« Last post by paul cotter on Today at 19:10:50 »
Glad to hear that, mnd in it's various forms is a dire diagnosis.
So the integral we'd be interested in, representing the total probability of finding the electron at the screen from 'then'/ that time to infinity is finite << 1. Specifically we can assume the electron would never be found at the screen, write it off and just fire the next electron.Sounds reasonable
Anyway, we were talking about a lack of detection at the screen as being a lack of measurement:Depends on your definition of measurement. In real life, measurement is epistemological. If the electron hits the lab wall, you're unaware of it and your epistemic wave function isn't altered by the event. In the sim, the sim would know that the wall was hit and the actual wave function would be altered, and the real wave function would collapse. The screen then also measures the collapse because the screen measures the wall; it becomes entangled with the wall state.
Well, that is still some measurement by the screen as far as I can see.Yes, you know it missed, so the epistemic wave function is altered by the knowledge, even if it isn't 100% certain.
It is NOT at the screen at any time, although there are lots of other places it can beUnless you're assuming a counterfactual interpretation, I think it a mistake to talk about where it is in the absence of measurement. But a lot of simulations do exactly that, so I suppose it depends how your sim is implemented. You know it missed, so the new wave function can yield odds of where it likely hit, and that's assuming that the lab is reasonably closed and it doesn't shoot off into space never to interact with anything, as so many photons never do.
Is it possible for a thing to exist despite the fact that it hasn't and will not in the future interact with anything else?A matter of definitions. What does it mean to exist? There's conservation laws, so of course it exists. It merely lacks a location/momentum.
For example, the electrons can encounter other particles and potentials en route to the barrier and/or screen.Always wondered about that. Do they regularly do the electron-gun thingy in a vacuum to avoid that sort of thing?
You seem to be asking if the electron misses the screen, is a measurement taken? Well, not by the screen (yet)We seem to agree that an electron (represented by a Gaussian wave packet initially) can "miss" the screen. It wouldn't matter if the screen is made infintely long parallel to the y-axis (and we fire the electron toward it along the x-axis). This is evidently quite different from a Newtonian view of particles and their movement, where the electron could not possibly be found beyond the screen without having impacted on the screen on the way. Hmmm... actually I might give the screen some potential above 0 in my computer model, for the sole purpose of reducing the number of electrons that will propagate through it. One issue with the simulation is - how long do you wait for the electron to have been detected by the screen? If the screen glows, great, you're done, you can fire the next electron. If it doesn't, then the wave packet is still spreading out to fill all of space as time progresses, so the probability of the electron being found at the screen never falls to 0. Clearly, for the purposes of a simulation you cannot wait forever. Once the group velocity of the wave packet has made it so that the wave packet is centred far beyond the screen, we must assume the electron has just "missed", the probability of it being found at the screen then starts to fall off exponentially with time as the distance from the screen increases. So the integral we'd be interested in, representing the total probability of finding the electron at the screen from 'then'/ that time to infinity is finite << 1. Specifically we can assume the electron would never be found at the screen, write it off and just fire the next electron.
or it never interacts, and is effectively nonexistent (according to any local interpretation at least).This might be philosophy. Is it possible for a thing to exist despite the fact that it hasn't and will not in the future interact with anything else? Anyway.... there's always gravity which we don't tend to include in any Quantum Mechanics, the electron is still providing some energy density and thus curving space, i.e. it is interacting with something else in some way (you would think).