Well, the correct answer up to this point is that we don’t know. We would need a theory of quantum gravity to understand what’s happening at this scale, and who knows how many ither step further we need to move to have a grasp of the “real” answer. Up to now, we only know that “something” is going to happen, and can make (motivated) conjectures.
It may indeed be that time is discretized in the end, and talking about fractions of planck time is meaningless: maybe the universe computes the next state based on the present one in discrete steps. In your case, it would be meaningless to say that an atom will decay in 10.5 Planck times, the only thing you could see is that at step 10 the atom hasn’t decayed and at step 11 it has (barring the correct remark of nsheperd that in practice the time span is too short for decoherence to be relevant). But, honestly, this is all just speculation.
Thanks for the response, that was helpful. 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?
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.
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 ;)
I read that too as soon as I saw thomblake’s reply. I’m a newcomer here, and I hadn’t heard of this view of physics before so it was very informative (though the quality of the wiki article isn’t that high, citation wise). I’ve also been talking to a physicist/philosopher about this (he’s been saying a lot of the same things you have) and he gave me the impression that if there’s a consensus view in physics, it’s that time is continuous...but that this is an open question.
Is this computationalist view of physics popular here, or rather, is it more popular here than in the academic physics community? It seems as though a computationalist view would on the face of it come into some conflict with the idea of continuous time, since between any state and any subsequent computed therefrom there would be an intermediate state containing different information than the first state. But I’m way out of my depth here.
Well, the correct answer up to this point is that we don’t know. We would need a theory of quantum gravity to understand what’s happening at this scale, and who knows how many ither step further we need to move to have a grasp of the “real” answer. Up to now, we only know that “something” is going to happen, and can make (motivated) conjectures. It may indeed be that time is discretized in the end, and talking about fractions of planck time is meaningless: maybe the universe computes the next state based on the present one in discrete steps. In your case, it would be meaningless to say that an atom will decay in 10.5 Planck times, the only thing you could see is that at step 10 the atom hasn’t decayed and at step 11 it has (barring the correct remark of nsheperd that in practice the time span is too short for decoherence to be relevant). But, honestly, this is all just speculation.
Thanks for the response, that was helpful. 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?
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.
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?
Just a side-note… I don’t think this was supposed to be a ‘metaphor’.
Fair enough. How does the view of the universe as a computer relate to the question of the continuity of time?
http://en.wikipedia.org/wiki/Digital_physics (It’s been years since I read that article; I’m going to read it again...)
I read that too as soon as I saw thomblake’s reply. I’m a newcomer here, and I hadn’t heard of this view of physics before so it was very informative (though the quality of the wiki article isn’t that high, citation wise). I’ve also been talking to a physicist/philosopher about this (he’s been saying a lot of the same things you have) and he gave me the impression that if there’s a consensus view in physics, it’s that time is continuous...but that this is an open question.
Is this computationalist view of physics popular here, or rather, is it more popular here than in the academic physics community? It seems as though a computationalist view would on the face of it come into some conflict with the idea of continuous time, since between any state and any subsequent computed therefrom there would be an intermediate state containing different information than the first state. But I’m way out of my depth here.