Can't continuousness be simulated by lazy evaluation? Also you're assuming the simulator is bound by the same physical limitations that exist inside the simulation which seems unreasonable to me. Simulations are usually vastly simpler than the substrate they run on.

Has this been actually proven? I remember multiple experiments trying to prove the opposite - both effectively a discrete-like and a grid-like universe. Wolfram for example has some ideas about discrete graphs https://writings.stephenwolfram.com/2020/04/finally-we-may-h...

> Has this been actually proven?

Neither proven nor disproven in any capacity.

Also I have no clue how anyone could assert that the universe being "continuous" (whatever that means) could be casually claimed by anyone to have any link to our universe being "a simulation" (whatever that means) or not.

>Simulations are usually vastly simpler than the substrate they run on.

So to simulate continuum you need a transfinite VM. It will be more efficient to just run the universe bare metal.

Quantum mechanics teaches us nature isn't continuous though.

The energy levels of electrons bound to atoms/molecules are quantized, and therefore the energy levels of photons emitted/absorbed (when those electrons change energy levels) are quantized.

But as far as I understand that is just the result of constraints imposed by the atom/molecule "box". Like how a guitar string can only vibrate at certain frequencies because an integer multiple of wavelengths of the standing wave must fit on the string.

Outside of such systems, energy levels are not quantized. For example, photons from distant galaxies appear to be redshifted on a continuous spectrum.

And even within the box the energy levels can be varied continuously if, for example, you squeeze the molecule or put it in an electric field.