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We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdfs results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. We separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropy for size-class distributions with uniform bin sizes., Comment: 8 pages

Employing the allegorical imagery from the film "The Matrix", we motivate and discuss our `Cyborg Astrobiologist' research program. In this research program, we are using a wearable computer and video camcorder in order to test and train a computer-vision system to be a field-geologist and field-astrobiologist., Comment: Updated biblio info

We show how the interplay of non-linear dynamics, self-gravity, and fluctuations leads to self-affine behavior of matter density correlations quite generically, i.e., with a power-law exponent whose value does not depend in a very direct way on the specific details of the dynamics. This we do by means of the Renormalization Group, a powerful analytic tool for extracting asymptotic behavior of many-body systems, Comment: Accepted for publication in Astronomy & Astrophysics. 10 pages using A&A style file; 2 eps figures

In a recent series of papers, Schwinger discussed a process that he called the Dynamical Casimir Effect. The key essence of this effect is the change in zero-point energy associated with any change in a dielectric medium. (In particular, if the change in the dielectric medium is taken to be the growth or collapse of a bubble, this effect may have relevance to sonoluminescence.) The kernel of Schwinger's result is that the change in Casimir energy is proportional to the change in volume of the dielectric, plus finite-volume corrections. Other papers have called into question this result, claiming that the volume term should actually be discarded, and that the dominant term remaining is proportional to the surface area of the dielectric. In this communication, which is an expansion of an earlier letter on the same topic, we present a careful and critical review of the relevant analyses. We find that the Casimir energy, defined as the change in zero-point energy due to a change in the medium, has at leading order a bulk volume dependence. This is in full agreement with Schwinger's result, once the correct physical question is asked. We have nothing new to say about sonoluminescence itself., Comment: 20 pages in double-column format; uses ReV_TeX 3.0; 8 encapsulated postscript figures; uses epsf.sty

The Universe that we know is populated by structures made up of aggregated matter that organizes into a variety of objects; these range from stars to larger objects, such as galaxies or star clusters, composed by stars, gas and dust in gravitational interaction. We show that observations support the existence of a composite (two--exponent) power law relating mass and size for these objects. We briefly discuss these power laws and, in view of the similarity in the values of the exponents, ponder the analogy with power laws in other fields of science such as the Gutenberg--Richter law for earthquakes and the Hutchinson--MacArthur or Damuth laws of ecology. We argue for a potential connection with avalanches, complex systems and punctuated equilibrium, and show that this interpretation of large scale--structure as a self--organized critical system leads to two $predictions$: (a) the large scale structures are fractally distributed and, (b), the fractal dimension is $1.65 \pm 0.25$. Both are borne out by observations., Comment: Total 15 pages: 10 text plus 2 figures and 3 tables

As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with time-- dependent viscosity in epochs of dissipation. As a consequence of the Dynamical Critical Scaling induced by noise and fluctuations, these equations describe the fractal behavior (with a scale dependent fractal dimension) observed at the smaller scales for the galaxy--to--galaxy correlation function and $also$ the Harrison--Zel'dovich spectrum at decoupling. By a Renormalization Group calculation of the two--point correlation function between galaxies in the presence of (i) the expansion of the Universe and (ii) non--equilibrium, we can account, from first principles, for the main features of the observed shape of the power spectrum., Comment: 13 pages with 2 encapsulated PostScript figures included, gzipped tar format

Rotation curves of spiral galaxies are known with reasonable precision for a large number of galaxies with similar morphologies. The data implies that non-Keplerian fall--off is seen. This implies that (i) large amounts of dark matter must exist at galactic scales or (ii) that Newtonian gravity must somehow be corrected. We present a method for inverting the integral relation between an elemental law of gravity (such as Newton's) and the gravitational field generated by a thin disk distribution with exponential density. This allows us to identify, directly from observations, {\it extensions} of Newtonian gravity with the property of fitting a large class of rotation curves. The modification is inferred from the observed rotation curve and is finally written in terms of Newton's constant or the effective potential of a test mass moving in the field generated by a point-like particle., Comment: 8 pages with 4 encapsulated PostScript figures included. Uses Astronomy & Astrophysics LaTeX macros. Submitted to A&A

