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Paper IPM / Physic / 7319  


Abstract:  
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 deBroglieBohm causal interpretation of quantum mechanics. We shall show that it is possible to understand the key character of deBroglieBohm theory, the quantum potential, as the conformal degree of freedom of the spacetime metric. In this way, gravity should give the causal structure of the spacetime, while quantum phenomena determines the scale. Some toy models in terms of tensor and scalartensor theories will be presented. Then a few essential physical aspects of the idea including the effect on the black holes, the initial BigBang 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 deBroglieBohm quantum theory out of a Weyl covariant theory. Extension to the case of many particle systems is discussed at the end.
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