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.

 

[Entropia]

The combination of Regge Calculus and Quantization is a promising approach to understanding the fundamental structure of spacetime. By using the triangulation method, we can discretize the continuous spacetime into small triangles, allowing us to compute the Riemann tensor and other geometric quantities. This can provide valuable insights into the curvature and dynamics of spacetime.

One of the key challenges in understanding the quantum nature of spacetime is defining a minimum unit of space and time. This is where the Regge Calculus can play a crucial role. By quantizing the area and volume of the triangulated spacetime, we can define a minimum quantum of space and time. This would allow us to probe the structure of spacetime at a more fundamental level and potentially uncover new physics.

However, there are still several open questions and challenges in this approach. For instance, how do we ensure that the quantization of space and time is consistent with the principles of quantum mechanics? Can we extend this approach to higher dimensions? These are important questions that need to be addressed in order to fully utilize the potential of Regge Calculus and Quantization in understanding the nature of spacetime.

Nevertheless, the combination of these two powerful techniques holds great promise in shedding light on the fundamental properties of spacetime and its connection to quantum mechanics. It is an exciting area of research that has the potential to revolutionize our understanding of the universe.