Why do you say that the time slices overlap? It seems on your set up, and mine, that they do not. The point seems to be just that nothing can happen in less than a Planck time, not that something cannot happen in 10.5 Planck times. The latter doesn’t follow from the former so far as I can see. But I’m not on firm ground here, and I may well be mistaken. (ETA: But at any rate my example above doesn’t involve anything happening in 10.5 Planck times. Everything I describe in that example can be said to occur in a whole number of planck times.)
And ‘now’ doesn’t imply infinite divisiblity: we could have moments of time whether or not time is infinitely divisible, and we would need to refer to them to talk about the limit between two planck times anyway. And we cannot arrive at moments by infinite divisibility anyway, since moments are extensionless, and infinite division will always yield extensions.
Ah, english is not my native language. With “event B happens in another timeslice that starts half a planck time after the slice of event A” I meant timeslice B starts half a planck length after timeslice A started, so the second half of A overlaps with the fist of B.
B does not happen at 10.5 planck times after now. It happens somewhere between 10 and 11 planck times after “now” and you cannot tell when. Do not visualize time as a sequence of slices.
Edit: My point is, it’s simply impossible to visualize time. If your brain insists on visualizing it, you will never understand. Because whenever you visualize a timeslice you visualize it with a clear cut start and a clear cut end. But that’s not how this works.
Edit2: Maybe I’m just reading your response wrong. My point is that the precision in your example is the problem. There is no event that happens at a time with a precision smaller than one planck length. So 10.5 is just as wrong as 0.5.
Ahh, I see, I think I misunderstood you. I’m not sure I understand why A and B overlap. The claim about Planck times is that nothing can happen in less time. Does it follow from that that all time must be measured in whole numbers of Planck times? A photon takes one Planck time to pass through one Planck length, but I can’t see anything problematic with a cosmic ray passing through one Planck length in 10.5 Planck times. In other words does the fact that the Planck time is a minimum mean that it’s an indivisible unit?
I don’t think anything in my example relies on visualizing time, or on visualizing it as a series of slices. But I may be confused there. Do you have reason to think that one cannot visualize time? I suppose I agree that time is not a visible object, and so any visualization is analogical, but isn’t this true of many things we do visualize to our profit? Like economic growth, say. What makes time different?
I don’t really doubt that you’re right. Most everything I read on the subject agrees with or is consistant with what you’re saying. But the idea is still very confusing to me, so I appreciate your explanations. Let me try to make my troubles more clear.
So far as I understand it, a Planck time is a minimum because that’s the time it takes the fastest possible thing to pass through the minimum possible length. If something were going 99% the speed of light, or 75% or any percentage other than 100%, 50%, 25%, 12.5% etc. then it would travel through the Planck length in a non-whole number of Planck times. So something traveling at 75% the speed of light would travel through the Planck length at 1.5 Planck times. Maybe we can’t measure this. That’s fine. But say something were to travel at a constant velocity through two Planck lengths in three Planck times. Wouldn’t it just follow that it went through each Planck length in 1.5 Planck times? It may be that we can’t measure anything with precision greater than whole numbers of Planck times, but in this scenario it wouldn’t follow from that that time is discontinuous.
Mathematically speaking, you can say “in average it travelled for 1 Planck length in 1.5 Planck time”. But physically speaking, it doesn’t mean anything. Quantum mechanics works with wavefunction. Objects don’t have an absolutely precise position. To know where the object is, you need to interact with it. To interact with it, you need something to happen. Due to Heinsenberg’s Uncertainity Principle (even if you consider it as a “certainity principle” as Eliezer does), you just can’t locate something more precisely in space than a Planck length, nor more precisely in time than a Planck time. Done at quantum level, objects don’t have a precise position and speed. So saying “it moves at 0.75c so it crosses 1 Planck length in 1.5 Planck time” doesn’t hold. It can only hold as an average once the object evolved for many Planck times (and moved many Planck length).
Mathematically speaking, you can say “in average it travelled for 1 Planck length in 1.5 Planck time”. But physically speaking, it doesn’t mean anything. Quantum mechanics works with wavefunction.
I see. But this raises again my original worry: does QM’s claim about Planck times actually say anything about the continuity of time? Or just something about the theoretical structure of QM? Or just something about the greatest possible experimental precision? Does a limit on the precision of time at this level imply that these are actual indivisible and discontinuous units?
Maybe I’m just too steeped in pragmatism to notice, but it seems your question has already been answered. For example:
Does a limit on the precision of time at this level imply that these are actual indivisible and discontinuous units?
No, a limit on precision tells you that it’s not meaningful to ask whether or not there are actual indivisible and discontinuous units. There’s no experiment that could tell the difference.
I think pragmatism is a fine approach here, but could you clarify for me what your think the answer to my question is exactly? If it’s not meaningful to ask whether or not there are indivisible and discontinuous units, then is the answer to my question “Does QM’s claims about Planck time imply that time is discontinuous?” simply “No” because QM says nothing meaningful about the question one way or the other?
In ‘pure’ QM (without gravity), the Planck length has no special significance, and spacetime is assumed to be continuous. But we know that QM as we know it must be an approximation because it disagrees with GR (and/or vice versa), and the ‘correct’ theory of quantum gravity might predict weird things at the Planck scale. So far, most proposed theories of quantum gravity have little more predictive power than “The woman down the street is a witch; she did it”, though some do predict stuff such as the dispersion of gamma rays I’ve mentioned elsewhere.
is the answer to my question “Does QM’s claims about Planck time imply that time is discontinuous?” simply “No” because QM says nothing meaningful about the question one way or the other?
We’re trying to dissolve the question by pointing out that there exists a third option besides “continuous” or “discontinuous”. So the answer to “Does QM’s claims about Planck time imply that time is discontinuous?” would be “No, but neither is it continuous, but a third thing that tends to confuse people.”
