Re:Physicists Create World’s First Time Crystal
by lisper on Friday October 07, 2016 @04:44PM
(#12663781)
That is a really good question, and a complete answer would be way too complicated for an HN comment but I'll give it my best shot.
First let us observe that even in the classical universe there are discrete quantities. Atoms, for example, are discrete. You can't have half a uranium atom because that's not a uranium atom any more, it's some other kind of atom. But aside from these discrete quantities most of the things that describe the state of the classical world seem to be continuous: you can position an atom anywhere, you can move it at any speed (including zero), etc. and hence the atom can have any value for its total energy.
This turns out to be only an approximation to the truth. It turns out that classical systems in fact can only have energies that are discrete multiples of some very small number. This number is not Planck's constant, but it's derived from Planck's constant in a way that depends on the physical setup. This is why, for example, to see quantum effects you have to control the setup very carefully, which generally means making things very cold so they don't jiggle around too much. This is one of the complications that I can't get into here. But the details don't really matter. What matters is that it turns out that some of the quantities we thought were continuous are in fact discrete, it's just that the units are so small that it's not apparent until things are very small and/or very cold. And in particular, energy is discrete.
But the underlying math of QM is not discrete, it's continuous. So how do we get from the continuous math of the quantum wave function to the discrete behavior we observe in reality? We don't really know. If we really understood that we could explain why Planck's constant has the value that it does, and we can't do that (yet). One possibility is that space and time are discrete just like energy it, but it's just not apparent because the units into which nature slices up space and time are too small for us to access experimentally. If space and time do turn out to be discrete, then the continuous math of QM will turn out to be merely a very (very!) good approximation.
But the distinction that really matters between the quantum and the classical is that states in the quantum universe are described by complex numbers and states in the classical universe are described by real numbers. That is the thing that makes quantum and classical fundamentally different, and it's the thing that makes the quantum world "weird" to us, because that's how you get things like entanglement and destructive interference. The quantization part is, ironically, a relatively unimportant detail, at least when it comes to talking about things like time crystals. (It's incredibly important for other things, like semiconductors.)
First let us observe that even in the classical universe there are discrete quantities. Atoms, for example, are discrete. You can't have half a uranium atom because that's not a uranium atom any more, it's some other kind of atom. But aside from these discrete quantities most of the things that describe the state of the classical world seem to be continuous: you can position an atom anywhere, you can move it at any speed (including zero), etc. and hence the atom can have any value for its total energy.
This turns out to be only an approximation to the truth. It turns out that classical systems in fact can only have energies that are discrete multiples of some very small number. This number is not Planck's constant, but it's derived from Planck's constant in a way that depends on the physical setup. This is why, for example, to see quantum effects you have to control the setup very carefully, which generally means making things very cold so they don't jiggle around too much. This is one of the complications that I can't get into here. But the details don't really matter. What matters is that it turns out that some of the quantities we thought were continuous are in fact discrete, it's just that the units are so small that it's not apparent until things are very small and/or very cold. And in particular, energy is discrete.
But the underlying math of QM is not discrete, it's continuous. So how do we get from the continuous math of the quantum wave function to the discrete behavior we observe in reality? We don't really know. If we really understood that we could explain why Planck's constant has the value that it does, and we can't do that (yet). One possibility is that space and time are discrete just like energy it, but it's just not apparent because the units into which nature slices up space and time are too small for us to access experimentally. If space and time do turn out to be discrete, then the continuous math of QM will turn out to be merely a very (very!) good approximation.
But the distinction that really matters between the quantum and the classical is that states in the quantum universe are described by complex numbers and states in the classical universe are described by real numbers. That is the thing that makes quantum and classical fundamentally different, and it's the thing that makes the quantum world "weird" to us, because that's how you get things like entanglement and destructive interference. The quantization part is, ironically, a relatively unimportant detail, at least when it comes to talking about things like time crystals. (It's incredibly important for other things, like semiconductors.)