Abstract
A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy). Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity), the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement). In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum affects geometry of multidimensional phase space and gravity changes in any point the torsion in the ordinary four-dimensional Lorenz space-time metric.
Highlights
The advantage of a geometric representation of physical phenomena is the elegance, and and above all the immediate visualization of processes
In the first part of the article, we will consider the entropy of a quantum system as a vector of the superposition of many different entropies whose values are conditioned by the observer and will provide a new suggestive reading to Rovelli’s relational quantum mechanics
From Vector of Boltzmann Entropies to Bohm’s Quantum Potential In Section 2, we have shown that a non classical entropy space can lead to a new interesting reading of Rovelli’s relational quantum mechanics
Summary
The advantage of a geometric representation of physical phenomena is the elegance, and and above all the immediate visualization of processes. In the second part of the article, fixed the background of the rectangular coordinates of the entropy, we will show that the non linear relation of the average values of the phase space with the different observed entropy generates an information manifold of the phase space with Fisher metric. By the covariant derivatives in a general form represented by the Morphogenetic system illustrated in the mathematical appendix, the Bohm quantum potential by a minimum principle of the average action is obtained as Fisher metric or information metric in the phase space. In this approach, the Bohm quantum potential emerges as a consequence of the classical equilibrium condition in the quantum entropy space. All the quantum phenomena disappear when the vacuum curvature in phase space is zero, the Fisher metric is the Euclidean metric and the Weyl-like gauge potential that is function of all particles’ positions is zero
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