It's a research paper that definitively needs an ELI25. My attempt (that perhaps is wrong):
Looking at collisions of neutron stars, perhaps it's possible to find difference from the predictions of General Relativity that may be helpful to discover an extension of the theory.
How bad is that? I'd love to read any correction or improvement from someone that is working in a related topic.
I also need the ELI25, however I think that the paper might be indicating that following the same procedure for spontaneous scalarization to vector fields may yield unphysical results. That being said, I can't tell if the belief is that a ghost instability is inherently a mathematical object - or something that may be physical but we simply do not know.
> Lastly, we stress that our results are relevant for most
known extensions of spontaneous scalarization to other
fields, not just the vectors, and our study can be considered
as a first step to obtain a no-go theorem for extending
spontaneous scalarization to other fields. For vector fields,
Garcia-Saenz et al. [51] has identified the presence of ghost
and gradient instabilities in the background of compact
objects in a broad class of generalized Proca theories
[84,85]. Similar concerns were also raised in the context
of cosmology in Ref. [86]. Going beyond vector fields, all
known formulations of nonminimally coupled spin-2 fields
that could spontaneously grow are known to lead to ghost
instabilities as well [75]. Likewise, p-form fields also have
the same constraint structure we discussed in Sec. V, hence
they suffer from similar divergent terms [87]. Spontaneous
growth of spinor fields as it was introduced in Ref. [88] also
contains divergent terms.
What I grasp is roughly the following, we know, that you could construct a scalar field, part of a spacetime that solves relativity, that would show almost no effect on a weak gravity environment (it's mostly undetectable, unless close to a massive object). But in massive environments, we could in principle detect the effects of a non-trivial field (i.e. make predictions, and try to observe them).
Essentially, build a theory (perturb the theory), and make a testable prediction that works on the large scale, but would be hard or impossible to observe on a weak gravity environment (for some definition of weak, I think they mean something less massive than a star).
They ask whether or not you can do something like this with a more complex, vector field (i.e. a new force/particle).
It's all very theoretical.
But it may give an avenue to find new physics, maybe even explain dark matter/energy.
I hope this helps. In order to get anywhere close to "25" I will ignore some factors and engage in a bit of "lie to students" terminological and notational abuse.
> ... may be helpful to discover an extension of the theory.
The authors have a set of families of alternatives to General Relativity, and are exploring whether they are viable as a physical description of gravitation in our universe, and if not (spoiler: they're not; they admit this up front) whether any of them can be adapted into a good physical description.
The second author of the (purely theoretical) headline paper in [(headline)paper ref [43]] explored variations on Brans-Dicke (BD) scalar-tensor gravitation.
Briefly, BD adds an additional scalar field to the familiar Einstein curvature tensor of General Relativity. The field is physically interpretable as a gravitational potential, or more precisely, a value that takes the global value of the gravitational constant G to a local effective gravitational constant G_{eff}. One as a result has to adapt the relationship between the curvature and the distribution of stress-energy, by introducing a coupling between matter and the scalar field. In BD, this is the Brans-Dicke coupling constant \omega. The higher the value of \omega, the more matter couples to the tensor part and the less to the scalar part of the scalar-tensor gravity. The value of \omega is not constrained by the theory: one has to look at the behaviour of the distribution of matter to constrain \omega.
In General Relativity, matter at a point can completely determine the Einstein curvature tensor at that point. In B-D, however, the scalar potential also has a role. So if the matter sources a solution in General Relativity, one needs an appropriate \omega to source a solution in B-D for a given value of the scalar potential.
The more we look at astrophysical phenomena, and the more we do direct tests in our solar system, the more strongly positive the lowest physically compatible value of \omega can be, or the closer to zero the magnitude of the scalar must be, or both.
If the value of the scalar is everywhere zero, it can simply be elided, and one gets General Relativity.
At \omega -> \infty BD has for all practical purposes identical behaviour to General Relativity for any value of the scalar. Parsimony in that case would favour GR: the scalar field, even at its |strongest|, would just not affect matter.
A goal of theoreticians trying to keep scalar-tensor theory alive and relevant as a physical possibility therefore is to have \omega very high everywhere except near compact objects such as (stellar!) black holes and neutron stars. Around them, they might hope, the strength of the self-interaction of the scalar field (like the self-interaction of the Einstein curvature tensor in General Relativity, and the tensor part of scalar-tensor) leads to interesting differences from General Relativity.
