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Bekenstein's rival to Dark Matter

  1. Dec 29, 2004 #1


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    Bekenstein just posted a new paper on his relativistic MOND
    which obviates dark matter

    An alternative to the dark matter paradigm: relativistic MOND gravitation

    This is a followup of an earlier Bekenstein paper which was published in Physical Review Series D this year. Here is the preprint:

    Relativistic gravitation theory for the MOND paradigm

    He claims it gives the right gravitational lensing results and has the right limits. It seems to be a modification of
    General Relativity, actually, rather than newtonian dynamics
  2. jcsd
  3. Dec 30, 2004 #2


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    Thank you. The new paper basically restated the previous one from this year, but is designed to be more readable.

    The bottom line, of course, is that Bekenstein's TeVeS formulation of MOND is consistent with GR except that it explains the vast majority of the behavior associated with dark matter (both in galactic dynamics and lensing). Moreover, TeVeS has no obvious theoretical problems (e.g. failure to observe conservation laws).

    This is no crackpot theory.
  4. Dec 30, 2004 #3


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    I agree. Also the dateline on the paper that just came out was
    harvard physics dept Jefferson Lab where they may as well have a sign on the door "no cracks in the pot" :smile:
    I think Bekenstein stock is high.
    I find reading his paper tough going. I fell asleep this afternoon (maybe I shouldnt have tried reading it on the couch)

    the trouble is his modified version of General Relativity seems to have more moving parts, more cogwheels and levers to keep track of, than the original Einstein version.

    this curious vector gothic U or else script U
    on page 9 of the new paper he says To put it picturesquely, U "seeks out" the frame in which matter is at rest...

    wow. I wish he would put more things picturesquely. that sounds interesting.

    this vector U was in gothic font in the March 2004 paper and now it is in a script font in this December paper. What shall we call it among ourselves?
    It seems to be a key player.

    I guess you have studied this TeVeS thing longer than I have. I am glad you express confidence in it. gives some hope that something like it will eventually turn out right and banish Dark Matter from the land
    Last edited: Dec 31, 2004
  5. Dec 31, 2004 #4


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    well Ive kept gnawing at it
    read some more (mostly in the long paper) last night

    willeke, would you to try to paraphrase or explain a bit of this?
    say some of the obvious things about the chief rival of DM?

    not-completely-lousy new year everybody
    (if i could understand Teves better and see some more development in Dynamulation gravity, it would brighten the gloom some)
  6. Jan 3, 2005 #5


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    The very basics:

    1. MOND and all theories spawned from it, say that the odd galactic dynamics and other phenomena attributed to dark matter can be more parsimoniously explained by tweaking the law of gravity so that in the spherically symmetric, weak field limit, it acts as a 1/r force instead of a 1/r^2 force, once the field reaches a point a sub zero at which the accelleration due to gravity is 1.2*10^-8 cm/s^2.

    Comparisons of this theory to the data show that it explains the dynamics of galactic sized systems very well (the predictions are almost always well within the error bars of the data) without assuming any dark matter. In particular, it makes predictions about galaxies such as low surface brightness galaxies, whose existence was not known. It has made bona fide predictions that have born out, rather than post-dictions. It does this with basically one parametere (a sub zero) as the other potential variable in the theory (the mass to light ratio) is nearly 1 for almost all galactic objects.

    Even if MOND is dead wrong and a space probe bonks its sensors on a big chunk of dark matter tomorrow and definitely proves that the stuff is completely made of WIMPZILLAs or whatever, MOND still creates a puzzle for DM theorists. DM theory doesn't say much about how dark matter must be distributed. It looks at a system looks at what Newtonian theory would predict and explains where the DM has to be for the Newtonian theory to match the result using about three parameters for any given galaxy. This calculation by the way has been show to requires a distribution that is impossible to fit with baryonic matter, i.e. matter made up primarily of protons and neutrons like the matter we know and love. But, MONDs successes show that even if DM is right that DM must have a very specific distribution in relation to the luminous matter in a galaxy. This is particularly problematic in ellipitcal galaxies which are formed from the merger of spiral galaxies because ellipitical galaxies do not show dark matter expectations consistent with a merger of two spiral galaxy DM halos, but do behave consistent with MOND. Galaxy formation theories do a poor job of explaining how such a uniform distribution of DM relative to luminous matter could arise.

    MOND has failed primarily in three areas.

    2. One, it has not predicted any dark matter in galactic clusters (which are within the area where MOND effects are not predicted in the basic theory). But, experimental data seem to show a 50%-80% DM content in those systems. This could be due to massive neutrinos (at about 2eV each) or it could be due to differences between basic MOND theory and advanced MOND theory. Still, considering that many kinds of galaxies are off by factors of 100+ and that MOND does not create a mass deficit and would not need non-bayronic matter to make up the deficit in galactic clusters, this isn't a great failing.

    3. MOND has never made any specific prediction about lensing. It hasn't had a relativistic formulation and there has been doubt about whether it was even theoretically possible to great a formulation of MOND that was both well behaved and consistent with GR in non-MOND settings. MOND has not made any strong predictions cosmologically for the same reason The lack of a GR generalization has been cited as a major reason for rejecting MOND over DM.

    I made a first shot at paraphrasing the technical details, and found my paraphrase even worse than the original (which is damn ugly in its notation and less than elegant in its exposition). So, lets start with the bottom line conclusions:

    1. TeVes is designed so that it reduces, mathematically, to General Relativity in situations where gravitational fields are more than negligable. Only at weak gravitational fields do its unique characteristics come out. As a result, on a solar system scale (where graviational fields are sufficiently strong) and in essentially all the other places we have tested GR, TeVeS makes the same predictions.

