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.
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
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.
If you go deep enough in physics, you don’t have “wood”. You just have a wavefunction.
Fair enough, but surely the idea is to explain wood and the changes therein by reference to more fundamental physics. So even if the idea of change doesn’t show up at the very most fundamental levels, there must be some level at which change becomes a subject of physics. Otherwise, I don’t see how physics could profess to explain anything, since it would have nothing to do with empirical (and changable) phenomena.
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.
I’d love to talk more about that. Do you see configurations as platonic? And if our configuration is in constant flux (as is hard to doubt) on some level, do we therefore need to distinguish essential aspects of the configuration from accidental ones? And wouldn’t this view admit of two distinct persons having the same personal identity? That seems odd.
Well, I will say that a movie is “the same movie”, whatever it is stored on analog film, optical support, magnetic support or ssd storage. The content and the physical support are different issue. I’ll say that a movie “changed” if you cut or add some scene, or add subtitles, … but not if you copy the file from your magnetic hard disk to an USB key, even if there are much more differences at physical level between the HD and the USB key.
The same is true for personal identity, in my point of view. The personal identity is in the configuration of neurons, and even in the way changes propagate on the neural network, not in the specific matter distribution. Then, personal identity is not binary (am I the same I was one week ago ? and 20 years ago ?). But to a point yes, you can theoretically have two distinct “persons” with the “same” personal identity, if you can duplicate, or scan, a person.
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.
Fair enough, but surely the idea is to explain wood and the changes therein by reference to more fundamental physics. So even if the idea of change doesn’t show up at the very most fundamental levels, there must be some level at which change becomes a subject of physics. Otherwise, I don’t see how physics could profess to explain anything, since it would have nothing to do with empirical (and changable) phenomena.
I’d love to talk more about that. Do you see configurations as platonic? And if our configuration is in constant flux (as is hard to doubt) on some level, do we therefore need to distinguish essential aspects of the configuration from accidental ones? And wouldn’t this view admit of two distinct persons having the same personal identity? That seems odd.
Well, I will say that a movie is “the same movie”, whatever it is stored on analog film, optical support, magnetic support or ssd storage. The content and the physical support are different issue. I’ll say that a movie “changed” if you cut or add some scene, or add subtitles, … but not if you copy the file from your magnetic hard disk to an USB key, even if there are much more differences at physical level between the HD and the USB key.
The same is true for personal identity, in my point of view. The personal identity is in the configuration of neurons, and even in the way changes propagate on the neural network, not in the specific matter distribution. Then, personal identity is not binary (am I the same I was one week ago ? and 20 years ago ?). But to a point yes, you can theoretically have two distinct “persons” with the “same” personal identity, if you can duplicate, or scan, a person.