The result is a "cloud" of scalar self-interaction around compact objects caused by the very high but still not infinite coupling constant, and the presence of matter. This is called "spontaneous scalarization". In [paper ref [43]] the headline paper's second author explores whether there might be "spontaneous vectorization" if one substitutes a vector field for the scalar field. It does, and then generalizes to spontaneous "self-gravitating gravitational cloud" formation in any theory where matter couples to an additional gravitational component beyond the Einstein tensor.
Boiling this down: 2nd author Ramazanoğlu has been keen on finding some extra knobs to twiddle in strong gravity while ensuring the knob-twiddling produces no measurable effect in weak gravity, and he has a preference for vector-tensor rather than scalar-tensor gravity. In these, it's a dynamical vector field that couples to matter (only) gravitationally, so again one has a coupling constant to choose. Although the details of parametrizin...
* It's very strange that omega is not constant everywhere. I've read stranger things, but it's suspicious that it must change in a very specific way.
* This is not a mainline extension of GR. (Does this sentence even make sense? I mean, it's not like the supersymmetry extension of the standard model, that has a big chunk of the community behind it, but it's still far from confirmed.)
* When I read in the title "ghosts", I though it was a stupid press article translation of "perturbations" or something. I was confusing reading the paper. But now I understand it has a very specific technical meaning of a weird faster than light thing in weird objects (or they equations). If confirmed, are they real things, or just a math effect like in the phase vs group velocity problems?
Again, small caveat that to keep this close to ELI25, I am abusing some things (including changes in sign) in a way an expert will notice [they can refer to [1] where the signs and frames are dealt with carefully], but I believe this does not qualitatively affect the explanations you're looking for.
The Brans-Dicke (BD) coupling constant \omega can be constant everywhere in a specifically-modelled universe, and usually is. What varies by point in spacetime is the strength of the scalar field. \omega just relates the strength of that scalar field to its gravitational effects on matter. A BD universe with a higher \omega needs a higher absolute scalar value to deviate from General Relativity (which has no scalar potential field, and no \omega parameter).
One can vary anything in a theory, so a f(\omega)+f(scalar) theory is certainly something you can write down and explore the material consequences of. Usually you get an obviously unphysical theory. Even if the theory is not obviously unphysical, if it forces one to add more parameters that one proceeds to counter-tunes to match the good physical theory without these parameters, what is being gained? Maybe a deeper understanding of the more physical of the theories?
No theory that has an auxiliary gravitational field is properly an extension of General Relativity, it is an alternative to GR. This seems like a fine distinction, but auxiliary fields tend to produce astonishingly different outcomes for matter compared to General Relativity. One has to do headstands to suppress these differences or one gets a pretty different set of orbits (visible in signal-timings between spaceships, or lasers bouncing off the moon, etc) in our solar system, a very different count and/or average shape of galaxies, or a very different "texture" to the cosmic microwave background.
To be a candidate for a physical theory of gravitation, the alternative theory must of course match observations at least as well as General Relativity does. GR is supported by a lot of observations, especially in the weak field limit, and especially where GR differs from Newtonian gravitation far from masses.
The authors show that when they do a headstand to make the effects of the vector auxiliary gravitational field vanish in our solar system but not around neutron stars or small black holes, then matter around the black holes can trigger a gravitational avalanche, making the small black hole bigger than is possible by throwing all the nearby matter into it. In fact, it can run away and grow without bound, with the central mass M exceeding all the matter in the modelled universe.
This is caused by ghosts appearing when one does three things: (1) make the auxiliary scalar or vector field dense around and within these compact massive objects but sparse at a distance, (2) make the coupling of matter to the auxiliary field relevant (rather than vanishingly weak) and (3) add a quantum mechanical matter field. Fluctuations in the quantum matter produce fluctuations in the scalar field, and those fluctuations can take a one-way trip across some notional zero: rather than fluctuating from e.g. + -> 0 -> - and then back again - -> 0 -> +, a ghost gets in the way and keeps the fluctuated mode always negative (which means stronger gravitation than one expects from the local distribution of quantum matter).
> ... very specific technical meaning ...
Ghosts are almost always unphysical -- their presence breaks symmetries of nature that are well-tested, such as the local conservation of the proton mass, or a proton's passive or active gravitational charge. The passive charge is how a proton responds to a large nearby mass, while the active charge is how the proton affects the large nearby mass. One well-tested symmetry is that passive gravitational charge = active gravitational charge = mass.
Breaking the symmetries of the Poincaré group (the symmetries of Special Relativity: invariance under translation, rotation, and boost) with re...
Nice explanation! (I still don't understand all of the details.)
I hope to see you in the next GR discussion.
