The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is primordially deterministic, seems to be unsuitable. The statistical ensemble of stochastic (or deterministic) systems is considered to be the main object of dynamics. At such a logical reloading the statistical description becomes a component of dynamics, and capacities of dynamics increase. At such an approach one can describe deterministic, stochastic and quantum particles by means of the uniform technique. The quantum particle is described as a stochastic particle, i.e. without a reference to the quantum principles. Besides, by means of this technique one can describe classical inviscid fluid. There are four different versions of the formalism: (1) description in Euler dynamic variables, (2) description in Lagrange dynamic variables, (3) description in terms of the generalized stream function, (4) description in terms of the wave function. The uniform formalism is purely dynamic. Even describing stochastic systems, it does not refer to probability and probabilistic structures. In relativistic case the uniform formalism can describe pair production and pair annihilation.
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is primordially deterministic, seems to be unsuitable. The statistical ensemble of stochastic (or deterministic) systems is considered to be the main object of dynamics. At such a logical reloading the statistical description becomes a component of dynamics, and capacities of dynamics increase. At such an approach one can describe deterministic, stochastic and quantum particles by means of the uniform technique. The quantum particle is described as a stochastic particle, i.e. without a reference to the quantum principles. Besides, by means of this technique one can describe classical inviscid fluid. There are four different versions of the formalism: (1) description in Euler dynamic variables, (2) description in Lagrange dynamic variables, (3) description in terms of the generalized stream function, (4) description in terms of the wave function. The uniform formalism is purely dynamic. Even describing stochastic systems, it does not refer to probability and probabilistic structures. In relativistic case the uniform formalism can describe pair production and pair annihilation.
The formalism of dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is primordially deterministic, seems to be unsuitable. The statistical ensemble of stochastic (or deterministic) systems is considered to be the main object of dynamics. At such an approach one can describe deterministic, stochastic and quantum particles by means of the uniform technique. The quantum particle is described as a stochastic particle, i.e. without a reference to the quantum principles. Besides, by means of this technique one can describe classical inviscid fluid. There are four different versions of the formalism. One of versions uses equations, which describes evolution of the labelling (Lagrangian coordinates at fixed initial conditions for the density and the momentum density. These fixed initial conditions enter in the evolution equations. A nonuniqueness of irrotational flow and the mismatch between the velocity and the momentum density appear at this description. The mismatch is determined by the fluid vorticity and by some arbitrary parameter. Appearance of mismatch may be associated with the turbulence. The united formalism is purely dynamic. Even describing stochastic systems, it does not refer to probability and probabilistic structures.
In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special concepts, and this procedure cannot be repeated. In the model conception of quantum phenomena (MCQP) the quantum particle is a partial case of a stochastic particle, and the quantum dynamics is a special case of the stochastic particle dynamics. In MCQP the quantization is a dynamical procedure, where a special quantum term is added to the Lagrangian of the statistical ensemble of (classical) particles. This procedure can be repeated many times, because it is not accompanied by introduction of new concepts. It is very convenient from the formal viewpoint, because the set of dynamic quantizations forms a one-parameter group, which allows one to separate the dynamical and statistical (stochastic) properties.
