טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentLudwin Doron Moshe
SubjectApplications of Manifestly Covariant Quantum Theory In
Bohm-Aharonov Theory and General Relativity
DepartmentDepartment of Physics
Supervisors Professor Amos Ori
Professor Larry Horowitz
Full Thesis textFull thesis text - English Version


Abstract

One of the main obstacles standing in the way of unifying Quantum Mechanics and General Relativity is the role of time in both theories. In non-relativistic quantum mechanics, one makes use of a global time that has causal meaning, where for each value of t, the quantum states interfere coherently. A measurement at an instant t0 has a simultaneous effect on the entire wave-function spread in the universe at that same instant. In General Relativity, however, t is just another coordinate axis (though with time-like character). Trying to use t as the causal parameter of quantum mechanics in a relativistic environment causes difficulties due to the fact that t cannot be treated covariantly as the causal parameter.

In general relativity, since the coordinate t is also the parameter of evolution, we must describe any materialistic body as spreading over a world line, un-localized in the time axis and its appearance as a localized body in space is merely an illusion of our mind that cannot perceive the coordinate nature of time.

Accepting that Newton’s time and Einstein’s time are both needed, either by the covariant nature of the world or by our empirical experience, brings us to suggest that they are both present. Suppose that the universe is indeed evolving on the background of a 4D space, however the coordinate axis t is not the parameter of evolution. This means that we no longer need to conceive matter as spread in the t axis on a world line, but rather be localized very well in the 4D picture. The same way a ball rolls in a spatial direction, leaving its previous location empty, the only place we shall find matter will be in the present.

The Stueckelberg-Horwitz-Piron formalism is based on the idea that there is an invariant parameter τ of evolution of the system; wave functions, as covariant functions of space and the Einstein time t, form a Hilbert space (over R4) for each value of τ . The invariant parameter τ could be thought of as the generalization of Einstein’s proper time to quantum mechanics.

In the thesis, we study applications of the Stueckelberg-Horwitz-Piron theory in two interesting situations. One is in the Schwarzschild Black-Hole environment and the other is in a gravitational analogue of the Electric Aharonov-Bohm effect.