DETERMINISTIC FOUNDATIONS OF QUANTUM MECHANICS
Volodymyr Krasnoholovets,
Department of Theoretical Physics, Institute of Physics,
National Academy of Sciences, Prospect Nauky 46, UA-03028 Kyiv, Ukraine
(web page http://www.inerton.kiev.ua)
STATEMENT OF THE PROBLEM
Orthodox quantum mechanics represents a remarkable physical theory that allows the calculation
of main characteristics of the system studied in its stationary states. The characteristics are the system's
energy, momentum, moment of momentum, and position. All the calculations are based on the
employing the Schroedinger or Dirac probabilistic formalisms in which the wave
y-function or spinor are fundamental.
The wave function and the spinor are mathematical functions, which specifically include a phase that
in turn contains links between the said characteristics (and it is also implied that the phase involves
information on wave characteristics of the particle under consideration, i.e. some frequency
n and wavelength
l). It is believed that the absolute value of
the wave function |y| depicts the probability
amplitude that along with the phase f
completely describe the quantum system studied.
Notwithstanding the practical success of quantum mechanics,
researchers are interested in the reasons of such unusual behaviour of particles, which is very
distinguished from that of classical particles. Such studies fall within the subject --
the foundations of quantum mechanics. We can distinguish several major directions, which
concern the foundations. First of all this is the investigation of mathematical problems of interpretation
of quantum mechanical laws. Then we should mention problems, associated with so-called hidden
variables, though quantum mechanical vectors of states can be in accord only with the statistical
distribution of these variables but not with their definite values. Besides, there are problems, which
have been revealed in the course of recent studies associated with the phenomenon of entanglement
states; these ones touch a possibility for nonlocality of quantum theory. Nonetheless, all these approaches
are based on indeterminism, a very important starting point of all the contemporary quantum theories.
Pioneers of determinism, de Broglie and Bohm, still believed that some hidden variables would clarify
peculiarities of the quantum mechanical behaviour of particles. In particular, de Broglie was searching
for the interpretation of quantum mechanics by the double solution theory, when in addition to the standard
solution new equations would give the other solution that should disclose the inner reasons of the particle
behaviour. It is interesting to note that in de Broglie's approach [1] a subquantum medium is presented
and it has to intervene in the particle behaviour. What kind of a medium? De Broglie had never examined
this issue, but he mentioned about it in passing saying that it would be an aether. Once Dirac [2] also
mentioned about the necessary of an aether, but his arguments were not caught up by the others until
the end of 1990s, when Rothwarf [3] dug his work up. Then Winterberg [4] has developed a detailed
theory of the Planck aether, which allowed him to derived quantum mechanics starting from Boltzmann's
kinetic equation; however, Winterberg's approach is statistical.
NEW LINE OF RESEARCH
A new line of research is needed to integrate an aether and determinism.
Why an aether, or a substrate? Because a specialist in condensed matter physics cannot
see particles that move and interact in an absolute emptiness, i.e. vacuum.
Note that in the case of condensed matter, particles move in a lattice of atoms/molecules.
The lattice can be ordered or disordered, but it always exists! Besides, we should not forget
that the notion of aether came to us from the ancient manuscripts and we could pay consideration
to the knowledge base of the ancients (for instance, in the Bhagavad-gita written down about 3,000
years ago one can read [Ch.8, Verse 20]: "There is another eternal unmanifest state higher
than manifested Nature, which does not perish when all being perish").
Why determinism? Because in condensed matter physics researchers first try to solve problems,
for instance, associated with the motion of particles, without using any mathematical means.
Especially it takes place when one employs the approximation of so-called strong connection of a
particle with the crystal lattice. In this case a particle is treated as a material point that does not possess
any wave properties. Moreover, in higher energy physics particles do not demonstrate wave properties
as well; they seem material points. Thus, wave properties of particles, which appear at low and intermediate
energies, can indeed be associated with an intervention of a subquantum medium (or an aether, or space)
that imposes the wave behaviour on moving particles.
