Re: [Phys-L] speed c

[John Denker <jsd@av8n.com>]

On 03/14/2013 01:42 PM, Bill Nettles wrote:
> I was having a discussion with a friend about light, spacetime, max
> speeds, etc. I mentioned that light passing through matter travels
> slower than c. He responded, "Then because there isn't any perfect
> vacuum [SpaceWeather.com today reports 8 protons/cm^3], light never
> really travels at c." Thinking about this drove me to Feynmann, Vol
> I, Chap 31 to read about refractive index.
>
> What I gleaned from a quick reading:
>
> 1)      All E&M fields (and changes thereto ) propagate at c ...
> always.
>
> 2)      Atoms (& electrons attached) oscillate in response to other
> E&M fields producing their own E&M field.
>
> 3)      We detect light/E&M radiation which is a sum of all the
> sources of E&M fields, some of which are strong and others which are
> ignorable.
>
> 4)      Light passing through (near??) matter is phase shifted so
> that it appears to have traveled slower through the matter than it
> would have without the matter.
>
> Did I understand Feymann properly?

Yes.

> If so, it seems that light passing through any field of matter (even
> 8 protons/cm^3) would produce other E&M fields which would produce
> the phase shifted field, giving the appearance of slower than c (even
> if it's 1 part per 10^15).  But the field from any individual source
> always propogates at c.

Understanding this is the easy part.  Explaining it to somebody who
does not already understand it the hard part.  That's because it can
easily degenerate into word games
 -- what does one mean by THE light?
 -- what does one mean by the LIGHT?

> From a fundamental theoretical physics point of view, THE light always
travels at the speed c.  Anything else is the result of superposition.
An out-and-out standing wave is an extreme example of superposition,
and it doesn't travel at all;  it just stands there.  Its speed is
zero, not c.

On the other hand, Landau and Lifschitz wrote an entire book called
_Electrodynamics of Continuous Media_.  From a fundamental theoretical
point of view, there are no continuous media, but that doesn't stop
people from thinking in those terms.  If somebody insists on thinking
in terms of easy-to-measure, classical, macroscopic, continuous-media 
quantities, there is no way to convince him that c is the right answer.

  This is analogous to other word games that arise in special relativity.
  From a fundamental point of view, proper length is THE length.  However, 
  that fact is exceedingly hard  to get across to someone who doesn't 
  already understand, i.e. someone who thinks that the projected length
  is "the" length.

==========

Far more fundamentally, the true meaning of the speed c is not based
on light.  The only reason we can even talk about a nontrivial c is
because we measure space in one set of units and time in another.  If
we look properly at the four-dimensional universe and measure space
and time in the same units, then the meaning of "c" is the same as the
meaning of "radian".  It is the natural unit of angle.  That is to
say, c is to rotations in the XT plane as radian is to rotations in
the xy plane.

The fact that c is relevant to electromagnetism is no more significant
than the fact that radians are relevant to electromagnetism.  Note that
c /and radians/ are relevant to a treeeemendous number of things other
than light:  
  *) general relativity 
   -- including gravitation, 
     ++ including gravitational waves in particular
  *) special relativity
   -- including rest energy, momentum, and kinetic energy
   -- including the projection of length and time onto another frame
  *) et cetera