Dear Jeff

Sorry, Cte means "constant".

So you look at events (m,t(0)) in H where t(0) is some fixed time that I

have named "Cte" in my previous post.. As H is an hyperboloid, these events

are on a conic, intersection of H in W = P x T with the plane t = t(0).

So you see why the Newtonian spacetime W is useful, allowing some synthetic

proofs in this difficult theory, even if it has no physical existence.

In fact you have a group G(alilean) acting not only on the set W of events

but also on the set of world lines, that's just the old theory of Galilean

relativity.

Of course, the (choo-choo) theory is the study of the subgroup of G leaving

hyperboloid H globally invariant. This group G' is known for a long time as

H is a ruled quadric.

G' is itself the union of 2 distinct subsets G" and G'" where G" is the

subgroup of G' leaving globally invariant each of the 2 set of generators of

H and G'" the subset (G'" is not a subgroup) of G' swapping these 2 distinct

sets of generators, that is to say G" is a subgroup of G' of index 2.

Friendly

Francois

On 4/1/07, Jeff Brooks <trigeom@...> wrote:

>

> Dear Francois,

>

> what is Cte?

>

> > I want to give a name to theses conicsbut I don't dare choose!

> > Geometrically they are the projections along time axis on plane P of

> > the sections of the hyperboloid H by the planes t = Cte.

>

> Sincerely, Jeff

>

>

>

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