Ph.D Student | Doron Moshe Ludwin |
---|---|

Subject | Applications of Manifestly Covariant Quantum Theory In Bohm-Aharonov Theory and General Relativity |

Department | Department of Physics |

Supervisors | Full Professor Ori Amos |

Full Professor Larry Horowitz | |

Full Thesis text |

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 *t*_{0} 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 *R*^{4}) 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.