We also must keep in mind conceptual difficulties of orthodox quantum mechanics. Among them we
have to name the following: the notion "wave-particle"; the pure probabilistic (i.e. abstract) interpretation
of the Schroedinger wave y-function (in contrast, the
diffraction experiments measuring the wave properties of matter say that the wave
y-function is filled with a physical sense); long-range
action; Heisenberg's uncertainty principle; Lorentz non-invariance of the Schroedinger equation, etc.
Following Louis de Broglie, it is worth noting that the probabilistic formalism is developed in the phase
space, but not in the real one. And that is why we can anticipate that elimination of the difficulties is
likely if we are able to develop quantum mechanics in the real space. In particular, classical mechanics
is constructed in the real space (i.e. in a 3D space or 4D space-time) where particles -- material points --
are endowed with such measurable characteristics as the position, velocity, momentum, and kinetic energy.
A classical wave is specified by measurable properties as well, namely, the wavelength and frequency.
Hence if we consider a particle that moves in a special substrate and take
into account the interaction of the particle with the substrate, we indeed can arrive at a mechanics that
will include deterministic links between characteristics of the particle and the substrate. In 1924 de Broglie,
when wrote his remarkable relationships
E=hn
and
l=h/p
(1)
for a particle, assumed that some real wave was connected with the moving particle and that the
wave guided the particle. In expressions (1) parameters E and p
(the energy and the momentum) belonged to the particle, but the frequency
n and the wavelength l
were characteristics of a wave that should accompany
the particle at its motion in the real space. Note that relationships (1) enable the simple derivation of the
Schroedinger equation [5]. Regretfully, de Broglie's transparent idea on a moving particle accompanied
by an actual wave did not receive any further development.
However, let us try to start just from de Broglie's idea and relationships (1). In addition we can construct
the real space as a substrate that shares discrete and continual properties and a particle can be treated as
a local deformation of the space. Thus, it turns out that matter is not distinguished from the space in principle
(and this is a widening the scope of conventional quantum mechanical laws), though this assertion becomes
in contrast to the main idea of the relativity (in which matter is determined independently from the space that
is treated as emptiness).
Having developed a mechanics of a moving particle, we shall restrict our consideration to the manifestation
of relationships (1), i.e. we shall assume that the moving particle emits excitations (or waves) colliding with
the space and then the particle absorbs excitations (waves) again. As it has been found (see, e.g. review
papers [6]) the process of emission and absorption of these excitations occurs on each section
l, i.e. de Broglie wavelength, along the whole particle
path. A cloud of excitations that accompanies the moving particle is characterised by amplitude
L=lc/u where u
and c are velocities of the particle and excitations. The latest was called "inertons" because they
represent inert properties of the particle. In such a manner, quantum mechanics developed appears as
the kinetics of a particle -- the parameters l and
L can be treated as the free path lengths for the particle
and its inerton cloud respectively. In the mechanics, relationships (1) appear as fundamental and this allows
the transition to the Schroedinger [7,8] and Dirac formalisms [9], with the satisfaction of all formulas of special
relativity.
Since the mechanics constructed takes into account subtle aspects of the constitution of the real space and
the particle behaviour, it has been called submicroscopic quantum mechanics. This mechanics operates
with inertons, which are carries of inert properties of particles. Forces of inertia do not appear in Newton's
classical mechanics as Newton's mechanics deals only with material points which do not feature any inner
structure. However, the forces including the axifugal force quite real and everyone has often undergone
them (for instance, when one goes in a bus driven by an unskilled driver). In the recent study on inertia in
classical mechanics by the Varenyks [10] the inertia forces appear as proper forces of bodies which are
considered as not rigid material points but objects that consist of a great number of material points linked
elastically. Such an approach extends the range of classical mechanics and makes it possible to draw inertia
even in inertial reference frames. In particular, the Varenyks note that the force of inertia cannot do without
special carriers that should be considered as carriers of the fundamental mechanical interaction. From the
author's viewpoint the role of such kind of carriers should play inertons, which appear already on the
submicroscopic scale, ~ 10-28 cm, and spread down to the scale limited by the range of
the universe, ~ 1028 cm (note that size 10-28 cm is determined in high
energy physics as the range at which all fundamental physical interactions come together).
