Difference between continuum and Planck-scale lattice limits

[anorlunda]

In elementary particle theory, professor Susskind encourages us to think of space-time as divided into a lattice of cells. We use annihilation and creation operators in the Lagrangian to consume a particle in a cell and to create a new particle in an adjacent cell. Repeated application of Lagrangians cause particles to move. The final step is to take the limit as lattice size approaches zero.

I imagine a delta A-B, where A is the limit as lattice size approaches zero, and B is the limit as lattice size approaches the Plank length. Is such a delta meaningful? If so, does the value of that delta reveal anything about the underlying quantization of space-time?

By the way, it thrills me that there exists a forum such as this where one can post such questions and get illuminating answers. Thank you all for being so generous with your time to assist amateurs struggling to understand.

 

[jfy4]

I'm not quite sure I understand your delta question, but I can tell you there is an in-the-making quantum theory of gravitation called "canonical quantum gravity," also known as "loop quantum gravity" for historical reasons. This is a quantum theory of spacetime that predicts a spacetime lattice. It is an active area of research, though the underdog of quantum gravity to be sure.