Time Localization Same As Indeterminacy?

[LarryS]

It seems to me that, by definition, QM particles are localized in time.

A “particle” in QM and the act of measuring its particle-like attributes are one and same.

But one cannot predict ahead of time the result of measuring, say, an individual particle’s position (I’m assuming that due to the experimental setup, position measurements are uncertain). So the “particle” has no past. Also, one cannot predict what the wave function will do after it collapses. So the particle has no future. It is localized in time.

Can anyone think of an example in which Time Localization and QM Indeterminacy are not equivalent?

As always, thanks in advance.

 

[elibj123]

You are half correct- after a measurement, a particle's past is not important. The Schrödinger equation is first-order in time, which means that only the current qunatum state (wave function) affects the future state, and not its past\immediate-past (as in the classic wave equation).

But a particle does have a future, not in the meaning that you can exactly predict its path in space, but in the meaning that given its quantum state at t=0 (the moment of measurement), you can determine exactly its quantum state at any t>0 (given no further measurements are done). Otherwise Schrödinger's Equation would be useless. The fact that the wave function collapses, doesn't mean you don't know the new wave function (otherwise there's no point of making measurements), and using that new wave function as initial condition, you can theoretically predict the wave function at any future time.