On 9-1-2011 3:37, Darren New wrote:
> andrel wrote:
>> one time, with a distance between 2 points defined by x^2+Y^2+z^2-ct^2
>
>> OTOH if this is not observed in our universe, we either have more than
>> 4 space/time dimensions or laws are not invariant, both do not seem
>> compatible with reality.
>
> Except you just included "c" as a constant in that formula, which was
> the point. If "c" varies depending on how fast you're going, that whole
> formula falls apart.

?? I defined a metric on my space, that is all. OK, I added a 'c' to 
keep consistent with ordinary people*. No self respecting theoretical 
physicist would do that. (But then they sometimes don't know what their 
formulas mean in real life as they lost track what the power of 'c' is 
in their formulas; 'c' is in their system a constant of 1). That the c 
turns out to have a meaning in real life is a surprise.
In fact it doesn't, remember we were just doing maths. All we know is 
that there are coupled vector and scalar fields, with solutions that 
propagate out with a speed 'c'. If we identify those with the E and B 
field what propagates out is light, but then we are in the physical world.

A more consistent implementation of your proposal would be to define a 
distance as (px)^2+(qy)^2+(rz)^2-(ct)^2 where p,q,r, and c depend on 
position in space and/or velocity (and/or on higher orders derivatives). 
I am sure there are some mathematicians studying those too. Perhaps some 
of those can even be forced to be Galileo or Lorentz invariant too.

*) Note that I forgot to square it, the dimensions don't add up. 
Probably my teacher first did it without this constant or with another 
constant to remind us later that it had a dimension of (m/s)^2

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