Difference between revisions of "Discrete or Continuous"

Revision as of 09:35, 20 April 2023

Full Title or Meme

The search for understanding about how the discrete events of an Eventful Universe can co-exist with the continuous models of space and time.

Context

Remarks on Lubos Motl’s blog definately describe the reason why Physicists trained in calculus think discrete just won't work :

“There is strong scientific evidence today that the world isn’t discrete (and it isn’t simulated).

We do encounter integers and discrete mathematical structures in physics but in all the cases, we may see that they’re derived or emergent. They’re just limited discrete aspects of a more general and more fundamental underlying continuous structure, or they’re a rewriting of a continuous structure into discrete variables (eigenstates in a discrete spectrum) which makes it impossible to understand the value of certain parameters.

Quite generally, if the Universe were fundamentally discontinuous, it couldn’t have continuous symmetries such as the rotational symmetry, the Lorentz symmetry, and even descriptions in terms of gauge symmetries (which aren’t real full-fledged symmetries but redundancies) would be impossible. In a fundamentally discrete world, many (or infinitely many) continuous parameters would have to be precisely fine-tuned for the product to “look” invariant under the continuous transformations.”

References

Other Material

In computing a similar dichotomy is described as Digital versus Analog Computing.