6 ms·

I wonder if, as we get to smaller scales, do things start quantizing? Are we far from it?

by badosu 7y ago

viraptor 7y ago
There's some research suggesting that yes, it is. It plays nicely with the simulated universe theory. https://www.quora.com/Is-the-space-quantized-If-yes-then-are-the-size-of-quanta-also-increasing-with-the-expanding-universe https://www.quora.com/Is-the-space-quantized-If-yes-then-are...
gus_massa 7y ago
Nobody knows, but the current guess is that the interesting part is near the "Planck length" https://en.wikipedia.org/wiki/Planck_length https://en.wikipedia.org/wiki/Planck_length The problem is that > The Planck length is about 10E−20 times the diameter of a proton. so we need a biiiiiiiiiiiiiiiiiiig particle accelerator or that someone think some smart trick to use some cosmic event to explore this.
- raattgift 7y ago
  We don’t need anything at Planck energies to see a conflict between quantum field theories (QFTs) and General Relativity in the face of non-classical behaviour of matter which generates a strong signal in the stress-energy tensor. The main problem is that that such behaviours are “washed out” by the rest of the stress-energy tensor’s coupling to matter that is “in the classical limit”, and we don’t yet know how to recover classical physics from QFTs. The interesting-to-theorists quantum gravity stuff is near the centres of neutron stars and black holes, and in the distant past of our universe: all regions we have yet to be figure out how to explore. And all those regions are surrounded by extremely hot and noisy matter: the ultradense nuclear pasta and hot atmosphere and so forth in neutron stars, the accretion regions of black holes, and the “fog” of the surface of last scattering (and the equivalent for neutrinos and possibly equivalent(s) for other non-charged particles or whatever the hell dark matter is). The closest neutron stars and black holes are already a depressingly long way away by RADAR-distance, so there’s no real hope of soon sending a probe close to them to try to gather up and report back observations. So theorists who want to abolish General Relativity’s gravitational singularity, or alternatively quantum things like unitarity, are struggling to extract (even in principle) signal from noisy relics of these extreme-and-hidden things. However, there is still interesting stuff possible to test near us: if we can develop a laboratory-based object with strongly non-classical behaviour even at sufficient mass to influence lab gravimeters (that is, it will rise above the background stress-energy) then there are all sorts of things we can do to test theories of quantum gravity. We expect that semiclassical gravity will be blown away by such an experiment (there is a member of https://www.npl.washington.edu/eotwash/node/1 https://www.npl.washington.edu/eotwash/node/1 here on HN, for instance). An example might be to bring a milligram-or-more coherent mass into a superposition for at least a few milliseconds and see which way an array of lab gravimeters point. That’s already a difficult experiment! (the subsection heading is wildly optimistic, but explains the expected result of such an experiment: https://en.wikipedia.org/wiki/Semiclassical_gravity#Experimental_status https://en.wikipedia.org/wiki/Semiclassical_gravity#Experime... ) I’m not certain the Planck length is anything more than mixing some physical constants into a unit of length, rather than something important to nature. It is interesting to see Planck-scale dimensionful units are frame-invariant — they might not be, which is the premise of Doubly-Special Relativity, for instance. On the other hand, Special Relativity and its deformations might not be the right tool anyway, as a Planck scale object may generate enough spacetime curvature (by virtue of the Planck scale object’s local stress-energy) to blow away the global symmetries of the flat spacetime that form the background for these theories (which are NOT background-independent!). We’re not going to be probing Planck scale objects in the near future, and so there are few limits on speculative theories other than re-re-re-reconfirmations of local Lorentz invariance at lower (stress-)energies in a variety of backgrounds, including that of the Standard Model of Cosmology (the red-shifting of spectra from supernovae, the Lyman-alpha forest, and so on), that of effectively flat spacetime (labs on earth, and in space vehicles around the solar system), and that of significantly curved spacetime (spectra of neutron stars, for instance). And that same information is also evidence favouring one QFT: the Standard Model of Particle Physics (“SM”), which incorporates Lorentz invariance (but not gravitation, so SM is background-dependent, and enjoys the fact that General Relativity predicts the correct background for SM in every sufficiently small region in the universe, even if the background between SM-event-at-A and SM-observer-at-B is such that a region covering A and B is clearly not flat spacetime []). - — [] we can adapt to that by using generally covariant physical theories; unfortunately not all physical theories have been “promoted” into general covariance, and anyway tensors are hard so people will use cut-downs of generally covariant theories adapted to some special background. One can study gauge fixing to figure out how well this works for physical theories, and whether the “comma-goes-to-semicolon” rule of “promoting” theories into general covariance actually ends up with something that works in an arbitrary background. Lots of perfectly-good-here-on-Earth physical theories fall apart in different spacetime backgrounds.
  - salawat 7y ago