Anyway, one last question:
Did you choose the mass of the proton in the example because it's special? (The mass of the proton is not just the sum of the mass of the quarks, moreover, the mass of the quarks is quite small.) Is it equivalent to use the mass of the electron? (That has no inner parts (almost).)
I chose the proton mass because it dominates the ordinary matter component of the universe.
Chemistry and the absorption lines or astrophysical maser emissions of molecular clouds (of water, ammonia, and so on) works in all directions and at all scales, or we would very excitedly notice differences in the equivalents of the Lyman-alpha forest and wonder what was happening to protons in different parts of the universe. As far as we can tell, protons interact gravitationally, electromagnetically, and via weak interactions in identical fashion everywhere and everywhen.
We could certainly talk about electrons instead of protons. Focusing on baryons and discussing baryonic matter, rather than things like leptons, is more cultural than anything. For example: https://astronomy.swin.edu.au/cosmos/B/Baryonic+Matter
(Electrons and neutrons are practically always dancing with protons; for the most part it's only protons that you find going solo in large numbers in ionized clouds.
Likewise, where do you find most of the universe's quarks and gluons? In protons.)
Of course one could also say that as far as we can tell from observation, the Standard Model works well everywhere in the observed universe. There may be some small correcting terms yet to be added to make it work better or in regimes or regions not yet observed, but "small" is important there. (Personally, when I hear "SM" I hear relativistic QFT on curved spacetime, and start thinking of the behaviour of dozens of fields, and in that context electrons are already messy (cf. dressed electrons), and protons are almost incomprehensible: https://profmattstrassler.com/articles-and-posts/largehadron... just scratches the surface!)
"At the perturbative level it manifests as a tachyonic instability around spacetimes that solve Einstein’s equations."
At that early point, I realised that the article was either going to be bafflegab, or it was way over my head. Can anyone explain what a "tachyonic instability" is?
"Tachyon" literally means "speedy particle". It's used to refer to a particle traveling faster than the speed of light. Special relativity relates velocity to elapsed time for a particle, and the upshot of that is that anything with positive squared mass must be traveling at less than the speed of light.
When you learn about quantum field theory you find out that particles can be modeled as linearized modes of fields. e.g. the photon is a mode of the electro-magnetic field. This is a more general theory than just treating particles as fundamental, because it makes predictions for creation and annihilation of particles. Again, squared mass appears in these formulea.
If you write down a field theory with a squared mass term that is _negative_, you might naively think that this gives you particles that travel faster than the speed of light. However, the modes of such a field would not oscillate - they would grow exponentially (at least until they get out of the linear regime).
This is what is meant by a "tachyonic instability".
Question: as I recall the standard Schwarzchild metric allows for particles to move faster than light while falling into the black hole.
Would it be reasonably plausible that such instabilities get covered up by appropriate event horizons? E.g. how do we know that such tachyonic instabilities aren’t a physical effect of some kind?
My understanding of the paper is that it's pretty damn hard to get a new theory of gravity, other than general relativity. You might try and it might be ok at the perturbative level, but once you go to the strong field regime you are screwed, with development of instabilities. Their conclusion is applicable to a large class of modified theories of gravity.
14 comments
[ 0.22 ms ] story [ 40.8 ms ] threadLooking at collisions of neutron stars, perhaps it's possible to find difference from the predictions of General Relativity that may be helpful to discover an extension of the theory.
How bad is that? I'd love to read any correction or improvement from someone that is working in a related topic.
> Lastly, we stress that our results are relevant for most known extensions of spontaneous scalarization to other fields, not just the vectors, and our study can be considered as a first step to obtain a no-go theorem for extending spontaneous scalarization to other fields. For vector fields, Garcia-Saenz et al. [51] has identified the presence of ghost and gradient instabilities in the background of compact objects in a broad class of generalized Proca theories [84,85]. Similar concerns were also raised in the context of cosmology in Ref. [86]. Going beyond vector fields, all known formulations of nonminimally coupled spin-2 fields that could spontaneously grow are known to lead to ghost instabilities as well [75]. Likewise, p-form fields also have the same constraint structure we discussed in Sec. V, hence they suffer from similar divergent terms [87]. Spontaneous growth of spinor fields as it was introduced in Ref. [88] also contains divergent terms.
Essentially, build a theory (perturb the theory), and make a testable prediction that works on the large scale, but would be hard or impossible to observe on a weak gravity environment (for some definition of weak, I think they mean something less massive than a star).
They ask whether or not you can do something like this with a more complex, vector field (i.e. a new force/particle).