In our experimental studies we in fact could fix the influence of inertons
generated by both quantum systems [11,12] and a macroscopic system, namely, the Earth [13].
The force of inertia, or quantum mechanical force, whose carriers are inertons, makes itself evident also
in the macroscopic range. A simple device that measures the inerton radiation of the Earth has just been
elaborated by my colleagues and myself in our Institute.
THE PROSPECTS FOR NEW STUDIES
Here we have considered the quantum mechanical behaviour of particles moving in the real space.
However, we have not yet addressed details of the constitution of the space as well as the issue of
oscillating motion of inertons. That is, why inertons emitted from a particle then come back to it again.
These problems are beyond the subject of quantum mechanics, although they are very important for
the understanding the foundations of physics.
In our recent work [14] we have presented the introductory foundations supporting a new theory of space.
Some necessary and sufficient conditions allowing a previously unknown space to be explored through
scanning operators are re-examined with respect to measure theory. Topology, set theory, and fractal
geometry have been used to prove the necessity of the existence of the empty set, which allows the
topological spaces result in a "physical universe". The empty hyperset has ensured a formal structure
that enables the correlation with a degenerate cell (or ball, or superparticle) of space and supports
conditions for the existence of a universe.
In paper [15] the process of inerton emission is treated in detail. It has been shown that in addition
for such characteristics as the position, momentum, and kinetic energy inertons as quasi-particles
carry also local deformations from the particle to the tesselattice of the space. This means that the
gravitation phenomenon, i.e. the attraction, appears as a contraction of the space tesselattice between
material objects. This is the first interpretation of Newton's gravitational law 1/r that is based on
the detailed theory of the constitution of the real space and principles of motion of matter.
[1] L. de Broglie, Ann. de la Fond. L. de Broglie 12 (1987) 399.
[2] P. A. M. Dirac, Nature 168 (1951) 906.
[3] A. Rothwarf, Phys. Essays 11 (1998) 444.
[4] F. Winterberg, An attempt for a finistic theory of elementary particles,
Verlag relativistischer Interpretationen - VRI, Karlsbad (2000).
[5] L. de Broglie, Heisenberg's uncertainty relations and the probabilistic
interpretation of wave mechanics (Mir, Moscow, 1986), p. 42 (Russian translation).
[6] V. Krasnoholovets, Spacetime & Substance 1 (2000) 172 (also quant-ph/0106106);
Int. J. Comput. Anticipat. Systems (2002), in press (also quant-ph/0103110).
[7] V. Krasnoholovets and D. Ivanovsky, Phys. Essays 6 (1993) 554
(also quant-ph/9910023).
[8] V. Krasnoholovets, Phys. Essays 10 (1997) 407 (also quant-ph/9903077).
[9] V. Krasnoholovets, Ind. J. Theor. Phys. 48 (2000) 97 (also quant-ph/0103110).
[10] P. A. Varenyk and Yu. P. Varenyk, Spacetime & Substance 3 (2002) in press.
[11] V. Krasnoholovets, Ind. J. Theor. Phys. 49 (2001) 1 (also quant-ph/9906091).
[12] V. Krasnoholovets, submitted (also cond-mat/ 0108417).
[13] V. Krasnoholovets and V. Byckov, Ind. J. Theor. Phys 48 (2000) 1 (also quant-ph/0007027);
see in web page http://inerton.cjb.net in Recent Events.
[14] V. Bounias and V. Krasnoholovets, submitted.
[15] V. Krasnoholovets, submitted.