Permittivity-Permeability-Scale symmetry in Classical Electromagnetics Is this statement true: "If we double the permittivity and the permeability of the entire universe, then shrink it down to half; we wouldn't be able to tell the difference (within classical electromagnetics)"?
I know that many things would remain the same after such a transformation ($2\times \epsilon$,$\ 2 \times \mu$, $0.5\times\text{Scale}$) but how robust of a symmetry is it? I suspect such a transformation could be revealed by quantum mechanics, but what about just classical electromagnetics? (I also have an inclination that conductivity $\rho$ should also be doubled, but we could absorb the conductivity into the complex $\epsilon$)
Also, how would the effects be any different if we applied the transformation: $4\times \epsilon$,$\ 1 \times \mu$, $0.5\times\text{Scale}$ ? All electromagnetic fields will have the same shape, but the ratio between E and H fields would be halved. So things like wave impedance $\eta$ and transmission line characteristic impedance would also be halved. It feels like all electronic devices would still work fine, but what would change?
I don't have a particular concrete question, I just want to learn more about this idea.
Would my cell phone work exactly the same, for example (except for GPS, with relativity things can get iffy)?
 A: I believe that changing the permittivity of the universe would change the speed of light itself, with all that it entails.  Here is a portion of my speculative paper on a theory of gravity:
Paraphrasing from Arvin Ash; Why are µ0 and ɛ0 these exact values?  These are the constants of nature. These are properties of free space that tell us how fast magnetic fields and electric fields can interact with each other.  This sets a limit on how fast these fields can propagate through space.  In a different substance, or in a different universe, these constants could be different.   Thus if ɛ0, the permittivity of space was lower, c would increase.  Likewise if ɛ0 was larger, as with the dilation of particulate space, c would decrease as we see with time dilation in gravity.
Paraphrasing from Review of the Universe, “Just as space is defined by a network's discrete geometry, time is defined by the sequence of distinct moves that rearrange the network.  Time flows not like a river but like the ticking of a clock, with "ticks" that are about as long as the Planck time: 10-43 second. Or, more precisely, time in the universe flows by the ticking of innumerable clocks - in a sense, at every location in the network where a quantum "move" takes place, a clock at that location has ticked once.”
To show how this works in a gravitational field, we want to compare the permittivity of free space versus the permittivity of space on the surface of the gravitational body:
•   In Free Space:  c=√(1/µ0ɛ0), where µ0=1.25663706 x 10-6 and ɛ0=8.85418782 x 10-12
•   And using the Schwarzschild metric to determine time dilation relative to free space:  t!=t/√(1-2Gm/rC2)
On the Earth:       Mass=5.9722x1024kg   Radius=6.371x106m
We find a time dilation factor of tE=1.000,000,000,699,68
Thus we find a permittivity factor of ɛE = ɛ0 x tE=8.85418783x10-12
This works out to 21 centimeters per second in the relative speed of light
On the Sun:         Mass=1.989x1030kg  Radius=6.9634x108m
We find a time dilation factor of tS =1.000,002,121,041,69
Thus we find a permittivity factor of ɛS = ɛ0 x tS=8.85420660x10-12
This works out to 635 metres per second in the relative speed of light
On star R136a1: Mass=6.263x1032kg  Radius=2.089x1010m
(The largest known star)    We find a time dilation factor of tS =1.000,002,226,755,19
Thus we find a permittivity factor of ɛR = ɛ0 x tR=8.85438498x10-12
This works out to 6,675 metres per second in the relative speed of light
