Galaxy groups and the modified dynamics

I estimate Modified-Dynamics (MOND), median M/L values for recently published catalogues of galaxy groups. While the median, Newtonian M/L values quoted for these catalogues are 110-200 solar units, the corresponding values for MOND are less than 10 solar units.Comment: 5 pages, Latex, to appear in Astrophys. J. Let

Cosmological fluctuation growth in bimetric MOND

I look at the growth of weak density inhomogeneities of nonrelativistic matter, in bimetric-MOND (BIMOND) cosmology. I concentrate on matter-twin-matter-symmetric versions of BIMOND, and assume that, on average, the universe is symmetrically populated in the two sectors. MOND effects are absent in an exactly symmetric universe, apart from the appearance of a cosmological constant, Lambda~(a0/c)^2. MOND effects-local and cosmological-do enter when density inhomogeneities that differ in the two sectors appear and develop. MOND later takes its standard form in systems that are islands dominated by pure matter. I derive the nonrelativistic equations governing small-scale fluctuation growth. The equations split into two uncoupled systems, one for the sum, the other for the difference, of the fluctuations in the two sectors. The former is governed strictly by Newtonian dynamics. The latter is governed by MOND dynamics, which entails stronger gravity, and nonlinearity even for the smallest of perturbations. These cause the difference to grow faster than the sum, conducing to matter-twin-matter segregation. The nonlinearity also causes interaction between nested perturbations on different scales. Because matter and twin matter (TM) repel each other in the MOND regime, matter inhomogeneities grow not only by their own self gravity, but also through shepherding by flanking TM overdensitie. The relative importance of gravity and pressure in the MOND system depends also on the strength of the perturbation. The development of structure in the universe, in either sector, thus depends crucially on two initial fluctuation spectra: that of matter alone and that of the matter-TM difference. I also discuss the back reaction on cosmology of BIMOND effects that appear as "phantom matter" resulting from inhomogeneity differences between the two sectors.Comment: 14 pages. Some clarifications added. Version published in Phys. Rev.

Non-linear conformally invariant generalization of the Poisson equation to D>2 dimensions

I propound a non-linear generalization of the Poisson equation describing a "medium" in D dimensions with a "dielectric constant" proportional to the field strength to the power D-2. It is the only conformally invariant scalar theory that is second order, and in which the scalar $phi$ couples to the sources $\rho$ via a $\phi\rho$ contact term. The symmetry is used to generate solutions for the field for some non-trivial configurations (e.g. for two oppositely charged points). Systems comprising N point charges afford further application of the symmetry. For these I derive e.g. exact expressions for the following quantities: the general two-point-charge force; the energy function and the forces in any three-body configuration with zero total charge; the few-body force for some special configurations; the virial theorem for an arbitrary, bound, many-particle system relating the time-average kinetic energy to the particle charges. Possible connections with an underlying conformal quantum field theory are mentioned.Comment: Revtex, 16 pages. To be published in Phys. Rev.

Dark matter and non-Newtonian gravity from General Relativity coupled to a fluid of strings

An exact solution of Einstein's field equations for a point mass surrounded by a static, spherically symmetric fluid of strings is presented. The solution is singular at the origin. Near the string cloud limit there is a $1/r$ correction to Newton's force law. It is noted that at large distances and small accelerations, this law coincides with the phenomenological force law invented by Milgrom in order to explain the flat rotation curves of galaxies without introducing dark matter. When interpreted in the context of a cosmological model with a string fluid, the new solution naturally explains why the critical acceleration of Milgrom is of the same order of magnitude as the Hubble parameter.Comment: 12 pages, REVTeX, no figure

