[ExI] QT and SR

[scerir]

Mike Dougherty:
> Since this is all theoretical anyway... I'd like to introduce the answer
> that as these collections of spaceships, strings, molecules, atoms, etc
> approach the speed of light the number of reference frames exceeds the
> computational ability of the universe to "render" a consistent result.
> [...]
> Please feel free to school me for talking out of turn.

Talking out of turn? Au contraire. After 100 years there are
still uncertainties, conceptual uncertainties in SR.
(The solution of these comceptual difficulties may also
solve, at least partially, the conceptual divergence between
SR and QT?)

The first question might be: Is there too much relativism
in SR [1]? The second might be: Is it correct to say that,
according to SR, one-way velocities are devoid of physical
interest [2][3]? The third might be: Given that SR define
a "relative" simultaneity is it possible to define an "absolute"
simultaneity [4]?

One-way velocities are rather natural properties of physical
objects - like photons going from a point to another point.
It seems strange, or maybe paradoxical, that one-way velocities
are not reflected in the conceptual basis of a theory. Even in
the conceptual basis of an operational theory like SR.

But there are different, or more general approaches [5].
According to which the usual SR is just an important, special
case of a broader class of theories. These theories are also
consistent with the existent experimental results. The usual
Lorentz Transformations are just an important but special case
of a broader class of transformations, sometimes called Equivalent
Transformations (and among them the Inertial Transformations).
The Equivalent Transformations contain a free parameter reflecting
the well-known clock synchronisation conceptual arbitrariness.
Lorentz Transformations are recovered for a particular value
of that parameter. Actually all performed SR experiments (Michelson,
aberration, etc.) seem to be insensitive to the choice of that
parameter.

Two points somehow relevant here (since we are discussing the
Bell's spaceships paradox).
- The lenght of a moving rod can only be obtained by marking
the simultaneous position of its both end points. Therefore it
depends on the definition of simultaneity of (distant) events.
A theory which defines the "absolute" (and not the relative)
simultaneity of distant events would help a lot!
- Imagine Bell's spaceships, and their dynamics exactly as in
that paradox. Imagine each spaceship has its own clock,
synchronised with a clock on Earth. We can say that, since
spaceship A and B have at every instant of time exactly the
same velocity, their clocks accumulate exactly the same delay
with respect to the clock on Earth. So two events simultaneous
on Earth - taking place at points near which spaceships A & B
are passing - must be simultaneous also for the travellers of
A & B. We are facing here an "absolute" simultaneity which cannot
be explained by Lorentz Transformations (but can be explained
via Equivalent Transformations).

Paradoxical aspects of SR sometimes may have something to do
with the conceptual uncertainties of the theory.

[1] The best source is this one (maybe). F. Selleri (ed.),
    "Open Questions in Relativistic Physics", Apeiron,
    Montreal, 1998.
[2] A.Einstein, "Relativity, The Special, The General
    Theory", Methuen, London, 1920, see page 18. A similar
    statement also by H.Poincarè.
[3] One could also say that one-way velocity of light
    has never been measured, since SR assumes one clock
    and a mirror and ... a two-way velocity of light.
    (To measure a one-way velocity it is usually said one
    would need two clocks, and they have to be synchronised,
    and again synchronisation is a tricky concept and a
    conventional choice in SR. I do not think this is correct
    anymore.)
[4] "Absolute simultaneity" does not mean "absolute time"!
[5] Only to mention here papers by Reichenbach, Jammer,
    Mansouri & Sexl (1977), Croca, Selleri, etc.