If Special Relativity is formulated within the framework of Aristotle
space-time and if the relativistic boost invariance of any phenomenon
which satisfies this symmetry is interpreted as an intrinsic property
of this phenomenon rather than a very property of space-time itself,
Special Relativity is compatible
* with possible causal links between space-like separated events,
* with a realistic interpretation of the wave function,
* with an interpretation of quantum collapse as an objective,
instantaneous and ubiquitous phenomenon (rather than a shear change in
the knowledge of the observer)
* with an interpretation of Alain Aspect experiment as an action at
a distance
* with an interpretation of the propagation of particles at faster
than light speed trough a potential barrier thanks to quantum
tunnelling as the propagation of a faster than light interaction.

Bernard Chaverondier

Compatibility of possible interactions propagating faster than light
with the formulation of Special Relativity in the framework of
Aristotle absolute spacetime

http://perso.wanadoo.fr/lebigbang

References

[1] Alain Aspect, Three experimental tests of Bell inequalities by the
measurement of polarization correlations between photons. Thèse de
doctorat présentée à Orsay le 1er février 1983

[2] A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 1935. V.47.
P.777.

[3] Bohmian Mechanics Sheldon Goldstein
http://www.math.rutgers.edu/~oldstein/index.html

[4] "Hidden Variables and Nonlocality in Quantum Mechanics", Douglas
L. Hemmick http://www.intercom.net/~tarababe/dissertation.pdf

[5] Erich Joos, Elements of Environmental Decoherence. To be published
in the proceedings of the Bielefeld conference on "Decoherence:
Theoretical, Experimental, and Conceptual Problems", edited by P.
Blanchard, D. Giulini, E. Joos, C. Kiefer, and I.-O. Stamatescu
(Springer 1999)
http://xxx.lanl.gov/abs/quant-ph/9908008

[6] Michael D. Westmoreland (1), Benjamin Schumacher (2), OH 43022 USA
Quantum Entanglement and the Nonexistence of Superluminal Signals
(1) Department of Mathematical Sciences, Denison University,
Granville,
(2) Department of Physics, Kenyon College, Gambier,
http://www.arxiv.org/PS_cache/quant-...01/9801014.pdf

[7] Is Faster Than Light Travel or Communication Possible?
Updated 14-January-1998 by PEG, Original by Philip Gibbs 14-April-1997
http://math.ucr.edu/home/baez/physic...Light/FTL.html
[8] J.S. Bell, Physics, 1, 195 (1964); et "Speakable and Unspeakable"
in Quantum Mechanics. Cambridge Univ. Press, (1987)

[9] Claude Cohen Tannoudji, Bernard Diu, Franck Laloë, Mécanique
Quantique tome I, éditions Hermann, complément DIII et EIII § 3 b/

[10] Christoph Schiller, Motion mountain,
http://www.motionmountain.org/
paragraph 21 "Superposition and probabilities in Quantum Mechanics "
sub paragraph What is all the fuzz about measurements in quantum
theory ?

Bernard Chaverondier wrote:
If Special Relativity is formulated within the framework of Aristotle
space-time and if the relativistic boost invariance of any phenomenon
which satisfies this symmetry is interpreted as an intrinsic property
of this phenomenon rather than a very property of space-time itself,
Special Relativity is compatible
* with possible causal links between space-like separated events,
* with a realistic interpretation of the wave function,
* with an interpretation of quantum collapse as an objective,
instantaneous and ubiquitous phenomenon (rather than a shear change in
the knowledge of the observer)
* with an interpretation of Alain Aspect experiment as an action at
a distance
* with an interpretation of the propagation of particles at faster
than light speed trough a potential barrier thanks to quantum
tunnelling as the propagation of a faster than light interaction.


Exactly how do you answer the following argumnet.

Consider sending information from P to Q FTL at some speed U in some
inertial frame S. Chose coordinates so both events occur on the x axis and
let their time and distance representations be delta t and delta x
respectfully. Consider another inertial reference frame S' moving at
velocity v so we have from the Lorentz transformation:

delta t' = lambda (delta t - v delta x/c2) = lambda delta t (1 - Uv/c2).
Choose v such that c2/U v c then delta t' would be less than 0 implying
in that frame the signal left before it arrived. This violates causality so
FTL signaling is not possible.

Thanks
Bill

"Bill Hobba" wrote in message ...

Bernard Chaverondier
If Special Relativity is formulated within the framework of Aristotle
space-time and if the relativistic boost invariance of any phenomenon
which satisfies this symmetry is interpreted as an intrinsic property
of this phenomenon rather than a very property of space-time itself,
Special Relativity is compatible
with possible causal links between space-like separated events,

Bill Hobba
Consider sending information from P to Q FTL at some speed U in some
inertial frame S. Chose coordinates so both events occur on the x axis and
let their time and distance representations be delta t and delta x
respectfully. Consider another inertial reference frame S' moving at
velocity v so we have from the Lorentz transformation:

delta t' = lambda (delta t - v delta x/c2) = lambda delta t (1 - Uv/c2).
Choose v such that c2/U v c then delta t' would be less than 0 implying
in that frame the signal left before it arrived. This violates causality so
FTL signaling is not possible.


