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Ali Shojai

Publications and source records attributed to Ali Shojai.

36 records · Page 2Linked to original sources
arXiv2004

Understanding Quantum Theory in Terms of Geometry

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.

gr-qc↗
arXiv2003

Constraints Algebra and Equations of Motion in Bohmian Interpretation of Quantum Gravity

It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general coordinate transformations to the spatial and temporal diffeomorphisms. The quantum Einstein's equations are derived and it is shown that they are manifestly covariant under the above diffeomorphisms, as it would be.

gr-qc↗
arXiv2003

On The Relation of Weyl Geometry and Bohmian Quantum Mechanics

It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is built, and it is shown that both gravity and quantum are present at the level of equations of motion.

gr-qc↗
arXiv2003

Bohmian Quantum Gravity in the Linear Field Approximation

In this paper we have applied Bohmian quantum theory to the linear field approximation of gravity and present a self--consistent quantum gravity theory in the linear field approximation. The theory is then applied to some specific problems, the Newtonian limit, and the static spherically symmetric solution. Some observable effects of the theory are investigated.

gr-qc↗
arXiv2002

Quantum Effects and Cluster Formation

The causal interpretation of quantum mechanics is applied to the universe as a whole and the problem of cluster formation is studied in this framework. It is shown that the quantum effects be the source of the cluster formation.

astro-ph↗
arXiv2001

Quantum Einstein's Equations and Constraints Algebra

In this paper we shall address this problem: Is quantum gravity constraints algebra closed and what are the quantum Einstein equations. We shall investigate this problem in the de-Broglie--Bohm quantum theory framework. It is shown that the constraint algebra is weakly closed and the quantum Einstein's equations are derived.

gr-qc↗
arXiv2001

About Some Problems Raised by the Relativistic Form of De-Broglie--Bohm Theory of Pilot Wave

The standard relativistic de-Broglie--Bohm theory has the problems of tacyonic solutions and the incorrect non-relativistic limit. In this paper we obtain a relativistic theory, not decomposing the relativistic wave equations but looking for a generalization of non-relativistic Bohmian theory in such a way that the correct non-relativistic limit emerges. In this way we are able to construct a relativistic de-Broglie--Bohm theory both for a single particle and for a many-particle system. At the end, the theory is extended to the curved space-time and the connection with quantum gravity is discussed.

quant-ph↗
arXiv2001

Pure Quantum Solutions of Bohmian Quantum Gravity

In this paper we have investigated the pure quantum solutions of Bohmian quantum gravity. By pure quantum solution we mean a solution in which the quantum potential cannot be ignored with respect to the classical potential, especially in Bohmian quantum gravity we are interested in the case where these two potentials are equal in their magnitude and in fact their sum is zero. Such a solutions are obtained both using the perturbation and using the linear field approximation.

gr-qc↗
arXiv2000

Quantum, Gravity, and Geometry

Recently, it is shown that, the quantum effects of matter are well described by the conformal degree of freedom of the space-time metric. On the other hand, it is a wellknown fact that according to Einstein's gravity theory, gravity and geometry are interconnected. In the new quantum gravity theory, matter quantum effects completely determine the conformal degree of freedom of the space-time metric, while the causal structure of the space-time is determined by the gravitational effects of the matter, as well as the quantum effects through back reaction effects. This idea, previousely, is realized in the framework of scalar-tensor theories. In this work, it is shown that quantum gravity theory can also be realized as a purely metric theory. Such a theory is developed, its consequences and its properties are investigated. The theory is applied, then, to black holes and the radiation-dominated universe. It is shown that the initial singularity can be avoided.

gr-qc↗
arXiv2000

Nonminimal Scalar-Tensor Theories and Quantum Gravity

Recentely, it is shown that the quantum effects of matter determine the conformal degree of freedom of the space-time metric. This was done in the framework of a scalar-tensor theory with one scalar field. A point with that theory is that the form of quantum potential is preassumed. Here we present a scalar-tensor theory with two scalar fields, and no assumption on the form of quantum potential. It is shown that using the equations of motion one gets the correct form of quantum potential plus some corrections.

gr-qc↗
arXiv1999

Conformal Transformations and Quantum Gravity

Recently\cite{BQG}, it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space-time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e. changing the metric), or by making a conformal transformation (i.e. changing all physical quantities). These two ways are investigated and compared. Also, it is argued that, the ultimate formulation of such a quantum gravity theory should be in the framework of the scalar-tensor theories.

gr-qc↗
arXiv1999

Scalar-Tensor Theories and Quantum Gravity

Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space-time metric. So both gravity and quantum are geometrical features. Gravity determines the causal structure of the space-time, while quantum determines the scale of the space-time. In this article, it is shown that it is possible to use the scalar-tensor framework to build a unified theory in which both quantum and gravitational effects are present.

gr-qc↗
arXiv1999

Nonlocal Effects in Quantum Gravity

It is shown explicitly that in the framework of Bohmian quantum gravity, the equations of motion of the space-time metric are Einstein's equations plus some quantum corrections. It is observed that these corrections are not covariant. So that in the framework of Bohmian quantum gravity the general covariance principle breaks down at the individual level. This principle is restored at the statistical level.

gr-qc↗
arXiv1996

Direct particle interaction as the origin of the quantal behaviours

It is argued that the quantal behaviours may be understood in the framework of direct particle interactions. A specific example is introduced. The assumed potential predicts that at sufficiently large distances quantal behaviours arise, while at very large distances gravitational-like forces are present. The latter is true provided all particles have internal structures.

quant-ph↗
arXiv1996

Some Observable Results of the Retarded Bohm's Theory

It is shown that the retarded Bohm's theory has at least four novel properties. (1) The center of mass of an isolated two-body system is accelerated. (2) Hydrogen-like atoms are unstable. (3) The distribution function differs from the standard one. (4) The definition of energy needs some care.

quant-ph↗
arXiv1996

On the position operator for massless particles

It is always stated that the position operator for massless particles has non-comutting components. It is shown that the reason is that the commutation relations between coordinates and momenta differs for massive and massless particles. The correct one for massless particles and a position operator with commuting components are derived.

quant-ph↗
arXiv1996

On the Relativistic Quantum Force

In the extension of the de-Broglie-Bohm causal quantum theory of motion to the relativistic particles, one faces with serious problems, like the problem of superluminal motion. This forces many authors to believe that there is not any satisfactory causal theory for particles of integer spin. In this paper, it is shown that the quantal behaviour is the result of direct-particle-interaction of the particle with all of its possibilities. The formulation is, then, extended to the relativistic particles of arbitrary spin. The presented theory has the following advantages. (1) It leads to a deeper understanding of the quantal behaviour. (2) It has no superluminal motion. (3) It is applicable to any spin. (4) It provides a framework for understanding the problem of creation and annihilation of particles. (5) It provides a framework for understanding the spin-statistics relationship. (6) It does not need the two fundamental assumptions of the de-Broglie-Bohm quantum theory of motion, i.e., the guiding-formula postulate and the statistical postulate.

quant-ph↗