Exploring the EPR Paradox: Reconciling QM and SR

[rjbeery]

But to give up something fundamental for preserving the effective symmetry group of a wave equation?

That's the real crux, isn't it? What exactly shall we sacrifice? Causality mustn't be completely sacrificed if one adopts John Cramer's "Weak Causality" in lieu of "Strong Causality".

Strong Causality is defined as requiring that all causes precede effects, while Weak Causality allows for quantum causes to follow their effects. It is my opinion that this is the least offensive solution to the EPR paradox. Look at what is recovered - Objective Reality, Locality, Determinism (potentially), single history; other interpretations are not able to do this. Our Classical intuitions which QM has taught us to question or outright throw out the window can be recovered. This is attractive to me.

(but the number of states in QM is finite event function is continious so the numbe rof cats is very big but finite)

Unless you are implying "quantized time" (which I am not opposed to) I do not understand how a poison gas being triggered by an atomic decay process does not produce an infinite number of outcomes. Also, I do not believe that the Universe is infinite.

 

[LaserMind]

That's the real crux, isn't it? What exactly shall we sacrifice? Causality mustn't be completely sacrificed if one adopts John Cramer's "Weak Causality" in lieu of "Strong Causality".

I have researched weak causality which allows effect before cause, here is a 'good' letter on it (even though I do not agree with it):

Quote:
Physics Letters A 349 (2006) 411–414
Causality in quantum mechanics
David T. Pegg
Abstract
We show explicitly how the causal arrow of time that follows from
quantum mechanics has already been inserted at a deeper level by the choice
of normalisation conditions. This prohibits information being sent backwards
in time but does not determine a time direction for state propagation"


"To find out where the asymmetry associated with
causality is inserted into our basic quantum postulates, we first
consider the case in which the evolution is removed by allowing
the interval between preparation and measurement to be much
shorter than the characteristic evolution time. We must then be
careful to avoid first inserting the asymmetry into our probabil-
ity postulate. We proceed, therefore, by adopting a fundamental
postulate that time is symmetric in preparation and measurement."

End Quote

I question whether it is sensible to allow "We proceed, therefore, by adopting a fundamental
postulate that time is symmetric in preparation and measurement"

Is this sensible? It leads to backwards time phenomena (in BM) where the particle knows its goal when it starts out.

 

[rjbeery]

In a way I think it's more sensible that time obeys no directional arrow since any Physics equation involving a time parameter is reversible. You may point to entropic processes but my feeling is that there is a correlation between human experience and entropy which is independent of time's "arrow".

 

[Dmitry67]

In a way I think it's more sensible that time obeys no directional arrow since any Physics equation involving a time parameter is reversible. You may point to entropic processes but my feeling is that there is a correlation between human experience and entropy which is independent of time's "arrow".

Whats about the microscopic arrow of time, known as CP violation = T symmetry violation?
Standard Model is explicitly T-assymetric (the parameter is called 'CP violation phase', I believe)

 

[rjbeery]

I'm certainly no QFT expert but the apparent CPT symmetry violation is not necessarily the final edict on the subject. I read a proposal recently...let me try finding it.

 

[Ilja]

That's the real crux, isn't it? What exactly shall we sacrifice? Causality mustn't be completely sacrificed if one adopts John Cramer's "Weak Causality" in lieu of "Strong Causality".

Strong Causality is defined as requiring that all causes precede effects, while Weak Causality allows for quantum causes to follow their effects. It is my opinion that this is the least offensive solution to the EPR paradox. Look at what is recovered - Objective Reality, Locality, Determinism (potentially), single history; other interpretations are not able to do this. Our Classical intuitions which QM has taught us to question or outright throw out the window can be recovered. This is attractive to me.


Unless you are implying "quantized time" (which I am not opposed to) I do not understand how a poison gas being triggered by an atomic decay process does not produce an infinite number of outcomes. Also, I do not believe that the Universe is infinite.

I see absolutely no reason to replace classical common sense causality by some notion of "weak causality" which can lead to closed causal loops. Quantum nonlocality has a simple causal solution: Take a preferred frame and classical causality in this preferred frame.

Relativistic symmetry is emergent. I think, this is a quite natural conclusion, once one has understood that it appears in every wave equation. Wave equations in condensed matter theories are, last not least, not fundamental, but emergent.

But if relativistic symmetry is emergent, there is no reason at all not to take a preferred frame.

Then, I don't understand how you can think of some sort of backward causal influence and talk at the same time about "Our Classical intuitions can be recovered". The way to recover classical intuitions is clearly and obviously pilot wave theory.

