May21-04, 06:26 PM
talking about the hydrogen atom spectrum (energy levels)
reminds me of an outstanding question in modern theoretical physics
What is the area spectrum in Simplicial Quantum Gravity?"
SQG is Ambjorn's name used interchangeably for the dynamical triangulation approach to quantum gravity.
computer simulations using this approach recently
generated a 4D world (the Ambjorn Jurkiewicz Loll paper that Baez was talking about)
so Simplex Gravity works or so it appears, there is still plenty to check.
this means a major question, maybe the next big question in quantum gravity, is to calculate the spectra of the geometric operators, area and volume
like roughly 100 years ago Bohr realized the energy and angular momentum in the electron orbit were discrete and he made a discrete (quantum step) model of it and calculated what colors light
and now Ambjorn (and Loll and others) are guessing space is discrete in a certain way and modeling it with a swarm of simplices
(a simplex is the analog of triangle in more than 2 dimensions)
and those people or colleagues should be able to derive
a discrete spectrum of the (not energy this time but) area operator
this has already been done in Loop gravity
it turns out that the area eigenvalues are various fractional multiples of the basic Planck area (fractions and the like, some square roots too but basically simple)
so naturally one wonders if doing it in Simplex quantum gravity gives the same eigenvalues.
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