Photon dilemma for MOND-like dark matter

[mitchell porter]

TL;DR Summary

whether to couple or not

"Superfluid dark matter in tension with weak gravitational lensing data" (Mistele, McGaugh, Hossenfelder)

Regarding this paper, Sabine Hossenfelder tweets

It's about superfluid dark matter but highlights what I believe is a general problem of hybrid approaches.

The issue is roughly speaking this. You introduce a new field that reproduces modified gravity in some regime and CDM in some other regime. Question is, do you couple it to photons or not.

If you do couple it to photons you get a problem with reproducing observations from GW170817 that require photons to travel pretty much like gravitaitonal waves inside galaxies.

If you don't couple it to photons then kinematic measurements (inferred from the motion of stars and gas) will generically not match to lensing observations. Alas the data say they do.

One comment summarizes this as

"if it's coupled to photons then it should scatter them but we don't see that,

but if it's not then why are photons affected by its gravity like everything else"

 

[kodama]

does this affect modify gravity ?

 

[ohwilleke]

It is a dark matter particle hypothesis that has properties that reproduce MOND in some circumstances.

 

[Hornbein]

Matter with a special kind of gravity that doesn't bend the path of light? Weird.

 

[Demystifier]

What about bimetric theories, where different kinds of matter see different geometries?

 

[Madeleine Birchfield]

What about bimetric theories, where different kinds of matter see different geometries?

One of the authors of the paper, Stacy McGaugh, said on his blog that while he hasn't yet had time to read Milgrom's bimetric MOND paper, he hopes that some time in the future he could read Milgrom's paper

https://tritonstation.com/2023/03/06/ask-and-receive/

https://arxiv.org/abs/2208.10882

 

[strangerep]

What about bimetric theories, where different kinds of matter see different geometries?

I get the impression from Milgrom's paper arxiv:22209.10882 (linked above) that the two metrics are indeed intended to inhabit one spacetime. But I don't understand what the 2nd metric (Milgrom's "$\hat g_{\mu\nu}$") actually does in the geometry. He constructs 2 affine connections $\Gamma^\lambda_{~\mu\nu}$ and $\hat \Gamma^\lambda_{~\mu\nu}$, then calls their difference $$C^\lambda_{~\mu\nu} ~:=~ \Gamma^\lambda_{~\mu\nu} ~-~ \hat \Gamma^\lambda_{~\mu\nu}$$ a "relative acceleration tensor" (see p3).
His footnote 4 at the bottom of p3 says:

The tensor $C^\lambda_{~\mu\nu}$ may be thought of as the "relative acceleration field", of $g_{\mu\nu}$ with respect to $\hat g_{\mu\nu}$, in the sense that in a frame where $\hat g_{\mu\nu}$ is locally flat at some $\hat x$ [i.e., $\hat \Gamma^\lambda_{~\mu\nu}(\hat x) = 0]$], we have $d^2 x^\mu/d\tau^2 |_{\dot x} = -C^\lambda_{~\alpha\beta} \dot x^\alpha \dot x^\beta$, on a geodesic of $g_{\mu\nu}$ through $\hat x$.

So (clearly?) the 2 metrics participate somehow in the same geometry (e.g., congruences of worldlines) on a base manifold.

This is (so far) not making much sense to me, but I'll keep reading...

 

[martinbn]

I get the impression from Milgrom's paper arxiv:22209.10882 (linked above) that the two metrics are indeed intended to inhabit one spacetime. But I don't understand what the 2nd metric (Milgrom's "$\hat g_{\mu\nu}$") actually does in the geometry. He constructs 2 affine connections $\Gamma^\lambda_{~\mu\nu}$ and $\hat \Gamma^\lambda_{~\mu\nu}$, then calls their difference $$C^\lambda_{~\mu\nu} ~:=~ \Gamma^\lambda_{~\mu\nu} ~-~ \hat \Gamma^\lambda_{~\mu\nu}$$ a "relative acceleration tensor" (see p3).
His footnote 4 at the bottom of p3 says:

So (clearly?) the 2 metrics participate somehow in the same geometry (e.g., congruences of worldlines) on a base manifold.

This is (so far) not making much sense to me, but I'll keep reading...

I am not sure what you call geometry here, and what exactly confuses you. The same manifold can have many metrics, that is not a problem. It is another question what they are for.

 

[strangerep]

I am not sure what you call geometry here, and what exactly confuses you.

You picked up on that, huh?

So,... do you feel that you understand Milgrom's paper well? If so, I'd appreciate a summary explanation of the bimetric MOND theory in your own words, since I've never found Milgrom to be good at explaining things clearly.

The same manifold can have many metrics, that is not a problem. It is another question what they are for.

Indeed, the latter is what I'm struggling with, i.e., the correspondence between the math and the real-world physics.

Among other things, Milgrom says (1st para, p3) that the other metric $\hat g_{\mu\nu}$ couples to "twin matter", which is assumed not to interact directly with matter. So... "twin matter" is like "dark matter"??

Oh, but no, because... in footnote 10 on p13 he seems to contradict this when he says that, in the MOND regime, matter and twin-matter repel each other.

 

[martinbn]

Oh, no, you are far ahead. I gave up after the introduction. I was just curious if you had any mathematical objections.

 

[strangerep]

I was just curious if you had any mathematical objections.

I have none at this stage -- but I have not studied the gory detail in the depths. (If the physical correspondences are unclear/missing, I tend to lose interest.)

 

[Ken G]

I'm sure it's a common question, but wouldn't bimetric approaches have causality problems? It seems to me they would need to share the same null geodesics, else you could use the null geodesics of one metric to violate the causality of another. I guess the idea is you completely remove any interactions between the two species other than gravity, so the only way they communicate is by joint effects on each others' metrics, and each metric has its own null geodesics so causality is enforced. Is that the idea? If so, there could never be direct detection of dark matter, which probably means it will always seem like a speculative explanation. It would also seem to complicate unifying gravity with the other forces, because it seems like it really requires gravity as a metric effect but not as a force carrier, is that not so?

 

[Madeleine Birchfield]

What about bimetric theories, where different kinds of matter see different geometries?

One of the authors of the paper, Stacy McGaugh, said on his blog that while he hasn't yet had time to read Milgrom's bimetric MOND paper, he hopes that some time in the future he could read Milgrom's paper

https://tritonstation.com/2023/03/06/ask-and-receive/

https://arxiv.org/abs/2208.10882

Update: Stacy McGaugh says that "My understanding is that photons do see the MOND effect in bimetric theories, so the same concern doesn’t apply."

https://tritonstation.com/2023/05/19/commentary-on-wide-binaries/comment-page-1/#comment-21286