The Geometry of Quantum Potential

The following sections are included:

• Contents
• Introduction

The following sections are included:

• Bohm’s Original 1952 Approach on the Quantum Potential
• The Geometrodynamic Information of the Quantum Potential
  • Grössing’s thermodynamic approach to the quantum potential
  • Quantum potential as an information channel of a special superfluid vacuum
• About the Link Between Weyl Geometries and the Quantum Potential
  • Weyl’s conformal geometrodynamics
  • Santamato’s geometric interpretation of quantum mechanics
  • Novello’s, Salim’s and Falciano’s approach of quantum mechanics as a manifestation of the non-euclidean geometry
• The Quantum Potential in the Relativistic Domain
  • The quantum potential in Bohm’s approach to Klein-Gordon relativistic quantum mechanics
  • About a Bohmian approach to the Dirac relativistic quantum mechanics
• The Quantum Potential in Relativistic Quantum Field Theory
  • The quantum potential in bosonic quantum field theory
  • The quantum potential in fermionic quantum field theory
• The Quantum Potential in Bohmian Quantum Gravity
  • Bohm’s quantum potential in relativistic curved space-time
  • Bohm’s quantum potential in quantum gravity
• The Quantum Potential in Bohmian Quantum Cosmology
  • F. Shojai’s and A. Shojai’s geometrodynamic approach to Wheeler-de Witt equation
  • Pinto-Neto’s results about bohmian quantum cosmology
  • The quantum potential … and the cosmological constant
• About the Quantum Potential in the Treatment of Entangled Qubits

De Broglie-Bohm theory can receive a new interesting and suggestive reading which is based on the idea that all the features of the quantum potential derive from a fundamental physical quantity that can be appropriately called “quantum entropy”.

One of the most intriguing features of the geometry of space determined by quantum theory is certainly represented by the existence of non-local correlations between subatomic particles. In the quantum domain, the state of an object may be strongly correlated with the state of another object at a large distance from the first, such that no classical communication (involving signals which do not travel faster than light) between them is possible. As we have seen in chapter 1.1, in the de Broglie-Bohm approach, the nonlocal geometry of the quantum world is determined by the quantum potential. Bohm’s theory manages to make manifest quantum non-locality by means of the geometric properties of space described and expressed by the quantum potential. On the basis of Bohm’s and Hiley’s research, the ordinary space-time manifold cannot explain and reproduce the non-local correlations characterizing the geometry of the quantum world. In particular, Bohm’s and Hiley’s research suggest that the non-local geometry determined by the quantum potential can be reproduced in the context of a fundamental geometrodynamic background (the Bohmian implicate order, or also the analogous Hiley’s pre-space and notion of underlying process of quantum phenomena) which redesigns the behaviour of the particles.

The following sections are included:

• The Space-time Arena and the Quantum Vacuum
• Bohm’s Quantum Potential Approach as the Epistemological Foundation of the Quantum Vacuum
• From Bohm’s View to Kastner’s Possibilist Transactional Interpretation and Chiatti’s and Licata’s Approach about Transactions
• From Transactions … to a Three-dimensional Timeless Non-local Quantum Vacuum … to the Emergence of the Geometrodynamics of Standard Quantum Theory from the Non-local Quantum Vacuum
• About the Behaviour of Subatomic Particles in the Three-dimensional Timeless Non-local Quantum Vacuum
• Unifying Perspectives of the Non-local Quantum Potential of the Vacuum

The following sections are included:

• Conclusions
• References
• Index