While it’s weird to think of a baseball moving that way, I’m not sure it’s any weirder than other behaviors at the quantum level. When you think of the object as a wave or probability distribution, then you don’t have a jagged or pixelated line as it moves. Rather, you have a very large number of space quanta that all have some probability of containing the particle. (So if we think of it in terms of Photoshop, we’re not using the pencil tool to paint 1 pixel at a time; we’re using the diffuse paint brush to paint 1000 pixels at a time.)
Are these probabilities discrete or continuous? 
Dam
I think the energy of a photon is discrete. Einstein was convinced of it.
I yield. As I said, I was basing my answer on my best recollection of Brian Greene’s writing.
The energy of photons of a given frequency is discrete. I.e. if you restrict yourself to a single frequency f, you can only have a collection of photons with energy nhf, where n is a non-negative integer.
But if you allow the frequency to vary, you can have photons of any energy. If I have a photon with energy hf and want one with energy hf/2, I just make a photon with half the frequency.
“Energy is discrete” is a bit of an overstatement. “The energy states of a collection of photons with a given frequency” is more accurate (but doesn’t roll off the tongue as well).
If we’re talking about the Planck length being the size of a space quanta, then the probability distribution is going to be effectively continuous. In fact, the motion of most particles would appear quite continuous even without thinking of them as a wave - a proton has a diameter of a billion billion Plank lengths (10^20).
How a distribution of probabilities over cells would look like? Does it ever effectively become zero? Or is it possible (but very very very unlikely) for a particle to instantaneously “travel” from one cell to another 100 light years away?
I touched on a similar topic, colloquially and semi-facetiously, in this thread.
Damn, I thought of another problem: What would happen after the “jump”? Would probabilities map be simply instantaneously translated to another cell together with particle or would it be a lot more complex function?
Well - if you think of the universe as a state machine made up of Planck-size cells, then there is no such thing as a “particle”. A particle would be a formation of cells in a particular set of states.
If the universe is a state machine, with each generation taking a Planck time, and each cell a Planck size, then you can see how the finite speed of light (or, basically, the maximum speed beyond which no effect can propagate) immediately follows. That’s no surprise, though, seeing how Planck time has been calculated by taking speed of light into account, so it doesn’t in any way prove anything.
But I think there is something very elegant about the universe as a gigantic state machine. So I prefer to think there’s something to it.
Personally I would prefer a continuous space-time. It would seem more poetic. When contemlating a cellular automata view I immediately think of an idea that universe may be just a simulation on some higher beings bored scientist’s PC…
Energy is not quantized in general. It’s quantized for bound systems, but it’s a different quantization for every bound system, and anyway, not all systems are bound, and free systems can have any energy at all. Plus, even with spectra from bound systems, there’s some wiggle room due to the uncertainty principle, and you can shift those energies around with things like Doppler shifts.
And it would be extremely difficult to construct any sort of geometry that’s self-consistent, discrete on small scales, but still closely approximates continuous on large scales. In most square-grid cellular automata, for instance, c is different in different directions due to interactions along the diagonals, and this anisotropy persists no matter how large a scale you look at. Now, there are some very smart people working on the problem of constructing such a geometry, and I won’t swear that they’ll never work it out, but let’s just say that I’m not holding my breath.
It’s hypothesized that the entire universe (as we think we know it) is nothing more that a simulation that God is running – one of many, most likely – before he commits to actually, you know, creating one of them.
I think I have always imagined any quantised space-time as a form of foam. Where individual cells have no regular size or shape, but there are statistical properties that hold for the cells. For instance, the average size in any dimension is the Plank length. But like a foam of soap bubbles any individual cell may have a wide range of neighbours, from 4 to infinity for a 3D foam. I had figured that the large scale properties (like c) would work out. Then again, I’m no physicist, and this was more my assumption as to how the theorists were looking at making it work. One could imagine it working with rules where individual cells could combine and also fission, perhaps retaining an average cell size in the face of expansion (or indeed compression) of space, and also providing some wiggle room for other emergent effects.
What happens in space stays in space.
According to QM, yes, it can. Or, billions of light years away.
The problem with the state machine model is that it’s hard to harmonize that with relativity. If the cells have fixed locations, that blows relativity because it provides a fixed frame of reference, which relatively emphatically denies. If they don’t have fixed locations, then where are they and how do they move?
It’s possible that there are quantized properties of space (just as there are quantized properties of energy, but that doesn’t mean the energy level isn’t continuous). As mentioned above, there is a minimum distance, under which it’s meaningless to discuss: the planck length. But that doesn’t mean that the universe is a grid of planck-length cells.
Also, note that for a universe that’s a grid, all distances wouldn’t be integral multiples of planck length. Obvious example: if it’s a square array, move one cell left and one cell up.
Space has quantum properties, but there’s no evidence that it might be a grid, and some powerful arguments that it can’t be. The more we learn about space, the more we realize that whatever properties it does have, they won’t be particularly intuitivel, any more than QM is.
I always find it amusing that Creationists (including Intelligent Design proponents) attack Darwinism as counterintuitive, but don’t discuss QM. If QM controverted any of their cherished beliefs, they’d have quite a bit more of a field day making scientists look ridiculous to the ignorant (so easy that would be!)
LOL
God has anti-aliasing software he runs on space. He’s a pro.