    I was with you for the most part until >One can study gauge fixing to figure out how well this works for physical theories, and whether the “comma-goes-to-semicolon” rule of “promoting” theories into general covariance actually ends up with something that works in an arbitrary background. Lots of perfectly-good-here-on-Earth physical theories fall apart in different spacetime backgrounds. What? What is this "comma-goes-to-semi-colon" rule of "promoting" theories. This is either some superdense jargon I haven't been in the right place to encounter, or the research world has entered far stranger realms of symbolic representation than I've imagined possible. Seriously, what am I missing? I'm assuming it has something to do with proving the consistency of theoretical frameworks by correlating them with empirical confirmation, but I'm not 100% sure I'm not stripping out important nuance.
    - raattgift 7y ago
      > what am i missing ? Comma and semicolon typographical notation for partial resp. covariant derivatives. The comma is used to indicate a partial derivative: V^{\alpha}_{\comma\beta} = \partial_{\beta}V_{\alpha}. The semicolon V^{\alpha}_{\semicolon\beta} turns somewhat complicatedly (via Christoffel symbols) into \nabla{\beta}V^{\alpha}. There’s more detail at https://en.wikipedia.org/wiki/Covariant_derivative#Notation https://en.wikipedia.org/wiki/Covariant_derivative#Notation These notations are reflected in “comma-goes-to-semicolon” which is discussed in MTW chapter 20 & 22 (esp. §22.4, Electrodynamics in Curved Spacetime) and other textbooks. Carroll’s online lecture notes at https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll4.html https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll... discusses it briefly starting with the paragraph beginning “Our next task is to show how the remaining laws of physics…” and in particular (starting with) that paragraph’s penultimate sentence. Even more briefly, we need generally covariant physics to escape the flat spacetime background into general curved spacetime and still get sensible electromagnetism and so on. Even more briefly: the semicolon indicates a valid tensor equation, showing that we are fine when the basis vectors are not constant. Switching , to ; when it works hides away a bunch of work with Christoffel symbols, and what makes it work is the Equivalence Principle. Semicolon-goes-to-comma always works by gauge fixing, but unfortunately V^{a}_{,b} -> V^{a}_{;b} sometimes doesn’t; doing the full expansion by hand (well, or with modern automation) is one way to see if your physical theory is really generally covariant/background independent. > superdense Yes! As an example, and I haven’t really done more than scrub through it, and he really doesn’t go into any details beyond what you’d get in a standard textbook: https://www.youtube.com/watch?v=DfHln-nzpv0 https://www.youtube.com/watch?v=DfHln-nzpv0 (note LOCAL equations only in this video and its predecessor https://www.youtube.com/watch?v=XqNVxFY-lCs https://www.youtube.com/watch?v=XqNVxFY-lCs) Which leans heavily on https://en.wikipedia.org/wiki/Einstein_notation https://en.wikipedia.org/wiki/Einstein_notation Putting the extra typographical dot on top of the , giving a ; can literally represent several pages of dense equations. > jargon Yes! A lot of writing that turns out to generally be really mechanical has been squashed out of General Relativity through the years. Unfortunately the notation itself — as typography — tends to “leak out”, so we talk about indices being in the basement or upstairs, Greek vs Roman, etc etc.
raattgift 7y ago
LIGO is extremely far from quantum gravity. The gravitational waves in question have no quantum properties, either because they have so many quantum numbers in them that classical behaviour is recovered, or because they are classical “all the way down”. LIGO, its siblings, and their foreseeable successors are unlikely to help resolve this. The results have already constrained the space of quantum gravity theories from which General Relativity must be recoverable, but that is not the same as preferring (much less indicating) any particular approach to quantum gravity that will be consistent with LIGO et al.’s results. That said, LIGO’s detector itself relies upon the details of quantum mechanics, as it is also sensitive to quantum noise from its immediate environment. However the quantum mechanics in question are purely local, and have nothing to do with distant events like binary black hole mergers. (LIGO is not sensitive to those distant quantum mechanics — it’s either outright blind to them, or at best they blur into classicality — and it’s hard to envisage a human-buildable detector that would be sensitive to their gravitational influence within our solar system).
- emiliobumachar 7y ago
  Is there such a thing as real phenomena that's classical “all the way down”, as you have put it? If yes, which such phenomena is easiest to understand? I was under the impression that all of classical physics was special cases of quantum and relativistic physics, just like the relativistic equations of motion "degrade" into classical equations of motion when we postulate that all velocities involved are much lower than the speed of light.
  - jfengel 7y ago
    In this sense "classical" means "not quantum". General relativity is "classic" in the sense that position and momentum are variables rather than operators. They have real values rather than functions. So it's distinct from "classical" meaning "Newtonian" (or, perhaps "Newtonian + Maxwellian"), which is the sense in which "all of classical physics was special cases of quantum and relativistic physics".
    - raattgift 7y ago

