How Does Regge Calculus Define a Minimum Quantum of Spacetime?

[Klaus_Hoffmann]

Let be a (3+1) spacetime so we use triangularization of it computing 'Riemann Tensor' and so on, the problem is How can we define a 'minimum' Quantum of Space time (Area and Volume of the Surface should be quantizied) involivng the Regge Calculus ??

 

[marcus]

Let be a (3+1) spacetime so we use triangularization of it computing 'Riemann Tensor' and so on, the problem is How can we define a 'minimum' Quantum of Space time (Area and Volume of the Surface should be quantizied) involivng the Regge Calculus ??

Klaus as far as I know area and volume are not in any sense discrete in Regge approach.

that is not unusual in non-string QG

for example in CDT approach you let the size of the simplexes go to zero.

also in the Spinfoam approach there is AFAIK no smallest distance or area or volume----no discreteness.

however in canonical LQG there IS a discreteness result---the theory is not based on a discrete space, it is based on a continuum, but you can PROVE (in this one particular approach) that the area and volume operators have discrete spectrum. this should not be taken to mean that space is "made" of "atoms of space", it just means that certain observables representing the result of certain measurements have a discrete spectrum of possible outcomes.

quantization does not mean atomization. A quantum theory of spacetime geometry does not mean that there are atoms of space or time. There can be that in some approaches and NOT be that way in other approaches.