# MOND - general discussion

• I
• haushofer
In summary, the conversation discusses the concept of scale invariance and its relation to MOND, a modified theory of gravity that attempts to explain the observed discrepancy between the predicted and observed motion of galaxies. The conversation also touches upon the Galilean Conformal Algebra and its potential connection to MOND, as well as the theories of Skordis and Zlosnik and their use of a timelike vector field to account for dark matter effects.

#### haushofer

I was glancing through

https://arxiv.org/abs/1605.07458

I don't fully get why scale invariance kicks in below a certain acceleration. Is this because the centripetal force becomes constant? I do see that Newton's second law with the centripetal force included is scale invariant. This symmetry reminds me about the Galilean Conformal Algebra (as opposed to the Schrödinger algebra). Is there any relation between this GCA and MOND?

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haushofer said:
Some of the earlier papers are a bit better at explaining these things, e.g., this and this.

haushofer said:
I don't fully get why scale invariance kicks in below a certain acceleration.
No one really knows the fundamental reason behind this.

haushofer said:
Is this because the centripetal force becomes constant? I do see that Newton's second law with the centripetal force included is scale invariant.
The phenomenological motivation for inferring some kind of transitioning from the well-known non-uniform scale invariance (underlying Kepler's 3rd law) to uniform scale invariance is as follows. If ##v_{tan}## becomes constant over a certain span of radii, that implies scale invariance (since if ##r \to \lambda r## and ##t \to \lambda t##, then ##v_{tan}## stays constant). However, comparing galaxies of similar type, but different sizes, shows that this transition is not governed by a length scale, but rather an acceleration scale. These 2 pieces of empirical information inform the 2nd tenet of MOND, namely that, in the deep-MOND limit (##a_0 \to \infty##) the equations of motion can be written in a form where the constants ##G##, ##a_0##, and all masses ##m_i## in the problem, appear only as the product ##m_i G a_0##.

haushofer said:
This symmetry reminds me about the Galilean Conformal Algebra (as opposed to the Schrödinger algebra). Is there any relation between this GCA and MOND?
In arXiv:0810.4065 (and elsewhere) there's a reference to some of Milgrom's earlier work on this. In particular, on p5 it says
Milgrom said:
[...] in Milgrom (1997) [I showed] that the deep-MOND limit of the Bekenstein and Milgrom
(1984) formulation for the field equation for the potential is, in fact, invariant under the whole group of conformal space transformation (which includes space scaling). The above deep-MOND action is not invariant, but is multiplied by a constant under scaling.
... but I have not yet studied this region of the MOND literature.

haushofer
Deur's analysis is that in spiral galaxies MOND arises from the self-interaction of the gravitational field in a non-spherically symmetric matter field that is approximately a disk. http://dispatchesfromturtleisland.blogspot.com/p/deurs-work-on-gravity-and-related.html

Others have noted the apparent connection between the MOND acceleration and the diameter of the observable universe, which might suggest a horizon effect.

A few new MOND thoughts. Item 1 I think is significant. Items 2 and 3 are really just questions that I've asked myself, but haven't had time to answer...

(1) Probably the most important item: astronomer Stacy McGaugh, who has been a crucial advocate for MOND in recent years, just blogged that he considers the "aether scalar tensor" theory (AeST) of Skordis and Zlosnik (papers 1 2) to be the best theory at this point. That's a huge endorsement.

AeST contains a "timelike vector field" A (that's the "aether"), a scalar field, and the usual metric tensor.

(2) I recall that Sabine Hossenfelder's theory also had a vector field, called the "imposter field".

Is there anything in common between how Hossenfelder's imposter field, and Skordis and Zlosnik's aether field, account for dark matter effects?

(3) This item is really stretching things, but anyway... We've discussed Peter Woit's "Euclidean Twistor Unification" a few times. From the abstract: "Reconstructing a Lorentz signature theory requires introducing a degree of freedom specifying the imaginary time direction..."

Could that have anything in common with the timelike vector field of Skordis and Zlosnik?

kodama and ohwilleke
mitchell porter said:
A few new MOND thoughts. Item 1 I think is significant. Items 2 and 3 are really just questions that I've asked myself, but haven't had time to answer...

