Time Uncertainty and the Collapse of the Wavefunction

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Discussion Overview

The discussion centers on the conceptual differences between uncertainty in position and time within quantum mechanics, particularly regarding wavefunction collapse. Participants explore the implications of time not being treated as an observable in quantum mechanics and how this affects interpretations of measurement and collapse.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion about why position is treated as uncertain and collapsible, while time is not, suggesting a fundamental difference in how these concepts are treated in quantum mechanics.
  • It is noted that time is not considered an observable in standard quantum mechanics, which may contribute to the differing treatment of position and time.
  • One participant points out that there is inherent uncertainty in predicting when a measurement occurs, indicating that 'when' is not strictly definable in quantum terms.
  • Another participant argues that in standard quantum mechanics, position is an observable while time is a parameter, and this distinction leads to different interpretations of measurement and collapse.
  • There is mention of the idea that collapse is not universally accepted as part of quantum mechanics, with some interpretations treating it differently and suggesting that a deeper understanding requires an axiomatic approach.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the treatment of time versus position in quantum mechanics. Multiple competing views are presented regarding the nature of wavefunction collapse and the role of time as an observable.

Contextual Notes

Limitations include the lack of a time operator in quantum mechanics, the dependence on interpretations of wavefunction collapse, and the unresolved nature of how time and position are fundamentally treated in the context of quantum theory.

JasonWuzHear
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I'm having a hard time understanding why it makes sense to say that the particle has an uncertain position to which it can collapse, but not to say that the particle has an uncertain time to which it can collapse.

Similarly, why do we consider when the particle collapses as when we measure it, but we do not consider where the particle collapses as where we measure it? (Or maybe we do and I'm mistaken?)

I figure it has to do with the fact that there's no time operator in QM, but I'm curious if there's any difference to interpreting wave function collapse either way (uncertain where/when vs. it collapses where/when we measure it) conceptually.
 
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Yes, time is not an observable.
 
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You cannot even say, strictly speaking, 'when' you measure something. There is a fundamental (quantum) uncertainty, and you cannot predict beforehand 100% when the outcome will appear.
 
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JasonWuzHear said:
I'm having a hard time understanding why it makes sense to say that the particle has an uncertain position to which it can collapse, but not to say that the particle has an uncertain time to which it can collapse.

That's because in standard QM time is a parameter and position an observable. When QM is combined with relativity you have to treat time and position on equal footing so position also becomes a parameter. The other way of doing that, making time an observable, was also tried but ran into insurmountable problems.

JasonWuzHear said:
Similarly, why do we consider when the particle collapses as when we measure it, but we do not consider where the particle collapses as where we measure it? (Or maybe we do and I'm mistaken?)

Collapse isn't really a part of QM - only some interpretations. QM is a theory about observations in a general sense - its not concerned with the exact way you do an observation ie where and when you do it.

JasonWuzHear said:
I figure it has to do with the fact that there's no time operator in QM, but I'm curious if there's any difference to interpreting wave function collapse either way (uncertain where/when vs. it collapses where/when we measure it) conceptually.

Like I said collapse isn't really part of QM. To really understand it you need to see an axiomatic treatment. You can find such in Ballentine - Quantum Mechanics - A Modern Development.

Thanks
Bill
 
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