I wonder if the question of the continuity of time bears on the idea of the universe computing its next state: if time is discreet, this will work, but if time is continuous, there is no 'next state' (since no two moments are adjacent in a continuous extension). Would this be important to the question of determinism?

I don't think continuous time is a problem for determinism: we use continuous functions every day to compute predictions. And, if the B theory of time turns out to be the correct interpretation, everything was already computed from the beginning. ;)

Finally, notice that my example doesn't suggest that anything happens in 10.5 planck times, only that one thing begins 10 planck times from now, and another thing begins 10.5 planck times from now. Both processes might only occupy whole numbers of planck times, but the fraction of a planck time is still important to describing the relation between their starting moments.

What I was suggesting was this: imagine you have a Planck clock and observe the two systems. At each Planck second the two atoms can either decay or not. At second number 10 none has decayed, ad second 11 both have. Since you can't observe anything in between, there's no way to tell if one has decayed after 10 or 10.5 seconds. In a discreet spacetime the universe should compute the wavefunctions at time t, throw the dice, and spit put the wavefunctions at time t+1. A mean life of 10.5 planck seconds from time t translates to a probability to decay at every planck second: then it either happens, or it doesn't. It seems plausible to me that there's no possible Lorentz transformation equivalent in our hypothetical uber-theory that allows you to see a time span between events smaller than a planck second (i.e. our Lorentz transformations are discreet, too). But, honestly, I will be surprised if it turns out to be so simple ;)

Warning: wild speculations incoming ;)

I don't think continuous time is a problem for determinism: we use continuous functions every day to compute predictions. And, if the B theory of time turns out to be the correct interpretation, everything was already computed from the beginning. ;)

What I was suggesting was this: imagine you have a Planck clock and observe the two systems. At each Planck second the two atoms can either decay or not. At second number 10 none has decayed, ad second 11 both have. Since you can't observe anything in between, there's no way to tell if one has decayed after 10 or 10.5 seconds. In a discreet spacetime the universe should compute the wavefunctions at time t, throw the dice, and spit put the wavefunctions at time t+1. A mean life of 10.5 planck seconds from time t translates to a probability to decay at every planck second: then it either happens, or it doesn't. It seems plausible to me that there's no possible Lorentz transformation equivalent in our hypothetical uber-theory that allows you to see a time span between events smaller than a planck second (i.e. our Lorentz transformations are discreet, too). But, honestly, I will be surprised if it turns out to be so simple ;)

Do you think you could explain this metaphor in some more detail? What does 'computation' here represent?