(1) Probably the most important item: astronomer Stacy McGaugh, who has been a crucial advocate for MOND in recent years, just blogged that he considers the "aether scalar tensor" theory (AeST) of Skordis and Zlosnik (papers 1 2) to be the best theory at this point. That's a huge endorsement.

AeST contains a "timelike vector field" A (that's the "aether"), a scalar field, and the usual metric tensor.

(2) I recall that Sabine Hossenfelder's theory also had a vector field, called the "imposter field".

Is there anything in common between how Hossenfelder's imposter field, and Skordis and Zlosnik's aether field, account for dark matter effects?

(3) This item is really stretching things, but anyway... We've discussed Peter Woit's "Euclidean Twistor Unification" a few times. From the abstract: "Reconstructing a Lorentz signature theory requires introducing a degree of freedom specifying the imaginary time direction..."

Could that have anything in common with the timelike vector field of Skordis and Zlosnik?
Not a full response, but the first relativistic generalization of MOND, the TeVeS theory by Bekenstein was (aside from a pun in Hebrew) a tensor-vector-scalar theory. So was Moffat's MOG theory.

GR research has done a lot of work in tensor-scalar theories which typically describe GR plus dark energy phenomena, but not necessarily dark matter phenomena, while most, although not necessarily all, GR modifications that describe dark matter phenomena have a vector component.

mitchell porter said:
A few new MOND thoughts. Item 1 I think is significant. Items 2 and 3 are really just questions that I've asked myself, but haven't had time to answer...

(1) Probably the most important item: astronomer Stacy McGaugh, who has been a crucial advocate for MOND in recent years, just blogged that he considers the "aether scalar tensor" theory (AeST) of Skordis and Zlosnik (papers 1 2) to be the best theory at this point. That's a huge endorsement.

AeST contains a "timelike vector field" A (that's the "aether"), a scalar field, and the usual metric tensor.

(2) I recall that Sabine Hossenfelder's theory also had a vector field, called the "imposter field".

Is there anything in common between how Hossenfelder's imposter field, and Skordis and Zlosnik's aether field, account for dark matter effects?

(3) This item is really stretching things, but anyway... We've discussed Peter Woit's "Euclidean Twistor Unification" a few times. From the abstract: "Reconstructing a Lorentz signature theory requires introducing a degree of freedom specifying the imaginary time direction..."

Could that have anything in common with the timelike vector field of Skordis and Zlosnik?

is there a quanta with timelike vector field or a scalar field?

how is this any different from introducing new dark matter with timelike vector field or a scalar field?

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ohwilleke said:
Others have noted the apparent connection between the MOND acceleration and the diameter of the observable universe, which might suggest a horizon effect.
McCulloch tried to develop this idea, but my impression is that his attempt (which seems now to have launched off into fairy land, imho, -- see "quantized inertia", "horizon drive" if you're a masochist) has been debunked. There are even youtube video(s) about this.

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mitchell porter said:
(1) Probably the most important item: astronomer Stacy McGaugh, who has been a crucial advocate for MOND in recent years, just blogged that he considers the "aether scalar tensor" theory (AeST) of Skordis and Zlosnik (papers 1 2) to be the best theory at this point. That's a huge endorsement.
I saw that blog post, but haven't yet had time to re-study the SZ theory in detail. Note however, that Prof McGaugh is primarily an experimentalist and he says of himself (in another blog post, iirc) that he is unlikely to come up with a foundational theory underpinning MOND phenomenology.

mitchell porter said:
AeST contains a "timelike vector field" A (that's the "aether"), a scalar field, and the usual metric tensor.

(2) I recall that Sabine Hossenfelder's theory also had a vector field, called the "imposter field".