Chaverondier
That way :

Causality is not violated in your example. You haven't built a causal
loop ending at the same location and before the moment it has begun.

Now, your remark reminds that the relativist time ordering between
spacelike separated events isn't an absolute ordering. It depends on
observer's velocity. Consequently, the relativist time ordering is not
fitted to be a cause-effect ordering satisfying the causality
principle outside of the light cone. Indeed possible causal links
between spacelike separated events with a cause-effect order that
would depend on observer's velocity would allow to build causal loops
thanks to a simple change of observer.

Now, if you assume the set of physical phenomena to contain possible
phenomena that violate the boost symmetry and satisfy only the
SE(1)xSE(3) Aristotle group symmetry (SE(1)xSE(3)is a strict subgroup
of the connected component of the Poincaré group P4), boost invariance
of phenomena which satisfy it (noteworthy mechanics and
electromagnetism) is interpreted as an intrinsic property of such
phenomena occuring in this Aristotle spacetime. Phenomena like
possible FTL signals (that don't satisfy the relativist boost symmetry
because they propagate Faster Than Light) are not any more prohibited
in Aristotle spacetime. Such FTL signals would be prohibited in a
Minkowski spacetime modelisation, resting on the more demanding
Poincaré group symmetry, because FTL signals violate the relativist
boost invariance.

Aristotle space time is foliated in 3D Euclidean slices of absolute
simultaneity. In this spacetime, the time arrow points from any event
of the absolute present to any event of a future slice of absolute
simultaneity. The Aristotle spacetime chronological order isn't
dependant on observer's motion. Hence it is up to define an absolute
cause-effect arrow preventing any causal loop to occur even when
causal links between spacelike separated events are involved.

Now, to come back to your question, whatever the spacetime model, FTL
isn't up to give rise to possible causality principle violation.
Indeed, to get such a violation, it would be necessary to build a
causal loop ending at the same location and before the moment it has
begun (in some inertial frame). You cannot get such a causal loop with
FTL signals...
....unless you assume these Faster Than Light signals to be isotropic
and to have the same speed in any evenly moving frame of reference
(that's to say to assume these FTL signals to satisfy the relativist
invariance they violate).

Bernard Chaverondier
Compatibility between possible faster than light propagating
interactions with a formulation of Special Relativity in the framework
of Aristotle absolute spacetime
http://perso.wanadoo.fr/lebigbang

Bernard Chaverondier
If Special Relativity is formulated within the framework of Aristotle
space-time and if the relativistic boost invariance of any phenomenon
which satisfies this symmetry is interpreted as an intrinsic property
of this phenomenon rather than a very property of space-time itself,
Special Relativity is compatible
with possible causal links between space-like separated events,

Bill Hobba
Consider sending information from P to Q FTL at some speed U in some
inertial frame S. Chose coordinates so both events occur on the x axis
and
let their time and distance representations be delta t and delta x
respectfully. Consider another inertial reference frame S' moving at
velocity v so we have from the Lorentz transformation:

delta t' = lambda (delta t - v delta x/c2) = lambda delta t (1 - Uv/c2).
Choose v such that c2/U v c then delta t' would be less than 0
implying
in that frame the signal left before it arrived. This violates
causality so
FTL signaling is not possible.

Bernard Chaverondier
Causality is not violated in your example. You haven't built a causal
loop ending at the same location and before the moment it has begun.

I think you need to expand you reasoning. My point is that in one frame the
signal leaves the emitter before hitting the receiver. In another it leaves
the receiver (which is not even designed to emit a signal) before being
received by the emitter (which is not even designed to receive a signal).
The consequence of this can be made even plainer by considering what would
happen if you had a setup where the receiver reemitted the signal and sent
it back to the transmitter that was rigged to destroy itself when it
received the signal. In the frame were the signal left before it arrived we
would have the transmitter being destroyed prior to being able to emit the
signal.

Thanks
Bill

"Bill Hobba" wrote in message ...

Bernard Chaverondier
If Special Relativity is formulated within the framework of Aristotle
absolute space-time and if the relativistic boost invariance of any
phenomenon which satisfies this symmetry is interpreted as an
intrinsic property of this phenomenon rather than a very property of
space-time itself, Special Relativity is compatible with possible
causal links between space-like separated events.


