Welcome to the Homepage of

Associate Professor of Physics Department of Chemistry and Physical Sciences Pace University Pleasantville, New York 10570 e-mail: mshirigarakani [at] pace [dot] edu Phone: (914)773-3430 Fax: (914)773-3418

Research Fellow Center for Philosophy and Natural Sciences CPNS

LINKS My CV(in pdf) Pace Univeristy My Official Webpage at Pace University Department of Physics at Harvard

EDUCATION Ph.D., 2004, Georgia Intitute of Technology Thesis: Finite Quantum Theory of the Harmonic Oscillator, Advisor: Prof. David Finkelstein M.S., 1997, University of Akron Thesis: Statistical Behavior of Light Rays in Curved Spacetime Manifolds, Advisor: Prof. Gregory Townsend B.S., 1993, Tehran Polytechnic Thesis: A Qualitative Analysis of the Dark Matter, Advisors: Prof. M.H Khajehpour, Prof. J.Pashaie-Rad   POSITIONS Assistant Professor of Physics, Director, Physics/Engineering Program, Department of Chemistry and Physical Sciences, Pace University, New York, 2005-now Research Fellow, Center for Philosophy and Natural Sciences, University of California, Sacramento 2008-now Assistant Editor, International Journal of Theoretical Physics, 2002-now. Visiting Fellow, Department of Physics, Harvard University, Cambridge, 2006-2007 Instructor of Physics, Department of Chemistry and Physics, Augusta State University, Georgia, 2004-2005   RECENT PUBLICATIONS David R. Finkelstein and Mohsen Shiri-Garakani, Finite Quantum Dynamics, accepetd, to appear in International Journal of Theoretical Physics (2011) Mohsen Shiri-Garakani and David R. Finkelstein and, Finite Quantum Kinematics of the Harmonic Oscillator, J. Math. Phys, 47, 032105 (2006), arXiv: quant-ph/0411203 David R. Finkelstein, M. Shiri-Garakani, Expanded Quantum Linear Harmonic Oscillator.  Proceedings of the 3rd International Symposium on Quantum Theory and Symmetries (QTS3), Cincinnati, Ohio, September (2003) J. Baugh, D. R. Finkelstein, A. Galiautdinov, and M. Shiri-Garakani, Transquantum Dynamics, Foundations of Physics, 33, 1267, (2003). arXiv: hep-th/0304031 (Under the title Ultraquantum Dynamics). James Baugh, David Ritz Finkelstein, Andrei Galiautdinov, Heinrich Saller and Mohsen Shiri, Transquantum Space-Time, Proceedings of the 5th International Symposium of Fundamental Physics, Birla Science Center, Hyderabad, January 2003. James Baugh, Andrei Galiautdinov, David Ritz Finkelstein, Mohsen Shiri-Garakani and Heinrich Saller and, Elementary operation, Based on a talk given at the 5th International Quantum Structure Association Conference, Cesena, Italy, 2001. To appear in the International Journal of Theoretical Physics. arXiv: quant-ph/0411213   RESEARCH INTERESTS Quantum Spacetime (Unified Quantum Theory of Gravity) Philosophy and History of Modern Physics Quantum Logic, Quantum Philosophy   TEACHING I teach a variety of courses in physics, and sometimes in mathematics and related fields, at different levels. These include introductory physics, astronomy, classical mechanics, electrodynamics, thermodynamics and statistical physics, mathematical physics, history and philosophy of physics, and basic geology.   CURRENT RESEARCH Quantum Spacetime-Unified Gravity I began my quest for a unified thoery in physics as early as when I was an undergraduate student of physics at Tehran Polytechnic. I initially focused more on cosmology but later my focus shifted toward quantum theory. I began to work on a very unique and philosophically rich approach to quantum gravity when I joined David Finkelstein's Quantum Relativity group at Georgia Tech in 1997 as a graduate student. The long-awaited quantum theory of gravity has turned out to be the most challenging problem in theoretical physics, with its roots back in the mid 20th century. This would be a unification of the Standard Model and General Relativity into a (finite) quantum theory. Our approach to this problem is quite different from the main stream String Theory and the less well-known Loop Quantum Gravity. In short, we follow two mottos: Simple is Beautiful (and survives) and History Repeats. In details, we are inspired by a 1952 paper by Irving Segal [1] and a 1953 paper by Inönü and Wigner [2]. Segal pointed out that the usual quantum theory could be a limiting (approximate) theory of yet a more accurate, more complete theory with a simple group (algebra). The usual quantum thoery is described by the Heisenberg algebra:   [p,q] = - iħ [q,i] = 0 [i,p]= 0 Clearly one recovers classical (Newtonian) mechanics by letting the Plank constant ħ go to zero. Segal's important observation was that one could similarly recover