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But "quantum universe" doesn't actually mean that we're working with quanta(s), which translates to infinitesimally small but discrete quantities ? Aren't Pla

But "quantum universe" doesn't actually mean that we're working with quanta(s), which translates to infinitesimally small but discrete quantities ? Aren't Planck constants all about that ?

speeder 10y ago
He is referring to spacetime actually. quanta we are sure are the smallest objects in space. Spacetime is a sort of cartesian representation of space and time, with probably 4 axes (x, y, z, time). Many relativity concepts obey this, for example stuff moving in space at the speed of light, move literally zero on the time axis. And you can calculate the relationship between time and speed by rotating vectors. So back to quanta: we don't know if time is discrete. We don't even know if time actually exists, or its properties, because the math right now has results that are quite weird (like implying moving backwards in time should be normal and common as moving forward...), also there are arguments over the shape of "spacetime" with most people assuming it is a 4d cube, but maybe it ins't.
- Senji 10y ago
  What's been on my mind about these things is, we don't need to have "space" to be a "thing" that "exists". You can simulate a universe where "space" is encoded in each "particle"'s state as a scalar distance to some other particle. Thus you don't have a "full dimensional vector {x,y,z}" but you have a bunch of particles each keeping a list of variables with distances to other particles around them. Maybe I'm not explaining it right, but no one has proposed anything like this as far as I know.
  - Jarwain 10y ago
    I get what you're trying to say, and it's an interesting viewpoint on the matter. However, i still think of "space" as a useful abstraction in this case
    - Senji 10y ago
      Would it even be possible to devise an experiment to test for this? It doesn't seem likely to me.
  - raattgift 10y ago
    General Relativity, as a metric theory of gravitation, works exactly like this. Einstein's resolution to the Hole Argument[0] was to realize that spacetime itself has no properties other than the intervals between events, or equivalently, the sum of every 4-distance between a state of matter and another state of matter. In the standard cosmology, we use quantum fields that permeate the whole of spacetime and carry values at each point in spacetime. Some of the fields have values at each point that correspond to the presence of absence of a particle at that point (e.g. the electron field), while other fields provide a mechanism for one field to influence the state of another. In General Relativity we have the metric tensor, which is a field that carries information relevant to the causal structure of spacetime, and is determined by the values of the other fields (roughly, matter determines curvature, which in this case is a component of the distance in space and time from one configuration of matter to the next). So, rather than saying spacetime doesn't exist, we say instead that spacetime is only relevant when there is a configuration of matter within it that can be used to established one or more systems of coordinates (e.g. the matter states converge, diverge or oscillate). However, in Special Relativity there is no spacetime curvature (by definition) and so we do not need to use a metric tensor (we could naturally use the Minkowski tensor to describe the Minkowski spacetime, which is the spacetime of Special Relativity), but commonly attach a 4-vector to particles or bound collections of them. As with any spacetime in General Relativity, there is nothing special about a Minkowski spacetime that has nothing in it, or that has any other always-unchanging configuration of mass-energy. The Standard Model of Particle Physics is a group theory with the Poincaré group as a subgroup; the Poincaré group is the isometry group of Minkowski spacetime, or in other words, in Special Relativity, when you move something following the rules of the Poincaré group, you do not change the fundamental states of the thing you are moving. The Poincaré group in 3+1 spacetime has 3 (bidirectional) linear spacelike translation components, 3 components of (bidirectional) rotation, 3 components of Lorentz boost, and one timelike translation. So if you do a particle-smashing experiment today and the same experiment tomorrow (or in a lab across campus), you will get the same result. One can represent the action of the Poincaré group in several different ways. There is no harm in either approach in your second paragraph, as long as one is careful about how one manipulates either representation (especially, for example, swapping one representation for the other). [0] https://www.wikiwand.com/en/Hole_argument https://www.wikiwand.com/en/Hole_argument
- raattgift 10y ago
  "stuff moving in space at the speed of light, move literally zero on the time axis" No, on a Minkowski diagram with the x axis as a one space-like dimension coordinate (e.g. radius in metres) and the y axis as the time-like coordinate (e.g. -ct, where t is in seconds and c is the speed of light; - because of the sign convention[0]), something travelling at the speed of light traces out a 45 degree angle.[1] This is a fundamental property of Minkowski spacetime, the spacetime of Special Relativity (and the spacetime in local sections of the fibre bundle in General Relativity). Indeed, in a hyperbolic solution in General Relativity, everything moves at one second per second on the timelike axis measuring each object's proper time. This is one of many properties of time we do know very well; what's unclear is whether the property is emergent in the behaviour of systems of small objects, or whether it is fundamental to physics and applies to every object everywhere. General Relativity requires that the manifold be infinitely differentiable, and thus continuous, rather than discrete. Anything that seeks to explain gravitation and the observables from tests of relativity will have tremendous trouble introducing discretization on the background while retaining compatibility with those tests. For all practical purposes, that's true for everything outside the event horizon of a black hole and more recent than the first 1e-38 seconds after the big bang. [0] https://en.wikipedia.org/wiki/Sign_convention https://en.wikipedia.org/wiki/Sign_convention [1] https://en.wikipedia.org/wiki/File:Minkowski_diagram_-_photon.svg https://en.wikipedia.org/wiki/File:Minkowski_diagram_-_photo...
lisper 10y ago
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.)