The observable Universe is described by a collection of equal mass galaxies linked into a common unit by their mutual gravitational interaction. The partition function of this system is cast in terms of Ising model spin variables and maps exactly onto a three-dimensional stochastic scalar classical field theory. The full machinery of the renormalization group and critical phenomena is brought to bear on this field theory allowing one to calculate the galaxy-galaxy correlation function, whose critical exponent is predicted to be between 1.530 to 1.862, compared to the phenomenological value of 1.6 to 1.8, Comment: Based on a talk presented at the International Workshop on Elementary Particle Physics, Valencia, Spain, June 1995. Six pages using the macro which is appended at the end of the paper. Runs using standard LaTex 2.09. Strip off this macro and place in separate file to be named sprocl.sty

The partition function of a system of galaxies in gravitational interaction can be cast in an Ising Model form, and this reformulated via a Hubbard--Stratonovich transformation into a three dimensional stochastic and classical scalar field theory, whose critical exponents are calculable and known. This allows one to {\it compute\/} the galaxy to galaxy correlation function, whose non--integer exponent is predicted to be between 1.530 and 1.862, to be compared with the phenomenological value of 1.6 to 1.8., Comment: Uses RevTeX 3.0

In this paper we study the influence of the threshold effects due to massive degrees of freedom in the evolution with scale of gauge coupling constants. We first describe in detail the (standard) mass dependent renormalization prescription we use. This guides us to introduce and work with effective couplings, which are finite, process independent, and include complete threshold effects. We compute the evolution of the effective couplings in both, the Standard Model and its Minimal Supersymmetric extension, from \mz\ to the high energy region. We find that the effects from thresholds due to the standard massive gauge bosons are non--negligible, contrary to what is generally assumed when using other, less--accurate, descriptions of the thresholds, as for example in the step--function approximation. Moreover, we find that thresholds are relevant when studying perturbative SUSY unification, changing the conclusions reached when using the step--function approach. We find that threshold effects bring conflict between the known experimental data at $m_Z$, the naturalness upper bound on the masses of SUSY partners and the $perturbative$ unification of couplings., Comment: 33 pages, Revtex-3.0

We study the effect from a general ultralocal supermetric on primordial nucleosynthesis for Friedmann-Robertson-Walker Cosmology. The parameter $\lambda$ of the supermetric changes the effective number of degrees of freedom, $g_*$, which modifies the Friedmann equation. This modification produces variations in the production of primordial $^4He$. The observations of the primordial abundances of light elements ($^4He$, $D$, $^3He$ and $^7Li$) allow to estimate bounds on the values of $\lambda$ consistent with these observations. We obtain $0.87 \le \lambda \le 1.04$. In addition we analyze the importance of $\lambda < 1$ to explain possible incompatibilities in the standard Big-Bang nucleosynthesis., Comment: 15 pages, 2 PostScript figures

We know that the generally accepted theories of gravity and quantum mechanics are fundamentally incompatible. Thus, when we try to combine these theories, we must beware of physical pitfalls. Modern theories of quantum gravity are trying to overcome these problems. Any ideas must confront the present agreement with general relativity, but yet be free to wonder about not understood phenomena, such as the dark matter problem and the anomalous spacecraft data which we announce here. This all has led some ``intrepid" theorists to consider a new gravitational regime, that of antimatter. Even more ``daring" experimentalists are attempting, or considering attempting, the measurement of the gravitational force on antimatter, including low-energy antiprotons and, perhaps most enticing, antihydrogen., Comment: Written version of invited contribution to LEAP'94: Third Biennial Conference on Low-Energy Antiproton Physics. LaTeX, 9 pages

We propose that the dynamic Casimir effect is a mechanism that converts the energy of neutron starquakes into $\gamma$--rays. This mechanism efficiently produces photons from electromagnetic Casimir energy released by the rapid motion of a dielectric medium into a vacuum. Estimates based on the cutoff energy of the gamma ray bursts and the volume involved in a starquake indicate that the total gamma ray energy emission is consonant with observational requirements., Comment: This paper uses ReVTeX version 3.0