I wonder if, as we get to smaller scales, do things start quantizing? Are we far from it?

by badosu 7y ago

I wonder if, as we get to smaller scales, do things start quantizing? Are we far from it?

There's some research suggesting that yes, it is. It plays nicely with the simulated universe theory. https://www.quora.com/Is-the-space-quantized-If-yes-then-are-the-size-of-quanta-also-increasing-with-the-expanding-universe https://www.quora.com/Is-the-space-quantized-If-yes-then-are...

gus_massa 7y ago

Nobody knows, but the current guess is that the interesting part is near the "Planck length" https://en.wikipedia.org/wiki/Planck_length https://en.wikipedia.org/wiki/Planck_length The problem is that > The Planck length is about 10E−20 times the diameter of a proton. so we need a biiiiiiiiiiiiiiiiiiig particle accelerator or that someone think some smart trick to use some cosmic event to explore this.

raattgift 7y ago
We don’t need anything at Planck energies to see a conflict between quantum field theories (QFTs) and General Relativity in the face of non-classical behaviour of matter which generates a strong signal in the stress-energy tensor. The main problem is that that such behaviours are “washed out” by the rest of the stress-energy tensor’s coupling to matter that is “in the classical limit”, and we don’t yet know how to recover classical physics from QFTs. The interesting-to-theorists quantum gravity stuff is near the centres of neutron stars and black holes, and in the distant past of our universe: all regions we have yet to be figure out how to explore. And all those regions are surrounded by extremely hot and noisy matter: the ultradense nuclear pasta and hot atmosphere and so forth in neutron stars, the accretion regions of black holes, and the “fog” of the surface of last scattering (and the equivalent for neutrinos and possibly equivalent(s) for other non-charged particles or whatever the hell dark matter is). The closest neutron stars and black holes are already a depressingly long way away by RADAR-distance, so there’s no real hope of soon sending a probe close to them to try to gather up and report back observations. So theorists who want to abolish General Relativity’s gravitational singularity, or alternatively quantum things like unitarity, are struggling to extract (even in principle) signal from noisy relics of these extreme-and-hidden things. However, there is still interesting stuff possible to test near us: if we can develop a laboratory-based object with strongly non-classical behaviour even at sufficient mass to influence lab gravimeters (that is, it will rise above the background stress-energy) then there are all sorts of things we can do to test theories of quantum gravity. We expect that semiclassical gravity will be blown away by such an experiment (there is a member of https://www.npl.washington.edu/eotwash/node/1 https://www.npl.washington.edu/eotwash/node/1 here on HN, for instance). An example might be to bring a milligram-or-more coherent mass into a superposition for at least a few milliseconds and see which way an array of lab gravimeters point. That’s already a difficult experiment! (the subsection heading is wildly optimistic, but explains the expected result of such an experiment: https://en.wikipedia.org/wiki/Semiclassical_gravity#Experimental_status https://en.wikipedia.org/wiki/Semiclassical_gravity#Experime... ) I’m not certain the Planck length is anything more than mixing some physical constants into a unit of length, rather than something important to nature. It is interesting to see Planck-scale dimensionful units are frame-invariant — they might not be, which is the premise of Doubly-Special Relativity, for instance. On the other hand, Special Relativity and its deformations might not be the right tool anyway, as a Planck scale object may generate enough spacetime curvature (by virtue of the Planck scale object’s local stress-energy) to blow away the global symmetries of the flat spacetime that form the background for these theories (which are NOT background-independent!). We’re not going to be probing Planck scale objects in the near future, and so there are few limits on speculative theories other than re-re-re-reconfirmations of local Lorentz invariance at lower (stress-)energies in a variety of backgrounds, including that of the Standard Model of Cosmology (the red-shifting of spectra from supernovae, the Lyman-alpha forest, and so on), that of effectively flat spacetime (labs on earth, and in space vehicles around the solar system), and that of significantly curved spacetime (spectra of neutron stars, for instance). And that same information is also evidence