Currently, the Lorentz Ttransform does not map 4space to 3space
anywhere. Correct ?

It probably does but you might have asked if it maps
'everywhere'.

It seems like it might do some weird stuff because of the nonlinear
terms.

There is no such thing as a _formalized_ nonexistence in GR or SR, or
even QM. No ?




What I mean is that successive frames of reference are basically
isomorphic unless we're talking about black holes or something - no ?

Who cares? ) When you say isomorphic fourspace that is
the equivalent of using 5 axes for the abstracion of time.

I need to make the question more precise.



If you have successive frames which are less than Planck length, I want
to map them to --- Minkowski(3+0) space.

I measure things less that a metre with a meter stick.
Are you afraid you won't have enough room under the
fraction bar? Just tape more sheets to your work page
until all the digits will fit. )

Well, according to Planck, the number of reference frames from t1 to t2
is always finite. Yet Einstein treats time like it's continuous ?


Do you just define it to be so - or do you need algebra ? I think that
in the case of time you can get away with just defining it to be so,
but length is trickier. You have the same exact situation with length,
but I think that this must have some implications for the algebra of
the transform.

Review Fitzpatrick's description of the tranform and it may
become clearer what is being represented.

Lengths less than Planck Length must also map to Minkowski(3+0) space.
They will.


I consider Minkowski(3+0) to be the equivalent of nonexistence because
time is not there - existence becomes trivial.

Is it standard practice in physics to map lengths in 4space Planck
Length to 3space ?



Maybe that's the trick. instead of playing around with balls of radius
r and bla bla bla, just incorporate scale right into Lorentz transform.

Pythagoras didn't have to resort to that.



Is that what Nottale did ? Anybody know ?
I doubt any but Nottale know what he did.
http://arxiv.org/abs/hep-th/0307093

Reading the preface - it hardly makes any sense whatsoever. It's like a
Peano curve of twisting logic. I got a hell of a lot further with a
momentary glance at time scale calculus.


Sue...