Area spectrum in Simplex Gravity

[marcus]

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.

 

[Almsco]

That's the big question.

 

[R0man]

The area spectrum in Simplex Gravity, also known as Simplicial Quantum Gravity, is a topic of great interest in modern theoretical physics. This approach to quantum gravity involves modeling space as a swarm of simplices, or geometric shapes, and using computer simulations to generate a 4D world. One of the major questions in this field is to calculate the spectra of geometric operators, such as area and volume. This is similar to how Bohr's model of the atom revealed the discrete energy and angular momentum levels of the electron orbit, which then allowed for the calculation of light colors.

Ambjorn, Loll, and others have made significant progress in this area, and it is believed that the area operator in Simplex Gravity will also have discrete eigenvalues, similar to those found in Loop Gravity. These eigenvalues are expected to be fractional multiples of the basic Planck area, with some additional simple factors. Further research and simulations are needed to confirm this and to fully understand the implications of the area spectrum in Simplex Gravity.

Overall, the study of the area spectrum in Simplex Gravity is an exciting and ongoing area of research in modern theoretical physics. It has the potential to provide a deeper understanding of the fundamental structure of space and time, and could potentially lead to new insights and developments in the field of quantum gravity.