Edit: retracted because I don’t think this is helpful.
Why do you say that the time slices overlap? It seems on your set up, and mine, that they do not. The point seems to be just that nothing can happen in less than a Planck time, not that something cannot happen in 10.5 Planck times. The latter doesn’t follow from the former so far as I can see. But I’m not on firm ground here, and I may well be mistaken. (ETA: But at any rate my example above doesn’t involve anything happening in 10.5 Planck times. Everything I describe in that example can be said to occur in a whole number of planck times.)
And ‘now’ doesn’t imply infinite divisiblity: we could have moments of time whether or not time is infinitely divisible, and we would need to refer to them to talk about the limit between two planck times anyway. And we cannot arrive at moments by infinite divisibility anyway, since moments are extensionless, and infinite division will always yield extensions.
Ah, english is not my native language. With “event B happens in another timeslice that starts half a planck time after the slice of event A” I meant timeslice B starts half a planck length after timeslice A started, so the second half of A overlaps with the fist of B.
B does not happen at 10.5 planck times after now. It happens somewhere between 10 and 11 planck times after “now” and you cannot tell when. Do not visualize time as a sequence of slices.
Edit: My point is, it’s simply impossible to visualize time. If your brain insists on visualizing it, you will never understand. Because whenever you visualize a timeslice you visualize it with a clear cut start and a clear cut end. But that’s not how this works.
Edit2: Maybe I’m just reading your response wrong. My point is that the precision in your example is the problem. There is no event that happens at a time with a precision smaller than one planck length. So 10.5 is just as wrong as 0.5.
Ahh, I see, I think I misunderstood you. I’m not sure I understand why A and B overlap. The claim about Planck times is that nothing can happen in less time. Does it follow from that that all time must be measured in whole numbers of Planck times? A photon takes one Planck time to pass through one Planck length, but I can’t see anything problematic with a cosmic ray passing through one Planck length in 10.5 Planck times. In other words does the fact that the Planck time is a minimum mean that it’s an indivisible unit?
I don’t think anything in my example relies on visualizing time, or on visualizing it as a series of slices. But I may be confused there. Do you have reason to think that one cannot visualize time? I suppose I agree that time is not a visible object, and so any visualization is analogical, but isn’t this true of many things we do visualize to our profit? Like economic growth, say. What makes time different?
No. The claim is that nothing is located in time with a precision smaller than the planck time.
I don’t really doubt that you’re right. Most everything I read on the subject agrees with or is consistant with what you’re saying. But the idea is still very confusing to me, so I appreciate your explanations. Let me try to make my troubles more clear.
So far as I understand it, a Planck time is a minimum because that’s the time it takes the fastest possible thing to pass through the minimum possible length. If something were going 99% the speed of light, or 75% or any percentage other than 100%, 50%, 25%, 12.5% etc. then it would travel through the Planck length in a non-whole number of Planck times. So something traveling at 75% the speed of light would travel through the Planck length at 1.5 Planck times. Maybe we can’t measure this. That’s fine. But say something were to travel at a constant velocity through two Planck lengths in three Planck times. Wouldn’t it just follow that it went through each Planck length in 1.5 Planck times? It may be that we can’t measure anything with precision greater than whole numbers of Planck times, but in this scenario it wouldn’t follow from that that time is discontinuous.
Mathematically speaking, you can say “in average it travelled for 1 Planck length in 1.5 Planck time”. But physically speaking, it doesn’t mean anything. Quantum mechanics works with wavefunction. Objects don’t have an absolutely precise position. To know where the object is, you need to interact with it. To interact with it, you need something to happen. Due to Heinsenberg’s Uncertainity Principle (even if you consider it as a “certainity principle” as Eliezer does), you just can’t locate something more precisely in space than a Planck length, nor more precisely in time than a Planck time. Done at quantum level, objects don’t have a precise position and speed. So saying “it moves at 0.75c so it crosses 1 Planck length in 1.5 Planck time” doesn’t hold. It can only hold as an average once the object evolved for many Planck times (and moved many Planck length).
I see. But this raises again my original worry: does QM’s claim about Planck times actually say anything about the continuity of time? Or just something about the theoretical structure of QM? Or just something about the greatest possible experimental precision? Does a limit on the precision of time at this level imply that these are actual indivisible and discontinuous units?
Maybe I’m just too steeped in pragmatism to notice, but it seems your question has already been answered. For example:
No, a limit on precision tells you that it’s not meaningful to ask whether or not there are actual indivisible and discontinuous units. There’s no experiment that could tell the difference.
I think pragmatism is a fine approach here, but could you clarify for me what your think the answer to my question is exactly? If it’s not meaningful to ask whether or not there are indivisible and discontinuous units, then is the answer to my question “Does QM’s claims about Planck time imply that time is discontinuous?” simply “No” because QM says nothing meaningful about the question one way or the other?
In ‘pure’ QM (without gravity), the Planck length has no special significance, and spacetime is assumed to be continuous. But we know that QM as we know it must be an approximation because it disagrees with GR (and/or vice versa), and the ‘correct’ theory of quantum gravity might predict weird things at the Planck scale. So far, most proposed theories of quantum gravity have little more predictive power than “The woman down the street is a witch; she did it”, though some do predict stuff such as the dispersion of gamma rays I’ve mentioned elsewhere.
We’re trying to dissolve the question by pointing out that there exists a third option besides “continuous” or “discontinuous”. So the answer to “Does QM’s claims about Planck time imply that time is discontinuous?” would be “No, but neither is it continuous, but a third thing that tends to confuse people.”
Edit: retracted because I don’t think this is helpful.