What Happens When an Electron Interacts with a Photon in an Empty Space?

[frogsong]

The other day the following question occurred to me and I was wondering if anyone here might have the answer. Imagine a large piece of space that is really quite empty. Just a few electrons and photons whizzing about. Since these particles rarely interact, most of the time their wave funtions are not collapsed. Now let us suppose that an electron has an encounter with a photon and the electron's wave function collapses and it now has a spin etc. For how long does this collapsed state persist before we can no longer "see" the electron? And furthermore, since most of the particles in this system are not collapsed most of the time, would this system exhibit any unusual properies? I would think that, in fact, a good deal of the universe is rather like this. Thanks for your attention
Frogsong

 

[selfAdjoint]

For how long does this collapsed state persist before we can no longer "see" the electron?

Hi frogsong, great handle! Since we can't see the electron without bouncing at least one photon off it, it will keep those observable values until it next meets something. The wave function carries along the state (it is better to think of states: the electron is presumably in a superposition of all possible states before the interaction, and after, it is in a particular state; it will stay in that state till something happens to change it.

 

[dextercioby]

The other day the following question occurred to me and I was wondering if anyone here might have the answer. Imagine a large piece of space that is really quite empty. Just a few electrons and photons whizzing about. Since these particles rarely interact,

What do you mean...?They interract whenever they meet.

most of the time their wave funtions are not collapsed.

What's your idea of "wavefunction collapse"...?

Now let us suppose that an electron has an encounter with a photon and the electron's wave function collapses and it now has a spin etc.

The electron ALWAYS CARRIES SPIN...

For how long does this collapsed state persist before we can no longer "see" the electron?

That's just a weird question...If is doesn't interact ever again,his evolution would be dictated by the free particle Hamiltonian.(See SE).

And furthermore, since most of the particles in this system are not collapsed most of the time,

Weird...

I'd suggest to reread the V-th principle.And don't take the word "collapse" literally.

Daniel.

 

[frogsong]

Ok thanks for the response. I know the electron (for example) has a number of properties assiciated with it but for siimplicity let's just think about spin. So as I understand it, before the interaction with the photon there is no definite spin, just a probablity that the spin is x or y. After the interaction the spin is definite. No more nasty probabilities. Then some time later the photon comes back (or another photon comes along) and Whack! the spin is now indefinite again. So we look once, we see the electron, we look twice and it disappears.
OK, now here is a related question. When the photon interacts with the photon, how long does the interaction take? And what is going on while the photon is adjusting the wave function of the electron? What I am really asking here is can a physical state (like spin) change in zero time. And a change can be going from unknown to known. It would seem a strange world where things could change in zero time. I don't think I even know what zero time means.

Thanks again for your thoughts

 

[masudr]

If is doesn't interact ever again,his wavefunction would stay the same.

No. The wavefunction evolves according to the Schrodinger equation.

 

[dextercioby]

Sorry,of course,you're right...I was thinking of a stationary state and the conservation of probability...

Daniel.