All what we have to "give up" in pilot wave theory is a rather strange and non-intuitive thing if we think about it as fundamental - relativistic symmetry. The symmetry group which appears as emergent in every wave equation.

 

[debra]

Then, I don't understand how you can think of some sort of backward causal influence and talk at the same time about "Our Classical intuitions can be recovered". The way to recover classical intuitions is clearly and obviously pilot wave theory.

"Our Classical intuitions can be recovered" is a backward step IMO.

 

[ThomasT]

Perhaps you might find this interesting:
http://fqxi.org/data/essay-contest-files/Nikolic_FQXi_time.pdf

Demystifier, thanks for the link. I read the paper. It was interesting, but I've learned to think about time a bit differently. Whether we're talking about subjective or objective records of the world, the past is different from the present. This means that the spatial configurations that we're indexing are transitory, that the universe is in a continual state of flux.

I think that all time arrows can be reduced to the radiative time arrow. I see this as the fundamental dynamic of our universe, and it can be expressed in precise mathematical terms.

 

[Ilja]

"Our Classical intuitions can be recovered" is a backward step IMO.

Why? There is nothing inherently bad with them. They have made science the greatest success story of humanity.

And if one recognizes that relativistic symmetry is simply the emergent symmetry which appears in a natural way with every wave equation, there is no reason to follow the fundamental spacetime program which was developed at a time when symmetry groups were something new in physics.

 

[Demystifier]

"Our Classical intuitions can be recovered" is a backward step IMO.

Quite generally, a backward step is not allways a bad thing to do.
Humans make mistakes occasionally, and backward steps are often the best strategies in such occasional situations.

 

[rjbeery]

I see absolutely no reason to replace classical common sense causality by some notion of "weak causality" which can lead to closed causal loops. Quantum nonlocality has a simple causal solution: Take a preferred frame and classical causality in this preferred frame.

Ilja: I want to better understand your perspective. Could you provide an example of a closed causal loop due to a Weakly-Causal world? Also, could you please expand on relativistic symmetry and what it would mean to give it up? Are you suggesting that there IS a preferred reference frame?

 

[Ilja]

Ilja: I want to better understand your perspective. Could you provide an example of a closed causal loop due to a Weakly-Causal world? Also, could you please expand on relativistic symmetry and what it would mean to give it up? Are you suggesting that there IS a preferred reference frame?

With giving an example for closed causal loops I have a problem: The theory I prefer does not have them (it has a preferred frame), the alternative (the usual interpretation(s)) don't have a realistic notion of causality (realistic in Bell's meaning).

Causality (and, as well, a lot of other theoretical principles like realism) are best understood as properties of theories, not as theory-independent properties of the world. For a given theory, we can decide in a simple way if it is causal, or realistic, or whatever else. Moreover, defining these principles as properties of theories is very simple too.

If we want to define causality, this can be nicely seen: From experience we cannot derive it, because we have only one universe. From theory we can: In the theory, we can look what happens for other initial conditions.

One property which one would like to postulate is that there are no closed causal loops. The violation of BI allows two realistic explanations: A->B or B->A. Only one of them can be true, else we would already have a causal loop A->B->A. Which of them is true is something the theory should tell us. It should tell us the answer for arbitrary pairs A,B. If it does so, one can easily construct a preferred foliation: T(A)>T(B) if the answer for the pair A, B is B->A.

A hidden preferred foliation has no influence at all on observable effects, that's why it is named "hidden". But this may change below some critical length, similar to the usual sound wave equations, which have, for the sound waves, the same relativistic symmetry, only with another characteristic speed, but only for distances larger than the critical one which is of order of atomic distances.

And, yes, I'm suggesting that there really is a preferred frame. I have a theory of gravity for it (http://ilja-schmelzer.de/glet" ), which is published.

 

[Dmitry67]

The theory I prefer does not have them (it has a preferred frame),

OMG!
Yes, sure, there is a preferred frame: the one where the giant turtle is at rest :)

 

[rjbeery]

Ilja: what you have written is interesting to me, and I will make the effort to read your paper, but I would like to clarify that retro-causality does not necessitate closed-causal loops.

The violation of BI allows two realistic explanations: A->B or B->A.

The Transactional Interpretation allows for advanced and retarded quantum wavefunctions. John Cramer defines two types of causality.

Strong-causality principle: A cause must always precede all of its effects in any reference frame. Information, microscopic or macroscopic, can never be transmitted over a spacelike interval or over a negative timelike or negative lightlike interval.

