Locality in QM and commutators

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Discussion Overview

The discussion revolves around the concepts of causality and locality in quantum mechanics (QM) and quantum field theory (QFT), particularly focusing on the implications of micro-causality and non-locality as seen in phenomena like entanglement and the Aharonov-Bohm effect. Participants explore how these ideas interact and whether adjustments to second quantization have been considered in light of these non-local aspects.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how micro-causality in QFT, where commutators between fields vanish for spacelike intervals, aligns with the non-local nature of QM, citing entanglement and the Aharonov-Bohm effect.
  • Another participant emphasizes that while commutators between spacelike-separated regions A and B are zero, correlations between these regions can only be understood through a future region C, which includes both A and B within its past lightcone.
  • There is a reference to a philosophical concept called "simultaneous causality," which suggests that outcomes and their causes can occur at the same time, with a participant asking for clarification on this idea in relation to entanglement.
  • One participant expresses a need to think through the implications of the previous points, indicating a level of uncertainty or contemplation about the discussion.
  • A participant notes their unfamiliarity with philosophy forums and requests more specific references to engage with the topic of simultaneous causality.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between causality and correlation in the context of QM and QFT. There is no consensus on the interpretation of simultaneous causality or its implications for entanglement.

Contextual Notes

Some assumptions about the nature of causality and the interpretation of quantum phenomena remain unresolved, particularly regarding the implications of non-locality and the philosophical interpretations of causation.

haushofer
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Hi,

I have a conceptual question concerning causality and locality in QM.

Causality plays a role in second quantization when doing QFT, which one calls "micro-causality"; the commutators between fields disappear when the interval between them is spacelike.

However, how does this fit in the fact that QM is non-local (entanglement, Aharonov-Bohm effect)? Did people consider adjusting second quantization because of this?

Probably this has been asked before :)
 
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haushofer said:
Causality plays a role in second quantization when doing QFT, which one calls "micro-causality"; the commutators between fields disappear when the interval between them is spacelike.

However, how does this fit in the fact that QM is non-local (entanglement, Aharonov-Bohm effect)?

This is the old chestnut: "correlation is not causation".

Suppose there's some events at two spacelike-separated spacetime regions A & B.
And suppose these are recorded by observers within those regions. Correlations
between the data at A & B cannot be calculated except within some future spacetime
region C whose past lightcone includes both A and B -- so that information from
both A & B can be transmitted to C.

The fact that commutators between fields in A and B are zero doesn't matter,
since commutators between C & A, and between C & B, are not zero.
 
strangerep said:
This is the old chestnut: "correlation is not causation".

Suppose there's some events at two spacelike-separated spacetime regions A & B.
And suppose these are recorded by observers within those regions. Correlations
between the data at A & B cannot be calculated except within some future spacetime
region C whose past lightcone includes both A and B -- so that information from
both A & B can be transmitted to C.

The fact that commutators between fields in A and B are zero doesn't matter,
since commutators between C & A, and between C & B, are not zero.


I have noticed a thread on some philosophy forums claiming there is somehting called "simulatenous causality" where an outcome and its cause occurr at the same time. It has been claimed that entanglement is an example of this. Your answer philosophy seem to imply that this is not correct, do you agree? Can you elaborate?
 
strangerep said:
This is the old chestnut: "correlation is not causation".

Suppose there's some events at two spacelike-separated spacetime regions A & B.
And suppose these are recorded by observers within those regions. Correlations
between the data at A & B cannot be calculated except within some future spacetime
region C whose past lightcone includes both A and B -- so that information from
both A & B can be transmitted to C.

The fact that commutators between fields in A and B are zero doesn't matter,
since commutators between C & A, and between C & B, are not zero.
I have to think this a bit more through, but I think I get your point. Thanks! :)
 
skydivephil said:
I have noticed a thread on some philosophy forums claiming there is somehting called "simulatenous causality" where an outcome and its cause occurr at the same time. It has been claimed that entanglement is an example of this. Your answer philosophy seem to imply that this is not correct, do you agree? Can you elaborate?

I don't follow philosophy forums, so I'm unable comment without a more specific reference.
 

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