Diffusion Equations, Quantum Fields and Fundamental Interactions

The paper concerns an “ab initio” theoretical model based on the space-time quantum uncertainty and aimed to identify the conceptual root common to all four fundamental interactions known in nature. The essential information that identifies unambiguously each kind of interaction is inferred in a straightforward way via simple considerations involving the diffusion laws. The conceptual frame of the model is still that introduced in previous papers, where the basic statements of the relativity and wave mechanics have been contextually obtained as corollaries of the quantum uncertainty. Understanding the fundamental interactions of nature is certainly one among the most challenging topics of the modern physics; a unified theory able to account for the fundamental forces is a dream of the physicists since a long time [1, 2]. The science of the fundamental interactions progressed with the advancement of the physics of the elementary particles [3], whose properties could be tested by examining their way of interacting with other particles. The theoretical models bridging quantum and relativistic theories [4, 5] progressed along with the merging of the physics of the elementary particles and quantum fields [6] with that of the fundamental interactions. All this culminated with the formulation of the standard model [7] and with the superstring theory [8]. The way the particles interact involves significantly even the cosmology [9, 10]. The GU theories [11, 12] share some general concepts about the four fundamental interactions, their basic idea to model the force between quantum particles is in principle simple: to exchange appropriate elementary particles that transfer momentum and energy between the interacting partners. The vector bosons are acknowledged to mediate the forces between particles according to their characteristic features of lifetime and action range [13]. These messenger particles, quanta of the respective fields, are said to mediate the interaction that propagates with finite velocity and perturbs the space-time properties. This way of thinking suggests reasonably the key role of the displacement mechanism of the particles that propagate the interaction, e.g. the different transport rates of massive or massless messengers; this means, in particular, that the space in between a set of interacting particles is filled with the vector bosons mutually exchanged. As clouds of these latter flow throughout the spacetime, it is reasonable to expect that the global properties of the resulting interaction should depend on the ability of the messengers to spread around the respective partners. Eventually, since the mutual positions of each particle in the set are in general functions of time, even random local density gradients of these messengers are expectedly allowed to form throughout the space-time. These preliminary considerations feed the idea of implementing a model of fundamental interactions based on a appropriate mechanism of transport of matter/ energy, sufficiently general to be suitably extended from sub-nuclear to infinite range interactions. Among the possible transport mechanisms deserves attention the particle diffusion, driven by a gradient law originated by a non-equilibrium situation; as it has been shown in a previous paper [14], this law is strictly connected with the global entropy increase of an isolated thermodynamic system, the diffusion medium plus the diffusing species both tending to the equilibrium configuration in the state of maximum disorder. So the driving force of the diffusion process is actually the second principle of thermodynamics, i.e. a law so general to hold at the nano-micro-macro scales of interest in the present context. As a matter of fact, it has been found that this law allows describing not only the concentration gradient driven mass transport but also other important laws of physics: for instance Ohm’s electric conductivity or Fourier’s heat conductivity or Poiseuille pressure laws [14]. So, in agreement with the quantum character of the approach therein introduced, appears stimulating in principle the idea of testing via the diffusion laws even the exchange of vector bosons to describe the fundamental interactions. This hint leads in a natural way to the idea of dynamical flux of messenger particles, by consequence of which are exchanged momentum and energy of the interacting partners. This assumption merely requires that the messengers of the forces are exchanged as clusters of particles randomly flowing through the space-time and thus characterized in general by local concentration gradients. The physics of the four fundamental interactions has been already concerned in a dedicated paper [15]; in that paper the interactions have been described starting directly from the concept of space-time uncertainty. Here this problem is reformulated via the diffusion laws only in a surprisingly simple way. This paper aims to show that the key features of the fundamental forces are obtained by elaborating purposely the diffusion laws; it will be emphasized that these laws provide interesting hints also for relativistic and thermodynamic considerations. Of course the purpose of the paper is not that of providing an exhaustive description of the fundamental interactions, which would require a much longer review of the huge amount of literature