"Physical system" in quantum mechanics ?

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Discussion Overview

The discussion revolves around the concept of a "physical system" in quantum mechanics, particularly in relation to the Hilbert space formulation. Participants explore the definitions, implications, and challenges associated with delineating physical systems, including the division between a quantum object and its environment, and the role of decoherence in this context.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question what constitutes a physical system, emphasizing the importance of the Hamiltonian in defining it.
  • There is a suggestion that the division between a physical quantum object and its environment is arbitrary, yet it significantly influences decoherence.
  • One participant references a specific case where defining subsystems is complex due to the Hilbert space not being a tensor product, linking this to entanglement entropy and reduced density matrices.
  • Another participant mentions the factoring problem, indicating it has been a topic of debate within the forum.
  • Participants express interest in exploring previous discussions on the factoring problem for further insights.

Areas of Agreement / Disagreement

Participants generally agree that the object/environment cut is arbitrary and that decoherence is dependent on this division. However, the complexity of defining physical systems and the implications of the factoring problem remain contested and unresolved.

Contextual Notes

The discussion highlights limitations in defining physical systems and the challenges posed by the infinite dimensionality of Hilbert spaces, as well as the unresolved nature of certain quantum mechanical principles.

microsansfil
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Hello

In the usual Hibert-space formulation of quantum mechanics, to each physical system is attached a separable Hilbert Space (generally infine-dimentionnal) over complex field.

A crucial ingrediant in the description of a physical system is the notion of state and evolution of state, however what is a physical system ? Moreover, cutting physical system in "physical quantum object + environment" is arbitrary ?

Behind is the question about Quantum decoherence between physical quantum object and environment. This division into physical sub-system is it always trivial to do ?

Patrick
 
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This is a very good question!

In practice, I would say, one can say "what is a physical system" when one has the Hamiltonian. The Hamiltonian is a function of the form H(Q,P), and the system is essentially Q, that is, the set of all dynamical configuration variables.

The object/environment cut is arbitrary, but decoherence depends on this cut.
 
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Here is one case where the subsystem seems difficult to define because the Hilbert space is not a tensor product of the Hilbert space of the subsystems: http://arxiv.org/abs/1406.7304. Donnelly is discussing the entanglement entropy which does depend on the reduced density matrix, just like decoherence.

Another place where it seems more natural to talk about the operators associated with subsystems is in strict quantum field theory, where one talks about operators at spacelike separation. When the Hilbert space is infinite dimensional, it seems that the full extent to which quantum mechanics violates the Bell inequalities is still unknown: http://arxiv.org/abs/1008.1142.
 
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Demystifier said:
The object/environment cut is arbitrary, but decoherence depends on this cut.

This is the so called factoring problem.

It has led to a bit of debate on this forum.

A search will bring up the gory detail.

Thanks
Bill
 
bhobba said:
This is the so called factoring problem.

It has led to a bit of debate on this forum.

A search will bring up the gory detail.

Thanks
Bill

To find the debates on this interrogation, I use the filter "factoring problem" in my search on this forum ?

Patrick
 

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