Re: What is the history of relativity theory? (continuation of Poincare thread)
- From: "Ilja Schmelzer" <Ilja.Schmelzer@xxxxxxxxxxxxxxxx>
- Date: Wed, 7 Sep 2005 06:24:08 +0000 (UTC)
"Harry" <harald.vanlintel@xxxxxxx> schrieb
> "Ilja Schmelzer" <Ilja.Schmelzer@xxxxxxxxxxxxxxxx> wrote
> > "Harry" <harald.vanlintel@xxxxxxx> schrieb
> > > - Lorentz did not just "give the Lorentz contraction". I invite you to
> > > show
> > > how Lorentz' theory as corrected by Poincare - and which for
> > > experimental
> > > physics happens to be indistinguishable from that of Einstein - can be
> > > less
> > > predictive than that of Einstein.
> >
> > Ok.
> >
> > Assume we have a hidden preferred frame. In this preferred frame,
> > hidden information transfer is possible.
>
> It's not at all clear to me what you mean. I can imagine a laser and photo
> detector, together inside a black box that is at rest in the
> Ether/Space/Vacuum, whatever you want to call it. That would be "hidden
> information transfer in the preferred frame", but of course it would be
> hidden in all frames.
Indeed. I mean something completely different - the hidden variables
of realistic QM interpretations, for example.
> -> Looking below where you mention Bell: perhaps you mean hidden
information
> transfer that is much faster than light?
>
> > This hidden information
> > transfer can lead to violations of Bell's inequality. Example: Bohmian
> > mechanics, which has a preferred frame and violates Bell's inequality.
>
> I'm unfamiliar with Bohmian mechanics - a separate thread on that could be
> instructive!
Look for Duerr and Goldstein on arxiv.org.
In BM reality consist of two parts: The wave function Psi(Q), and the state
Q. For the wave function we have the usual Schrödinger equation, for
Q the guiding equation
d_t Q = (Psi^* J Psi) / (Psi^* Psi)
If we have a state with probability distribution for Q named quantum
equilibrium:
rho(Q) = Psi^*(Q) Psi(Q)
it remains in this state forever.
Q is the configuration of our world (say, Q in R^3 for one particle,
in R^3N for N particles, some functional space in field theory) in a fixed
moment t.
> > Assume the notion of causality should be Lorentz-covariant. In this
> > case we obtain Einstein causality, hidden information transfer in some
> > hidden preferred frame is impossible. We can prove Bell's inequality.
> >
> > Thus, Bell's inequality is an additional falsifiable (and falsified)
> > prediction of the Einstein-Minkowski version of SR, which is not
> > possible in the Lorentz-Poincare ether.
>
> Maybe you want to elaborate on this? According to all, light speed is the
> limit speed.
The theory is deterministic, but has absolute time, and the
trajectory of a single particle depends on the whole state of the world,
even if the resulting distributions rho(Q) don't.
> Perhaps you mean that faster-than-light information transfer might in
> principle enable the detection of the frame that according to
> Lorentz-Poincare can't be detected, while it would lead to
> self-contradiction in Einstein's theory.
> If so, IMO both hypotheses are equally predictive, but a failure of the
> prediction would have other consequences for Einstein-Minkowski
metaphysics
> than for that of Lorentz-Poincare. Please correct me if this is wrong.
This consideration is correct, I agree with it, but this is not what I mean.
The statistical predictions of BM in equilibrium and QM are identical, and
the preferred frame cannot be detected by statistical observation in above
theories.
The situation with predictive power is more complex than often imagined
if we talk about the "predictive power of theories". The problem is that
to make a prediction we need more than one theory. For example, in the
theory of gravity we need not only GR but also a theory of matter to
make predictions. (In principle, we have to include theories about the
behavious of measurement instruments and so on too. Even theories about the
reliability of certain experimenters.) Thus, in some sense we have to talk
about the predictive
power of groupes of theories.
Nonetheless, it seems justified that we can compare the "predictive power of
two theories T1, T2" if we use the same set of additional theories Tx,Ty,Tz,
that means,
if T1 + Tx + Ty + Tz allows to make a prediction which cannot be made in
T2 + Tx + Ty + Tz, T1 has more predictive power.
In this case, we use a set of assumptions I name "realism". Deterministic
theories
which predict the outcome of all experiments as depending on a (possibly
hidden) initial state (like Bohmian mechanics) are realistic. In the Lorentz
ether, reality itself may not be Lorentz-invariant, especially because the
ether is part of this reality. In Einstein's SR reality itself should be
Lorentz-invariant, there is no place for an ether
with a preferred frame, and also no place for BM which also needs a
preferred frame. Causality means Einstein causality.
Now a hidden variable theory for QM which meets the "metaphysical"
restrictions imposed by SR (Einstein causality not only for observations but
for hidden variables too) is impossible. This is Bell's theorem:
realism + Einstein causality => Bell's inequality
(Here "realism" denotes all explicit and implicit assumptions beyond
Einstein causality used by Bell, thus, a search for loopholes in Bell's
theorem does not
invalidate these considerations. At best, they can show that there are
other, weaker notions of realism which do not allow to prove this theorem.)
But there is no such theorem for the Lorentz ether. Instead, BM defines a
counter-example: BM is realistic, even deterministic, it is compatible with
Lorentz ether
metaphysics, but Bell's inequality does not hold (as in QM).
Ilja
.
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