Is there anything in common between how Hossenfelder's imposter field, and Skordis and Zlosnik's aether field, account for dark matter effects?
When I asked Sabine about this similarity, (which is also noted in Milgrom's Scholarpedia Article), her reply was a tad indignant at the suggested comparison, but istm that it's the same class of theory, the difference being down in the detail. I need to study both theories again. (But sheesh, I really wish Sabine would write her technical papers with a bit more helpfully detailed explanations -- I always feel like I'm wading through a swamp when I try to read her papers. )

mitchell porter said:
(3) This item is really stretching things, but anyway... We've discussed Peter Woit's "Euclidean Twistor Unification" a few times. From the abstract: "Reconstructing a Lorentz signature theory requires introducing a degree of freedom specifying the imaginary time direction..."

Could that have anything in common with the timelike vector field of Skordis and Zlosnik?
Yes, that really is stretching things beyond the speculations tolerated in the BTSM forum...

Try getting a scale-invariant force law out of anything in Euclidean Twistor Unification. Sure, something like that should be in there somewhere, since twistors are the spinors of the conformal group in which dilation invariance is prominent. But there's a long way still to go. There needs to be some kind of interpolation between Newtonian-scale phenomena and deep-MOND scale-invariant phenomena.

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kodama said:
is there a quanta with timelike vector field or a scalar field? How is this any different from introducing new dark matter with timelike vector field or a scalar field?
Well, there's the massive vector bosons of the weak interaction, but they have non-gravitational interactions.

You could try massive Proca fields with only gravitational interaction, but I don't know if they have any real-world presence. I noticed some papers about Proca fields interacting with gravity -- hence in the same ballpark as "Einstein-Aether" (distinguished vector field) theories, but I haven't studied them in detail.

The Higgs is a scalar field of course, but it's not an interact-only-with-gravity type of particle.

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kodama
ohwilleke said:
[...] the first relativistic generalization of MOND, the TeVeS theory by Bekenstein was (aside from a pun in Hebrew) a tensor-vector-scalar theory. So was Moffat's MOG theory.
IIRC/IIUC, in TeVeS the interpolation function must still be put in by hand. If that's right, then it's not a foundational theory. I.e., not a "Fundamond". **

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** I first saw the term "Fundamond" coined by Milgrom in Models of modified-inertia formulation of MOND:
Milgrom said:
[...] MOND, as we know it now, and as described by any of its presently-known formulations, is, arguably, an effective theory, an approximation, that must have roots in a more fundamental theory – a “Fundamond”.

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strangerep said:
IIRC/IIUC, in TeVeS the interpolation function must still be put in by hand. If that's right, then it's not a foundational theory. I.e., not a "Fundamond". **

-------------------------------------
** I first saw the term "Fundamond" coined by Milgrom in Models of modified-inertia formulation of MOND:

Deur is the best game in town when it comes to providing a Fundamond. Far better, for example, than aether theories.

ohwilleke said:
Deur is the best game in town when it comes to providing a Fundamond.
... if it actually worked the way he claims. but his papers do not contain enough detail to assess that reliably. Too much hand waving, imho.

ohwilleke said:
Far better, for example, than aether theories.
An Einstein-Aether (distinguished vector field) theory is of course not a Fundamond, if the origin of the vector field remains a mystery.

strangerep said:
... if it actually worked the way he claims. but his papers do not contain enough detail to assess that reliably. Too much hand waving, imho.

An Einstein-Aether (distinguished vector field) theory is of course not a Fundamond, if the origin of the vector field remains a mystery.
The only other real Fudamond candidate out there with any significant development is probably Verlinde's work.

If we speak of Verlinde's work, then we must also speak of Hossenfelder's covariant version (although she does not claim it to be fundamental in the way that Verlinde did, since she does not embrace Verlinde's interpretation of the distinguished vector field).

In this vein, I (belatedly) just noticed the following paper:

Mistele, McGaugh, Hossenfelder,
Galactic mass-to-light ratios with superfluid dark matter

wherein they compare the predictions of Mistele+Hossenfelder's Covariant Emergent Gravity (CEG) / Superfluid Dark Matter (SFDM) theory (in which the additional field in CEG is interpreted as being in a superfluid phase) against the McGaugh's SPARC database.

The conclusion of this paper says:

We have found that it is difficult to reproduce the achievements of MOND with the models that have so far been proposed for SFDM.

kodama and ohwilleke