favouring one QFT: the Standard Model of Particle Physics (“SM”), which incorporates Lorentz invariance (but not gravitation, so SM is background-dependent, and enjoys the fact that General Relativity predicts the correct background for SM in every sufficiently small region in the universe, even if the background between SM-event-at-A and SM-observer-at-B is such that a region covering A and B is clearly not flat spacetime []). - — [] we can adapt to that by using generally covariant physical theories; unfortunately not all physical theories have been “promoted” into general covariance, and anyway tensors are hard so people will use cut-downs of generally covariant theories adapted to some special background. One can study gauge fixing to figure out how well this works for physical theories, and whether the “comma-goes-to-semicolon” rule of “promoting” theories into general covariance actually ends up with something that works in an arbitrary background. Lots of perfectly-good-here-on-Earth physical theories fall apart in different spacetime backgrounds.
- salawat 7y ago
  I was with you for the most part until >One can study gauge fixing to figure out how well this works for physical theories, and whether the “comma-goes-to-semicolon” rule of “promoting” theories into general covariance actually ends up with something that works in an arbitrary background. Lots of perfectly-good-here-on-Earth physical theories fall apart in different spacetime backgrounds. What? What is this "comma-goes-to-semi-colon" rule of "promoting" theories. This is either some superdense jargon I haven't been in the right place to encounter, or the research world has entered far stranger realms of symbolic representation than I've imagined possible. Seriously, what am I missing? I'm assuming it has something to do with proving the consistency of theoretical frameworks by correlating them with empirical confirmation, but I'm not 100% sure I'm not stripping out important nuance.
  - raattgift 7y ago
    > what am i missing ? Comma and semicolon typographical notation for partial resp. covariant derivatives. The comma is used to indicate a partial derivative: V^{\alpha}_{\comma\beta} = \partial_{\beta}V_{\alpha}. The semicolon V^{\alpha}_{\semicolon\beta} turns somewhat complicatedly (via Christoffel symbols) into \nabla{\beta}V^{\alpha}. There’s more detail at https://en.wikipedia.org/wiki/Covariant_derivative#Notation https://en.wikipedia.org/wiki/Covariant_derivative#Notation These notations are reflected in “comma-goes-to-semicolon” which is discussed in MTW chapter 20 & 22 (esp. §22.4, Electrodynamics in Curved Spacetime) and other textbooks. Carroll’s online lecture notes at https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll4.html https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll... discusses it briefly starting with the paragraph beginning “Our next task is to show how the remaining laws of physics…” and in particular (starting with) that paragraph’s penultimate sentence. Even more briefly, we need generally covariant physics to escape the flat spacetime background into general curved spacetime and still get sensible electromagnetism and so on. Even more briefly: the semicolon indicates a valid tensor equation, showing that we are fine when the basis vectors are not constant. Switching , to ; when it works hides away a bunch of work with Christoffel symbols, and what makes it work is the Equivalence Principle. Semicolon-goes-to-comma always works by gauge fixing, but unfortunately V^{a}_{,b} -> V^{a}_{;b} sometimes doesn’t; doing the full expansion by hand (well, or with modern automation) is one way to see if your physical theory is really generally covariant/background independent. > superdense Yes! As an example, and I haven’t really done more than scrub through it, and he really doesn’t go into any details beyond what you’d get in a standard textbook: https://www.youtube.com/watch?v=DfHln-nzpv0 https://www.youtube.com/watch?v=DfHln-nzpv0 (note LOCAL equations only in this video and its predecessor https://www.youtube.com/watch?v=XqNVxFY-lCs https://www.youtube.com/watch?v=XqNVxFY-lCs) Which leans heavily on https://en.wikipedia.org/wiki/Einstein_notation https://en.wikipedia.org/wiki/Einstein_notation Putting the extra typographical dot on top of the , giving a ; can literally represent several pages of dense equations. > jargon Yes! A lot of writing that turns out to generally be really mechanical has been squashed out of General Relativity through the years. Unfortunately the notation itself — as typography — tends to “leak out”, so we talk about indices being in the basement or upstairs, Greek vs Roman, etc etc.

