How does the electric field of an electron compare to its probability wave?

[DarkMattrHole]

TL;DR

Is there a relationship between the two?

A single electron sitting in a void has an electric field that spreads out evenly in all directions as far as there is open empty space to allow it, is this roughly a correct statement?

Let's say we now introduce a singe proton into the void, 100 miles from the electron - it will also have an electric field, is that correct?, of the opposite sign.

Now the electric field of the electron will be distorted, as will that of the proton. It will be easier for the electron field to spread into the direction of the proton, and so it will, and all the electric field lines will edge towards the imaginary line between electron and proton, and edge away from the opposite direction and wrap around on a long arc towards the proton, correct? The electric field has been redirected and covers a bit less volume of space, as the strength of field is concentrated to a region in the vicinity around the electron and proton. From a distance of 1000 miles the electric field would look like an electric dipole. From a much greater distance no field would be detected as the field would appear locally neutralized.

The electron goes where the field lines tell it to go, and the field lines go mostly towards the proton (and vise versa) so the particles approach each other. When the particles unite and the electron is snug in an orbital the electric field will have 'collapsed' into a single place in space - the orbital.

Is the former description even close to accurate?
How does the collapse of the electric field - perhaps when an electron hits a proton on the back-wall of double split electron experiment - compare and contrast to the collapse of the probability wave in that experiment? How separate are these two things? I know that one is a physical field and the other is a calculation, so it's how closely the two things relate that I'm interested. If you got this far in my long winded question, thanks.

 

[PeterDonis]

Is the former description even close to accurate?

Not if you're talking about a quantum description, no. Trying to mix classical and quantum concepts just causes confusion.

 

[Nugatory]

How does the collapse of the electric field...

Even classically, there’s no such thing. No matter how we add or remove charges or move them around, the electric field is calculated by summing the contributions from all the charged particles, allowing for the $1/r^2$ effect of distance from the charge.

The wave function of a charged particle is completely unrelated to its electric field, and wave function collapse has completely different mathematical properties.

 

[DarkMattrHole]

Thanks, Nugatory. That's good to know. I was wondering if there could be a correlation because the electric field of the electron also sort of collapses onto the detector, or a wall, or wherever the electron ends up residing.

Also related to the question if i may - I am familiar with the Fenyman QED book explanation of counting beans using spin and transit time to predict probabilities, but the descriptions didn't go into the evolution of the probability waveform over time, however, i think Feynman suggests it spreads out uniformly in three dimensions, taking all paths and reflections as it spreads until the electron ultimately gets captured by one of the detectors, or it shows up stuck in an orbital in a wall atom somewhere, or elsewhere, all with probabilities according to the wave function. Feynman was describing partial reflection of light through sheets of of glass but didn't specify, does this spreading of the wave function proceed at the speed of light? If so, does the wave function for an electron also spread out at C? Thanks.

 

[DaveE]

In classical EM, you need to learn about superposition. The total field can be found by adding each of many separate solutions to Maxwell's equations.

Let's say we now introduce a singe proton into the void, 100 miles from the electron - it will also have an electric field, is that correct?, of the opposite sign.

Now the electric field of the electron will be distorted, as will that of the proton.

No the E-field of the electron doesn't change when the proton is added. The total E-field changes, it is just the sum of the two E-fields.

 

[PeroK]

Also related to the question if i may - I am familiar with the Fenyman QED book explanation of counting beans using spin and transit time to predict probabilities, but the descriptions didn't go into the evolution of the probability waveform over time, however, i think Feynman suggests it spreads out uniformly in three dimensions, taking all paths and reflections as it spreads until the electron ultimately gets captured by one of the detectors, or it shows up stuck in an orbital in a wall atom somewhere, or elsewhere, all with probabilities according to the wave function. Feynman was describing partial reflection of light through sheets of of glass but didn't specify, does this spreading of the wave function proceed at the speed of light? If so, does the wave function for an electron also spread out at C? Thanks.

You have got confused between three subjects: Classical EM, which involves the electric field of charged particles, such as electrons; QM, which involves the wavefunction for a particle such as the electron; and, QED, which is a more advanced quantum theory for the behaviour of light and matter.

These are three separate theories and you cannot mix and match concepts from them.

QM does not describe the propagation of the wavefunction. And, in fact, ultimately this leads to the breakdown of the non-relativistic theory of QM and the need for QED and relativistic QFT.