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.

 

[Entropia]

I would say that the concept of time localization in quantum mechanics is closely related to the uncertainty principle, but not exactly the same as indeterminacy. Time localization refers to the idea that a quantum particle can be localized or confined to a specific region in time, while indeterminacy refers to the inherent unpredictability of certain properties of a quantum particle.

In other words, while time localization may limit the possible time range in which a particle can exist, indeterminacy refers to the fact that we cannot precisely determine certain properties of the particle at any given time. This is a fundamental aspect of quantum mechanics and is not limited to just the concept of time localization.

To address the question of whether there are any examples where time localization and indeterminacy are not equivalent, I would say that it is possible for a particle to be localized in time but still have some level of indeterminacy in its properties. This could occur, for example, if the particle is confined to a specific time interval but its position within that interval is uncertain.

Overall, both time localization and indeterminacy are important concepts in quantum mechanics and play a crucial role in understanding the behavior of particles at the quantum level. While they may seem similar, they are distinct concepts that should not be conflated.