I Galaxy with no dark matter? (NGC1052-DF2)

[PeterDonis]

Its clear that space time is not constant density, hence the variance of gravitational effects that have resulted in galaxy clusters.

This is due to variations in the density of matter (and energy, pressure, etc.--all the things that go into the stress-energy tensor). It is not due to variations in "the density of spacetime". There is no such thing as "the density of spacetime" unless you want to use that term to describe the cosmological constant, but then, as I've already said, it must be constant if it's going to be a property of spacetime (as opposed to a property of matter, energy, pressure, etc.).

The energy density of space-time, is always measured to be the same locally, only marginally less that matter.

I have no idea what you are talking about here. Can you give an actual equation, and a reference for where you are getting it from?

 

[phinds]

We see X. Where X = gravitational effects on space-time in turn effecting matter and light. We know that matter can have this effect on space-time. But am I wrong or we really don't really understand what makes up space-time, and why massive objects cause it to bend?

Since you put "bending" in quotes in a previous post, I assume you understand the following, but just in case you don't, space-time does NOT bend / stretch, or do anything that matter does. We SAY that it bends because objects in space-time with no external force being applied to them follow geodesics, which are STRAIGHT lines in space-time but are "curved" only when looked at by improperly applying Euclidean Geometry to a domain where it is not valid but where you need instead Riemann Geometry (actually, I've been told it's "pseudo" Riemann Geometry but in any case it's not Euclidean and nothing bends/stretches/curves, etc).

 

[JMz]

This is not necessarily true. The main issue is how DM behaves and for a DM candidate that is thermally produced in the early Universe, you typically need it to be heavier than neutrinos to constitute cold dark matter. However, thermal production at a relatively late stage is not the only possibility. A very popular DM candidate these days is axion DM, which is very appealing from many perspectives. Axions typically have very (very!) light masses and the corresponding DM halos are not built from particles as much as from coherent states, i.e., essentially classical fields.

Very nice. This makes the unit of field construction some kind of clump of many axions. Presumably the effective number of degrees of freedom of such a field is far smaller than the number of axions comprising it, right? (My guess, from this reasoning, is that the d.f. ratio is much larger than the neutrino/axion mass ratio.)

 

[Orodruin]

where you need instead Riemann Geometry (actually, I've been told it's "pseudo" Riemann Geometry but in any case it's not Euclidean and nothing bends/stretches/curves, etc).

Just to make this clear. Riemann geometry describes a manifold that is equipped with a metric tensor, which by definition is positive definite. Euclidean geometry is a special case of Riemannian geometry so its really not excluding Euclidean to state Riemannian. A pseudo-Riemannian geometry involves a pseudo-metric, which instead of being positive definite has the requirement of being non-degenerate. If you want to split hairs further, Lorentzian geometry has a pseudo-metric with a 1+n or n+1 signature. Minkowski space is to Lorentzian geometry what Euclidean space is to Riemannian geometry.

 

[phinds]

Just to make this clear. Riemann geometry describes a manifold that is equipped with a metric tensor, which by definition is positive definite. Euclidean geometry is a special case of Riemannian geometry so its really not excluding Euclidean to state Riemannian. A pseudo-Riemannian geometry involves a pseudo-metric, which instead of being positive definite has the requirement of being non-degenerate. If you want to split hairs further, Lorentzian geometry has a pseudo-metric with a 1+n or n+1 signature. Minkowski space is to Lorentzian geometry what Euclidean space is to Riemannian geometry.

So do you think space-time really "bends"?

 

[Orodruin]

Very nice. This makes the unit of field construction some kind of clump of many axions. Presumably the effective number of degrees of freedom of such a field is far smaller than the number of axions comprising it, right? (My guess, from this reasoning, is that the d.f. ratio is much larger than the neutrino/axion mass ratio.)

Yes. As with any coherent state, the field expectation value satisfies the classical equations of motion and it does not contain a well-defined number of axions (it is not an eigenstate of the axion number operator). If I understand correctly, a dark matter halo in the axion DM models is essentially a soliton solution to the classical field equations, but I am not an expert in axion DM.

 

[Orodruin]

So do you think space-time really "bends"?

"Bend" is not a well defined term. Also, we all know that "really" is a bit subjective. Please define what you mean by "spacetime bends".

 

[JMz]

Labeling an unknown gravitational phenomena a form of matter, tends to narrow one's thinking about the problem, and put it in a box. Does it not? We haven't had to contend with an potential alternate theory of gravity until the confirmation that the effects of "dark matter" exist.

I think you are downplaying the huge variety of theories of gravity that have been proposed in the century+ since GR was proposed. Many of these generated creative thinking about new experiments that could distinguish them from GR. So far, no theory has done better than GR.

As recently as last year, a whole swath of alternative theories were ruled out by the single observation of the LIGO/Virgo observation of the kilonova. Why did they exist? Because people are contending with, and proposing, alternative theories of gravity, all the time.

 

[phinds]

"Bend" is not a well defined term.

I think it is quite well defined to say, for example, "a metal rod bends". It really bends Does space-time?

 

[Orodruin]

I think it is quite well defined to say, for example, "a metal rod bends". It really bends Does space-time?

Again, "bends" has no well defined meaning in the context. Please define what you mean by the word if you want to make a question.

 

[phinds]

Again, "bends" has no well defined meaning in the context. Please define what you mean by the word if you want to make a question.

Sorry, I meant to say in the previous post that I agree w/ you that "bends" is ill defined in the context of space-time, so I think it's a bit of a meaningless argument, I just don't like seeing people say "space-time bends" because that, to me, makes a false assumption that space-time is material that can be bent / stretched, etc and that is a misunderstanding that can lead to other misunderstandings.