Weak-causality principle: A macroscopic cause must always precede its macroscopic effects in any reference frame. Macroscopic information can never be transmitted over a spacelike interval or over a negative timelike or negative light-like interval.

Cramer's TI makes a distinction between micro- and macroscopic causes in a Weakly Causal world. This in itself could avoid closed-causal loops, but not necessarily, because his Weak-Causality Principle avoids addressing the possibility of microscopic causes preceding micro- or macroscopic effects.

My personal interpretation differs from Cramer's in that I do not draw a distinction between macro- and microscopic causes, but rather wavelike and particle causes. This wave-particle time asymmetry avoids closed causal loops while allowing for retro-causality because the causal ordering of two events is resolved in the definition of wavelike vs particle.

In this picture all particle causes of event E are shaded in blue, while all wavelike causes of event E are shaded in green. This cleanly resolves the EPR paradox because the entangled particles A and B are seen to possesses a distinct spin at the time of their emission due to the advanced waves of their future measurements. Similarly, the results of their future measurements are determined in a retarded manner by the particles themselves traveling forwards in time. Note that the absolute speed of waves and particles being capped at c persists in this model, which means that Relativity is not violated. The result would be an Objectively Real, (Weakly-) Causal, Local and Deterministic Universe...

 

[Dmitry67]

Deterministic?
It was non deterministic when I learned it
Check also here: http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics#Comparison
is it a typo?

 

[rjbeery]

Before someone asks, I must add that Determinism surfaces from my interpretation because I believe that both wavelike and particle pathing choices are made via the Principle of Least Action.

 

[rjbeery]

Ahh! Dmitry you type too fast. Since this interpretation is unique (AFAIK) I'm not sure what wikipedia would have to say about it. I do welcome criticisms from the fine minds on this forum, though.

 

[DrChinese]

... Local and Deterministic Universe...

Yea, I'd have to question the deterministic part as well. I think the big item in this is the mechanism for effecting the apparently non-local phenomena we all know and love - without being non-local. :)

 

[rjbeery]

DrChinese: The Local mechanism which displays non-locality is already encapsulated in the interpretation. The apparent non-local effects occurring at A and B particles' measurement events is an illusion because both particles possessed a distinct spin at event E (where A and B Locally interacted) and proceeded to carry this spin with them to their respective measuring events. Remember it is the type of measurement taken at these measuring events that restricts the formulation of the advanced waves to ones producing a pair of particles at event E which concur with our QM findings.

 

[DrChinese]

DrChinese: The Local mechanism which displays non-locality is already encapsulated in the interpretation. The apparent non-local effects occurring at A and B particles' measurement events is an illusion because both particles possessed a distinct spin at event E (where A and B Locally interacted) and proceeded to carry this spin with them to their respective measuring events. Remember it is the type of measurement taken at these measuring events that restricts the formulation of the advanced waves to ones producing a pair of particles at event E which concur with our QM findings.

Yes, I am good with this part. I just don't think that makes it a deterministic interpretation. Deterministic (to me anyway) implies that something "caused" Alice and Bob to have the specific orientation at E. I do not think this interpretation implies that.

 

[rjbeery]

Determinism is the philosophical proposition that every event, including human cognition and behavior, decision and action, is causally determined by an unbroken chain of prior occurrences.

Literally using this definition, this interpretation is not Deterministic. Note that the above description of Determinism presumes that influences from the future cannot occur at all; it is merely dealing with the idea that everything happening now either is or is not a result of past events. And the answer to this question is deemed to be the sole arbiter of whether or not future history is set in stone. I say this is false, and that a future history can be set in stone even if some phenomena are retro-causal. When I say Deterministic I mean that there is a single history, from beginning to end, with no random, uncertain or acausal events. If all effects are the result of causes, and if Physics follows the Principle of Least Action for both particle and wavelike influences, then I believe this interpretation is Deterministic*. We could take Cramer's cue and call it Weak Determinism by removing the temporal restriction, if you wish...

* Deterministic under the mildly revised definition of being "the philosophical proposition that every event, including human cognition and behavior, decision and action, is causally determined".

 

[DrChinese]

Literally using this definition, this interpretation is not Deterministic. Note that the above description of Determinism presumes that influences from the future cannot occur at all; it is merely dealing with the idea that everything happening now either is or is not a result of past events. And the answer to this question is deemed to be the sole arbiter of whether or not future history is set in stone. I say this is false, and that a future history can be set in stone even if some phenomena are retro-causal. When I say Deterministic I mean that there is a single history, from beginning to end, with no random, uncertain or acausal events. If all effects are the result of causes, and if Physics follows the Principle of Least Action for both particle and wavelike influences, then I believe this interpretation is Deterministic*. We could take Cramer's cue and call it Weak Determinism by removing the temporal restriction, if you wish...

