More Experimental Evidence for MOND

[ohwilleke]

Why not?

Because the object is within a gravitational field significantly in excess of a₀ (which by construction, in MOND, can only arise from a gravitational source whose Newtonian gravitational acceleration at that point is in excess of a₀).

I only say "significantly" because, at the fine margins, the structure of the interpolation function matters. But, no planets or dwarf planets in the solar system are at the fine margins since the Newtonian gravitational acceleration from the Sun upon all of them far exceeds a₀. The Newtonian gravitational acceleration from the Sun on Pluto at its average distance from the Sun is about 32,500 times a₀.

 

[strangerep]

So in short, for small $r$ or big acceleration modifying gravity is not needed (the $1/r$ contribution is small compared to the $1/r^2$ contribution).

MOND interpolation functions are governed by an acceleration scale ($a_0$), not a length scale.

Thus MOND (simply from the math) applies numerically not to the interior of a star but very much so for objects distant enough from the star.

MOND "applies" to every point in spacetime. One calculates the total $\nabla\Phi$ by conventional means, and then applies a $\nu()$ (force-side) interpolation function to get the physically relevant field at every point.

 

[ohwilleke]

MOND "applies" to every point in spacetime. One calculates the total $\nabla\Phi$ by conventional means, and then applies a $\nu()$ (force-side) interpolation function to get the physically relevant field at every point.

I think what is trying to be said is that MOND is indistinguishable from Newtonian gravity in the interior of a star (although, of course, all MOND physicists would agree that there are probably significant non-Newtonian GR effects in the interior of a star and that the the interior of a star is beyond the domain of applicability of simple toy model MOND).

 

[PeterDonis]

Milgrom discusses it generally at Scholarpedia

Ok, I've read this article and I'm still confused about the External Field Effect. Let me try to explain why.

First, compare with standard Newtonian gravity. The dynamical law, if we put it in terms of acceleration, is simple: $a = G M / r^2$. If we have multiple gravitating masses, we simply vector sum the accelerations due to each one to get the final acceleration. The Newtonian approximation to GR works the same way; in fact we can even go several orders into the post-Newtonian approximation in GR and still have things work the same way. (The standard framework for this is the Einstein-Infeld-Hoffman equations.)

What is the corresponding law for MOND? I don't see one explicitly given in the article, but from what I can gather the acceleration law is an interpolation between the above Newtonian one for $a >> a_0$ and the asymptotic law given in the article, $a = \sqrt{G M a_0} / r$ for $a << a_0$ (where I have substituted the formula given for $r_M$). But given that law for a single source with mass $M$, it would see like the law for multiple sources would work the same way as above: just vector sum the accelerations due to each source.

But if we just vector sum the accelerations due to each source, where is the need for any "External Field Effect"?

 

[PeterDonis]

Milgrom discusses it generally at Scholarpedia

Another thing in the article bothers me: the treatment of the "accelerations" involved as though they were proper accelerations, instead of recognizing that all of the objects involved are in free fall. For example, at one point the article states that an acceleration defines a length scale, and mentions the Unruh effect. But only proper accelerations define a length scale in this respect. "Accelerations due to gravity" do not. (For example, the article says that $c^2 / a$, the length scale for acceleration $a$, limits the size of a locally free falling frame that can be constructed centered on the object--but that is only true if $a$ is a proper acceleration. The only limit on the size of a locally free falling frame centered on a free falling object is spacetime curvature, which has nothing to do with the "acceleration due to gravity" on the object.)

 

[strangerep]

I think what is trying to be said

Huh? "Said" by who?

is that MOND is indistinguishable from Newtonian gravity in the interior of a star [...]

Deep in the interior of a sphere of gravitating matter, Newtonian gravity is very small. So there we must work with the total field, including any (usually very weak) field arising from source(s) outside the sphere.

 

[strangerep]

Another thing in the article bothers me: the treatment of the "accelerations" involved as though they were proper accelerations, instead of recognizing that all of the objects involved are in free fall. For example, at one point the article states that an acceleration defines a length scale, and mentions the Unruh effect. [...]

I, too, don't like the way Milgrom (and some other MONDian zealots) casually use Newtonian gravity, but flip over to relativistic concepts when it suits them.

I reckon the 5th (or is it 6th?) tenet of MOND should be: "read lots of other MOND authors besides Milgrom".

 

[strangerep]

First, compare with standard Newtonian gravity. The dynamical law, if we put it in terms of acceleration, is simple: $a = G M / r^2$. [...] What is the corresponding law for MOND?