quantum theory from a theory with the following simple Lie algebra structure: [p,q] = - i ħ [q,i] = - p ħ' [i,p] = - q ħ'' (There is another choice of signature so that the group will be SO(2,1) but for our purposes SO(3) is more suitable. Ultimately, when we simplify the group of relativity, we will comlexify and work with unitary groups so the signature wont matter.) ħ' and ħ'' here are two extra "Plank constants" and are members of a family of parameters that we label regularization paramters [3]. The imaginary unit in now an operator with finite descrete spectrum. What makes Segal's observation more important is the fact that several major revolutions of physical thoeries in the past, including the quantum theory and theories of relativity, exhibit the same type of behavior. In fact most fundamental physical constants, including k, c, G, ħ, and weak and strong coupling constants, control the non-commutativity and non-integrability of Lie algbras at various level of the physical theory. These constants act as switches that turn a "curvature" in the theory on or off. A remarkable feature of these constants is that each of them is associated with a fundamnetal unification. For instance, k unifies heat and work, c puts space and time (and energy and mass) in the same footing, G unifies spacetime with gravity and finally ħ connect energy and frequency together. We have applied the Segal's suggestion to the quantum harmonic ocsillator and obtained remarkable results quant-ph/0411203. The Finite Quantum Theory (FQT) of the harmonic oscillator predicts a finite (bounded) non-linear energy spectrum for the oscillator, while turning it to a rotator with momentum, position, and the imaginary unit now as angular momentum operators. FQT also predicts pronounced violation of uncertainty principle. History and Philosophy of Physics I. Philosophical Structure of Physical Regularizations The regularization program described above is quite rich in philosophical aspects. There are several significant features, involving general concepts in philosophy of science, common to almost all regualrizations of physics. We list them below, while describing each briefly in the context of the passage from Galileo to Special Relativity. We will also see below that why we could lable regularizations as reformations. Relativization of Absolutes An absolute or idol [4] of a physical theory is one of the fundamental quantities of the theory that remains unchanged under the dynamics of the theory. It couples to other variables of the theory through the fundamental equations but not the inverse. We call a two-way coupling reciprocity. In pre-Einstein relativity (Galileo relativity) , time is the absolute. It couples into space but the space has no effect on time. Time becomes a relative variable SR. Now there is a two-way coupling between time and space. New Non-Commutativities The new (regular) theory exhibits new non-commutativitie(s) previously not present in the new non-regular (singular)) theory. In Galileo relativity boosts (coordinate transformation to other inertial frames) along different directions do commute. But in SR, they do not in general. Removing Infinities (Singularities) The new non-commutativity is the result of introducing a finite parameter into the sigular theory, which was thought to be infinite (or zero). We call this parameter a regularization parameter. The speed of light in SR is finite. It was considered to be infinite in Galileo theory. Removing infinities is indeed a much broader aspect of the regularization process. In general, the regular theory is finite in that it suffers from no (or many less) singularities. For example, the finite quantum theory of the harmonic oscillator replaces the usual position and momentum operators with angular momentum operators with discrete and bounded spectrum. A discrete quantum spacetime would be free the the usual infinities associated with theories assuming a continuum of spacetime background. Points (events) are replaced by cells with finite dimensions and localization is confined to a physical limit. Stability The regular theory is stable against finite changes in the regularization parameter. Roughly speaking, an unstable theory is surrounded by infinite number of stable and mathematically isomorphic theories. A small change in the commutation relations of an unstable theory transforms it to one of the surrounding stable ones. A small change in commutation relations of Galileo theory (i.e., introducing a non-zero parameter as the inverse of speed of light), changes the theory