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[Phys-L] what is c? was: Travel distance in a waveguide.



On 02/23/05 10:35, Dan Crowe wrote:
I know that John is not going to like "speed of causation", given his
prior discussions on causation.

Actually I'm mostly happy with "speed limit of causation".

I'm not allergic to causation; I'm just allergic to
wrong; I squawk when people say wrong things about
causation. And referring to c as the speed limit of
causation is not wrong, as far as I know.

Similarly, IIRC, about a year ago Michael E. referred
to c as the speed limit of information, which comes
to essentially the same thing, so I'm mostly happy
with that, too.

But even that's not the whole story.

The quantity "c" is the speed at which massless exchange bosons (photons
& gravitons) propagate. It is also the natural speed limit for massive
particles. Are there other important characteristics of "c" that would
be useful in determining a better name for it?

I cannot think of a concise name that includes both important
characteristics.

There's a lot more than two.

When you think about boosts and rotations in special relativity,
_c_ is to boosts as _radian_ is to rotations.

This guarantees c will show up in lots of places. For
instance, if you take the relativistic expression for
energy versus momentum and expand it in a power series,
the zeroth order term is E = m c^2, the first-order term
is .5 m v^2, and then there an endless series of
higher-order terms. Every term except the first-order
term (not excepting the zeroth-order term) has an explicit
factor of c in it. The m c^2 term is nontrivial even at
zero speed, and the higher-order terms make nontrivial
contributions even when we are well below the speed limit.

My gut feeling is that the "most important" property is
_c_ is to boosts as _radian_ is to rotations
and that all the speed-limit stuff is a consequence of
this ... but I don't know how to formalize this idea.