But "quantum universe" doesn't actually mean that we're working with quanta(s), which translates to infinitesimally small but discrete quantities ? Aren't Planck constants all about that ?

speeder 10y ago

He is referring to spacetime actually. quanta we are sure are the smallest objects in space. Spacetime is a sort of cartesian representation of space and time, with probably 4 axes (x, y, z, time). Many relativity concepts obey this, for example stuff moving in space at the speed of light, move literally zero on the time axis. And you can calculate the relationship between time and speed by rotating vectors. So back to quanta: we don't know if time is discrete. We don't even know if time actually exists, or its properties, because the math right now has results that are quite weird (like implying moving backwards in time should be normal and common as moving forward...), also there are arguments over the shape of "spacetime" with most people assuming it is a 4d cube, but maybe it ins't.

Senji 10y ago
What's been on my mind about these things is, we don't need to have "space" to be a "thing" that "exists". You can simulate a universe where "space" is encoded in each "particle"'s state as a scalar distance to some other particle. Thus you don't have a "full dimensional vector {x,y,z}" but you have a bunch of particles each keeping a list of variables with distances to other particles around them. Maybe I'm not explaining it right, but no one has proposed anything like this as far as I know.
- Jarwain 10y ago
  I get what you're trying to say, and it's an interesting viewpoint on the matter. However, i still think of "space" as a useful abstraction in this case
  - Senji 10y ago
    Would it even be possible to devise an experiment to test for this? It doesn't seem likely to me.
- raattgift 10y ago
  General Relativity, as a metric theory of gravitation, works exactly like this. Einstein's resolution to the Hole Argument[0] was to realize that spacetime itself has no properties other than the intervals between events, or equivalently, the sum of every 4-distance between a state of matter and another state of matter. In the standard cosmology, we use quantum fields that permeate the whole of spacetime and carry values at each point in spacetime. Some of the fields have values at each point that correspond to the presence of absence of a particle at that point (e.g. the electron field), while other fields provide a mechanism for one field to influence the state of another. In General Relativity we have the metric tensor, which is a field that carries information relevant to the causal structure of spacetime, and is determined by the values of the other fields (roughly, matter determines curvature, which in this case is a component of the distance in space and time from one configuration of matter to the next). So, rather than saying spacetime doesn't exist, we say instead that spacetime is only relevant when there is a configuration of matter within it that can be used to established one or more systems of coordinates (e.g. the matter states converge, diverge or oscillate). However, in Special Relativity there is no spacetime curvature (by definition) and so we do not need to use a metric tensor (we could naturally use the Minkowski tensor to describe the Minkowski spacetime, which is the spacetime of Special Relativity), but commonly attach a 4-vector to particles or bound collections of them. As with any spacetime in General Relativity, there is nothing special about a Minkowski spacetime that has nothing in it, or that has any other always-unchanging configuration of mass-energy. The Standard Model of Particle Physics is a group theory with the Poincaré group as a subgroup; the Poincaré group is the isometry group of Minkowski spacetime, or in other words, in Special Relativity, when you move something following the rules of the Poincaré group, you do not change the fundamental states of the thing you are moving. The Poincaré group in 3+1 spacetime has 3 (bidirectional) linear spacelike translation components, 3 components of (bidirectional) rotation, 3 components of Lorentz boost, and one timelike translation. So if you do a particle-smashing experiment today and the same experiment tomorrow (or in a lab across campus), you will get the same result. One can represent the action of the Poincaré group in several different ways. There is no harm in either approach in your second paragraph, as long as one is careful about how one manipulates either representation (especially, for example, swapping one representation for the other). [0] https://www.wikiwand.com/en/Hole_argument https://www.wikiwand.com/en/Hole_argument
raattgift 10y ago
"stuff moving in space at the speed of light, move literally zero on the time axis" No, on a Minkowski diagram with the x axis as a one space-like dimension coordinate (e.g. radius in metres) and the y axis as the time-like coordinate (e.g. -ct, where t is in seconds and c is the speed of light; - because of the sign convention[0]), something travelling at the speed of light traces out a 45 degree angle.[1] This is a fundamental property of Minkowski spacetime, the spacetime of Special Relativity (and the spacetime in local sections of the fibre bundle in General Relativity). Indeed, in a hyperbolic solution in General Relativity, everything moves at one second per second on the timelike axis measuring each object's proper time. This is one of many properties of time we do know very well; what's unclear is whether the property is emergent in the behaviour of systems of small objects, or whether it is fundamental to physics and applies to every object everywhere. General Relativity requires that the manifold be infinitely differentiable, and thus continuous, rather than discrete. Anything that seeks to explain gravitation and the observables from tests of relativity will have tremendous trouble introducing discretization on the background while retaining compatibility with those tests. For all practical purposes, that's true for everything outside the event horizon of a black hole and more recent than the first 1e-38 seconds after the big bang. [0] https://en.wikipedia.org/wiki/Sign_convention https://en.wikipedia.org/wiki/Sign_convention [1] https://en.wikipedia.org/wiki/File:Minkowski_diagram_-_photon.svg https://en.wikipedia.org/wiki/File:Minkowski_diagram_-_photo...

lisper 10y ago

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.)