Locality in QM and commutators

[haushofer]

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 :)

 

[strangerep]

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.

 

[skydivephil]

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 philosphy 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 woudl seem to imply that this is not correct, do you agree? Can you elaborate?

 

[haushofer]

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! :)

 

[strangerep]

I have noticed a thread on some philosphy 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 woudl 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.