I Could the probability distribution itself be quantised?

Summary
The quantum multiverse would require infinite splitting for the probability function to be perfectly smooth, wouldn't it?
Everything is quantised when you look at it close enough. What about quantum probability waves themselves?

If the quantum multiverse interpretation were true, then each quantum decision leads to a splitting of the universe. But this isn't a binary choice, it's a probability distribution. For that graph to be smooth, the universe would have to split infinitely many times at each collapse of the wave function, wouldn't it?

So far we haven't encountered any true infinities in our universe. Space and time are probably quantised, not true continuums. What about the quantum wave function itself? I only have a lay person's understanding of any of this, but as I understand it, the multiverse interpretation says that rather than a quantum decision being random, all options are persued, and interact with each other somehow to produce the wave function. But unless the splitting is infinite, this function wouldn't be perfectly smooth.
 
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Everything is quantised when you look at it close enough.
This is not correct, though it is a common misconception. There are plenty of phenomena in quantum mechanics that are continuous, not discrete. A simple example is the energy and momentum of a free particle.

What about quantum probability waves themselves?
The wave function is continuous.

If the quantum multiverse interpretation were true, then each quantum decision leads to a splitting of the universe.
This is another common misconception that is not correct. We have plenty of threads on the MWI that discuss why; going into detail about that is probably better handled by starting a separate thread on that topic (preferably after spending some time reading previous threads on the topic).

this isn't a binary choice, it's a probability distribution
That depends on the specific measurement; for measurements where the results are quantized, there can indeed be a binary choice--a simple example is a spin measurement on a spin-1/2 particle.

Space and time are probably quantised, not true continuums.
"Probably" is way too strong given our current state of knowledge. It's a hypothesis, which at this point we can't to much to investigate, that's all.
 

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