Zenith Grant Awardee

Dr. Roderich Tumulka

Eberhard-Karls-Universitaet

Co-Investigators

Sheldon Goldstein, <i>Rutgers University</i><br>Tim Maudlin, <i>Rutgers University</i><br>Nino Zanghi, <i>Universita di Genova</i>

Project Title

Bohmian Mechanics at Space-Time Singularities

Project Summary

Quantum mechanics has been plagued by paradoxes since its inception, and was criticized for this particularly by Einstein. Arguably, the simplest and most elegant solution to these paradoxes known to date is a theory called Bohmian mechanics. It provides an explanation how quantum phenomena work, whereas conventional quantum mechanics limits itself to describing what observers see. In this project, we plan to use Bohmian ideas to develop a possible solution to another mystery of quantum physics: How do quantum particles behave inside a black hole, the object predicted by Einstein's General Theory of Relativity in which gravity is so strong that even light cannot escape, and into which no observer can look?

Our solution will require a new version of Bohm's law of motion, involving drastic changes from the normal version to make it suitable in the presence of a "singularity," the points inside a black hole where gravity becomes literally infinite. We want to confirm what has been suggested by preliminary research: that any matter touching the singularity gets destroyed, but for certain types of singularities, surprisingly, there arises the possibility of particle creation by the singularity in very much the same way that an electron can create photons.

Technical Abstract

Arguably the simplest and most elegant "quantum theory without observers" is Bohmian mechanics. It postulates that particles have trajectories, governed by a certain simple equation of motion. Under the assumption of a preferred foliation of space-time into space-like 3-surfaces given by a Lorentz invariant law, it is known that Bohmian mechanics possesses a natural generalization to relativistic space-time. The project is to extend Bohmian mechanics to space-time geometries with singularities.

Preliminary research suggests two interesting phenomena: First, time-like singularities naturally lead to the annihilation and creation of particles at the singularity, and thus to a process with a varying number of particles, involving a wave function from Fock space. The stochastic law of particle production that we want to formulate would fit exactly into a gap of lawlessness left open by classical physics. Second, in the presence of a space-like singularity, since it can absorb but not emit particles, the appropriate Bohm-type equation of motion should involve a density matrix instead of a wave function, which evolves not unitarily but should obey a Lindblad equation. The assumptions we have in mind include that the metric is a fixed background metric, but not necessarily asymptotically flat or stationary.