# ON A GEOMETRICAL DESCRIPTION OF QUANTUM MECHANICS

@article{Novello2011ONAG, title={ON A GEOMETRICAL DESCRIPTION OF QUANTUM MECHANICS}, author={M. Novello and J. Salim and F. Falciano}, journal={International Journal of Geometric Methods in Modern Physics}, year={2011}, volume={08}, pages={87-98} }

We show that quantum mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular affine space, which we call Q-wis. This is proved using the Bohm–de Broglie causal formulation of quantum mechanics. In the Q-wis geometry, the length of extended objects changes from point to point. In this formulation, deformation of physical distances are in the core of quantum effects allowing a geometrical formulation of the uncertainty principle.

#### 19 Citations

Weyl Geometries, Fisher Information and Quantum Entropy in Quantum Mechanics

- Physics
- 2012

It is known that quantum mechanics can be interpreted as a non-Euclidean deformation of the space-time geometries by means Weyl geometries. We propose here a dynamical explanation of such approach by… Expand

Quantum mechanics as the dynamical geometry of trajectories

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- 2015

We illustrate how non-relativistic quantum mechanics may be recovered from a dynamical Weyl geometry on configuration space and an `ensemble' of trajectories (or `worlds'). The theory, which is free… Expand

On the Geometrization of Quantum Mechanics

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Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success… Expand

Unification of Quantum and Gravity by Non Classical Information Entropy Space

- Computer Science, Physics
- Entropy
- 2013

A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided and the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. Expand

Bell Length as Mutual Information in Quantum Interference

- Computer Science, Mathematics
- Axioms
- 2014

This work shows a relation among the probabilities of a quantum system in terms of information of non-local correlation by means of a new quantity, the Bell length. Expand

Bell Length as Non-Local Correlation Distance

- 2015

A quantum correlation between two qubits in a Bohmian framework is here investigated. From the analysis of the quantum correctors in entropy it is possible to derive a characteristic length of… Expand

A Short Survey on a “Strange” Potential

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- 2014

The David Bohm work on quantum mechanics starts from de Broglie pilot wave theory, which can be considered as the most significant hidden variables theory equivalent to quantum mechanics as for… Expand

Metric Relativity and the Dynamical Bridge: Highlights of Riemannian Geometry in Physics

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We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations.… Expand

Mean value of the quantum potential and uncertainty relations

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- 2020

In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the… Expand

On physical meaning of Weyl vector

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- 2010

The present paper considers if the new proposed conformal geometrodynamics (CGD) can extend the Nature features compared with general theory of relativity (GTR). The answer for this question can be… Expand

#### References

SHOWING 1-10 OF 33 REFERENCES

Geometric derivation of the Schrödinger equation from classical mechanics in curved Weyl spaces

- Physics
- 1984

A theory physically equivalent to traditional nonrelativistic quantum mechanics is presented, in which both dynamical and probabilistic concepts enter in a classical way. Particle trajectories are… Expand

"Relative State" Formulation of Quantum Mechanics

- Physics
- 1957

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as… Expand

Particle trajectories in relativistic quantum mechanics

- Physics
- 1985

Abstract The causal stochastic approach to the relativistic scalar Klein-Gordon equation is shown to preserve the time-like character of particle trajectories provided additional physical assumptions… Expand

The Interpretation of Quantum Mechanics

- Physics
- 1987

The interpretation of quantum mechanics has been controversial since the introduction of quantum theory in the 1920s. Although the Copenhagen interpretation is commonly accepted, its usual… Expand

Elimination of negative probabilities within the causal stochastic interpretation of quantum mechanics

- Physics
- 1984

Abstract Negative probabilities resulting from the Klein-Gordon equation are eliminated from quantum theory within the stochastic interpretation of quantum theory (SIQM) for spin-zero particles. The… Expand

A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II

- Physics
- 1952

In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of hidden variables developed in a… Expand

Quantum mechanics and reality

- Physics
- 1970

Despite its enormous practical success, quantum theory is so contrary to intuition that, even after 45 years, the experts themselves still do not all agree what to make of it. The area of… Expand

Geometry of dislocated de Broglie waves

- Physics
- 1987

The geometrical structures implicit in the de Broglie waves associated with a relativistic charged scalar quantum mechanical particle in an external field are analyzed by employing the ray concept of… Expand

Quantum measurement and geometry.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1990

The classical limit of the theory is established by proving that the most general form of the Weyl field which gives an extremum of the action is restricted to be of a special form, and gives a correct description of the electromagnetic interaction of a point particle. Expand

Interpreting the wave function of the universe

- Physics
- 1986

Abstract The Many-Worlds Interpretation of quantum mechanics is used to determine the meaning of the universal wave function of quantum cosmology. More precisely, the Many-Worlds Interpretation is… Expand