Re: Download a new book on quantum mechanics and relativity.

From: chaverondier (bernard.chaverondier_at_wanadoo.fr)
Date: 10/04/04 

Date: 4 Oct 2004 13:05:06 -0700

Eugene Stefanovich <eugenev@synopsys.com> wrote in message news:<4160E7A0.5040306@synopsys.com>...

Eugene Stefanovich
> Could you please explain to me the meaning of "absolute
> synchronization" in your approach. I feel, it plays a
> significant role there, but I don't understand what it means.

Chaverondier
If all symmetries of relativity are satisfied, then, there can be
only one speed c at which interactions propagate at a speed
independent on the motion of their source.

If this speed of propagation is infinite you get the Galilean
Relativity and the space-time you get is the Newtonian
space-time with an absolute time, but no absolute space.

If the speed of propagation is c, then you get the Special
Relativity and the space-time you get is the Minkowski
space-time with no absolute time and no absolute space.

If space-time translations and space rotations
invariance are satisfied by any phenomean, but that
  * some interactions propagate at a speed
      c independent on their source
  * some interactions propagate at a speed
      C > c independent on their source

then, the principle of relativity of motion is broken (I will detail this
point later). You are not any more in Minkowski space-time. Lorentz
covariance is still possible (and so can be satisfied by free particles)
but is not any more required. You are in the Aristotle space-time.

In this framework, it is possible to define Lorentz inertial frames.
In such a frame R the relativist simultaneity means that an event
zA occurring at A and an event zB occurring at B are said to be
simultaneous (with regard to the simultaneity prevailing in frame R)
when a flash emitted at event zA located at A at rest in R and a flash
emitted at event zB at B at rest in R (both propagating at speed c)
reach the middle I of [AB] at the same time.

Only a class of frames R0 (images of each others by space-time
translation or space rotation) satisfies the requirement that when
I is the middle of points A and B at rest in R0, a signal propagating
at speed C emitted from I reaches A and B simultaneously according
to the relativist simultaneity prevailing in this frame. These preferred
frames R0 are Aristotle frames (ie motionless inertial frames).

Eugene Stefanovich
> [in Relativist Quantum Dynamics]
> the "signals" will depart and arrive simultaneously
> in all reference frames (see 12.3.3). This is guaranteed
> by interaction dependence of boost transformations.

Chaverondier

The possibility of FTL interaction doesn't bother me
too much because I believe that some Interactions may
propagate Faster Than Light. However, such interactions
cannot reach their emission and reception event at the
same time whatever the frame where they take place.

That would mean that the principle of relativity of motion
be satisfied _in 4D space-time_ (not in representation
Space which I doubt that it is the same condition)

Indeed, instantaneous interactions conflict with the
Principle of relativity of motion in 4D space-time
(which is the representation space of a free particles,
but not the representation space of interacting particles)

If you assume that a device is up to send signals at speed
C > c in an inertial frame R0 and assume nevertheless
the principle of relativity, then you are contrived to assume
that the same device, located in an other frame R2, would be
up to send back a signal at this same speed C.

So, let us choose inertial frames R0, R1 and R2 such that
  * speed of R1 with regard to R0 = v
  * speed of R2 with regard to R1 = v
  * vC/c^2 > 1

We can successively
  * transmit immediately at time t0 = t1 =0 a signal from A1
at rest in R1 to A0, located at the same place but at rest in R0,

  * send a signal at speed C from A0 to B0 (at rest in R0)
at speed C > c and receive this signal at B1 at rest in R1
located at the same place than B0 at time t0=(A0B0)/C in R0
and t1 in R1 such that
t1 = (t0 - vx0/c^2)/(1-v^2/c^2)^(1/2), ie
t1 = (x0/C)(1-vC/c^2)/(1-v^2/c^2)^(1/2) <0
(where x0 denotes the distance A0B0 measured in R0)

  * transmit immediately this signal from B1 at rest in R1 to
B2 at rest in R2 located at the same place than B1 at time t1,

  * send back a signal at speed C in R2, from B2 to A2
at rest in R2, so that observer located at A1 in R1 can
receive the answer to its message at time 2t1 <0 and
so can decide not to send it.

This provides the looked for contradiction.

Hence, FTL signalling is not compatible
with the principle of relativity of motion.

The possibility of signals propagating at speeds c and signals
propagating at speed C>c, both independent on the motion
of their sources, conflicts with the hypothesis of a principle
of relativity of motion applying to any phenomenon without
any exception (when 4D space-time is considered).
 