In (1), the notion of a stochastic classical action is introduced and a probability is linked to exp( constant * action). The objective of (1) is not to derive quantum mechanics, but to derive stochastic dynamics based on maximum entropy in action space. We have argued in a number of previous notes (2) that one may use the classical action to create a quantum free particle probability. This classical action, however, is not chosen a priori, but rather arises due to other considerations. We suggest that stochasticity is present in Newtonian mechanics at some time scale because dt is finite in dp/dt= Force (Newton’s second law) and so postulate that force delivery at some x,t is probabilistic within some dt and dx. A priori, dt and dx are not known, but if there is stochasticity, there should be a free particle probability, i.e. a probability(x,t) where x,t represent an x, t interaction point. Furthermore, the notion of dx and dt should arise naturally. We note that the form exp(i function(x,t,p,E) may be introduced because free particles have no distributed variable (like energy in the Maxwell-Boltzmann case). exp(i function(x,t)) immediately introduces periodicity, but we have argued that stochasticity can only exist within tiny, fixed dx, dt linked to dp/dt=F. In particular, one classical Newtonian scales this stochasticity is not seen. The periodicity should be directly in x and t space, suggesting exp( i A1 t + i A2 x). This expression, however, should be Lorentz invariant, and A1 and A2 should be constants, at least for a fixed mo and v. The reason that the one must have periodicity is that the dx and dt ranges of stochasticity in dp/dt=Fr must appear naturally. At this point, one is led to exp(-iEt+ipx) with -Et+px being a Lorentz invariant which satisfies the above criteria. This Lorentz invariant happens to be the classical action in both the relativistic and nonrelativistic cases, hence giving rise to action as being a stochastic variable (of (1)) because it is a function of the two scholastic variables x and t. Alternatively, one may choose the exp(iA1x+iA2t) due to its conservation properties. One may then argue that A1 and A2 could also be conserved for x,t held constant, i.e. A1 and A2 could be linked to Newtonian energy and momentum in elastic collisions. This allows one to solve for the special relativistic g(v) =1/sqrt(1-vv/cc). Given the idea of a conserved quantity form for a probability, one may argue that exp(i Action) satisfies a maximization of Shannon’s entropy subject to a conserved constraint (which is again a link with (1).) The question then becomes: Why should the Lorentz invariant A= -Et+px be the classical action.One may note that x,t usually refer to trajectory values and so for a free particle, one has x=vt. This means that one may factor out t, i.e. A= t( -E+pv), but this is automatically the form of the Lagrangian with E being the Hamiltonian. This holds relativistically and non-relativistically with the form: dL/dv partial = p. The remaining question is: Why should the classical action be Lorentz invariant? We consider E(v)-p(v) v = -L such that dE/dv - v dp/dv -p = -dL/dv partial. This means that dE/dv - v dpd/v = 0 ((1)). A Lorentz transformation, however, changes mo in a rest frame into p=mov/sqrt(1-vv/cc) and E=mocc/sqrt(1-vv/cc). One may see that this solution may be obtained from ((1)) showing a direct link between the classical action approach and special relativity. The connection may be carried further as Lt = -Et+px is a Lorentz invariant, but also the classical action (in both the relativistic and nonrelativistic cases). We argue that the use of the action in (1) as a stochastic variable is directly related to special relativity. In summary, from finite dt in dp/dt=F, t and x are stochastic variables within some naturally appearing dx and dt. One may write a linear combination of x and t and to create a stochastic Lorent invariant variable which should appear in exp(i Lorentz invariant) and create the dx and dt units. It may then be shown that this Lorentz invariant in E,p,x,t should be equivalent to the classical action.
It is shown that the classical description of pair production effect is possible, i.e. one can describe pair production without a reference to quantum principles. Pair production appears at statistical description of stochastic relativistic particles. There is a special force field which is responsible for pair production. This field is a reasonable consequence of quantum stochasticity. Consideration of quantum systems as stochastic systems and statistical description of them generates hydrodynamic interpretation of quantum phenomena. In the collision problem the hydrodynamic interpretation appears to be alternative to the conventional interpretation, based on quantum principles and on consideration of the wave function as a principal object of dynamics. Hydrodynamic interpretation leads to such a statement of the collision problem, which is alternative to the conventional S-matrix theory.
The tachyon model of neutrino is constructed, basing on the statement that quantum description is a statistical description of stochastically moving particles. Besides, the tachyon model contains two conceptual points: (1) universal formalism of particle dynamics, describing uniformly all particles: deterministic, stochastic and quantum, (2) discrete space-time geometry and skeleton conception of particle dynamics. The universal formalism is a result of a logical reloading, when the statistical ensemble becomes to be the basic object of particle dynamics instead of a single particle. Such a reloading admits one to describe uniformly the quantum, stochastic and deterministic particles in terms of a statistical ensemble without a reference to principles of quantum mechanics. Besides, one uses a relativistic state of a particle, when the state is described by the particle skeleton (several space-time points) instead of the point in the phase space, what is nonrelativistic concept of the particle state. Representing the Dirac equation in terms of the statistical ensemble, one concludes that in the deterministic approximation the world line of the Dirac particle may be a spacelike helix with timelike axis. The rotational component of the relativistic Dirac particle is described nonrelativistically. It shows that the world line may be spacelike, and the Dirac particle may be a tachyon. Neutrino is a Dirac particle, and it is a tachyon.