New coins from old, smoothly

Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be random. The work of Keane and O'Brien (1994) implies that such a simulation scheme with the probability $\P_p(N<\infty)$ equal to 1 exists iff $f$ is continuous. Nacu and Peres (2005) proved that $f$ is real analytic in an open set $S \subset (0,1)$ iff such a simulation scheme exists with the probability $\P_p(N>n)$ decaying exponentially in $n$ for every $p \in S$. We prove that for $\alpha>0$ non-integer, $f$ is in the space $C^\alpha [0,1]$ if and only if a simulation scheme as above exists with $\P_p(N>n) \le C (\Delta_n(p))^\alpha$, where \Delta_n(x)\eqbd \max \{\sqrt{x(1-x)/n},1/n \}. The key to the proof is a new result in approximation theory: Let \B_n be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree $n$. We show that a function $f:[0,1] \to (0,1)$ is in $C^\alpha [0,1]$ if and only if $f$ has a series representation $\sum_{n=1}^\infty F_n$ with F_n \in \B_n and $\sum_{k>n} F_k(x) \le C(\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$. We also provide a counterexample to a theorem stated without proof by Lorentz (1963), who claimed that if some \phi_n \in \B_n satisfy $|f(x)-\phi_n(x)| \le C (\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$, then $f \in C^\alpha [0,1]$.Comment: 29 pages; final version; to appear in Constructive Approximatio

Self-energy of a scalar charge near higher-dimensional black holes

We study the problem of self-energy of charges in higher dimensional static spacetimes. Application of regularization methods of quantum field theory to calculation of the classical self-energy of charges leads to model-independent results. The correction to the self-energy of a scalar charge due to the gravitational field of black holes of the higher dimensional Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in even dimensions, but it acquires non-zero value in odd dimensional spacetimes. The origin of the self-energy correction in odd dimensions is similar to the origin the conformal anomalies in quantum field theory in even dimensional spacetimes.Comment: 9 page

Simple relativistic model of a finite-size particle

Soluble model of a relativistic particle describing a bag of matter with fixed radius held together in perfect balance by a self-consistent combination of three forces generated by electromagnetic and massive scalar and vector fields is presented. For realistic values of parameters the bag radius becomes that of a proton.Comment: 10pages + 3 postscript figures included in the file, uses RevTe

Examples of the Zeroth Theorem of the History of Physics

The zeroth theorem of the history of science (enunciated by E. P. Fischer) and widely known in the mathematics community as Arnol'd's Principle (decreed by M. V. Berry), states that a discovery (rule, regularity, insight) named after someone (often) did not originate with that person. I present five examples from physics: the Lorentz condition defining the Lorentz gauge of the electromagnetic potentials; the Dirac delta function (x); the Schumann resonances of the earth-ionosphere cavity; the Weizsacker-Williams method of virtual quanta; the BMT equation of spin dynamics. I give illustrated thumbnail sketches of both the true and reputed discoverers and quote from their "discovery" publications.Comment: 36 pages, 8 figures. Small revisions, added material and references - Arnol'd's law, Emil Wiechert. Submitted to Am. J. Phy

Initial singlet and triplet spin state contributions to pp -> pp pi0

The PINTEX facility at the IUCF Cooler ring, dedicated to the study of spin dependence in nucleon-nucleon interactions, has been used to measure polarization observables of the reaction pp -> pp pi0 at beam energies between 325 and 400 MeV. The stored polarized proton beam had spin projections both in the longitudinal and the transverse directions with respect to the beam momentum. We report here on the measurements of the relative transverse and longitudinal spin-dependent cross sections, deltasigma_T/sigma_tot and deltasigma_L/sigma_tot, and how from these observables the initial spin singlet and triplet cross sections are obtained. Considering angular momentum states less or equal to one, the contribution of the Ps partial waves to the cross section can be extracted.Comment: Contribution to PANIC99, XVth Particles and Nuclei International Conference, June 10-16, 1999, Uppsala, Sweden. Latex, 5 pages, 3 figure

Experimental search for evidence of the three-nucleon force and a new analysis method

A research program with the aim of investigating the spin dependence of the three-nucleon continuum in pd collisions at intermediate energies was carried out at IUCF using the Polarized INternal Target EXperiments (PINTEX) facility. In the elastic scattering experiment at 135 and 200 MeV proton beam energies a total of 15 independent spin observables were obtained. The breakup experiment was done with a vector and tensor polarized deuteron beam of 270 MeV and an internal polarized hydrogen gas target. We developed a novel technique for the analysis of the breakup observables, the sampling method. The new approach takes into account acceptance and non-uniformities of detection efficiencies and is suitable for any kinematically complete experiment with three particles in the final state.Comment: Contribution to the 19th European Few-Body Conference, Groningen Aug. 23-27, 200

Faster-than-c signals, special relativity, and causality

Motivated by the recent attention on superluminal phenomena, we investigate the compatibility between faster-than-c propagation and the fundamental principles of relativity and causality. We first argue that special relativity can easily accommodate -- indeed, does not exclude -- faster-than-c signalling at the kinematical level. As far as causality is concerned, it is impossible to make statements of general validity, without specifying at least some features of the tachyonic propagation. We thus focus on the Scharnhorst effect (faster-than-c photon propagation in the Casimir vacuum), which is perhaps the most plausible candidate for a physically sound realization of these phenomena. We demonstrate that in this case the faster-than-c aspects are ``benign'' and constrained in such a manner as to not automatically lead to causality violations.Comment: Plain LaTeX2E; 25 pages; 4 embedded figures (LaTeX pictures). V2: Some discussion clarified, minor rearrangements, references updated, no change in physics conclusions. To appear in Annals of Physic

Dependence of pp->pp pi0 near Threshold on the Spin of the Colliding Nucleons

A polarized internal atomic hydrogen target and a stored, polarized beam are used to measure the spin-dependent total cross section Delta_sigma_T/sigma_tot, as well as the polar integrals of the spin correlation coefficient combination A_xx-A_yy, and the analyzing power A_y for pp-> pp pi0 at four bombarding energies between 325 and 400 MeV. This experiment is made possible by the use of a cooled beam in a storage ring. The polarization observables are used to study the contribution from individual partial waves.Comment: 6 pages, 1 table, 4 figures, corrected equations 2 and

Towards Longitudinal Beam Polarization in the Cooler

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Spin Correlation in PP Scattering at 200 MeV

This research was sponsored by the National Science Foundation Grant NSF PHY-931478