* Deterministic under the mildly revised definition of being "the philosophical proposition that every event, including human cognition and behavior, decision and action, is causally determined".

I see this point, however, I really don't think this restores any kind of determinism. We still don't have any explanation of WHY correlated photons Alice and Bob have spin up vs. spin down, etc. There is no apparent possibility of answering this either. (Now please keep in mind that I don't in any way consider that a weakness or a criticism.) Instead, you end up postulating some kind of stochastic mechanism which is still outside of the interpretation... just as you might in any interpretation. And that doesn't really make it deterministic.

In other words: with this interpretation, we can answer the question ["how do apparently non-local correlations arise"] but we cannot answer the question ["where are the hidden variables"] ? We would say that SOME of the hidden variables where found to reside in the future. But clearly some variables are missing (since the actual observed values are not explained anywhere), and there is clear contextuality as well (I question whether any contextual interpretation can also be deterministic, although I am not certain about that).

 

[Dmitry67]

wait, wait, "weak causality" is a good point, but even without it TI is explicitly non-deterministic. Just on a first found link:

http://www.npl.washington.edu/npl/int_rep/tiqm/TI_38.html#3.8

The TI also clarifies, but does not solve, the problem of predictivity. As was discussed in Section 3.2, the beginning of a transaction can be viewed as the emitter sending out a retarded "offer" wave in various directions and receiving an "echo" back from the absorber in the form of an advanced confirmation wave which has an amplitude proportional to * (where is the complex OW evaluated at the absorber locus). In the usual circumstance there are a very large number of potential future absorbers, and if all provide such echoes, the emitter, at the instant of emission, has a large menu of possible transaction possibilities from which to choose. In a single quantum event the boundary conditions will permit only one event to occur.

Born's probability law is therefore a statement that the probability of occurrence of a given transaction is proportional to the magnitude of the echo corresponding to that transaction which the emitter receives.

 

[rjbeery]

but we cannot answer the question ["where are the hidden variables"] ?

I'm not sure about that (meaning, I'm not sure one way or the other). As you mentioned, this interpretation already provides the "hidden variable" source regarding which axes the spins shall be restricted to; yet it does not immediately answer which particle will be up vs down. However, given the postulate that retro-causal effects are determined by the Principle of Least Action just as traditional causal effects are, isn't it possible that the measured spin itself is determined by the same principle? If one accepts the postulate it almost seems that one must accept a unique solution to "least action"*. I grant that we may never know the Least Action formulation, so claiming a Deterministic Universe may be unfalsifiable or even meaningless, but I believe that it may be possible to structure experiments that account for all advanced wavelike causes (including those that occur both after E and also after particle measurement at A and B)! Could I describe such an experiment? No, but I enjoy thinking about it.

* I know that mathematically this is not always true. I understand that a function may have more than one minimum but idealizations rarely apply to the real world.

Dmitry: My response to DrChinese is pertinent to your post as well. The Principle of Least Action postulate is not the heart of my interpretation but I feel it is valuable. Feynman's http://en.wikipedia.org/wiki/Path_integral_formulation" gives a unique solution to QM effects, so I don't feel like introducing it here is an overly radical thing to do.

The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics.

 

[jsg]

This is a little off the track, but it seems to me that a parallel can be drawn between the collapse of the wave function and Descartes' "cogito." It works like this: Just as the collapse of the wave function reduces an infinite number of possible states to a single perceived one, so the "cogito"–"I think therefore I am"–reduces the infinite web of causality to a single agent, the "I" that does the thinking.

I find this interesting since neither the collapse nor the "cogito" cancels out the underlying possible states of the system on the one hand or the causal conditions behind an action on the other. But the parallel ends there since the collapse identifies an actual state while the "cogito" creates the necessary but misleading fiction of a single causal agent.

 

[alxm]

jsg, read the forum rules - don't highjack threads with off-base ideas.

 

[rjbeery]

Yes, that is interesting. My personal perspective, though, assigns nothing special to measurement or even knowledge in the quantum world beyond the principle of least action. As an analogy, the path that water "chooses" to flow down a mountainside is set before it makes its journey. There are not an infinite number of possible paths, but one, which is predestined (i.e. the path of least resistance). The measurement of a quantum system would be analogous to carving a trench at some point in the mountainside - yes, the water's flow does not remain unaffected by this but that does not give the measurement itself any more of an elevated status than the mountain's pre-existing topography had the trench not been dug...