We define an entropy for a quantum field theory by combining quantum fluctuations, scaling and the maximum entropy concept. This entropy has different behavior in asymptotically free and non--asymptotically free theories. We find that the transition between the two regimes (from the asymptotically free to the non--asymptotically free) takes place via a continuous phase transition. For asymptotically free theories there exist regimes where the ``temperatures" are negative. In asymptotically free theories there exist maser--like states mostly in the infrared; furthermore, as one goes into the ultraviolet and more matter states contribute to quantum processes, the quantum field system can shed entropy and cause the formation of thermodynamically stable {\it entropy--ordered} states. It is shown how the known heavier quarks can be thus described., Comment: uses ReVTeX 2.1, 13 pages + 5 figures (available by request to the author), LAEFF-93/017

We discuss a natural notion of entropy in quantum field theory and apply it to asymptotically free theories in their perturbative regimes. We then specialize to QCD and find that quark flavor states can be described as entropy--ordered states of QCD, and that the masses for the $s\bar{s}$--state, charm, $c\bar{c}$--state, bottom and $b\bar{b}$--state can all be fitted by requiring that the entropy of each of these states be the same. The resulting Pearson correlation coefficient between theory and experiment is better than 0.99, and the known quark masses can be accounted for with less than an 8\% error., Comment: uses ReVTeX, 11 pages + 2 figures (available by request to the author), LAEFF-93/015

In this paper we study and compare susy unification using two different approaches in order to take into account the effect of light particle thresholds on the evolution of gauge couplings: the step--function approximation, on the one hand, and a mass dependent procedure, which gives a more accurate description of the dependence of the results on the masses, on the other. We also include the effect of heavy thresholds, when $SU(5)$ is chosen as the unifying group. We find that the mass--dependent procedure excludes scenarios where all susy masses are below $1\;TeV$, and favors a value of $\alpha_3(m_Z)$ near its upper experimental bound, contrary to the results obtained with the step--function approximation. We underline the dependence of the results on the procedure chosen to deal with light thresholds., Comment: 18 pages,LAEFF-93/014,REVTEX-2.1, 5 figures not included, available upon request (include FAX number)#

We discuss the effect of the renormalization procedure in the computation of the unification point for running coupling constants. We explore the effects of threshold--crossing on the $\beta$--functions. We compute the running of the coupling constants of the Standard Model, between $m_Z$ and $M_P$, using a mass dependent subtraction procedure, and then compare the results with $\bar{MS}$, and with the $\theta$-- function approximation. We also do this for the Minimal Supersymmetric extension of the Standard Model. In the latter, the bounds on susy masses that one obtains by requiring perturbative unification are dependent, to some extent, on the procedure., Comment: 22 pages, REVTEX-2.1, 6 Post-Script figures are included

Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range approximation, and adopt for it a statistical interpretation. This virtual charge density has fractal structure, and it is seen that, independently of whether the theory is or is not asymptotically free, it describes a system where the equilibrium state is at its classical limit ($\hbar \rightarrow 0$). We also present a simple analysis of how diffusion of the charge density proceeds as a function of the distance at which the system is probed., Comment: RevTeX, 13 pages plus 4 Figures (available from the author upon request), LAEFF--93/006

We study how the effects of quantum corrections lead to notions of irreversibility and clustering in quantum field theory. In particular, we consider the virtual ``charge" distribution generated by quantum corrections and adopt for it a statistical interpretation. Then, this virtual charge is shown to ($a$) describe a system where the equilibrium state is at its classical limit ($\hbar \rightarrow 0$), ($b$) give rise to spatial diffusion of the virtual cloud that decays as the classical limit is approached and ($c$) lead to a scenario where clustering takes place due to quantum dynamics, and a natural transition from a ``fractal" to a homogeneous regime occurs as distances increase., Comment: LaTeX, 14 pages plus 4 Figures (available from the author upon request), LAEFF--93/003

We show how, by considering the cumulative effect of tiny quantum gravitational fluctuations over very large distances, it may be possible to: ($a$) reconcile nucleosynthesis bounds on the density parameter of the Universe with the predictions of inflationary cosmology, and ($b$) reproduce the inferred variation of the density parameter with distance. Our calculation can be interpreted as a computation of the contribution of quantum gravitational degrees of freedom to the (local) energy density of the Universe., Comment: 13 pages, LaTeX, (3 figues, not included)