What Brown saw and you can too

A discussion is given of Robert Brown's original observations of particles ejected by pollen of the plant \textit{Clarkia pulchella} undergoing what is now called Brownian motion. We consider the nature of those particles, and how he misinterpreted the Airy disc of the smallest particles to be universal organic building blocks. Relevant qualitative and quantitative investigations with a modern microscope and with a "homemade" single lens microscope similar to Brown's, are presented.Comment: 14.1 pages, 11 figures, to be published in the American Journal of Physics. This differs from the previous version only in the web site referred to in reference 3. Today, this Brownian motion web site was launched, and http://physerver.hamilton.edu/Research/Brownian/index.html, is now correc

Scalar Field Quantum Inequalities in Static Spacetimes

We discuss quantum inequalities for minimally coupled scalar fields in static spacetimes. These are inequalities which place limits on the magnitude and duration of negative energy densities. We derive a general expression for the quantum inequality for a static observer in terms of a Euclidean two-point function. In a short sampling time limit, the quantum inequality can be written as the flat space form plus subdominant correction terms dependent upon the geometric properties of the spacetime. This supports the use of flat space quantum inequalities to constrain negative energy effects in curved spacetime. Using the exact Euclidean two-point function method, we develop the quantum inequalities for perfectly reflecting planar mirrors in flat spacetime. We then look at the quantum inequalities in static de~Sitter spacetime, Rindler spacetime and two- and four-dimensional black holes. In the case of a four-dimensional Schwarzschild black hole, explicit forms of the inequality are found for static observers near the horizon and at large distances. It is show that there is a quantum averaged weak energy condition (QAWEC), which states that the energy density averaged over the entire worldline of a static observer is bounded below by the vacuum energy of the spacetime. In particular, for an observer at a fixed radial distance away from a black hole, the QAWEC says that the averaged energy density can never be less than the Boulware vacuum energy density.Comment: 27 pages, 2 Encapsulated Postscript figures, uses epsf.tex, typeset in RevTe

The history of mass assembly of faint red galaxies in 28 galaxy clusters since z=1.3

We measure the relative evolution of the number of bright and faint (as faint as 0.05 L*) red galaxies in a sample of 28 clusters, of which 16 are at 0.50<= z<=1.27, all observed through a pair of filters bracketing the 4000 Angstrom break rest-frame. The abundance of red galaxies, relative to bright ones, is constant over all the studied redshift range, 0<z<1.3, and rules out a differential evolution between bright and faint red galaxies as large as claimed in some past works. Faint red galaxies are largely assembled and in place at z=1.3 and their deficit does not depend on cluster mass, parametrized by velocity dispersion or X-ray luminosity. Our analysis, with respect to previous one, samples a wider redshift range, minimizes systematics and put a more attention to statistical issues, keeping at the same time a large number of clusters.Comment: MNRAS, 386, 1045. Half a single sentence (in sec 4.4) change

The Quantum Interest Conjecture

Although quantum field theory allows local negative energy densities and fluxes, it also places severe restrictions upon the magnitude and extent of the negative energy. The restrictions take the form of quantum inequalities. These inequalities imply that a pulse of negative energy must not only be followed by a compensating pulse of positive energy, but that the temporal separation between the pulses is inversely proportional to their amplitude. In an earlier paper we conjectured that there is a further constraint upon a negative and positive energy delta-function pulse pair. This conjecture (the quantum interest conjecture) states that a positive energy pulse must overcompensate the negative energy pulse by an amount which is a monotonically increasing function of the pulse separation. In the present paper we prove the conjecture for massless quantized scalar fields in two and four-dimensional flat spacetime, and show that it is implied by the quantum inequalities.Comment: 17 pages, Latex, 3 figures, uses eps

Gravitational Waves in Bianchi Type-I Universes I: The Classical Theory

The propagation of classical gravitational waves in Bianchi Type-I universes is studied. We find that gravitational waves in Bianchi Type-I universes are not equivalent to two minimally coupled massless scalar fields as it is for the Robertson-Walker universe. Due to its tensorial nature, the gravitational wave is much more sensitive to the anisotropy of the spacetime than the scalar field is and it gains an effective mass term. Moreover, we find a coupling between the two polarization states of the gravitational wave which is also not present in the Robertson-Walker universe.Comment: 34 papers, written in ReVTeX, submitted to Physical Review

Enhanced Geometry Fluctuations in Minkowski and Black Hole Spacetimes

We will discuss selected physical effects of spacetime geometry fluctuations, especially the operational signatures of geometry fluctuations and their effects on black hole horizons. The operational signatures which we discuss involve the effects of the fluctuations on images, and include luminosity variations, spectral line broadening and angular blurring. Our main interest will be in black hole horizon fluctuations, especially horizon fluctuations which have been enhanced above the vacuum level by gravitons or matter in squeezed states. We investigate whether these fluctuations can alter the thermal character of a black hole. We find that this thermal character is remarkably robust, and that Hawking's original derivation using transplanckian modes does not seem to be sensitive even to enhanced horizon fluctuations.Comment: 13 pages, 3 figures, based on a talk presented at the Peyresq 12 worksho

Quantum Inequalities and Singular Energy Densities

There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of apparent failures of the quantum inequalities, which involve passage of an observer through regions where the negative energy density becomes singular. We argue that this type of situation requires one to formulate quantum inequalities using sampling functions with compact support. We discuss such inequalities, and argue that they remain valid even in the presence of singular energy densities.Comment: 18 pages, LaTex, 2 figures, uses eps

Quantum Inequalities for the Electromagnetic Field

A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential, and the sampling function used to weight the energy integrals is left arbitrary up to the constraints that it be a positive, continuous function of unit area and that it decays at infinity. Examples of the quantum inequality are developed for Minkowski spacetime, Rindler spacetime and the Einstein closed universe.Comment: 19 pages, 1 table and 1 figure. RevTex styl