How Do Electron Orbitals Work at Relativistic Speeds?

[Arubi Bushlee]

So I was wondering... for no particular reason:

Say you have a proton and your right arm is a particle accelerator. You throw the proton at about 90% the speed o' light. The you take your left arm which also happens to be a particle accelerator and you shoot an electron out right next to it. Conveniently the two particles are the distance at which they would normally be if they were an atom at room temperature of about 300k. Could they form an atom?

What I'm trying to get at if you didn't get that is: if you have a proton moving at the almost speed o' light and you have an electron that relative to that proton is stationary. (Of course the electron is also moving at 90% the speed of light but relative to the proton it is stationary). Like two cars going at 100mph. If you took away the road and wind resistance nobody in the cars would be able to tell if they were moving because they would have nothing to compare themselves to. It's like how the Earth is spinning a thousand miles per hours but we don't feel it because we are spinning with the Earth. Does the same apply to protons and electrons. Are they to each other stationary?

To be redundant in case you missed it what I am getting at is if you take a proton and electron and accelerate them in the same direction next to each other with the same speed can they form an atom? i.e. stable electron orbit, or would the two subatomic particles ionize? Please explain why or why not. :)

<- This atom looks pretty cool, thought I'd put it in. Anyways thanks for reading.

 

[Drakkith]

To be redundant in case you missed it what I am getting at is if you take a proton and electron and accelerate them in the same direction next to each other with the same speed can they form an atom? i.e. stable electron orbit, or would the two subatomic particles ionize? Please explain why or why not. :)

They can indeed. As you've said, they aren't moving relative to each other and would be able to bind together into an atom.

 

[mfb]

Physics is the same in every reference frame. Every hydrogen atom in your room moves at 90% the speed of light relative to some (hypothetical) observer speeding past earth. Your hydrogen atom would be no different.

 

[ChrisVer]

really, by what means would you accelerate an electron+proton to move along each other?
the electrons are negatively charged, the protons are positively charged... move them through a magnetic field and their directions will change... you can't move them in an electric field either (the one would move forward, the other back)...
At the end in order to accelerate the electron and proton in such a way that they would be together along their paths, you would have to use Electric or Magnetic fields that change drastically within a distance of a nanometer...or you could accelerate them and then try to bring them together? In such a case nothing would happen...the atom could be formed, and the only difference for you would be its spectral lines (they would be pretty much doppler shifted) relative to what you'd get from the same atoms moving with v~sqrt(kT/m) relative to you...

 

[mfb]

really, by what means would you accelerate an electron+proton to move along each other?

Electron cooling for proton (or ion) beams does that.
The beams are combined with a (macroscopic) magnetic field, because it deflects the two beams in opposite directions, so you can merge them and separate them again later.

The actual cooling application: the electrons are cool, the protons and electrons get in thermal equilibrium (hydrogen formation is rare), which means the protons in the accelerator get cooled while the electrons take some of their thermal energy. Electrons get separated and dumped, beam is cooled.