Time Uncertainty and the Collapse of the Wavefunction

[JasonWuzHear]

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.

 

[atyy]

Yes, time is not an observable.

 

[JK423]

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.

 

[bhobba]

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.

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.

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