raattgift 7y ago

LIGO is extremely far from quantum gravity. The gravitational waves in question have no quantum properties, either because they have so many quantum numbers in them that classical behaviour is recovered, or because they are classical “all the way down”. LIGO, its siblings, and their foreseeable successors are unlikely to help resolve this. The results have already constrained the space of quantum gravity theories from which General Relativity must be recoverable, but that is not the same as preferring (much less indicating) any particular approach to quantum gravity that will be consistent with LIGO et al.’s results. That said, LIGO’s detector itself relies upon the details of quantum mechanics, as it is also sensitive to quantum noise from its immediate environment. However the quantum mechanics in question are purely local, and have nothing to do with distant events like binary black hole mergers. (LIGO is not sensitive to those distant quantum mechanics — it’s either outright blind to them, or at best they blur into classicality — and it’s hard to envisage a human-buildable detector that would be sensitive to their gravitational influence within our solar system).

emiliobumachar 7y ago
Is there such a thing as real phenomena that's classical “all the way down”, as you have put it? If yes, which such phenomena is easiest to understand? I was under the impression that all of classical physics was special cases of quantum and relativistic physics, just like the relativistic equations of motion "degrade" into classical equations of motion when we postulate that all velocities involved are much lower than the speed of light.
- jfengel 7y ago
  In this sense "classical" means "not quantum". General relativity is "classic" in the sense that position and momentum are variables rather than operators. They have real values rather than functions. So it's distinct from "classical" meaning "Newtonian" (or, perhaps "Newtonian + Maxwellian"), which is the sense in which "all of classical physics was special cases of quantum and relativistic physics".
  - raattgift 7y ago