2004/04/24 by Fatimah Shojai, Shojai, Fatimah, Ali Shojai +1 · 2 citations
Physics and Astronomy · #Astrophysics (astro-ph) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Relativity and Gravitational Theory #astro-ph #gr-qc #quant-ph
paper · pdf · doi:10.48550/arxiv.gr-qc/0404102
88 Pages, 6 figures. To appear in Progress in Quantum Physics Research, Nova Science Publishers, Inc., 2004
arxiv created 2004/04/24 · openalex publication_date 2004/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Understanding quantum theory in terms of a geometric picture sounds great. There are different approaches to this idea. Here we shall present a geometric picture of quantum theory using the de-Broglie--Bohm causal interpretation of quantum mechanics. We shall show that it is possible to understand the key character of de-Broglie--Bohm theory, the quantum potential, as the conformal degree of freedom of the space--time metric. In this way, gravity should give the causal structure of the space--time, while quantum phenomena determines the scale. Some toy models in terms of tensor and scalar--tensor theories will be presented. Then a few essential physical aspects of the idea including the effect on the black holes, the initial Big--Bang singularity and non locality are investigated. We shall formulate a quantum equivalence principle according to which gravitational effects can be removed by going to a freely falling frame while quantum effects can be eliminated by choosing an appropriate scale. And we shall see that the best framework for both quantum and gravity is Weyl geometry. Then we shall show how one can get the de-Broglie--Bohm quantum theory out of a Weyl covariant theory. Extension to the case of many particle systems and spinning particles is discussed at the end.