Re: On the Incompleteness of Relativization

On Mar 24, 2:10 am, Hendrik van Hees <Hendrik.vanH...@xxxxxxxxxxxxxxxx
giessen.de> wrote:
I don't think that your criticism of relativity is justified. First of
all it's based on well established empirical facts.

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Moderator's note: I heavily disagree with the notion of science propagated
already by your first paragraph: If the just quoted sentence of mine is
irrelevant to your argument, it's irrelevant for physics since physics
is all about empirical facts and their theoretical description. HvH.
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Except there was no criticism of what Relativity IS and what it DOES
say, but a criticism of what it is NOT and what it does not say --
hence the subject header. As stated clearly at the beginning of the
article, the very issue you're bringing up is precisely the issue that
is not relevant here!

The issue you're alluding to was already covered by paragrph (a2),
therefore your criticism (which has nothing to do with paragraph (b),
which is the main focus of the article) is irrelevant.

Yes, we know that the empirical differences favor the representation
space of the Poincare' group over the parallel representation space of
the Galilei group, wherever one can draw the paradigm arrow from B -->
A. None of this, however, has any bearing on the reverse arrow A -> B.
Emprical tests are irrelevant to the A -> B direction.

Rather, what's relevant here is what lies on the A side that is not
already included on the B side.

Here, this means: what lies in the representation space given by the
Galilei group (the A side) that is not already included by whatever
representation space is adopted in the "relativization" transformation
A -> B. The domain of A -> B is not complete, hence not everything
that is known to have held up to 1905 is known to be incorporated in
B.

There may not even be a "completion" in this respect. I think it's
already the case that NO finite-dimensional symmetry group containing
the Poincare' group as a subgroup has a representation space that
completely maps onto the representation space of the Galilei group.
(Among other things, the vector and spinor representations don't even
begin to exhaust the full representation space of the Galilei group).

I don't know enough about the representation theories (yet) to say
anything more definite, though what I read in the literature appears
to be very negative on this issue and seems to allude to what one
might call the "c^2-Tower Problem"; e.g. the necessity of ALL orders
of the expansion t = s - (1/c)^2 u + (1/c)^2 t_2 + ...) in a complete
representation theory ... we begin already to see this with the
necessary appearance of the (1/c)^4 terms in any theory that bridges
the gap between Galilei and Lorentzian gravity in such a way as to
include Newtonian gravity as a special case.

As stated at the start of the article, there are oblique ways to a
paradigm to be attacked. This is a case in point. "Oblique" means the
vanguard and "what's already occupied and established" is left
completely untouched, while the forces wrap around the unguarded
flanks.

(This was a technique introduced as an innovation by Alexander 2300
years back).

The most clear-cut cases in point of the incompleteness, of course,
are the absence of the B side to the projective representations on the
A side (apart, perhaps from various ad hoc after-the-fact kludges that
might be imposed to write them in by hand). This you already begin to
see with gamma_5 (which naturally emerges in the projective
representations), the B field (which is A_5 in the projective
representation) the better accounting for the mass-energy relation,
etc.

The other reply, which purports to use "my own examples" to "refute"
the point will be looked at in closer detail shortly. I wasn't
expecting to see this thread in spr, and just spotted it.

.