Why is Quantum Field Theory Local?

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Discussion Overview

The discussion centers around the nature of locality in Quantum Field Theory (QFT) compared to nonrelativistic Quantum Mechanics, particularly in the context of entanglement and relativistic principles. Participants explore the implications of locality in QFT, its mathematical formulation, and the philosophical interpretations of locality and non-locality.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants argue that QFT is local because it accommodates special relativity, which is fundamentally a local theory.
  • Others clarify that QFT includes entanglement, which complicates the notion of locality, as entangled particles exhibit correlations that do not conform to classical definitions of locality.
  • A participant explains that QFT is local in the sense that spacelike separated measurements must commute, meaning their outcomes do not depend on the order of measurement.
  • There is a discussion about the definition of a local Hamiltonian, with examples provided to illustrate local and nonlocal Hamiltonians.
  • One participant emphasizes that locality in QFT is realized through the construction of field operators that commute at spacelike separations, ensuring causality and the unitarity of the S-matrix.
  • Another participant points out that the terminology around "non-locality" can lead to confusion, as some physicists and philosophers interpret entangled correlations differently.
  • A later reply challenges the notion that correlations from entanglement do not imply non-locality, stating that the broader physics community generally accepts these correlations as evidence of quantum non-locality.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of locality and non-locality in the context of QFT and entanglement. There is no consensus on the implications of entanglement for the concept of locality, with some asserting that it does not contradict locality while others argue that it does.

Contextual Notes

The discussion highlights the complexity of defining locality in quantum theories, particularly the dependence on specific definitions and interpretations within different scientific communities. The terms "local" and "non-local" are used variably, leading to potential misunderstandings.

  • #181
Kolmo said:
Regarding (b), all GPTs allow updating but by "Bayesian" we mean there is a unique way to update in late of data. In GPTs going beyond the Tsirelson bound ##2\sqrt{2}## there is an element of arbitrary choice in how one updates in light of data. This is what leads to a recent phrase: it's the most general GPT where one can still learn.
Could you give some references?
 
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  • #183
atyy said:
Could you give some references?
To be more explicit there is also also a third condition proved to be equivalent in this paper, so the full list is that the theory is obeys the following which are all equivalent:

(a) The most general theory satisfying the Exclusion principle. Namely that if each of the pairs from a set of observables ##A,B,C## are compatible/co-measurable, then the whole set is co-measurable

(b) The most general one that permits Bayesian updating.

(c) The most general one which assigns probabilities to any repeatable ideal measurements.

(a) was originally a conjecture of Ernst Specker. Cabello proved (c) implies (a) and from there proves (a) in the paper I linked. After that he later proved (b) in (PDF free access):
https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.042001.
 
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