It is doubtless that the
true space-time model is necessary for a correct description of physical
phenomena. One needs to choose a true geometry from the list of possible
space-time geometries. If the list of possible geometries is incomplete, one is
doomed to use of a false space-time geometry. Fortunately, in this case
one can introduce additional suppositions, compensating negative features
of the false space-time geometry. Using these additional hypotheses, one
can describe correctly several experimental date and observations. But
another experimental data appear not to be described in proper way, and one
needs to introduce another additional suppositions to explain new experimental
data and observations. In other words, it is impossible to introduce such
additional suppositions which would explain all experimental data.
Such a situation took
place many years ago, when the Ptolemaic conception of the celestial
mechanics used a false statement about nonrotating Earth. It was compensated by
the means of additional statements about epicycles and differentials and
provided quite impressive accuracy in predicting astronomical events. Such
conceptions, using incorrect suppositions and compensating them by additional
hypotheses, will be referred to as compensating, or Ptolemaic conceptions.
The author of this work
strongly believes that the contemporary theoretical physics has the same
problem arising from the usage of Minkowski space-time model which is incorrect
at small distances. The quantum mechanics with its strange axioms and
properties appears to be a compensating construction, which is necessary
to achieve agreement of theory with experimental data (and it does an excellent
job on that). But it is valid only for nonrelativistic quantum mechanics.
Construction of relativistic quantum theory (quantum field theory) needs
additional suppositions which sometimes are incompatible with principles of nonrelativistic
quantum mechanics. In other words, the quantum theory has typical features of a
Ptolemaic construction.
One could eliminate
additional suppositions and solve problems of the quantum phenomena
description, using a true space-time geometry. But to choose the true
space-time geometry, one needs to posses the list of all possible geometries. Then
one could choose from this list the most appropriate geometry. The list
of possible geometries is determined by the method of the geometry construction.
There are several methods (geometric conceptions) of constructing the proper
Euclidean geometry. They are presented in the table.
|
title of conception of
geometry |
non-numerical (verbal) information |
numerical information |
|
Euclidean CG |
Euclidean axioms |
empty set |
|
Riemannian CG |
continuity, manifold, coordinate system |
dimension n, metric tensor g_ik |
|
topological-metric CG |
topology, curve |
nonnegative metric S(x,x') and constraints on metric |
|
pure metric CG |
empty set |
real world function G(x,x')=S(x,x')S(x,x')/2 |
Any geometric conception
contains non-numerical information and numerical one. At some values of
numerical information all geometric conceptions generate (CG) the proper
Euclidean geometry. Varying the numerical information, one obtains another
geometries, associated with the given CG. The more numerical information is
contained in the geometric conception, the more powerful class of geometries,
generated by this CG. The most powerful class of geometries is generated by the
pure metric CG, because it contains only numerical information. The
Euclidean CG does not generate other geometries, because it does not contain
numerical information. The Riemannian CG, used usually for construction of the
space-time geometry, hold intermediate place between the Euclidean CG and pure
metric CG.
The Riemannian CG generates
only one uniform isotropic flat geometry. This is the Minkowski
geometry, which can be described completely by the world function G_M. The pure metric CG generates a class
L of uniform isotropic flat
geometries, labelled by a function D(G_M). The Minkowski geometry belongs to
this class (if D(G_M)=0). The list of geometries, generated by the pure metric CG is the most
complete one. It is this list L that is to be used for choosing an appropriate space-time geometry.
Motion of a free particle
in any space-time geometry except for Minkowski geometry is stochastic. Real
microparticles are stochastic, and it is not reasonable to choose the Minkowski
geometry as a space-time geometry, where free motion of particles is
deterministic. But what geometry of the class L should be chosen. There is a lot of them. The answer is as follows. One should
choose such a space-time geometry, so that the statistical description of
the stochastic particle motion coincides with experimental data. As far as all
experimental data on nonrelativistic motion of microparticles are described by
quantum mechanics very well, it is sufficient to choose the space-time geometry
in such a way that the statistical description of the stochastic particle
motion would coincide with the quantum mechanical description. This constraint
determines the distortion function D(G_M) in the form D(G_M)=d=h/(2bc)
for G_M>G_0, where h is the quantum constant, c is the speed of the light, and b is a new universal constant. Then
the world function
G=G_M+D(G_M)
depends on the quantum
constant, and quantum constant becomes to be an attribute of the space-time
geometry. Using this space-time geometry, one does not need additional
(Ptolemaic) suppositions, know as principles of quantum mechanics.
Quantum principles and
quantum axiomatics are considered in this work as secondary physical laws generated
by a statistical description of the stochastic behavior of particles. In this
description the stochastic world lines of particles are conditioned by the
space-time properties. This approach reminds the interplay between the
thermodynamics and the statistical physics, where thermodynamical principles
appear to be generated by the statistical description of the random molecular
motion. Such an approach to quantum mechanics is substantiated in the presented
papers.
For more formal statement of the problem click here
.