Our universe is most likely a computer simulation

[daaron]

139. The model of wave-particle duality says "Yes."

What do you mean by "really analog?" or "really digital?" Really in reality? QM is a model for the subatomic reality, and how we interpret QM in regards to reality is, like I said, a question most theoretical physicists leave for philosophers and Dr. Davies. It's "really" both analog AND digital, at the same time. Hence when we talk about a probability wave collapsing to a binary 'decision', so to speak, in the math yes, it's a continuous transformation. The analog probability wave(s) have a state that is best modeled as a binary state. Conversely, given a binary state and information about the particle in that state, we can deduce the solution to the wave equation that gives it. To answer the 1st two questions, then: Yes (and digital). Yes (and digital).

As for wavelengths less than Planck scale... sure, no problem; the math admits such empirical errors, but then we get quantum foam - particles popping in an out of existence. That's the famous problem with relativity, which doesn't work across foamy spacetime. It needs a nice smooth manifold over which to correctly make predictions. String theory attempts to solve this problem by, in essence, making the Planck scale the minimum size (by, of course, a much more circumspect route than I make it seem). In the stringy universe, when one zooms in to Planck scale, one starts zooming back out again into the same universe.

As for all non-imaginary numbers potential wavelengths for energy or matter? More or less, within the limits of how much matter-energy there actually is in the cosmos (whatever that number). Why? Because all matter has a de Broglie wavelength. The bigger the matter, the longer the wavelength. So the de Broglie wavelength of a person, say, would be so big that quantum mechanical effects are almost completely smudged out of measure-ability. Similarly with relativity - at very slow speeds the effects just aren't really measurable, except under the most controlled of conditions. Obviously it wouldn't make much sense to speculate about an imaginary wavelength - lengths are always measured as scalar quantities, not vectors.

As for a photon with the wavelength of Pi... OK, but 3.14... what? That is, which units? Meters? mm's? LY's? The answer is 'why not', mathematically. Question is does nature have such a thing?