That over-simplified formula is highly error-prone when you're about to work with MOND. You should use the full formula involving something like the $(r_1 - r_2)$ vector that I described in my earlier long post. You can't validly go from this simplistic formula to a MONDian version. I explained why in my earlier post -- one immediately encounters violations of Newton's 3rd aw.

I don't see one explicitly given in the article, but from what I can gather the acceleration law is an interpolation between the above Newtonian one for $a >> a_0$ and the asymptotic law given in the article, $a = \sqrt{G M a_0} / r$ for $a << a_0$ (where I have substituted the formula given for $r_M$). But given that law for a single source with mass $M$, it would see like the law for multiple sources would work the same way as above: just vector sum the accelerations due to each source.

... which only has a slim chance of working if you use the full formulas, including the equation of motion for the CoM.

This is why it's better (i.e., less confusing) to use the MoG formulation of MOND, using a "force-side" $\nu()$ interpolation function rather than an "inertia-side" $\mu()$ interpolation function. Then you can just compute the total conventional field, and apply the $\nu()$ interpolation function thereto.

 

[PeterDonis]

one immediately encounters violations of Newton's 3rd aw

I guess that would be because the acceleration is not linear in $M$?

If so, how is MOND even a viable model at all? $F = ma$ still has to work, right? And if $F = ma$ works, but $F$ is not symmetric (i.e., Newton's third law is violated), then you simply have an inconsistent model, right?

 

[PeterDonis]

This is why it's better (i.e., less confusing) to use the MoG formulation of MOND, using a "force-side" $\nu()$ interpolation function rather than an "inertia-side" $\mu()$ interpolation function. Then you can just compute the total conventional field, and apply the $\nu()$ interpolation function thereto.

But this just puts me back to my earlier question: "compute the total conventional field" means including all of the potentials $\Phi$ from all sources. Once we've done that, and derived a force from it (using whatever "force-side interpolation" you like), where is there any room left for an "external field effect"?

 

[strangerep]

I guess that would be because the acceleration is not linear in $M$?

In the Wikipedia entry or AQUAL there's a sloppy, sketch of this, with vector and sign errors. But I managed to correct it for myself once I saw the general idea. (I'm sure you'd be able to do likewise -- see below for why I don't show it in detail right now).

If so, how is MOND even a viable model at all? $F = ma$ still has to work, right? And if $F = ma$ works, but $F$ is not symmetric (i.e., Newton's third law is violated), then you simply have an inconsistent model, right?

Please read my post #15 again, carefully. F=ma can be made to work as long as we work carefully with the vectors, and separate out the CoM and Rel motions. (I guess I'll have to add some more math to that post, but right now I'm traveling and won't able to post anything nontrivial until next week.)

Regardless, the above is the main reason why I find the formulation with a $\nu()$ "force-side" interpolation function easier to work with.

 

[strangerep]

But this just puts me back to my earlier question: "compute the total conventional field" means including all of the potentials $\Phi$ from all sources. Once we've done that, and derived a force from it (using whatever "force-side interpolation" you like), where is there any room left for an "external field effect"?

There isn't. That's why I think all this MONDian EFE stuff is just a big, unnecessary, misleading kerfuffle.

 

[PeterDonis]

F=ma can be made to work as long as we work carefully with the vectors, and separate out the CoM and Rel motions.

Why do we need to separate out the motions? If the altered behavior in the MOND model depends on (some interpolated function of) the gradient of the total potential, then it depends on the total potential. And that seems OK in itself: the objects don't know what part of the total potential is due to some particular neighboring object (such as the two stars in a wide binary) and what part is due to everything else. They just sense a single effect due to the total potential. So trying to separate out pieces doesn't seem right.

 

[Structure seeker]

Ceres:

$$g = \frac{GM}{r^2}$$
$$g = \frac{(6.67 \times 10^{-11})(9.1 \times 10^{20})}{(400 \times 10^{9})^2} \approx 0.003 a_0$$

Pluto is left as an exercise for the student.

I was admitting my mistake, seems I don't understand yet how the EFE works. I was only correct in the knowledge that it is a predicted and quantifiable phenomenon of MOND.

 

[strangerep]

Why do we need to separate out the motions?

That's only if one insists on trying to implement MOND via a modified inertia approach.

Whereas...

If the altered behavior in the MOND model depends on (some interpolated function of) the gradient of the total potential, then it depends on the total potential. And that seems OK in itself: the objects don't know what part of the total potential is due to some particular neighboring object (such as the two stars in a wide binary) and what part is due to everything else. They just sense a single effect due to the total potential. So trying to separate out pieces doesn't seem right.

...this is in a modified gravity implementation of MOND.