Bill Hobba
Consider sending information from P to Q FTL at some speed U in some
inertial frame S. Chose coordinates so both events occur on the x axis
and let their time and distance representations be delta t and delta x
respectfully. Consider another inertial reference frame S' moving at
velocity v so we have from the Lorentz transformation:

delta t' = lambda (delta t - v delta x/c2) = lambda delta t (1 -
Uv/c2).
Choose v such that c2/U v c then delta t' would be less than 0
implying
in that frame the signal left before it arrived. This violates
causality so
FTL signalling is not possible.


Bernard Chaverondier
Causality is not violated in your example. You haven't built a causal
loop ending at the same location and before the moment it has begun.


Bill Hobba
I think you need to expand you reasoning. My point is that in one
frame the signal leaves the emitter before hitting the receiver. In
another it leaves the receiver (which is not even designed to emit a
signal) before being received by the emitter (which is not even
designed to receive a signal).


Bernard Chaverondier
What you remind is that the frame dependant relativist time displayed
by the clock of the receiver at the moment it is hit by a possible FTL
signal can be less than the time displayed by the clock of the emitter
at the moment it is emitted. Of course, I agree with you about this
point. Now, this doesn't prove causality principle to be violated.
This proves the impossibility to assume the relativist time ordering
to be an absolute cause-effect ordering required outside of the light
cone. Indeed, this relativist time ordering lacks the independence on
the observer's motion which is needed to prevent causal loops to
occur.

If you want your time ordering to be respectful of causality
principle, you have to consider the appropriate space-time model. As
soon as possible FTL signals (hence signals violating the relativist
invariance) are assumed to exist, you can no longer consider that all
of the restricted Poincaré group symmetries of Minkowski spacetime are
always satisfied. Consequently only the Aristotle group Symmetries ie
the SE(1)xSE(3) symmetries (spacetime translations and spatial
rotations forming a strict subgroup of the restricted Poincaré group)
can still be assumed to be satisfied. This symmetry group give rise to
the absolute Aristotle space-time SE(1)xSE(3)/SO(3). It's a 4D affine
space-time foliated in 3D Euclidean slices of absolute simultaneity
(and 1D fix points). This foliation and the absolute chronological
order between slices of absolute simultaneity support an observer
independent cause-effect arrow which prevents any causal loop to
occur.

In the framework of Aristotle spacetime, the inertial frames where
relatively simultaneous events belong to the same slice of "causal
simultaneity" should be called motionless inertial frames or Aristotle
frames. The switch from an Aristotle frames to an other one is
mastered by Aristotle group action which preserves the Aristotle space
metric, the Aristotle time metric and the foliated structure of
Aristotle spacetime.


Bill Hobba
The consequence of this can be made even plainer by considering what
would happen if you had a setup where the receiver reemitted the
signal and sent it back to the transmitter that was rigged to destroy
itself when it received the signal. In the frame were the signal left
before it arrived we would have the transmitter being destroyed prior
to being able to emit the signal.


Bernard Chaverondier
To get a more intuitive understanding of your present causal absolute
ordering versus relativist time ordering and FTL question, let us
consider a physical metaphor using a relativist sound synchronisation
process between distant clocks on a moving barge. So,

* let us consider a long barge with one clock at the rear end A,
one clock at the front end B and a klaxon located at the middle I of
AB.
* let us consider a sound emitted by the Klaxon reaching A at event
z1 and B at event z2. In our metaphor, events z1 and z2 are said to be
"sound simultaneous".

In the framework of our present metaphor, let us consider the light
speed to be approximately infinite. From the point of view of
cause-effect ordering, (ie from the point of view of an infinitely
fast propagating signal synchronisation hence, an observer's motion
independent synchronisation process), clock B is late with regard to
clock A when the barge is moving in direction AB.

That's because the forward sent phonon is running behind the escaping
front end B of the Barge. Hence, in Aristotle absolute spacetime, this
phonon has more space to travel than the phonon sent backward (which
is going to the encounter of the rear end A of the barge).
Consequently, from the point of view of "sound synchronisation induced
time ordering", when the barge is moving in AB direction, a fast
enough Faster Than Sound signal is up to hit point B before it has
leaved the emitter located at the rear end A.

Now, if you interpret this "sound synchronisation induced time
ordering" to be an absolute cause-effect time ordering outside of the
sound cone, you will conclude that you can receive at A a "Faster Than
Sound back propagated answer" coming from B before the emitter at A
has sent his Faster Than Sound propagated question. Actually, the
Faster Than Sound signal will come back to A at the same time it
leaves in the case of an infinitely fast propagating signal and a
little later (in nice agreement with causality principle) if it
propagates only much Faster Than Sound but not infinitely fast.

Bernard Chaverondier
Compatibility of possible Faster Than Light propagating interactions
with a formulation of Special Relativity in the framework of Aristotle
absolute spacetime http://perso.wanadoo.fr/lebigbang