It's all very theoretical.
But it may give an avenue to find new physics, maybe even explain dark matter/energy.
> ... may be helpful to discover an extension of the theory.
The authors have a set of families of alternatives to General Relativity, and are exploring whether they are viable as a physical description of gravitation in our universe, and if not (spoiler: they're not; they admit this up front) whether any of them can be adapted into a good physical description.
The second author of the (purely theoretical) headline paper in [(headline)paper ref [43]] explored variations on Brans-Dicke (BD) scalar-tensor gravitation.
Briefly, BD adds an additional scalar field to the familiar Einstein curvature tensor of General Relativity. The field is physically interpretable as a gravitational potential, or more precisely, a value that takes the global value of the gravitational constant G to a local effective gravitational constant G_{eff}. One as a result has to adapt the relationship between the curvature and the distribution of stress-energy, by introducing a coupling between matter and the scalar field. In BD, this is the Brans-Dicke coupling constant \omega. The higher the value of \omega, the more matter couples to the tensor part and the less to the scalar part of the scalar-tensor gravity. The value of \omega is not constrained by the theory: one has to look at the behaviour of the distribution of matter to constrain \omega.
In General Relativity, matter at a point can completely determine the Einstein curvature tensor at that point. In B-D, however, the scalar potential also has a role. So if the matter sources a solution in General Relativity, one needs an appropriate \omega to source a solution in B-D for a given value of the scalar potential.
The more we look at astrophysical phenomena, and the more we do direct tests in our solar system, the more strongly positive the lowest physically compatible value of \omega can be, or the closer to zero the magnitude of the scalar must be, or both.
If the value of the scalar is everywhere zero, it can simply be elided, and one gets General Relativity.
At \omega -> \infty BD has for all practical purposes identical behaviour to General Relativity for any value of the scalar. Parsimony in that case would favour GR: the scalar field, even at its |strongest|, would just not affect matter.
A goal of theoreticians trying to keep scalar-tensor theory alive and relevant as a physical possibility therefore is to have \omega very high everywhere except near compact objects such as (stellar!) black holes and neutron stars. Around them, they might hope, the strength of the self-interaction of the scalar field (like the self-interaction of the Einstein curvature tensor in General Relativity, and the tensor part of scalar-tensor) leads to interesting differences from General Relativity.
The result is a "cloud" of scalar self-interaction around compact objects caused by the very high but still not infinite coupling constant, and the presence of matter. This is called "spontaneous scalarization". In [paper ref [43]] the headline paper's second author explores whether there might be "spontaneous vectorization" if one substitutes a vector field for the scalar field. It does, and then generalizes to spontaneous "self-gravitating gravitational cloud" formation in any theory where matter couples to an additional gravitational component beyond the Einstein tensor.
Boiling this down: 2nd author Ramazanoğlu has been keen on finding some extra knobs to twiddle in strong gravity while ensuring the knob-twiddling produces no measurable effect in weak gravity, and he has a preference for vector-tensor rather than scalar-tensor gravity. In these, it's a dynamical vector field that couples to matter (only) gravitationally, so again one has a coupling constant to choose. Although the details of parametrizin...
My takeaway:
* It's very strange that omega is not constant everywhere. I've read stranger things, but it's suspicious that it must change in a very specific way.
* This is not a mainline extension of GR. (Does this sentence even make sense? I mean, it's not like the supersymmetry extension of the standard model, that has a big chunk of the community behind it, but it's still far from confirmed.)
* When I read in the title "ghosts", I though it was a stupid press article translation of "perturbations" or something. I was confusing reading the paper. But now I understand it has a very specific technical meaning of a weird faster than light thing in weird objects (or they equations). If confirmed, are they real things, or just a math effect like in the phase vs group velocity problems?
The Brans-Dicke (BD) coupling constant \omega can be constant everywhere in a specifically-modelled universe, and usually is. What varies by point in spacetime is the strength of the scalar field. \omega just relates the strength of that scalar field to its gravitational effects on matter. A BD universe with a higher \omega needs a higher absolute scalar value to deviate from General Relativity (which has no scalar potential field, and no \omega parameter).
One can vary anything in a theory, so a f(\omega)+f(scalar) theory is certainly something you can write down and explore the material consequences of. Usually you get an obviously unphysical theory. Even if the theory is not obviously unphysical, if it forces one to add more parameters that one proceeds to counter-tunes to match the good physical theory without these parameters, what is being gained? Maybe a deeper understanding of the more physical of the theories?
