Classical states and decoherence

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Discussion Overview

The discussion revolves around the concept of classical states and their relationship with decoherence, particularly in the context of quantum mechanics and macroscopic objects. Participants explore the implications of decoherence on classical states, the phenomenon of environment-induced superselection (Einselection), and the nature of observable states in quantum systems.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants question the robustness of classical states against decoherence and speculate on what would happen if classical states could decohere, using the example of a table.
  • Others clarify that decoherence occurs when a quantum object interacts with its environment, leading to classical probabilities and loss of interference, while the quantum system remains in superposition with the environment.
  • A participant introduces the concept of Einselection, stating that it refers to the selection of preferred states (pointer states) that are least perturbed by environmental interactions.
  • There is a discussion about whether classical states can be decohered and the implications of this on observable quantities like position and momentum, with some suggesting that if decoherence affected classical states, it could alter our perception of reality.
  • One participant expresses confusion about how Einselection relates to macroscopic objects and questions the validity of using examples like the Buckingham Palace windows to illustrate these concepts.
  • Another participant asserts that decoherence leads macroscopic objects to be in eigenstates of position, suggesting that typical interactions with the environment stabilize these states.
  • There are references to specific literature and technical details regarding the nature of interactions and the implications for understanding quantum mechanics.

Areas of Agreement / Disagreement

Participants express differing views on the robustness of classical states against decoherence, the implications of Einselection, and the applicability of examples like the Buckingham Palace windows. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Participants reference various sources and technical literature to support their claims, indicating a reliance on specific definitions and interpretations of quantum mechanics. The discussion highlights the complexity of the relationship between quantum states and classical observations, with unresolved assumptions about the nature of decoherence and its effects on macroscopic objects.

  • #91
bhobba said:
Its simple. It's got to do with the difference between a proper and an improper mixed state. The mixed state is Σ pu |u><u| + pd |d><d|. If you observe that with the up-down observable you will get |u><u| with probability pu and |d><d| with probability pd. Now is that because it was in state |u><u| with probability pd and similarly for |d><d|? If so the observation did nothing - no change. In interpretations like BM or GRW that actually is the case and is how they resolve the measurement problem. But they may not be true - the observation may have changed the mixed state to a pure one - there is no way of telling. Remember this is a mixed state - not a superposition - interference terms have been suppressed.

Thanks
Bill

is the "state |u><u| with probability pd and similarly for |d><d|" the improper mixed state in the example (noting that entangled electron with spin up and spin down are entangled so you can't use proper mixed state).. but why did you use proper mixed state in Σ pu |u><u| + pd |d><d|?
 
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  • #92
lucas_ said:
is the "state |u><u| with probability pd and similarly for |d><d|" the improper mixed state in the example (noting that entangled electron with spin up and spin down are entangled so you can't use proper mixed state).. but why did you use proper mixed state in Σ pu |u><u| + pd |d><d|?

Both proper and improper mixed states are mathematically the same, pu |u><u| + pd |d><d| is proper or improper - you can't tell from observing it - only by knowing how it was prepared. |u><u| and |d><d| are pure - not mixed.

Thanks
Bill
 

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