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ABrooks comments on Welcome to Less Wrong! (2010-2011) - Less Wrong
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I have a Physics question for you: is time continuous? I mean, is any given extent of time always further divisible into extents of time?
As far as I understand it : any time smaller than Planck's time (around 10^-43 second) is not meaningful, because no experiment will ever be able to measure it. So the question is kinda pointless, for all practical purpose, time could be counted as integer units of Planck's time.
I've read that too, but I get confused when I try to use this fact to answer the question. On the one hand, it seems you are right that nothing can happen in a time shorter than the Planck time, but on the other hand, we seem to rely on the infinite divisibility of time just in making this claim. After all, it's perfectly intelligible to talk about a span of time that is one half or one quarter of Planck time. There's no contradiction in this. The trouble is that nothing can happen in this time, or as you put it, that it cannot be meaningful. But does this last point mean that there is no shorter time, given that a shorter time is perfectly intelligible?
Suppose for example that exactly 10 planck times from now, a radium atom begins decay. Exactly 10 and a half planck times from now, another radium atom decays. Is there anything problematic in saying this? I've not said that anything happened in less than a Planck time. 10 Planck times and 10.5 Planck times are both just some fraction of a second and both long enough spans of time to involve some physical change. If there's nothing wrong with saying this, then we can say that the first atom began its decay one half planck length before the second. This makes a half Planck length a meaningful span of time in describing the relation between two physical processes.
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...)
In your example you're using the term "now". That term already implies a point in time and therfore an infinitely divisible time. The problem is that while you certainly could conceive of a half planck time you could never locate that half in time. I.e. an event does not happen at a point in time. It happens anywhere in a given range of time with at least the planck length in extend. Now suppose that event A happens anywhere in a given timeslice and event B happens in another timeslice that starts half a planck time after the slice of event A. You can not say that event B happens half a planck time after event A since the timeslices overlap and thus you cannot even say that event B happens at all after event A. It might be the other way round. So while in your mind this half planck length seems to have some meaning in reality it does not. Your mind insists on visualizing time as continuous and therefore you can't easily get rid of the feeling that it were.
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).
For a start the classical hallucination of particles and decay doesn't really apply at times on the planck scale (since there's no time for the wave to decohere). There's just the gradual evolution of the quantum wavefunction. It may be that nothing interesting changes in the wavefunction in less than a planck time, either because it's actually "blocky" like a cellular automata or physics simulation, or for some other reason.
In the former case you could imagine that at each time step there's a certain probability (determined by the amplitude) of decay, such that the expected (average) time is 0.5 planck times after the expected time of some other event. Such a setup might well produce the classical illusion of something happening half a planck time after something else, although in a smeared-out manner that precludes "exactly".
That's a good point about decay, but my example only referred to the beginning of the process of decay. I wasn't trying to claim that the decay could take place in less than one, one, or less than one trillion planck times. The important point for my example is just that the starting points for the two decay processes (however long they take) differ by .5 planck times. Nothing in the example involves anything happening in less than a Planck time, or anything happening in non-whole numbers of Planck times.
But the thing is : how can you measure that the decay differs by .5 Planck times ? That would require an experimental device which would be in a different state .5 Planck times earlier, and that's not possible, according to my understanding.
Good point. I agree, it doesn't seem possible. But this is what confuses me: no measuring device could possibly measure some time less than one Planck time. Does it follow from this alone that a measuring device must measure in whole numbers of Planck times? In other words, does it follow logically that if the planck time is a minimum, it is also an indivisible unit?
This is my worry. A photon travels across a planck length in one planck time. Something moving half light-speed travels across the same distance in two planck times. If Planck times are not only a minimum but an indivisible unit, then wouldn't it be impossible for some cosmic ray (A) to move at any fraction of the speed of light between 1 and 1/2? A cosmic ray (B) moving at 3/4 c couldn't cover the Planck length in less time than A without moving at 1 c, since it has to cover the planck length in whole numbers of planck times. This seems like a problem.
It could be like that something moving at 3/4 c will have, on each Planck time, a 3/4 chance of moving of one Planck length, and a 1/4 chance of not moving at all. But that's how I understand it from a computer scientist point of view, it may not be how physicists really see it.
But I think the core reason is that since no signal can spread faster than c, no signal can cross more than one Planck length over a Planck time, so a difference of less than a Planck time can never be detected. Since it cannot be detected, since there is no experimental setting that would differ if something happened a fraction of Planck time earlier, the question has no meaning.
If time really is discreet or continuous doesn't have any meaning, if no possible experiments can tell the two apart.
Of course, given any experiment, spacetime being discrete on a sufficiently small scale couldn't be detected, but given any scale, a sufficiently precise experiment could tell if spacetime is discrete at that scale. And there's evidence that spacetime is likely not discrete at Planck scale (otherwise sufficiently-high-energy gamma rays would have a nontrivial dependency of speed on energy, which is not what we see in gamma-ray bursts). See http://www.nature.com/nature/journal/v462/n7271/edsumm/e091119-06.html
Thanks for the post and for the very helpful link.
The difference between discreet or continuous time is a concern of mine because it bears on what it means for something to be changing or moving. But I'm very much in the dark here, and I don't know what physicists would say if asked for a definition of change. Do you have any thoughts?
Well, the nature of time is still a mystery of physics. Relativity killed forever the idea of a global time, nad QM damaged the one of a continuous time. Hypothesis like Julian Barbour's timeless physics (which has significant support here), or Stephen Hawking's imaginary (complex number) time could change it even more.
Maybe once we have a quantum gravity theory and an agrement over the QM interpretation we could tell more... but for now, we've to admit we don't know much about the "true nature" of change or movement. We can only tell how it appears, and since any time smaller than Planck time could never be detected, we can't tell apart from that if it's continuous or discreet.
I'm sorry, I really don't know. In fact, I don't think I even know what the majority opinion is among physicists (if there is one).
At the face of it, it seems like if spacetime is discrete, then up until now, the unit of discreteness is small enough to allow us to do calculus (which assumes continuity) with impunity, even at the smallest of scales our experiments go to. So, as far as experimental evidence goes, there's no reason to believe in discreteness. But I guess your question is whether there are any theoretical arguments which suggest discreteness... to which I really don't have an answer. If I understand some interesting argument in the future, I'll get back to you.
Thanks, I'll look forward to it.