Does length contraction affect the orbital path of a relativistic electron?

[neilparker62]

Hi

Just wondering about the orbital path of a high speed particle - eg electron in orbit. Is it length contracted? Then how do we manage nλ=2.π.r ?

Neil

 

[mfb]

nλ=2πr comes from Bohr's model, this has been replaced by quantum mechanics about 90 years ago.
With relativistic quantum mechanics, it is no problem to find orbitals for electrons even around heavy nuclei, where relativistic effects are important. It is problematic to switch to the view of the electron (because it does not have a fixed velocity).

 

[bcrowell]

Length contraction is a description of a difference in an observation between two different frames of reference. We're not doing any measurements in a frame of reference moving along with the electron, so there is no reason to convert to or from that frame.

 

[jartsa]

Hi

Just wondering about the orbital path of a high speed particle - eg electron in orbit. Is it length contracted? Then how do we manage nλ=2.π.r ?

Neil

Orbital path is length contracted, and wavelengths are length contracted. So we don't have a radius, and we have many different lambdas.

So we write: d = n * sum of lambdas, where d is distance traveled when going around the path once.

d changes smoothly when speed changes smoothly.(I assumed this was a question about a high speed hydrogen atom)