    2. TeVeS in the weak field is basically a Lagrangian formulation of MOND. The two are identical for point sources. The Lagrangian vector field skews naiive MOND predictions for mass distributions that are not spherically symmetric. The Lagrangian also tweaks the way the MOND acts when, e.g., two fields, one in the MOND limit and one in the ordinary limit are superimposed upon each other. The differences from naiive MOND are subtle (e.g. 10-15% adjustments in the MOND effect in some the areas of spiral galaxies), but have the effect of allowing center of gravity calculations, conservation of energy, etc.

    3. TeVeS tweaks GR to a great extent through tensor big U. Because there is a tensor formulation, the theory does not have a preferred coordinate system.

    4. TeVeS achieves a major result no prior theory of relativistic MOND did, its impact on light (twice the deflection created by gravitational effects acting on matter) is the same as GR. In other words, if the mass dynamics of a galaxy or other system are accurately described by both MOND in general and by DM as formulated in a particular system, then the lensing predicted by both theories will be the same.

    5. TeVeS, like all prior formulations of MOND, uses an arbitrary function to transition between the GR/Newtonian regime and the MOND regime. In TeVeS this function is called "F" and it is a horrible ugly beast that Bekenstein himself describes as a toy model. It fits the data, but is really just a placeholder.

    6. TeVeS is ugly in part because it is formulated not as a from scratch theory, but as a modification of GR. GR's actions can be basically broken into geometric and non-geometric components. TeVeS uses a four way split, modifying the two GR components modestly, and then adding two new components described as the vector and scalar field components. Heuristically one can think of the tensor part (the first two of the four components of the action) basically being old fashioned GR tweaks a little by the U tensor, the vector part connected with the adjustment in the Lagrangian necessary to make MOND well behaved, and the scalar part necessary to reproduce naiive MOND.
  7. Jan 3, 2005 #6


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    Thanks! this is clear and helpful exposition!
    I hope everybody at General A & C reads it.

    I had hoped that maybe this TeVes was more than an ugly toy duckling of a cobbled together working placeholder. But I will go with your perception because you have delved into it more. And at least there is real progress! Like with your point 4.
  8. Jan 3, 2005 #7


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    One point of encouragement is discussed in this thread:

    This good point is that a convincing argument is made that any quantum gravity theory must have a significantly different tensor expression than GR because a spin 2 graviton, while implying a rank-2 tensor, does not (as many quantum people had assumed but not checked) imply the particular rank 2 tensor found in GR. I think that it is entirely possible that the formulation of quantum gravity found in that paper generically with an "S" tensor in place of the "T" tensor may well prove to be mathematically equivalent to Bekenstein's MOND in the large outlines.

    The biggest important proof of Bekenstein's paper is that it shows that a fully workable relativistic MOND is theoretically possible. It is the opposite of a "no go" theorem.
    Last edited: Jan 3, 2005
  9. Jan 3, 2005 #8


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    I see, an "existence proof"

    one shows that at least one solution to a set of conditions exists,
    the set of solutions is nonempty
    then there remains the fun of finding the best among them
  10. Jan 3, 2005 #9


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    One of the bigger questions I have yet to think through is how MOND impacts gravitational time dialation.

    The formula in normal GR is well known for simple cases like spherically symmetric sources: https://www.physicsforums.com/showthread.php?t=58359

    But, the potential field for MOND has more energy than the potential field in GR, so the gravitational time dialation should be greater. And, because a 1/R field declines so much more slowly than a 1/r^2 field, there might even be some slight distance dependence to the spherically symmetric formula for gravitational time dialation.

    This shouldn't be an order of magnitude difference. The two potential fields (and hence gravitational time dialation effects) should be more or less identical out to a sub zero, but at greater distances there should be a detectable difference.
  11. Jan 18, 2005 #10


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    Phil Helbig puts in a good word for MOND

    Phil Helbig is a familiar presence on s.p.r.
    (may be one of the moderators now, they change around)
    He just started a thread to discuss TeVeS, or Bekenstein's MOND.
    he seems to like it and think it is worth studying

    ---quote from Helbig---
    In the cosmological community, the idea of dark matter is well
    established, though a significant minority think that the idea of a
    modified law of gravity might be a better explanation to explain things
    which dark matter explains. In particular, such theories have made
    testable predictions which a) differ from those of the dark-matter
    hypothesis and b) have been confirmed while c) having fewer parameters
    than the dark-matter hypotheses. Sounds like a good scientific theory
    to me.

    Of course, there are justified objections to the idea of MOND (Modified
    Newtonian Dynamics). However, the following papers go beyond the idea
    of the simple form of MOND to counter many of these objections:

    * astro-ph/0403694
    * astro-ph/0412652

    What do people who work in gravitational theory think of these papers?
    (They are by Jacob Bekenstein, who is certainly not a crackpot.) The
    astronomical community might be more open to modifications of the law of
    gravity since it a) is confronted by problems which require it OR a
    competing hypothesis like dark matter which is 1) not DIRECTLY verified
    and 2) has problems of its own (see the papers mentioned above) and b)
    most people in cosmology and astrophysics don't use full-blown GR in
    their day-to-day work so perhaps aren't as emotionally attached to it as
    a theory. The papers above, however, should be accessible and
    interesting to people on the other side of the fence. How big an issue
    is the idea of alternative theories of gravity in the field of
    gravitational research as opposed to the field of
    ----end quote---

    Helbig's threadstarter post is

    and is called "Non-GR Theories of Gravity"
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