VERY HIGH ENERGY PHENOMENA IN THE UNIVERSE 2014
A duality between the emission of microgravitational waves and Quantum Mechanics
Vo Van Thuan
Vietnam Atomic Energy Institute (VINATOM)
and
The Office of the State NEPIO for NPP
thuanvova@gmail.com & thuanvv@moit.gov.vn
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 inducedmatter 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
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16.
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