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nshepperd comments on Welcome to Less Wrong! (2010-2011) - Less Wrong
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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.
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.
Well, I'm not so much asking about the true nature of change or movement but rather just what we mean to say when we say that something is changing or has changed. I take it that if I told any layperson that a block of wood changed from dark to pale when left out in the sun, they would understand what I mean by 'changed'. If interrogated as to the meaning of change they might say something like "well, it's when something is in one condition at one time, and the same thing is in another condition at another time. That's a change."
But obviously that's quite informal and ill suited to theoretical physics. On the other hand, physicists must have some basic idea of what a change or motion is. Yet I cannot think of anything more precise or firm than what I've said above.
If you go deep enough in physics, you don't have "wood". You just have a wavefunction. The wavefunction evolves with time in "classical" QM physics, and just exists statically in timeless physics.
And "the same thing" doesn't mean much, since there is nothing like "this electron" but only "one electron".
Saying that a piece of wood changed is an upper-level concept, which you can't directly define in fundamental physics, but only approximates (like "pressure", or "wood", or "liquid"). The way you define your high level approximation doesn't really need to know if the lower level is continuous or not. The same way you won't define "liquid" differently just because we discovered that protons are not indivisible, but made of quarks.
Of course, lower level can be relevant : for example the fact there is no such thing as "this electron" contributes to saying that personal identity depends of configuration more than of "the same matter". But it's only a minor argument towards it, for me.