No theory that has an auxiliary gravitational field is properly an extension of General Relativity, it is an alternative to GR. This seems like a fine distinction, but auxiliary fields tend to produce astonishingly different outcomes for matter compared to General Relativity. One has to do headstands to suppress these differences or one gets a pretty different set of orbits (visible in signal-timings between spaceships, or lasers bouncing off the moon, etc) in our solar system, a very different count and/or average shape of galaxies, or a very different "texture" to the cosmic microwave background.
To be a candidate for a physical theory of gravitation, the alternative theory must of course match observations at least as well as General Relativity does. GR is supported by a lot of observations, especially in the weak field limit, and especially where GR differs from Newtonian gravitation far from masses.
The authors show that when they do a headstand to make the effects of the vector auxiliary gravitational field vanish in our solar system but not around neutron stars or small black holes, then matter around the black holes can trigger a gravitational avalanche, making the small black hole bigger than is possible by throwing all the nearby matter into it. In fact, it can run away and grow without bound, with the central mass M exceeding all the matter in the modelled universe.
This is caused by ghosts appearing when one does three things: (1) make the auxiliary scalar or vector field dense around and within these compact massive objects but sparse at a distance, (2) make the coupling of matter to the auxiliary field relevant (rather than vanishingly weak) and (3) add a quantum mechanical matter field. Fluctuations in the quantum matter produce fluctuations in the scalar field, and those fluctuations can take a one-way trip across some notional zero: rather than fluctuating from e.g. + -> 0 -> - and then back again - -> 0 -> +, a ghost gets in the way and keeps the fluctuated mode always negative (which means stronger gravitation than one expects from the local distribution of quantum matter).
> ... very specific technical meaning ...
Ghosts are almost always unphysical -- their presence breaks symmetries of nature that are well-tested, such as the local conservation of the proton mass, or a proton's passive or active gravitational charge. The passive charge is how a proton responds to a large nearby mass, while the active charge is how the proton affects the large nearby mass. One well-tested symmetry is that passive gravitational charge = active gravitational charge = mass.
Breaking the symmetries of the Poincaré group (the symmetries of Special Relativity: invariance under translation, rotation, and boost) with re...
I hope to see you in the next GR discussion.
Anyway, one last question:
Did you choose the mass of the proton in the example because it's special? (The mass of the proton is not just the sum of the mass of the quarks, moreover, the mass of the quarks is quite small.) Is it equivalent to use the mass of the electron? (That has no inner parts (almost).)
Chemistry and the absorption lines or astrophysical maser emissions of molecular clouds (of water, ammonia, and so on) works in all directions and at all scales, or we would very excitedly notice differences in the equivalents of the Lyman-alpha forest and wonder what was happening to protons in different parts of the universe. As far as we can tell, protons interact gravitationally, electromagnetically, and via weak interactions in identical fashion everywhere and everywhen.
We could certainly talk about electrons instead of protons. Focusing on baryons and discussing baryonic matter, rather than things like leptons, is more cultural than anything. For example: https://astronomy.swin.edu.au/cosmos/B/Baryonic+Matter (Electrons and neutrons are practically always dancing with protons; for the most part it's only protons that you find going solo in large numbers in ionized clouds. Likewise, where do you find most of the universe's quarks and gluons? In protons.)
Of course one could also say that as far as we can tell from observation, the Standard Model works well everywhere in the observed universe. There may be some small correcting terms yet to be added to make it work better or in regimes or regions not yet observed, but "small" is important there. (Personally, when I hear "SM" I hear relativistic QFT on curved spacetime, and start thinking of the behaviour of dozens of fields, and in that context electrons are already messy (cf. dressed electrons), and protons are almost incomprehensible: https://profmattstrassler.com/articles-and-posts/largehadron... just scratches the surface!)
At that early point, I realised that the article was either going to be bafflegab, or it was way over my head. Can anyone explain what a "tachyonic instability" is?
When you learn about quantum field theory you find out that particles can be modeled as linearized modes of fields. e.g. the photon is a mode of the electro-magnetic field. This is a more general theory than just treating particles as fundamental, because it makes predictions for creation and annihilation of particles. Again, squared mass appears in these formulea.
If you write down a field theory with a squared mass term that is _negative_, you might naively think that this gives you particles that travel faster than the speed of light. However, the modes of such a field would not oscillate - they would grow exponentially (at least until they get out of the linear regime).
This is what is meant by a "tachyonic instability".
Would it be reasonably plausible that such instabilities get covered up by appropriate event horizons? E.g. how do we know that such tachyonic instabilities aren’t a physical effect of some kind?