 

[Structure seeker]

MOND interpolation functions are governed by an acceleration scale (a0), not a length scale.

In a two body system the mass of the more massive object is also a factor yes. The other (attracted) mass is divided out in the force law and the gravitational constant is constant.

 

[PeterDonis]

That's only if one insists on trying to implement MOND via a modified inertia approach.

this is in a modified gravity implementation of MOND

So does that mean $F = ma$ no longer works in a modified gravity implementation of MOND? If so, how do you compute motions?

 

[ohwilleke]

This is why it's better (i.e., less confusing) to use the MoG formulation of MOND, using a "force-side" $\nu()$ interpolation function rather than an "inertia-side" $\mu()$ interpolation function. Then you can just compute the total conventional field, and apply the $\nu()$ interpolation function thereto.

MoG which is a theory of Dr. Moffat is a completely different theory than MOND by Dr. Milgrom, it is not a formulation of it. Basically, MoG is a scalar-vector-tensor theory. The only similarity is that they both seek to explain dark matter phenomena by modifying gravity.

 

[ohwilleke]

So does that mean $F = ma$ no longer works in a modified gravity implementation of MOND? If so, how do you compute motions?

F = ma still works.

 

[Vanadium 50]

You neded to use TeX for F=ma?

The answer is "maybe". Let's take a strep back - what problem are we trying to solve? That of too much acceleration in the outer parts of spiral galaxies. F = ma has three terms, and any one can be changedL

1. F is too small (modified gravity)
2. m is too big (dark matter)
3. a is too big (modified inertia)

I am keeping F = ma here as a definition of "force", You could redefine it, but that's likely to generate confusion over clarity. But anyway, those are the options.

 

[strangerep]

So does that mean $F = ma$ no longer works in a modified gravity implementation of MOND? If so, how do you compute motions?

Use $$a ~=~ \nu\left( \frac{|g_N|}{a_0} \right) \, g_N ~,$$where $g_N$ is the Newtonian gravitational acceleration, and the interpolation function $\nu(y)$ satisfies $\nu(y)\to 1$ for $y \gg 1$, and $\nu(y)\to y^{-1/2}$ for $y \ll 1$.

Alternatively, (and maybe preferably as it's more general), you can do it using a $\mu()$-type interpolation function inside a modified field equation for $\Phi$. The AQUAL Wiki page I mentioned earlier shows an example near the end. (Sorry, gotta run, so can't type it out properly here right now.)

 

[strangerep]

MoG which is a theory of Dr. Moffat is a completely different theory than MOND by Dr. Milgrom, it is not a formulation of it. Basically, MoG is a scalar-vector-tensor theory. The only similarity is that they both seek to explain dark matter phenomena by modifying gravity.

(Oh good grief.) Of course I meant "MoG" in the sense of "Modified Gravity formulation of MOND", given the entire context of this thread.

In any case, the term "MoG" is generic, not just for Dr Moffat's theory, so I refuse to allow him to hijack it exclusively.

 

[PeterDonis]

where $g_N$ is the Newtonian gravitational acceleration

The Newtonian acceleration due to all sources?

 

[Structure seeker]

what problem are we trying to solve? That of too much acceleration in the outer parts of spiral galaxies

It's much more than just that. I'll quote the most recent blog of Stacy:

I wrote the equation for the required effects of dark matter in all generality in McGaugh (2004). The improvements in the data over the subsequent decade enable this to be abbreviated to

$g_{DM} = g_{bar}/(e^{√(g_{bar}/a_0)} -1)$.
This is in McGaugh et al. (2016), which is a well known paper (being in the top percentile of citation rates). So this should be well known, but the implication seems not to be, so let’s talk it through. $g_{DM}$ is the force per unit mass provided by the dark matter halo of a galaxy. This is related to the mass distribution of the dark matter – its radial density profile – through the Poisson equation. The dark matter distribution is entirely stipulated by the mass distribution of the baryons, represented here by $g_{bar}$. That’s the only variable on the right hand side, $a_0$ being Milgrom’s acceleration constant. So the distribution of what you see specifies the distribution of what you can’t.

This is not what we expect for dark matter. It’s not what naturally happens in any reasonable model, which is an NFW halo. That comes from dark matter-only simulations; it has literally nothing to do with $g_{bar}$.

If you nevertheless choose to merely modify the mass, you run into problems such as these: https://tritonstation.com/2023/06/27/checking-in-on-troubles-with-dark-matter/

And here is a list of successful MOND predictions, the first (galaxy rotation curves) being what you mention: http://www.scholarpedia.org/article...phenomenology:_MOND_laws_of_galactic_dynamics

 

[Vanadium 50]

he Newtonian acceleration due to all sources?

