Permittivity in inertial reference frames

[wimms]

Suppose 2 inertial frames with relative relativistic velocities.
To discuss phenomena in other frame, we need to use Lorentz Transform for length and time. I got question: do we have to also use LT to talk about permittivity and permeability of other IRF? This seems strange. Permittivity has units of distance, which should be LT'ed. Thus we would conclude that permittivity of other IRF is different than that of ours? Are we to suppose that vacuum around other IRF has changes in permittivity just because it is in relative motion? If so, then how comes it is called "constant"? If not, then c must appear different in other IRF for us?

 

[jdavel]

wimms,

The permittivity and permeability of empty space are Lorentz invariant, just as c (the reciprocal of the sqrt of their product) is.

Consider permittivity. It shows up in Coulomb's law which gives the force between two charged particles separated by a distance. If permittivity changed with velocity, the force would change, and the two particles would accelerate differently. In other words, identical experiments on the motion of charged particles done in two labratories, in relative motion would yield different results. Or even stranger, an experiment done in January would yield different results from the same experiment done in June when the Earth's velocity around the sun has changed by 60,000miles/hr. No such difference has ever been observed (ditto for experments involving permeability). Everyone who understands what that means, believes that c is constant. Because what it means is that c is constant!

 

[jdavel]

wimms said: "Permittivity has units of distance, which should be LT'ed."

I got carried away and forgot to address this point explicitly. Permittivity does have units of length, and they do get LT'd. But it also has units of mass and time which get LT'd as well. The units of permittivity (SI) are:

coulomb^2/(meter^2*Newton) =

coulomb^2/(meter^2*kg*m/sec^2) =

coulomb^2/(kg*m)(m^2/sec^2)

Experiments in particle accelerators have shown with outrageous precision that charge is Lorentz invariant, so that takes care of the numerator.

The LT's cancel for (kg*m) because mass gets bigger but lengths get shorter.

The LT's for m/sec have to cancel in order for c to be invariant.

So, premittivity is invariant.

You can do the same thing with the units for permeability.