Relativistic Length Contraction and Electron Orbits
Date: Summer 2012
A consequence of the theory of relativity is that matter moving at extremely fast speeds contracts in the direction it is moving. What happens to the molecular structure of the matter when it contracts in one direction only? Do the electrons move in much different orbits? Is that contraction even possible?
I am not an expert in relativity, but I think your question has a much more complicated answer. You would have to start over with relativistic quantum mechanics with the corresponding definitions and mathematical properties. It “is not fair” to just do the molecular quantum mechanics ignoring relativity, then, at the end “plug in” relativity. Doing so leads to difficulties and probable errors. For example: Relativity treats the properties of matter in the presence of gravity, but quantum mechanics treats the properties of matter under conditions where gravity is negligible. Folding the two together correctly is still a debated problem. But one thing is sure. You cannot solve the relativity problem, then at the end say, “Oh! Now I am going to tag on quantum mechanics. Nor can you do the inverse. You cannot solve the quantum mechanical problem neglecting gravity, then at the end say, “Oh! Now I am going to paste in relativity.
An electron in orbit usually moves at about 2.2*10^6 m/sec. That is fast, but it is not quite 1% of c, 299,792,458 m/s. Generally, relativistic speeds approach 99% - 99.9% c.
When electrons are accelerated to 99.9% c, they are no longer in orbits and compression does occur. Accelerated electrons have been stripped from an atom and are in a beam, the result of a great deal of energy, The mass increase is from .0005 AMU at rest, to .001 AMU at 99.9% c.
Good question! PEHughes, Ph. D. Milford, NH
1. What happens to the molecular structure of the matter when it contracts in one direction only?
---------Length contraction is a decrease in length detected by an observer of objects at any non-zero velocity (usually noticeable near at the speed of light) relative to that observer. ( http://en.wikipedia.org/wiki/Length_contraction)
If we consider molecules as macroscopic objects, it will be same: contraction from the observer, nothing changed in the frame of the object. (But, we cannot simply as shown below.)
2. Do the electrons move in much different orbits?
---------An electron orbital is different from a moon orbital: it is a probability of finding an electron at a given place. (See the uncertainty principle of Heisenberg for more detail. Another, an electron behaves more as a wave than as a particle.)
While relativity describes macroscopic phenomena, quantum mechanics tends to explain microscopic phenomena such as photons and electrons. Although a couple of people have developed to unify two areas of physics, it’s still quite challenging. Simply, each cannot just apply to explain another, so we cannot apply relativity to electrons easily. (See these for further detail, although they are too technical to put here.
http://phys.columbia.edu/~cqft/physics.htm, http://www.arthurjaffe.com/Assets/pdf/Quantum-Theory_Relativity.pdf )
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Update: November 2011