Re: RAH and Light speed


Gerry Quinn wrote:

When you are finished with the mathematical digressions, please return
to the discussion of the assertions of specific physical theories, and
we will continue.

You cannot, ever, understand mathematical physics if you sneer at and
ignore mathematics. This *should* be painfully obvious.

If mathematics is indeed consistent, no amount of mathematical
manipulation will transform a theory in which the physical properties
of an object include position and velocity in spacetime into one in
which the notions are expressly ruled out, which is what you seem to be
saying.

If you bothered to read and understand what I said, instead of simply
sneering, you might have a clue what is and what is not ruled out. What
I was saying is that the geometry of special relativity is very much
analogous to Euclidean geometry and a whole host of other geometries
which the nineteenth century turned up. You can get at the more
abstract geometry by axioms (which can be and has been done for
relativity), but you can also get at it by considering more concrete
models of the geometry, and then defining isomorphisms. That's a basic
move in mathematics as a whole.

You can, incidentally, not only get Euclidean three-space and Minkowski
four-space in this way, you can get an abstract Galililean space+time
in this way. If you do that, objects in space+time do not have a
velocity as a determinate value, any more than points in Eucidean space
have Cartesian coordinates, but rather you have these things once you
choose a particular coordinate frame. This is really not much more of a
big deal than saying you don't get a specific number for velocity until
you choose units, and decide whether it is going to be measured in
miles per hour or furlongs per fortnight.

No one but you knows what Quinn-relativity is, if indeed it has a
single, coherent meaning at all. In the ordinary sense of the word,
what happended is that Galilean relativity was extended to be
Einsteinean relativity.

And after being extended, it was different, right?

It's different in that the group of transformations is no longer the
Galilean group but instead the Poincare group. The Galilean group can
be generated from space translations, time translations, velocity
boosts, and rotations (via an orthogonal matrix.) The Poincare group
can be generated from spacetime translations, rotations, and Lorentz
velocity boosts.

.

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