Time evolution of a detected particle

[PeterDonis]

Or just tunneling away

If the potential in the box walls has only a finite width, yes.

 

[anuttarasammyak]

If we had already the particle confined in a very narrow 1D box (to the extent of almost a point $x_0$), then the speed of particle seems meaningless let alone the light speed!

You must investigate by what materials you make the box so that it does not rupture by high pressure of the particle in it. Feeling pressure is measurement of particle momentum so velocity.

 

[Roberto Pavani]

what materials

I think there is a distinction between the mathematical model and the physical system. Once we start asking what materials the box is made of, we are talking about real-world physics. In that case, confinement requires a physical interaction and barriers are finite. Some of the arguments above, however, rely on idealized infinite walls that are mathematically useful but not physically realizable.

 

[flippiefanus]

The eye diagram makes my point rather than yours. It's a good tool for the problem it was built for. It's the wrong tool for the one under discussion, which is what "not with a quartz crystal" meant.

Ultrafast imaging doesn't derive frame times from an electronic clock at all. STAMP encodes them in pulse sequence and dispersion: https://www.nature.com/articles/s41377-018-0044-7. This group, https://opg.optica.org/josab/abstract.cfm?uri=josab-35-11-2822, set them with mirror-array path-length differences, where 1 µm of path is 3.34 fs. T-CUP and CUSP use temporal shearing and spectral–temporal mapping: https://www.nature.com/articles/s41467-020-15745-4. What you won't find anywhere are PLLs.

So, no nails here. The main problem to me, as a lowly incoming physics graduate student, is that the bubble nucleation in the bubble chamber might not happen fast enough. What I'm not worried about is image timing, because it's been done.

Not really the point of this thread though, and otherwise the post was relevant to the discussion.

I think the missing ingredient is the quantum Zeno effect. In the type of measurement represented in reply #3, the particle is measured over and over again by the medium through which it propagates. If at some point the measurement localized it at $x_0$ with some uncertainty, then a followup measurement that happens shortly after the previous one maintains the size of the uncertainty and the only change is the shift in position due to the velocity of the particle. So, although the wave function of the particle starts to disperse just after the initial measurement, based on its finite uncertainty in momentum (finite because the position uncertainty is finite), a subsequent measurement happening shortly after the initial measurement brings it back to the position and size that one would expect of a particle with a given velocity.