dramatically. SR, however, is stable against any finite change in the speed of light. Simplicity The regular theory is simple. By simple, we mean algebraic simplicity, which implies that the group of the theory is simple. A group is simple if it does not contain an invariant subgroup. A semi-simple (Lie) group is one whose Lie algebra has no solvable subalgebras, and is then a product of finite number of simple subgroups. A group which is not semi-simple, we term compound. (Mathematicians call this non-semi-simple). Roughly speaking, a compound group can not break into a product of subgroups, which are each related to transformation relevant to the absolute or idol of the main group. In Galileo group (in 1 + 1 dimension), time translations form an invariant subgroup. But the group does not break into the product of this subgroup and another one. This is the direct result of the fact that time is an absolute of the theory. So we point out that semi-simplicity implies reciprocity. Generalized Principle of Correspondence The regular theory reproduce the singular theory in the appropriate limit. In other words, old working theory must be recovered from the new theory in the limit where one or more regularization parameters go to zero. This is the generalized principle of correspondence. One recovers the Galileo relativity from SR when the reciprocal speed of light goes to zero. Here we see why reformation would be an appropriate term for the radical changes in physical theories. Almost all such revolutions are actually evolutions which leave the old theory alive in its own working framework. We emphasize here that reformations are physical regularization. In fact, the concept of regularization in physics is not new. Since the advent of field theories, several regularization methods have been introduced to remove the unwanted infinities out of physics. These are unphysical in that they are introduced just to hide the divergencies that enter field theories. There have not been direct experimental motivations for unphysical regularization. The three major regularization schemes are Pauli-Villars regularization [5], lattice regularization (lattice gauge theory) [6] and dimensional regularization [7,8,9]. In addition to theoretical motivation for regularization programs, sometimes experiments themselves lead to a more regular theory compared to the preceding one. The most famous example of a reformation process is Planck’s, which led to quantum theory. One idol (absolute) in classical mechanics is the system under study. In a measurement process, a classical system acts on the experimenter but not conversely. Consequently, classical measurements are commutative. Quantum theory is “simpler” than classical physics in that it does not separate measurements from transformation. A quantum system might changes as a result of an observation. Quantum observations do not commute in general. Compared to unphysical regularizations, physical regularizations affect the theories in a subtler way but their effects are rather dramatic. An unphysical regularization leaves the idol(s) of the theory untouched. But reformation of a theory results in dethroning one or more of its idols. The subtlety of a reformation process can be seen by studying its effect on the group structure of the theory. In fact, a reformation is a group regularization. We use the terms group flexing and group flattening for the mathematical process describing physical regualrization and its inverse [3]. We finally gather the ideas mentioned above into one principle: Segal Doctrine: Any compound (singular, unstable) physical theory is a flattening of a regular, more stable, more accurate theory, which we call its flexed theory. II. Quantum Logic, Logical and Causal Order, Physical Basis of Possibilities Coming Soon! References [1] Segal, I. E. Duke Math. J. 18, 221 (1951). [2] Inönü, E. and Wigner, E. P., Proc. Natl. Acad. Sci. U.S.A. 39, 510–524 (1953). [3] Shiri-Garakani, Mohsen, Finite Quantum Theory of the Harmonic Oscillator, Ph.D. Thesis, Georgia Institute of Technology (2004). [4] The term idol is borrowed from Bacon, F. Novum Organum. P. Urban and J. Gibson (tr. eds.) Peru, Illinois: Open Court Publishing Company, 1994. [5] Pauli, W. and Villars F. On the Invariant Regularization in Relativistic Quantum Theory, Rev. Mod. Phys. 21, 434-444, 1949. [6] Wilson, K.G. Phys. Rev. D10, 2445, (1974). [7] Bollini, C.G. and Giambiagi, J.J. Nuovo Cimento 31, 550, (1964). [8] Bollini, C.G. and Giambiagi, J.J. Phys. Lett. 40B, 566, (1972). [9] ’t Hooft G. and Veltman M. Nucl. Phys. B44, 189, (1972).