Errors in Ballentine (QM Textbook)?

[vanhees71]

Measurement is not a notion of QFT. Microcausality says by definition that field operators commute or anticommute at spacelike pairs of arguments. This implies (and is indeed equivalent to) the statement that arbitrary observables with spacelike separated support commute.

I don't understand the first sentence. QFT as any physical theory is about the mathematical description of observable facts of nature and thus it makes observable predictions (cross sections for scattering, the blackbody spectrum, etc.). Measurement is as much a notion of QFT as it is for non-relativistic QM.

 

[PeterDonis]

that's indeed what's usually understood to be "no causal effect"

Not in the many papers in the literature that struggle with how to interpret correlations that violate the Bell inequalities. Perhaps that's not a problem for you, but it is for many.

 

[vanhees71]

It's a problem for proponents of the collapse assumption. It's no problem for proponents of the ensemble interpretation.

 

[PeterDonis]

Moderator's note: Some posts have been moved to the "Difference Between Collapse and Projection" thread in the interpretations forum.

 

[atyy]

No, you need to take a partial trace and describe the evolution by some master equation. That can be FAPP a kind of "state reduction", but it's nothing outside the dynamical laws of QT!

This is wrong. The partial trace does not derive state reduction. The partial trace derives the state update for non-selective measurements. It does not derive the state update for selective measurements. Mathematically, this is because a mixed density matrix does not have a unique decomposition as a mixture of pure states.
https://pages.uoregon.edu/svanenk/solutions/Mixed_states.pdf (see comments #22 and #55-57)

 

[atyy]

See Weinberg, QT of fields vol. 1 for a comprehensive treatment of these issues for fields of arbitrary spin.

This QFT reference also give the state reduction postulate in Eq 2.1.7 (in the old fashioned way as part of the Born rule). Earlier in the chapter, he also writes that QFT is based on the same postulates as QM.

 

[PeterDonis]

The thread has gotten far away from just discussing errors in Ballentine, and we already have another thread in the interpretations forum for discussing different concepts of what "state reduction" means.

Thread closed.