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

[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).