The fundamental plane of elliptical galaxies with modified Newtonian dynamics

The modified Newtonian dynamics (MOND), suggested by Milgrom as an alternative to dark matter, implies that isothermal spheres with a fixed anisotropy parameter should exhibit a near perfect relation between the mass and the fourth power of the velocity dispersion. This is consistent with the observed Faber-Jackson relation for elliptical galaxies-- a luminosity-velocity dispersion relation with large scatter. However, the observable global properties of elliptical galaxies comprise a three parameter family; they lie on a ``fundamental plane'' in a logarithmic space consisting of central velocity dispersion, effective radius, and luminosity. The scatter perpendicular to this plane is significantly less than that about the Faber-Jackson relation. I show here that, in order to match the observed global properties of elliptical galaxies with MOND, models must deviate from being strictly isothermal and isotropic; such objects can be approximated by high-order polytropic spheres with a radial orbit anisotropy in the outer regions. MOND imposes boundary conditions on the inner Newtonian regions which restrict these models to a dynamical fundamental plane which may differ from that implied by the traditional virial theorem. Scatter about this plane is relatively insensitive to the necessary deviations from homology.Comment: 9 pages, 6 eps figures, mn style. Shortened and revised version includes more recent data on elliptical galaxies. Accepted for publication in MNRA

MOND and the lensing Fundamental Plane: No need for dark matter on galaxy scales

Bolton et al. (2007) have derived a mass-based fundamental plane using photometric and spectroscopic observations of 36 strong gravitational lenses. The lensing allows a direct determination of the mass-surface density and so avoids the usual dependence on mass-to-light ratio. We consider this same sample in the context of modified Newtonian dynamics (MOND) and demonstrate that the observed mass-based fundamental plane coincides with the MOND fundamental plane determined previously for a set of high-order polytropic spheres chosen to match the observed range of effective radii and velocity dispersions in elliptical galaxies. Moreover, the observed projected mass within one-half an effective radius is consistent with the mass in visible stars plus a small additional component of ``phantom dark matter'' resulting from the MOND contribution to photon deflection.Comment: Minor revisions in response to referee. Revised title. Accepted in MNRA

The Bright Side of Dark Matter

We show that it is not possible in the absence of dark matter to construct a four-dimensional metric that explains galactic observations. In particular, by working with an effective potential it is shown that a metric which is constructed to fit flat rotation curves in spiral galaxies leads to the wrong sign for the bending of light i.e. repulsion instead of attraction. Hence, without dark matter the motion of particles on galactic scales cannot be explained in terms of geodesic motion on a four- dimensional metric. This reveals a new bright side to dark matter: it is indispensable if we wish to retain the cherished equivalence principle.Comment: 7 pages, latex, no figures. Received an honorable mention in the 1999 Gravity research Foundation Essay Competition. Submitted to Phys. Rev. Let

Auction Theory

This paper discusses two central questions: Why do auction institutions continue to be so popular after thousands of years? and What accounts for particular details, like the popularity of sealed bid and ascending-bid auctions

Journeys in The Country of The Blind: Entanglement Theory and The Effects of Blinding on Trials of Homeopathy and Homeopathic Provings

The idea of quantum entanglement is borrowed from physics and developed into an algebraic argument to explain how double-blinding randomized controlled trials could lead to failure to provide unequivocal evidence for the efficacy of homeopathy, and inability to distinguish proving and placebo groups in homeopathic pathogenic trials. By analogy with the famous double-slit experiment of quantum physics, and more modern notions of quantum information processing, these failings are understood as blinding causing information loss resulting from a kind of quantum superposition between the remedy and placebo

Quasirents, Influence and Organization Form

When changing jobs is costly, efficient employment arrangements are characterized by complex contracts, rather than simply wages. Under these contracts, workers are not generally fully compensated for the effects of post-employment events or decisions. As a consequence, if there is a central office executive with discretionary authority to make decisions, employees will be led to waste valuable time in attempts to influence his decisions. Efficient organization design balances these “influence costs” against the benefits of improved appraisal, coordination, and planning that such an executive can provide. Identifying influence costs requires first identifying the kinds of decisions about which employees will care. We identify several: with efficient employment contracts, employees prefer more on-the-job consumption and better opportunities to learn and display their abilities and to acquire human capital. They also prefer to occupy jobs where continuity of employment is particularly important to the employer, because such jobs carry higher wages. Applications of our perspective, which focuses on influence processes and the trade-off between influence costs and improved decisionmaking appears to have wide and fruitful application to questions or organization theory, industrial organization, contract theory, and related areas