If your theory is correct, then the principle of relativity of
motion has to be restricted to free particles when applied in
a 4D space-time. When interacting particles are involved,
what has to be expressed is the Unitary representation of
the Poincaré group in the appropriate representation space
and the appropriate commutators of the Lie algebra of the
Poincaré group have to be considered.

Chaverondier
> > In your theory, the Poincaré group is not universal
> > because the speed of interactions which propagate
> > at a speed independent of their sources is not unique.
> > It depends on the type of interaction. Hence,
> > the universality of Poincaré group is broken.

Eugene Stefanovich
> I am telling you that there is just one Poincare group in my
> approach. The commutation relations of its Lie algebra are
> given in eq. (26) - (33) in subsection 2.2.1. The commutators
> of ANY representation of this algebra by Hermitian operators
> are given in eqs (50) - (56) in subsection 5.2.2. These
> commutators do not depend on observed physical system,
> interactions, etc. Yes, they depend on the constant 'c',
> but this has nothing to do with the speed of propagation of
> interactions. The group is always the same, however, there
> is infinite number of ways to define representations of
> this group in the Hilbert space of the system. For example,
> you can define a non-interacting representation (see 8.2.1
> for the case of 2 particles and 9.1.6 for the Fock space)
> or you can define interacting representation (one example
> is in 8.3.1, another example is interaction in QED 11.1.2).

Chaverondier
OK, the parameter c which represents the maximum
propagation speed of free particles is the one embedded
in your Poincaré group and, nevertheless, the representation
of the Poincaré group in the representation space of
interacting particles can give rise to infinite speed
of propagation of interactions in our 4D space-time.

I begin to think that the problem of inapplicability of Lorentz
Covariance to interacting particles (if you are right) is that the
good space to model interacting particles is the space of
representation of interacting particles.

Hence, the Minkowski space-time picture should be restricted to
Free particles.

If you are right, perhaps that the violation of Lorentz covariance
(which Is the expression of the principle of relativity of motion
in the 4D space-time which is the representation space of the free
particles) means that the principle of relativity has to be applied
in the appropriate representation space. Perhaps that the gauge
invariance principle fails to provide the right Hamiltonian because
it is inappropriate to apply it when the dynamics of interactions begin
to take place because we are not any more in the representation
space of free particles ?

Chaverondier
> > You cannot postulate inertial frames or 3D space geometry
> > and so on without providing a physical justification and
> > a mathematical demonstration that these geometrical
> > tools rest on a sound physical basis.
 
> > On the contrary, the restricted Aristotle sub-group of Poincaré
> > group encompasses only space-time translations and space rotations
> > groups which are unique. This subgroup is the same whatever
> > the particles, interactions, rods and clocks you consider.

Eugene Stefanovich
> I disagree. Time translations do depend on interaction.
> The generator of time translations is Hamiltonian H, right?
> I suppose, in your theory you write this operator as H = H_0 + V,
> where H_0 is Hamiltonian for free particles, and V is interaction-
> dependent term.

Chaverondier
The theory I wrote was only intended to prove that there was a geometrical
structure compatible with Faster Than Light interactions and with the
possibility to express the relativist symmetries of phenomena that satisfy
this symmetries. The possible users of this geometrical background can build
in this framework any Hamiltonian they wants. It's only a geometrical arena
compatible with FTL (hence violating the Lorentz covariance) and nevertheless
compatible with any phenomena satisfying Lorentz covariance.

That's the minimal modification of special relativity which allows for FTL
Interactions, so that you find in it all the geometrical tools you need.

A 3D Euclidean space
A 1D Euclidean time
Lorentz inertial frames

I cannot see how you can use geometrical tools without a proper
physical justification of their use and a mathematical construction
resting on satisfied symmetries and symmetry groups.
This is the basis for the derivation of a geometry.

Why should your theory conflict with time translation invariance
in 4D space-time ? (which is the only invariance of Aristotle space-time
which might perhaps be in possible conflict with your theory, though
presently, I doubt that there be a conflict despite the dynamical nature
of time translation which I know to be true)

Bernard Chaverondier
http://perso.wanadoo.fr/lebigbang/transformation.htm
Settlement of Lorentz transforms and "canonical" inertial
frames in the framework of Aristotle space-time.
http://perso.wanadoo.fr/lebigbang/epr.htm
Quantum determinism or Relativist locality ?

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