(10 04 2003)
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 and with an interpretation of Alain Aspect experiment [1], [2] as an action at a distance.
Bells inequalities violation [3], seemed to have been confirmed by Alain aspect experiment. This strongly suggests quantum collapse to be a non local phenomenon. Indeed, when interpreted as an objective phenomenon, the wave function collapse caused by a quantum measurement is an instantaneous action at a distance. Now, instantaneous actions at a distance and faster than light propagation of interactions don’t satisfy all of the symmetries of the Poincaré group, because they conflict with the relativistic boost invariance. Some authors like John G. Cramer [7] have resurrected the time symmetric Feynman-Wheeler absorber theory. So have done too Hoyle and Narlikar but within the context of a Steady State or Quasi Steady State cosmology [8]. Hence they support the possibility of action at a distance. However most authors still consider action at a distance to be incompatible with special Relativity [4], [5]. Consequently, for the sake of quantum physics and special relativity compatibility, the quantum collapse has to be interpreted as a shear change in the knowledge of the observer accordingly to the Copenhagen interpretation.
Now, let us consider the Aristotle space-time E1xE3, the set theoretic product of a one dimensional and a three dimensional Euclidean space. According to dynamical groups theory [6], E1xE3, is isomorphic to SE(1)xSE(3)/SO(3) and is a 4D affine space-time endowed with a rank 1 Euclidean time metric and a rank 3 Euclidean spatial metric. E1xE3 is foliated into 3D absolute simultaneity Euclidean folds and 1D Euclidean fix points which are the characteristic foliations of these two metrics. SE(1)xSE(3), the Aristotle group, is the restricted isometry group of Aristotle space-time. SE(1)xSE(3) encompasses the space-time translations and the spatial rotations. This symmetry group is embedded in the restricted Poincaré group. Hence, Aristotle spacetime is compatible with relativistic dynamical systems because any dynamical phenomenon satisfying all of the Poincaré group symmetries necessarily satisfies Aristotle group’s ones too and because, thanks to appropriate definitions, the physical effects of a relativistic boost can be proved to be covariant with regard to Aristotle group actions.
Dislike Minkowski space-time, Aristotle space-time is compatible with dynamical phenomena that possibly violate the relativistic boost invariance as soon as such dynamical phenomena satisfy the other symmetries of the Poincaré group. Indeed, the Aristotle group SE(1)xSE(3) encompasses all of the restricted Poincaré group symmetries but the relativistic boost invariance one. Hence Aristotle space-time enables possible faster than light interaction propagation as soon as they satisfy the covariance with regard to space-time translations and spatial rotations, ie the symmetries which give rise to the Aristotle group SE(1)xSE(3).
Actually, such possible interactions conflict only with the hypothesis according to which all of the restricted Poincaré group symmetries were satisfied by any physical phenomenon without any exception. This hypothesis is required for a Minkowski model of our space-time to be relevant (at least locally if gravity were accounted for). Aristotle space-time is somehow more tolerant than Minkowski space-time with regard to the required symmetries of phenomena which it authorizes to occur. Indeed, relativistic boost invariance is not anymore required. Within Aristotle absolute space-time framework, the relativistic interpretation of faster than c light propagation in Casimir effect experiment or of particles when passing through a quantum barrier thanks to quantum tunnelling effect [9] is not any more disputable.
Within Aristotle space-time framework, the relativistic boost invariance has to be interpreted as an intrinsic property of the phenomena which actually satisfy this symmetry, not as a very property of space-time itself applying to any phenomenon. Hence, Relativistic objections to the realistic interpretation of quantum waves and quantum collapses as well as to Alain Aspect experiment interpretation as an action at a distance disappear. Indeed, such objections rely on a conflict of this interpretation with the hypothesis of the relativistic boost-invariance. This requirement doesn’t apply within Aristotle space-time anymore.
The interpretation of Minkowski space-time as being a model of our space-time itself (even locally) is an efficient but compelling hypothesis. It is equivalent to assume any physical phenomenon to satisfy the relativist invariance. The interpretation of relativist symmetries as being intrinsic properties of physical phenomena which satisfy them instead of being very properties of our space-time enlarges the validity domain of Special Relativity up to possible phenomena violating the relativist invariance and authorizes without mathematical incoherences,
to interpret quantum non locality exhibitions as interactions propagating faster than light,
to interpret the quantum diffusion process as a very short violation of the relativist invariance between an intitial and a final stage satisfying this invariance.
to interpret the relativist invariance as a physical property modelling an equilibrium state of thermodynamical origin at an observation scale where the macroscopic observer isn't up to observe fluctuations around this equilibrium state (assumption similar to the local equilibrium hypothesis used to model thermodynamically irreversible processes)
[1] A. Einstein, B. Podolsky and N.Rosen, Phys. Rev. 1935. V.47. P.777.
[2] 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
[3] J.S. Bell, Physics, 1, 195 (1964); et"Speakable and Unspeakable"
in Quantum Mechanics. Cambridge Univ. Press, (1987)
[4] 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-ph/pdf/9801/9801014.pdf
[5] 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/physics/Relativity/SpeedOfLight/FTL.html
[6] J-M Souriau, Structure of dynamical Systems, Progress in mathematics, Birkhäuser.
[7] The Arrow of Electromagnetic Time and Generalized Absorber Theory
J. G. Cramer, Dept. of Physics FM--15, Univ. of Washington, Seattle, WA 98195, USA
http://www.npl.washington.edu/npl/int_rep/dtime/dtime.html
[8] INSTANTANEOUS ACTION AT A DISTANCE IN A HOLISTIC UNIVERSE
B.G. Sidharth, Centre for Applicable Mathematics & Computer Sciences
B.M. Birla Science Centre, Hyderabad 500 063 (India)
http://arxiv.org/abs/gr-qc/9812003
[9] Quantum Nonlocality in Two-Photon Experiments at Berkeley
Authors: Raymond Y. Chiao, Paul G. Kwiat, Aephraim M. Steinberg
http://xxx.lanl.gov/abs/quant-ph/9501016