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zonde said:
Any set of orthogonal vectors that span a Hilbert space must be eigenvectors of some Hermitian operator on that Hilbert space.
Is there an additional assumption in the PBR theorem?
- Context: Graduate
- Thread starter PeterDonis
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Discussion Overview
The discussion centers on the PBR theorem, specifically exploring whether there is an additional assumption regarding the ontic state during the measurement process. Participants analyze the implications of the theorem and question the assumptions made about the relationship between quantum states and ontic states, particularly in the context of entangled measurements.
Discussion Character
- Debate/contested
- Exploratory
- Technical explanation
Main Points Raised
- One participant suggests that the PBR theorem relies on the assumption that the ontic state does not change during the measurement process, questioning how this assumption holds when the quantum state transitions to an entangled state.
- Another participant refines the argument by outlining a chain of reasoning that leads to a contradiction if the ontic state before measurement is assumed to be the same as after measurement, suggesting that the measurement process might alter the set of possible ontic states.
- Concerns are raised about the implications of the measurement being entangled, which could lead to different ontic states being possible for entangled versus non-entangled quantum states.
- There is a discussion on whether changes in the quantum state should be interpreted in an ontic or epistemic sense, with one participant arguing that assuming a change in the ontic state would contradict the theorem's conclusions.
Areas of Agreement / Disagreement
Participants express differing views on the assumptions underlying the PBR theorem, particularly regarding the stability of the ontic state during measurement. No consensus is reached on whether the assumption about the ontic state changing is valid or necessary.
Contextual Notes
Participants note that the assumptions about the ontic state and its relationship to quantum states are crucial for the validity of the PBR theorem, but these assumptions remain unresolved and are subject to interpretation.
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