That's the issue.

Suppose I have a mass m at a distance r such that the Newtonian acceleration would be a0/10. In MOND, its acceleration would be a0. Now I put a sec`ond identical mass. next to the first In MOND the acceleration is still a0. Now I put lots of masses - say 100 total. In both models, the acceleration is 10a0.

This is a feature of the theory and many people consider it a problem. This is why I said "may not even be a field theory" - it is not clear that one can come up with a local function that correctly superposes fields from multiple distinct sources. In particular, if you have two big nearby masses and a small one far away, what do you do?

 

[fresh_42]

Since this is still a B-level thread, I dare to make a comment as a naive layman.

Firstly, MOND describes what is and makes predictions of what we measure. This is no valid argument in my mind. It is constructed to do exactly this. It is a minimal requirement. These models are accordingly fine-tuned. What lacks in my opinion is a good reason why nature should follow these tunings.

Secondly, the discussion reminds me of ether. Some medium that tells the central mass about the amount of mass far away in order to adjust its gravitation. Maybe I got it wrong, but I had the impression from reading the posts here, that it makes a difference whether two Jupiters surround each other very far away or a Jupiter and a tiny moon would. Or is all this just a different (from $r^{-2}$) potential?

 

[Structure seeker]

This is why I said "may not even be a field theory" - it is not clear that one can come up with a local function that correctly superposes fields from multiple distinct sources.

It wasn't clear at first, until TeVeS and AQUAL appeared. Nowadays, progress has been made with Einstein-Aether theories, BIMOND and perhaps even with just a slight modification in quantum field theory Deur's approach. It needs to be checked and recalculated by others and reformulated so clarity increases.

 

[Vanadium 50]

@fresh_42 I address your second point in post #18.

Your first point overstates (or maybe understates) the case. If every (rotationally supported) galaxy had its own a0, one could say "you got out what you put in - big whoop." But every galaxy has the same a0 - i.e. you can look at one galaxy and now you know the rotation curves of not just that galaxy, but all of them. In ΛCDM, every galaxy should be different - and observationally, that is not what we see.

Could there be an astrophysical explanation? I think that is likely. However, the battle lines have been drawn - you have people saying "gravity must be modified!" and others saying "the universality of a0 tells us nothing! I won't even look at it!" IMHO, neither path is the correct one.

 

[Structure seeker]

Firstly, MOND describes what is and makes predictions of what we measure. This is no valid argument in my mind. It is constructed to do exactly this. It is a minimal requirement. These models are accordingly fine-tuned. What lacks in my opinion is a good reason why nature should follow these tunings.

It was constructed for explaining galaxy rotation curves, not the baryonic TF-relation or velocity dispersions. But yes, a FUNDAMOND theory would be great for explaining why nature follows these tunings.

 

[PeterDonis]

it is not clear that one can come up with a local function that correctly superposes fields from multiple distinct sources

Sure you can, just add the potentials linearly and take the gradient of the total potential. That is what I understood was being done in the "modified gravity" version described earlier. My question is, if that's what is being done, there should not be any such thing as an "External Field Effect", nor should it make any difference whether we use, say, coordinates centered on the center of mass of a wide binary or coordinates centered on the center of mass of the Milky Way. But other posts in this thread have talked about an EFE and have at least implied that it does make a difference which coordinates we use. That's why I am confused about what MOND actually says.

 

[Vanadium 50]

just add the potentials linearly

But they don't add. That's the M in MOND and indeed, the whole point.

It may - or may not - be possible to combine them, using some other function. Since the interpolation function suggested by Milgrom is non-analytic, it would be best if it were a different, but similar function. (e.g. erf or tanh instead of a theta function)

 

[PeterDonis]

But they don't add

The last paragraph of @strangerep's post #43 says they do. It says compute the total conventional (i.e., Newtonian) field and then apply an interpolation function to it. That means adding the potentials linearly just like in Newtonian gravity, taking the gradient of the total (since that's the Newtonian field), and then applying an interpolation function.

At this point I'm going to bow out of this conversation because I can't get a clear explanation of exactly how MOND works. I'll just have to take the time to read the papers when I get a chance.

 

[Vanadium 50]

This is exactly the problem with composite objects.

 

[sbrothy]

Here's a much less "breathless" assessment by Ethan Siegel of this study:
https://bigthink.com/starts-with-a-bang/binary-stars-prove-modified-gravity/

Very sobering.

 

[strangerep]

Suppose I have a mass m at a distance r such that the Newtonian acceleration would be a0/10. In MOND, its acceleration would be a0.

Huh? How do you figure that?