Reviving Quantum Geometrodynamics

Tuesday, Nov. 14th
Susanne Schander, Perimeter Institute
Quantum Geometrodynamics
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By Jorge Pullin, LSU

Geometrodynamics is the name John Archibald Wheeler gave to the description of space-time completely in terms of geometry and its eventual quantization. The description of space-time is in terms of a metric of space that evolves in time. 

An approach to quantization that has been successful for the kind of theories that describe particle physics, like chromodynamics -which describes the strong interactions inside nuclei-, is the use of lattices. In it, one approximates the differential equations of the theory by finite differences. This has two upshots. On the one hand, infinities that tend to arise associated with the differential equations are eliminated. On the other hand, the resulting equations are amenable to be solved on a computer. The resulting approach is known as lattice gauge theory. Its application to the theory of strong interactions, lattice quantum chromodynamics, allows for instance to compute the mass of the proton.

Since the gauge theories of particle physics are typically represented in terms of a vectors like the potentials that appears in electromagnetism, attempts to apply lattice techniques to gravity have usually started from formulations of the theories in terms of potentials. The formulation used to set up loop quantum gravity would be an example. In this talk the use of lattices was explored with the traditional formulation of gravity used in geometrodynamics. Among the issues discussed was how to keep the metric of space yielding positive distances in the quantum theory. Moreover, a method to represent the symmetries of the theory on the lattice was given. Also the issue of the continuum limit, that is, how to retrieve from the discrete theory the continuum behavior we observe in space-time at large scales was addressed.

Quantum reference frames

Tuesday, March 7th
Flaminia Giacomini, ETH Zurich

Quantum reference frames
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By Jorge Pullin, LSU

It is generally accepted that the energies at which full quantum gravity effects will be relevant are so high that there is no chance of generating them in the laboratory. Full quantum gravity is only expected to be relevant in extreme environments like deep inside black holes or near the origin of the universe.

Nevertheless, there is interest is studying situations in which both quantum effects and gravity are important. Experiments can currently probe gravitational effects of masses as small as 90 milligrams, or quantum superpositions at scales of half a meter. These types of situations, though short of fully quantum gravitational in essence, can offer experimental guidance in a field that is notoriously short of it.

The talk focused on the issue of quantum reference frames. Reference frames are commonly used in physics and are treated as idealizations. In reality, any reference frame is a physical system and is subject to the laws of quantum mechanics like any other. Taking that into account leads to modifications in the form of the laws of physics from the one they take in idealized frames. In particular several important quantum properties like the "entanglement" that physical systems exhibit is a frame dependent phenomenon. Also the equivalence principle, the statement that all masses fall at the same acceleration in gravity, can be extended to be valid in quantum reference frames and in situations such as a massive object in a spatial quantum superposition.

The summary is that we do not currently know which experiments will prove definitively that gravity has quantum features, and probing regimes involving quantum mechanics and gravity can offer guidance on how to quantize gravity.