Recently on my mind is this question: Is the universe is ultimately continuous or discrete?
I will freely admit that I lack the knowledge and tools to have the answer, but I’m still curious about it. Here is what I’ve been considering, based on the Physics I’ve studied:
Matter was once thought of as continuous… Cut your gold into smaller and smaller pieces and it’s still gold. But then we learned about atoms, and found out that matter is comprised of individual, indivisible sub-elements. Any further divisions and it’s no longer gold. That’s discrete.
Consider electricity. You can talk about a current flowing through a wire as a continuous function in units of Amperes, but at the end of the day it’s really made up of an exact number of individual electrons moving around. That’s also discrete.
But then what about light and other electromagnetic waves? They’re one of those creepy things that apparently exhibits both discrete and continuous properties (particle and wave)… By my understanding, light is made up of photons, discrete mass-less particles produced by energy being released from electrons as they fall between discrete, calculable energy levels around an atom. So that seems to be discrete. But then I’ve also read about experiments where researchers will cut two slits in a piece of paper, and send photons through one-by-one. The photons create a diffraction (?) pattern on the wall behind the slits, as if they interacted with more photons passing through the other slit. This shouldn’t happen though, since the photons were actually released one-by-one and had nothing to interact with. Besides being creepy, that seems to be more like a continous thing.
Then how about ideas like time and distance? It seems to me that even if the particles in the universe are discrete, shouldn’t they still be moving through space that can be measured infinitely more precisely? That is, continuously? What is to say that I can’t measure 1/4 the length of a photon, or 1/10,000 the length of that?
And I don’t have the faintest clue what’s going on at the quantum scale… anybody know if that kind of stuff is continuous or discrete? After listening to Dr. Brian Greene’s presentation on String Theory a while back, it seems like quantum-sized strings might in fact be continuous again, seeing as they are little tiny waves. So if they are continuous, then are electrons and photons and other such “discrete” particles actually continuous in nature?
I don’t know if any of you have the answer for me, but by all means let me know if you do. I’m very curious.