 

[JMz]

Yes. As with any coherent state, the field expectation value satisfies the classical equations of motion and it does not contain a well-defined number of axions (it is not an eigenstate of the axion number operator). If I understand correctly, a dark matter halo in the axion DM models is essentially a soliton solution to the classical field equations, but I am not an expert in axion DM.

Thanks. Given how large the ratio must be, the "effective number in a clump", I would have been shocked if someone proposed an eigenstate that matched it, especially if it was supposed to be particularly stable against perturbations.

 

[Orodruin]

Sorry, I meant to say in the previous post that I agree w/ you that "bends" is ill defined in the context of space-time, so I think it's a bit of a meaningless argument, I just don't like seeing people say "space-time bends" because that, to me, makes a false assumption that space-time is material that can be bent / stretched, etc and that is a misunderstanding that can lead to other misunderstandings.

This likely comes from a misappropriation of "curved spacetime". People unfamiliar with nomenclature are likely to use them as essentially synonymous. If you use them as synonymous, then yes, spacetime is "bent" (i.e., "curved" in the well-defined mathematical sense of parallel transport around a loop not necessarily giving back the same vector) and the equations governing this curvature has the stress-energy tensor as its source term.

Thanks. Given how large the ratio must be, the "effective number in a clump", I would have been shocked if someone proposed an eigenstate that matched it, especially if it was supposed to be particularly stable against perturbations.

Even if it is not an eigenstate, as with any state you can of course compute the expectation value of the number operator ... It will be large.

 

[Grinkle]

This likely comes from a misappropriation of "curved spacetime".

I think it comes from a lack of math background.

I propose that a reasonable definition of bends is something that does not follow a geodesic. I speculate , as I do not have any formal mathematical understanding of geometries, that saying 'spacetime bends' is not a self-consistent statement, because its (spacetime's) shape is defined by some mathematical description which also defines consistent geodesics and it is therefore contradictory to say that spacetime bends. By definition, it can't. Its shape, whatever it is, defines straight. Any two points in a spacetime are connected by a geodesic.

If I am wrong that a geodesic is the shortest path length connecting two points for some given geometry, then the above make no sense. I can only hope it makes at least some sense otherwise.

edit:

In case that is too scattered to make sense of, an example of what I am thinking is 'curved Euclidean planes' - if a Euclidean plane is curved with respect to Euclidean geometry, its not Euclidean, its instead a plane in some other geometry.

 

[kimbyd]

Yes I am aware of the multiple ways gravitational effects can manifest itself, but what are referring to is how these gravitational effects result in the observable universe, so not sure how twisting forces are revenant here in regards to forming galaxy clusters. It relates to how space time reacts to massive objects, and how matter and energy react to the "bending" of space time. Dark matter may not be a particle at all.

The only other option besides a particle is modified gravity. And as I pointed out, modified gravity theories conceived to date do not fit with observation without at least some dark matter.

Edit: To clarify, based upon our understanding of quantum mechanics, everything in the universe is made out of fields, and fields can be quantized into particles.

 

[PeterDonis]

I propose that a reasonable definition of bends is something that does not follow a geodesic.

This is a reasonable definition of a path bending, yes; i.e., it's what it means to say that a circle, for example, is curved in Euclidean geometry, as opposed to a straight line. However, note that this definition of curvature is extrinsic--it depends on the curve being embedded in a higher dimensional space in a particular way.

However, when we say in GR that spacetime is curved, we are talking about intrinsic curvature--curvature that can be defined simply by the intrinsic features of the manifold, without making use of any embedding in any higher dimensional space. There is no such thing for a one-dimensional curve; the lowest dimension a manifold can have and have intrinsic curvature at all is 2. And in 2 or more dimensions, the definition of "curved" is "has a nonzero Riemann tensor"--or, to put it in more concrete terms, that parallel transporting a vector around a closed curve does not leave the vector unchanged.

Its shape, whatever it is, defines straight. Any two points in a spacetime are connected by a geodesic.

This is true, but it only means that we can always find a straight curve--straight in the sense of extrinsic curvature, i.e., no bending of the path, i.e., a geodesic--between any two points. It does not mean that there is no difference at all between, for example, a flat Euclidean plane and a 2-sphere like the surface of the Earth. There is; but that difference cannot be captured by just looking at individual geodesics. You have to look at how multiple geodesics "fit together", so to speak--for example, by looking at what happens to a vector when you parallel transport it around a closed curve composed of geodesic segments, which is what the Riemann tensor describes.

 

[Grinkle]

@PeterDonis Can you recommend a lay-person book or textbook on whatever math it is that is behind what you are describing?

I have in my (distant) past 4 semesters of calculus and 2 semesters (one undergrad and one grad) of engineering analysis, stated to give an idea of whether I am in any position to study this math.

 

[PeterDonis]

Can you recommend a lay-person book or textbook on whatever math it is that is behind what you are describing?

Carroll's online lecture notes on GR give a good introduction to the math of manifolds, tensors, and curvature in the first couple of chapters:

https://arxiv.org/abs/gr-qc/9712019

 

[Orodruin]

To clarify, based upon our understanding of quantum mechanics, everything in the universe is made out of fields, and fields can be quantized into particles.

I would not put it like this as it seems to put an equal sign between quantum fields and particles. Particles are a particular type of state of a quantum field, but the phenomenology would be so much more dull if they were the only type of state. Only considering particles you miss out on any non-perturbative effects as well as the coherent states (and thereby the classical limit).