VERY HIGH ENERGY PHENOMENA IN THE UNIVERSE 2014 A duality between the emission of micro- gravitational waves and Quantum Mechanics Vo Van Thuan Vietnam Atomic Energy Institute (VINATOM) and The Office of the State NEPIO for NPP & Quy Nhon, August 3rd - 9th, 2014.

Contents  Introduction  Symmetry with time-like extra-dimensions  Geodesic deviation for gravitational wave  Quantum equations and indeterminism  Continuity equation  Conclusions

1- Introduction (1)  A fundamental problem of physics is the consistency of quantum mechanics with general relativity.  Standard models of elementary particles (SM) based on the special relativity with flat space-time often ignores gravitational interaction.  Kaluza and Klein [1,2] were first to propose an extra-dimension (ED) with an additional space-like axis which is compacted on a cylinder and is almost hidden from observation.  In a relation to ED theories, the semi-classical approach to quantum mechanics is the fundamental concept of hidden variables introduced by de Broglie and Bohm [3,4].  Experimental evidence for violation of Bell inequalities [5,6] abandoned local hidden variable models, however, still leaving the door open to non-local hidden variables.  Most of ED models applied space-like extra-dimensions, while few models considered time-like EDs.  Our study follows the induced-matter models with time-like EDs.

1- Introduction (2) Examples of models applying time-like EDs:  Randall’s membrane models [7]  Induced matter models [8,9,10], in particular: - Wesson [8] proposed a space-time-matter model describing proper mass as a time-like extra-dimension. - A geometrical dynamic model for elementary particles proposed by Koch [10] with a time-like dimension which offered a method for derivation of relativistic Klein-Gordon equations in 4D-curved space-time from higher dimensional Einstein gravitational equations. - In our previous study of space-time symmetry [11] following the induced- matter approach a simplified geometrical dynamics was proposed for derivation of quantum mechanics equations.  In the present study we prove that the relativistic quantum wave equations in 4D-space-time can be identical to a general relativity’s geodesic description of curved ED time-space.  The work is done at a conceptual stage, not yet at a quantitative level.

2- Symmetry with time-like extra-dimensions (1)

2- Symmetry with time-like extra-dimensions (2)

2- Symmetry with time-like extra-dimensions (3)

2- Symmetry with time-like extra-dimensions (4)

2- Symmetry with time-like extra-dimensions (5)

2- Symmetry with time-like extra-dimensions (6)

2- Symmetry with time-like extra-dimensions (7)

3- Geodesic deviation for gravitational wave (1)

3- Geodesic deviation for gravitational wave (2)

3- Geodesic deviation for gravitational wave (3)

3- Geodesic deviation for gravitational wave (4)

3- Geodesic deviation for gravitational wave (5)

3- Geodesic deviation for gravitational wave (6)

3- Geodesic deviation for gravitational wave (7)

3- Geodesic deviation for gravitational wave (8)

3- Geodesic deviation for gravitational wave (9)

3- Geodesic deviation for gravitational wave (10)

4- Quantum equations and indeterminism (1)

4- Quantum equations and indeterminism (2)

4- Quantum equations and indeterminism (3)

4- Quantum equations and indeterminism (4)

4- Quantum equations and indeterminism (5)

5- Continuity equation (1)

5- Continuity equation (2)

5- Continuity equation (3)

5- Continuity equation (4)

5- Continuity equation (5) Equation (42) describes “classical motion” of the matter current of an individual electron and it seems able to describe the micro evolution of electron material point along a classical geodesic in an extended time-space. However, the reality is more complicated: Indeed, the measuring equipment cannot be in a stationary state, because the micro-structure of the sensors (detectors) evolves in a complex non-local 3D-time and should deform violently the time-space structure of micro-particle during a measurement.  As a result, an individual measurement has (almost) no way to extract physical information from an individual object. Measurements made on an ensemble (collective) of identical particles can obtain only statistically averaged values of the physical parameters, leading to a probabilistic interpretation.  It is in consistency with conventional quantum mechanics.

6- Conclusions (1)

6- Conclusions (2)

6- Conclusions (3)

References 1.T. Kaluza, Sitz. Preuss. Akad. Wiss. 33(1921) O. Klein, Z. f. Physik 37(1926) L. de Broglie, J. Phys. et Radium 8(1927) D. Bohm, Phys.Rev.85(1952)166, J.S. Bell, Physics 1(1964) S.J. Freedman and J.F. Clauser, Phys.Rev.Lett. 28(1972) L. Randall and R. Sundrum, Phys.Rev.Lett. 83(1999) P.S. Wesson, Phys. Lett. B276(1992) S.S. Seahra, P.S. Wesson, Gen.Rel.Grav. 33(2001) B. Koch, arXiv: v1[quant-ph], 2008; 11. B. Koch, arXiv: v2[quant-ph], Vo Van Thuan, IJMPA 24(2009) V. Fock, Z. f. Physik 39(1926) Ya.B. Zeldovich, Usp.Fiz.Nauk 95(1968) E. Schrödinger, Sitzungsb. Preuss. Akad. Wiss. Phys.-Math. Kl. 24(1930) W.Pauli, Rev.Mod.Phys. 13(1941)203.

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