# Questions on reversed Coulomb force.

1. Oct 3, 2007

### Robert Clark

Questions on reversed "Coulomb" force.

I've seen that with Moeller scattering, the attractive force between
the nucleus and the electron can become repulsive at high relativistic
velocities of the electron. What are the energies required for this to
occur?
Is there an analogous result between electrons, i.e., in electron-
electron scattering, where the repulsive force between them switches
to become attractive at high energies?
The strong nuclear force operates as an attractive force even between
protons at distances of the size of the nucleus, about 10^-15 m. This
works even for protons beamed towards a nucleus at short distances,
not necessarily already contained within a common nucleus.
But shouldn't this distance be frame dependent? If the protons are
aimed toward a nucleus but to be a longer distance away, shouldn't
they regard the distance to be Lorentz contracted at sufficiently high
velocity?
If the proton beam say was aimed to skirt the outside of an atoms
electron cloud at about 10^-10 m away from the nucleus, shouldn't a
Lorentz contraction factor of 10^5 cause the protons to regard the
distance to be within the 10^-15 distance to the nucleus at which the
strong force is active?
The proton has a rest energy of close to 1 GeV. So a Lorentz factor
of 10^5 would correspond to giving the proton an energy of 100 Tera
eV. Not even the LHC is expected to get this high. However, Fermilab
gets up to 1 TeV. If the proton beam was aimed to come within 10^-12 m
of the nucleus, where the strong force would not be expected to
operate, then Lorentz contraction should make the distance appear as
10^-15 m to the protons, where the strong force would operate. Has
such an effect been seen?

Bob Clark

2. Oct 4, 2007

### Uncle Al

Re: Questions on reversed "Coulomb" force.

Robert Clark wrote:
[snip]

> But shouldn't this distance be frame dependent? If the protons are
> aimed toward a nucleus but to be a longer distance away, shouldn't
> they regard the distance to be Lorentz contracted at sufficiently high
> velocity?
> If the proton beam say was aimed to skirt the outside of an atoms
> electron cloud at about 10^-10 m away from the nucleus, shouldn't a
> Lorentz contraction factor of 10^5 cause the protons to regard the
> distance to be within the 10^-15 distance to the nucleus at which the
> strong force is active?

[snip]

1) Lorentz contraction is external viewer perspective not a local
physical alteration. The wheels of a relativistic choo-choo are not
elliptical.

http://bkocay.cs.umanitoba.ca/Students/Theory.html
The distorted cube

2) Lorentz contraction is the body coming right at your nose. A
grazing miss is Terrell rotation instead.

http://prola.aps.org/abstract/PR/v116/i4/p1041_1
Lit. cite
http://www.math.ubc.ca/~cass/courses/m309-01a/cook/terrell1.html
http://www.ibiblio.org/lunar/school/library/finilite.html
http://en.wikipedia.org/wiki/Terrell_rotation

3) At relativsitic velocities electric and magnetic fields swap
identities. You've got a lot more calculation to do.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2