Re: No...

Neat, I'll have to look at that some more.

Just to close this issue - C is *not* a barrier or a limit or even the speed of anything in particular. It's a parameter that characterizes the actual world.

Note that Euclidean geometry has exactly such a parameter - but it is imaginary! That is, in relativistic geometry we can think of the equation

x^2 - (ct)^2 = 0

and factor this to

(x-ct)(x+ct) = 0

so either x/t = c or x/t = -c. The parameter then represents the relative scale of the space to the time axis.

Now, it turns out that metric geometry (with a Pythagorean-like theorem) is a special case of projective geometry, and that the special type of metric geometry (Euclidean or pseudo-Euclidean = relativistic) is determined by the equation for a "degenerate conic", which is one that looks like

x^2 + y^2 + ... = 0

Euclidean plane geometry is then characterized by the equation

x^2 + y^2 = 0

which can be factored into

(x+iy)(x-iy) = 0

The characteristic parameter of Euclidean geometry is i, the imaginary unit! The points x and y satisfying this equation are called the "circular points at infinity". So, in a sense, Euclidean geometry has a thing called "infinity" that is such that you can never get closer to it. This is exactly analogous to the parameter c in relativity, which has a speed that can never be attained. Thus

relativity = the light cone
Euclidean geometry = the points at infinity

Post #174,207 by deSitter 9/14/04 12:55:53 PM Reply	Re: No... I had a friend who measured the refractive index of something and came up with 6! :) Of course I meant "measurement" in the sense of the measurement problem, the "other half of quantum mechanics" that gives the formalism physical meaning. And of course you can accurately measure the angular momentum of, say, [link\|http://www.if.ufrgs.br/~betz/quantum/SGtext.htm\|silver atoms]. -drl
Post #174,212 by Another Scott 9/14/04 1:32:33 PM Reply	There are materials with negative refractive indexes. Lots of weird things are being discovered these days. [link\|http://physicsweb.org/articles/world/16/5/3/1\|Physics Web]. I think c will stand as a limit for a while though. :-) Cheers, Scott.
Post #174,217 by deSitter 9/14/04 1:53:55 PM Reply	Re: There are materials with negative refractive indexes. Neat, I'll have to look at that some more. Just to close this issue - C is not a barrier or a limit or even the speed of anything in particular. It's a parameter that characterizes the actual world. Note that Euclidean geometry has exactly such a parameter - but it is imaginary! That is, in relativistic geometry we can think of the equation x^2 - (ct)^2 = 0 and factor this to (x-ct)(x+ct) = 0 so either x/t = c or x/t = -c. The parameter then represents the relative scale of the space to the time axis. Now, it turns out that metric geometry (with a Pythagorean-like theorem) is a special case of projective geometry, and that the special type of metric geometry (Euclidean or pseudo-Euclidean = relativistic) is determined by the equation for a "degenerate conic", which is one that looks like x^2 + y^2 + ... = 0 Euclidean plane geometry is then characterized by the equation x^2 + y^2 = 0 which can be factored into (x+iy)(x-iy) = 0 The characteristic parameter of Euclidean geometry is i, the imaginary unit! The points x and y satisfying this equation are called the "circular points at infinity". So, in a sense, Euclidean geometry has a thing called "infinity" that is such that you can never get closer to it. This is exactly analogous to the parameter c in relativity, which has a speed that can never be attained. Thus relativity = the light cone Euclidean geometry = the points at infinity -drl

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