Many-worlds, Schroedinger, Heisenberg pictures

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Discussion Overview

The discussion revolves around the many-worlds interpretation (MWI) of quantum mechanics, particularly focusing on the relationship between the Schrödinger and Heisenberg pictures. Participants explore the implications of these interpretations in non-relativistic quantum mechanics, canonical quantum gravity, and relativistic quantum field theory (QFT).

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that in the many-world interpretation of non-relativistic quantum mechanics, the Schrödinger picture is more fundamental than the Heisenberg picture.
  • Others argue that in canonical quantum gravity, the two pictures are identical, suggesting a different relationship than in non-relativistic quantum mechanics.
  • A participant questions whether the lack of time evolution in canonical quantum gravity, described as a gauge transformation, affects the interpretation of the pictures.
  • There is a discussion about the status of relativistic QFT, with some suggesting that the Schrödinger picture is preferred for MWI, while others raise concerns about the implications of relativistic covariance.
  • One participant introduces the idea that the many-time formalism could be used to achieve covariance in the context of relativistic QFT.

Areas of Agreement / Disagreement

Participants express differing views on the fundamental nature of the Schrödinger and Heisenberg pictures within various frameworks, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

Limitations include the dependence on specific interpretations of quantum mechanics and the unresolved nature of time evolution in canonical quantum gravity and its implications for the many-worlds interpretation.

atyy
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I've usually heard the many-worlds interpretation described in the Schroedinger picture, in which the wave function evolves unitarily. Does a Heisenberg picture exist for many-worlds, or is the Schroedinger picture more fundamental in that interpretation?
 
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In the many-world interpretation of non-relativistic QM, the Schrödinger picture is certainly more fundamental than the Heisenberg one.
But this is not really so in canonical quantum gravity, where the two pictures are identical.
 
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Demystifier said:
In the many-world interpretation of non-relativistic QM, the Schrödinger picture is certainly more fundamental than the Heisenberg one.
But this is not really so in canonical quantum gravity, where the two pictures are identical.

Because there is no time evolution in canonical quantum gravity (time evolution is a gauge transformation)?
 
atyy said:
Because there is no time evolution in canonical quantum gravity (time evolution is a gauge transformation)?
Yes.
 
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How about relativistic QFT? Or do you think MWI doesn't satisfactorily address that, because MWI seems to pick a preferred foliation?

Also, how about canonical quantum gravity in AdS? I think canonical quantum gravity in AdS has time evolution (I think the Hamiltonian is not zero because of the AdS boundary condition, which is one of the reasons AdS/CFT is possible, since the bulk inherits its time evolution from the boundary CFT).
 
atyy said:
How about relativistic QFT?
In relativistic QFT Heisenberg and Schrödinger pictures are different, so Schrödinger picture is the preferred one for MWI.

The question of relativistic covariance is a separate issue. It can be made covariant by using many-time formalism.
 
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