Probability Distribution for Time of Measurement?

[dx]

Say we have an electron in a position eigenstate $\delta(P-x)$ at point $P$ at time $t_0$. We also have a detector at another point Q. At $t_0$, the probability of the detector registering the electron is zero. After a certain time $T$, the time evolution of the wave function generates a non-zero probability for the electron to be found at Q, but what can we say about the time of measurement? Is there a function $f(t)$ such that $f(t)dt$ gives the probability that the detector will register a measurement in the interval $(t, t+dt)$?

 

[jostpuur]

Excellent question!

Sorry for not answering it, though. I merely wanted to say that if you had not asked this, I might have been asking the same thing at some point. I had actually already started to preparing some kind of question about this topic (that's why I think this is an excellent question ), but I've still been too busy with some other problems, and replies to my other questions.

When you know that some theory exists, it is a simple thing to tell about it.

But when you don't know that some theory exists, it becomes dangerous to claim that it wouldn't exist. It could be that you just haven't heard about it, but somebody else has, and somebody could prove you wrong.

This probability density with respect to time seems to belong into this difficult category of topics, where everybody merely wants to keep mouth shut in order to avoid saying anything wrong. I've been speculating that some kind of "effective collapsing density" should exist, but I don't really know how it should work.

Fortunately we have some scientists who are ready to go through the effort of actually finding out what is known and what is not known, and I'm probably not wrong to guess that Demystifier belongs into this group? I'm looking forward to hear his comment on this (sorry for creating pressure )

 

[meopemuk]

You can get more info by searching the web and/or arXiv for "time of arrival"

 

[meopemuk]

Try this one

Norbert Grot, Carlo Rovelli, Ranjeet S. Tate, "Time-of-arrival in quantum mechanics"
http://arxiv.org/abs/quant-ph/9603021

 

[jostpuur]

Very interesting, meopemuk.