# Unification of Quantum and Gravity by Non Classical Information Entropy Space

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Quantum Mechanics from Vector of Boltzmann Entropies

- Theories of type 1 are deterministic. Single events are completely described by their known initial values and deterministic laws (differential equations). Classical mechanics is obviously such a theory. We include this type of theory, where probability does not play any role, in our classification scheme because it provides a basis for the following two types of theories. Theories of type 2 have deterministic laws but the initial values are unknown. Therefore, no predictions on individual events are possible, despite the fact that deterministic laws describing individual events are valid. In order to verify a prediction of a type 2 theory a large number of identically prepared experiments must be performed. We have no problems to understand or to interpret such a theory because we know it is just our lack of knowledge which causes the uncertainty. An example is given by classical statistical mechanics. Of course, in order to construct a type 2 theory one needs a type 1 theory providing the deterministic laws.
- It is possible to go one step further in this direction increasing the relative importance of probabilityeven more. We may not only work with unknown initial values but with unknown laws as well. In the type 3 theories there are no deterministic laws describing individual events, only probabilities can be assigned. There is no need to mention initial values for particle trajectories any more (initial values for probabilistic dynamical variables are still required).”

_{1}, S

_{2},….,S

_{n}). Now we have:

## 3. From Vector of Boltzmann Entropies to Bohm’s Quantum Potential

## 4. Curved Space-Time Embedded in Phase Space with Fisher Metric as Fusion of Quantum with Gravity

_{μ}with the covariant derivative ∇

_{μ}and by changing the Lorentz metric with the curved metric g

_{μν}inside Equations (28) and (29), it is possible to combine the Bohm quantum theory of motion and gravity and to interpret the quantum potential as the conformal degree of freedom of the space–time metric. In this picture, the quantum Hamilton-Jacobi equation of motion for a particle (of spin 0) in a curved background is the following:

_{μν}to:

## 5. Conclusions

## Appendix A

#### A.1. Tensor, Covariant and Contravariant Derivatives and Morphogenetic System

#### A.2. Commutators in Morphogenetic System and Tensor Derivative

## Conflicts of Interest

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**MDPI and ACS Style**

Resconi, G.; Licata, I.; Fiscaletti, D.
Unification of Quantum and Gravity by Non Classical Information Entropy Space. *Entropy* **2013**, *15*, 3602-3619.
https://doi.org/10.3390/e15093602

**AMA Style**

Resconi G, Licata I, Fiscaletti D.
Unification of Quantum and Gravity by Non Classical Information Entropy Space. *Entropy*. 2013; 15(9):3602-3619.
https://doi.org/10.3390/e15093602

**Chicago/Turabian Style**

Resconi, Germano, Ignazio Licata, and Davide Fiscaletti.
2013. "Unification of Quantum and Gravity by Non Classical Information Entropy Space" *Entropy* 15, no. 9: 3602-3619.
https://doi.org/10.3390/e15093602