilistic causation doesn't even work classically and is generally rejected as a conclusive theory of causality. One doesn't need quantum mechanics for that.

 

[Demystifier]

Reichenbach's principle is not a fundamental physical law,

I agree. It is a part of the standard scientific method, which is much more general that physics.

but a principle with only limited applicability.

I agree. The scientific method is very powerful, but it cannot solve all problems.

It is based on classical,

Not in the sense of classical physics, but yes in the sense of standard ("classical") scientific method.

deterministic

The Reichenbach principle just says that if there is a correlation between something, then there must be a cause for the correlation. It does not insist that everything is deterministic in the Laplace's sense.

and nonrelativistic reasoning.

The Reichenbach principle is not in contradiction with relativity. For instance, the Reichenbach principle is valid in classical relativistic physics.

 

[Demystifier]

Science does not depend on particular mathematical theories.

All science, from psychology and medicine to experimental QM, uses the same principles of statistics, which is based on the same theory of probability.

 

[Demystifier]

Reichenbach's common cause principle is not a principle of the scientific method. On the contrary, probabilistic causation doesn't even work classically and is generally rejected as a conclusive theory of causality. One doesn't need quantum mechanics for that.

Can you give a non-quantum example of science that rejects the Reichenbach's common cause principle?

 

[rubi]

I agree. It is a part of the standard scientific method, which is much more general that physics.

Don't you see how terribly poor and unscientific it is to dogmatically claim that some principle is part of the scientific method? There is no authority that defines what the scientific method is. The success of science critically depends on the ability of scientists to eventually reject wrong principles if they happen to disagree with our current best theories. If you need a dogma to justify your point of view, then you leave the realm of scienctific discussion.

All science, from psychology and medicine to experimental QM, uses the same principles of statistics, which is based on the same theory of probability.

If some field uses probability theory, then it is because probability theory just happens to suffice in the particular situation. If the data seems to be in conflict with with probability theory, people would explore different approaches. So far, this hasn't been necessary in psychology or medicine. However, experimental QM of course does not use probability theory. For example in quantum tomography, the statistics specifically reconstructs a quantum state rather than a classical probability distribution. If classical probability theory is used in some particular quantum experiment, then it is because in that situation, classical probability theory and quantum theory are the same.

Can you give a non-quantum example of science that rejects the Reichenbach's common cause principle?

Here's one example: https://www.journals.uchicago.edu/doi/abs/10.1086/psaprocbienmeetp.1986.1.193140
You will find many more if you look for them. (Edit: For example, this page has a few of them listed: https://plato.stanford.edu/entries/physics-Rpcc/#2)

 

[Mentz114]

There are always Lorentz frames in which Alice acts later than Bob observes, and others in which Bob acts later than Alice. So who can be said to cause (or affect) what?

Causality is simply inapplicable to an analysis of correlations at spacelike distances because any meaningful use of this notion depends on a notion of before and after, which doesn't exist in this case.

Given that there is no 'before/after' available then the instantaneous communication between the pair (they always have the same/opposite spin) has the same affect as the non-local correlations. There appears to be no way to decide experimentally which is a better hypothesis.

 

[PeroK]

I don't think I'm posulating anything. A is set up freely, no common cause with B. B depends on A. Therefore A causes B. What is the alternative?

Both. Which is absurd. Which is precisely why the paradigm used here must be faulty.

Let's assume that experiments went the other way and we have hidden variables. Now, that does not mean that each electron has a definite spin (about all three axes simultaneously) as would be expected classically and would be, let us say, a robust paradigm. Instead, we know from basic QM (without entanglement) that an electron has to decide when measured what spin measurement to return. Where is this information held? And how does the electron process this information? Given the nature of what happens when we measure about different axes that is a lot of information per electron - potentially an infinite amount of information.

It seems to me this is just as faulty a paradigm. Just as physically unjustifiable.

But, also, let's take a look at something apparently more robust: a particle following a geodesic or moving under a potential. How does the particle know which way to move? If we were to simulate this, we would have to do a certain number of measurements or calculations on behalf of the particle to determine the local spacetime or local change in potential. It can't logically be done without any measurement or calculation; yet nature does it! That something tests the surrounding locality in every direction and informs the particle which way to move - what is the alternative to that?

It seems to me if you really ask how nature achieves things, then all the paradigms are faulty. Perhaps, therefore, nature managing to correlate two remote measurements is not as absurd as you may think. And it doesn't imply that nature is sending information from A to B any more than information is being gathered and processed about local changes in spacetime or a potential field.

 

[PeterDonis]

Alice's and Bob's outcomes are known to themselves at the moment of observation.

Yes, but Bob doesn't know Alice's outcome when he knows his own (and vice versa).

B depends on A.

No, A and B are correlated. Correlation has no ordering.

the same experiments can be done under timelike separation. You can't then rule out the loophole of secret collusion between the particles but you have unambiguous causality violation

This is simply false. There is no causality violation in these experiments.

 

[Derek P]

Let's assume that experiments went the other way and we have hidden variables. Now, that does not mean that each electron has a definite spin (about all three axes simultaneously) as would be expected classically and would be, let us say, a robust paradigm. Instead, we know from basic QM (without entanglement) that an electron has to decide when measured what spin measurement to return. Where is this information held? And how does the electron process this information? Given the nature of what happens when we measure about different axes that is a lot of information per electron - potentially an infinite amount of information.

It seems to me this is just as faulty a paradigm. Just as physically unjustifiable.

But, also, let's take a look at something apparently more robust: a particle following a geodesic or moving under a potential. How does the particle know which way to move? If we were to simulate this, we would have to do a certain number of measurements or calculations on behalf of the particle to determine the local spacetime or local change in potential. It can't logically be done without any measurement or calculation; yet nature does it! That something tests the surrounding locality in every direction and informs the particle which way to move - what is the alternative to that?

It seems to me if you really ask how nature achieves things, then all the paradigms are faulty. Perhaps, therefore, nature managing to correlate two remote measurements is not as absurd as you may think. And it doesn't imply that nature is sending information from A to B any more than information is being gathered and processed about local changes in spacetime or a potential field.

I have never said that nature sends information from A to B. I have said that under the assumptions of the pardigm used here, nature must do so. nd you are using the same paradigm when you say "nature decides".
Incidentally "no hidden variable theory" includes "potentially an infinite amount of information."

 

[PeterDonis]

under the assumptions of the pardigm used here

As far as I can tell, @PeroK is not assuming anything or advocating any paradigm; he's basically saying we don't have a paradigm that works. The question is, given that we have a theory that makes correct predictions, why do we need a paradigm?

[Moderator's note: the rest of this post was off topic and has been deleted.]

 

[PeterDonis]

Thread closed for moderation.