High School More Experimental Evidence for MOND

[Vanadium 50]

The gravitational tug of planets on stars is Newtonian (six planets tug on the sun with much more than a0; Mars and Neptune just a bit more)

It isn't the mass of Ceres that is relevant. It is the mass of the Sun.

That's just totally wrong. It's freshman physics. The acceleration of the sun due to Ceres depends on Ceres' mass.

 

[ohwilleke]

That's just totally wrong. It's freshman physics. The acceleration of the sun due to Ceres depends on Ceres' mass.

The acceleration of Ceres' due to the Sun does not depend upon Ceres' mass, however.

The acceleration of the Sun due to Ceres mass is for all practical purposes irrelevant. The Sun has a mass of 1.9891 × 10³⁰ kilograms. Ceres' mass is 9.1* 10²⁰. The acceleration of Ceres due to the mass of the Sun swamps the acceleration of the Sun due to the mass of Ceres.

Yes, both masses contribute to the combined pull of gravity between the Sun and Ceres. But, the contribution of Ceres to the combined pull of gravity between them is a billion times smaller than the contribution of the Sun to the combined pull of gravity between them.

Equally important, freshman physics is about Newtonian gravity. MOND's very name, "MOdified Newtonian Gravity" makes clear that it isn't talking about the same thing that you learn in freshman physics because it is modified. If the acceleration from either of them on the other exceeds a₀ then MOND does not apply.

 

[Vanadium 50]

As they say inm lawyer-land, "If the law is against you argue the facts. If the facts are against you, argue the law. If they are both against you, pound your fist on the table and try and confuse the issue." But PF is not lawyer land.

I said that the pull of six plamets on the sun was well above a0. That is a fact. I also said that the pull of Ceres was substantially less than that. I backed that up with a calculation. You've claimed this is "WRONG!" without providing any evidence.

Huffing and puffing may work elsewhere, but not here.

 

[ohwilleke]

I said that the pull of six plamets on the sun was well above a0. That is a fact. I also said that the pull of Ceres was substantially less than that. I backed that up with a calculation.

What is wrong is your seeming conclusion from those statements made in reference to the MOND constant, that the pull of the planets on the Sun, separate and apart from the pull of the Sun on the planets, has any relevance whatsoever to MOND, or to whether wide binary stars tell us anything about MOND.

It doesn't.

When an object is within the Newtonian gravitational pull of an object giving rise to an acceleration due to gravity on that object which is far in excess of a₀, the mass of the object doesn't matter when it comes to determining if MOND applies. In that situation, you are simply in the land of ordinary general relativity without any modification, which is almost indistinguishable from Newtonian gravity in a solar system context outside the perihelion of Mercury (which is slightly different in GR than it is in Newtonian gravity due to strong field GR effect that close to the Sun) and some very subtle and slight frame dragging effects.

I was giving you the benefit of the doubt that what you meant to say in the somewhat odd sense of talking about the pull of the planets on the Sun was their mutual gravitational attraction, because it didn't occur to me that you meant what it seems that you really did mean, which is that the pull of any of solar systems bodies (other than the Sun) on the Sun has any relevance to anything.

 

[PeterDonis]

It doesn't.

Why not?

 

[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?