Jacob D. Bekenstein

The modified newtonian dynamics (MOND) paradigm of Milgrom can boast of a number of successful predictions regarding galactic dynamics; these are made without the assumption that dark matter plays a significant role. MOND requires gravitation to depart from Newtonian theory in the extragalactic regime where dynamical accelerations are small. So far relativistic gravitation theories proposed to underpin MOND have either clashed with the post-Newtonian tests of general relativity, or failed to provide significant gravitational lensing, or violated hallowed principles by exhibiting superluminal scalar waves or an a priori vector field. We develop a relativistic MOND inspired theory which resolves these problems. In it gravitation is mediated by metric, a scalar field and a 4-vector field, all three dynamical. For a simple choice of its free function, the theory has a Newtonian limit for nonrelativistic dynamics with significant acceleration, but a MOND limit when accelerations are small. We calculate the beta and gamma PPN coefficients showing them to agree with solar system measurements. The gravitational light deflection by nonrelativistic systems is governed by the same potential responsible for dynamics of particles. Consequently, the new theory predicts gravitational lensing by extragalactic structures that cannot be distinguished from that predicted within the dark matter paradigm by general relativity. Cosmological models based on the theory are quite similar to those based on general relativity; they predict slow evolution of the scalar field. For a range of initial conditions, this last result makes it easy to rule out superluminal propagation of metric, scalar and vector waves. Ethan Vishniac wrote: Hi, I don't have a reference for a skeptical review of MOND. As you might expect, this is considered a fringe hypothesis by most. However, there is an interesting paper you should see: astro-ph/0312273. Briefly, they examine a galaxy cluster with a strong sub-cluster, which has just passed through the main cluster for the first time (probably). Most of the baryonic mass is in the hot gas (by a factor of ten) so the initial pass has stripped the gas out of the sub-cluster. In fact, in the X-rays the subcluster is not evident. If stars and gas are all there is then there is no significant mass concentration associated with the sub-cluster. However, the sub-cluster is quite easy to see in the gravitational lensing map. Evidently, the mass of the sub-cluster has not been significantly reduced by losing all of the gas. (That is, the mass to light ratio for the sub-cluster is what one would expect for an isolated system.) This looks like a simple demonstration that most of the mass in galaxy clusters is non-luminous and dissipationless. There have also been attempts to disprove MOND by comparing time delays in strong lensing systems with MOND based models. Unfortunately, the real problem here is that there is no clear set of predictions for MOND. Ethan Vishniac He also wrote: BTW, one way to address MOND on its own terms is to try to follow galactic rotation curves out to very very great distances. If the dark matter model is correct, they will eventually turn over and fall as r^{-1/2}. This is hard, perhaps impossible, using gas. There is some work using the velocity dispersion of satellite galaxies around otherwise isolated bright galaxies (Prada et al., ApJ 598, 260-,2003). (The Sloan Digital Sky Survey makes it possible to get good statistics for very weak signals.) They claim to have detected a drop in the velocity dispersion by a factor of 2 between 20 and 350 kpc. This is roughly in line with expectations from cosmological simulations, and stands in contradiction to what one would expect from MOND. Finally, one can try to measure the shape of galaxy halos using weak lensing. The line of reasoning is a bit indirect, but the point is that an elliptical or disk-like distribution of mass at small radii gives rise to nearly spherical equipotential surfaces at large radii. On the other hand, dark matter halos are generally triaxial, and will appear elliptical on the sky. Hoekstra et al. (Astrophysical Journal, 606, 67-77, 2004) have done this and claim a strong elliptical signal in the weak lensing data. Finally, Renate Loll corrected an oversimplification in my account of her model: [...] I never claimed the geometries we find are nice *and smooth*, I think they almost certainly will be fairly wild individually, even at relatively large scales. Like the particle paths in the quantum mechanical path integral, the individual histories should not be taken too literally, the physics'll all be in suitable expectation values of course. ----------------------------------------------------------------------- "When I am working on a problem, I never think about beauty. I think only about how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong." - Buckminister Fuller ----------------------------------------------------------------------- Previous issues of "This Week's Finds" and other expository articles on mathematics and physics, as well as some of my research papers, can be obtained at http://math.ucr.edu/home/baez/ For a table of contents of all the issues of This Week's Finds, try http://math.ucr.edu/home/baez/twf.html A simple jumping-off point to the old issues is available at http://math.ucr.edu/home/baez/twfshort.html If you just want the latest issue, go to http://math.ucr.edu/home/baez/this.week.html