Table of contents

Cosmogony, unlike its bigger brother Cosmology, concerns the origin of planets, and not the Universe as a whole. As such, it is a much more relevant subject to the student of physics and astronomy. Living as we do on a fairly typical terrestrial planet, we, as inquiring scientists, must often wonder where our home came from. It is a short step from this general interest to questions concerning the similarities and differences between Earth and nearby Moon, Venus, Mercury and Mars, and the differences between our Sun's solar system and the planets that have recently been found around other stars. Few topics in astronomy lend themselves better to the detailed analysis and interpretation of physical observations, in the hope of answering the two big questions: 'how common are Earth-like planets, and do they have university physics departments?' and 'are other planetary systems similar to ours and, if not, why not?'

We examine the quantum mechanical eigensolutions of the two-dimensional infinite-well or quantum billiard system consisting of a circular boundary with an infinite barrier or baffle along a radius. Because of the change in boundary conditions, this system includes quantized angular momentum values corresponding to half-integral multiples of ℏ/2. We discuss the resulting energy eigenvalue spectrum and visualize some of the novel energy eigenstates found in this system. We also discuss the density of energy eigenvalues, N(E), comparing this system to the standard circular well. These two billiard geometries have the same area (A = πR²), but different perimeters (P = 2πR versus (2π + 2)R), and we compare both cases to fits of N(E) which make use of purely geometric arguments involving only A and P. We also point out connections between the angular solutions of this system and the familiar pedagogical example of the one-dimensional infinite-well plus δ-function potential.

The distinction between work and heat is obvious in most typical situations, but becomes difficult in certain critical cases. The subject is discussed in texts on thermodynamics and has long given rise to debate. This paper presents an approach based on a mesoscopic analysis, using a simple mechanical model, in which bodies are made up of particles (representing atoms and/or molecules) treated as material points interacting with forces that obey Newton's laws. The sum of the work done by these microscopic forces is split into two terms representing the macroscopic quantities work and heat.

We suggest an elementary scheme for introducing quasi-classical states of a particle that can move on the semi-axis x > 0 only, where it experiences a quadratic potential (a folded harmonic oscillator). Using an image method with coherent and other simple states of the harmonic oscillator, we analyse wavepackets that oscillate bouncing off a rigid wall set at x = 0.

Cartan proved an important theorem showing that Einstein's general relativity is essentially the only theory of gravity that involves the metric tensor, its first derivatives, and linear functions of its second derivatives. Weyl gave a simplified, less general version of this theorem, which we explain in detail. Both emphasize the centrality of the curvature scalar and the naturalness of general relativity.

The Ampère theorem and the Biot–Savart law are well known tools used to calculate magnetic fields created by currents. Their use is not limited to the case of magnetostatics; they can also be used in time-dependent problems. We show in this paper that the highly classical example of a straight wire, generally treated as a simple magnetostatics problem, should be considered in the framework of time-varying fields. This academic question is a nice illustration showing the generality of the Biot–Savart law, and especially how it implicitly takes into account the charge conservation law.

It is shown how point charges and point dipoles with finite self-energies can be accommodated in classical electrodynamics. The key idea is the introduction of constitutive relations for the electromagnetic vacuum, which actually mirrors the physical reality of vacuum polarization. Our results reduce to conventional electrodynamics for scales large compared to the classical electron radius r₀ ≈ 2.8 × 10⁻¹⁵ m. A classical simulation for a structureless electron is proposed, with the appropriate values of mass, spin and magnetic moment.

The problem considered here is that of a parallelepiped-shaped box, partially filled with liquid, that slides on a flat surface. The box is accelerated with a constant acceleration during a given time and then decelerated because of the frictional force. Due to the forces acting on the liquid during both phases (acceleration and deceleration), sloshing of the liquid takes place inside the container and such sloshing effects strongly affect the system dynamics. A simple experimental apparatus has been designed to analyse the sloshing effects and a simple theoretical model for the sloshing phenomenon has been developed. Experimental results obtained in the experimental set-up are presented and compared with theoretical predictions.

We obtain exact perturbation corrections to the energies and wavefunctions for the potential −α/r + βr and show that an adjustable parameter enables us to improve the perturbation series considerably. This straightforward approach is suitable for teaching at undergraduate level.

A video of the Reynolds transition experiment, developed for physics teaching, shows the continuous transition from laminar to turbulent flow. Additionally, the critical Reynolds number of the experimental set-up is determined approximately. By looking at it, the user of the video can measure all necessary data and then calculate a result.

An overlooked straightforward application of velocity reciprocity to a triplet of inertial frames in collinear motion identifies the ratio of their cyclic relative velocities' sum to the negative product as a cosmic invariant—whose inverse square root corresponds to a universal limit speed. A logical indeterminacy of the ratio equation establishes the repeatedly observed unchanged speed of stellar light as one instance of this universal limit speed. This formally renders the second postulate redundant. The ratio equation furthermore enables the limit speed to be quantified—in principle—independently of a limit speed signal. Assuming negligible gravitational fields, two deep-space vehicles in non-collinear motion could measure with only a single clock the limit speed against the speed of light—without requiring these speeds to be identical. Moreover, the cosmic invariant (from dynamics, equal to the mass-to-energy ratio) emerges explicitly as a function of signal response time ratios between three collinear vehicles, multiplied by the inverse square of the velocity of whatever arbitrary signal might be used.

We deduce the most general space–time transformation laws consistent with the principle of relativity. Thus, our result contains the results of both Galilean and Einsteinian relativity. The velocity addition law comes as a by-product of this analysis. We also argue why Galilean and Einsteinian versions are the only possible embodiments of the principle of relativity.

We present the details of the four year MPhys undergraduate degree provided by the University of Surrey. Integral to this course is a full year spent on a research placement, which in most cases takes place external to the university at a North American or European research centre. This paper outlines the basic rationale underlying the course and, by including a number of research student profiles, we discuss the triple benefits of this course for the students, the University of Surrey and the host institutions where the students spend their research year.

An illustrative example is presented concerning Thomson's theorem on the minimum energy of the equilibrium charge distribution on conductors. The theorem is used to find the density of the induced surface charge in the classical case of a point charge in front of an infinite planar conductor. The energy functional of the system can be minimized directly by simple considerations.

Following Marcella's approach to the double-slit experiment (Marcella T V 2002 Eur. J. Phys.23 615–21), diffraction patterns for two-dimensional masks are calculated by Fourier transform of the Mask geometry into momentum space.

We show that in order to account for the repulsive Casimir effect in the parallel-plate geometry in terms of the quantum version of the Lorentz force, it is possible to introduce virtual surface densities of magnetic charge and currents. The quantum version of the Lorentz force expressed in terms of the correlators of the electric and magnetic fields for planar geometries then yields the Casimir pressure correctly.

The two Numerical Recipes books are marvellous. The principal book, The Art of Scientific Computing, contains program listings for almost every conceivable requirement, and it also contains a well written discussion of the algorithms and the numerical methods involved. The Example Book provides a complete driving program, with helpful notes, for nearly all the routines in the principal book.

The first edition of Numerical Recipes: The Art of Scientific Computing was published in 1986 in two versions, one with programs in Fortran, the other with programs in Pascal. There were subsequent versions with programs in BASIC and in C. The second, enlarged edition was published in 1992, again in two versions, one with programs in Fortran (NR(F)), the other with programs in C (NR(C)). In 1996 the authors produced Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing as a supplement, called Volume 2, with the original (Fortran) version referred to as Volume 1. Numerical Recipes in C++ (NR(C++)) is another version of the 1992 edition. The numerical recipes are also available on a CD ROM: if you want to use any of the recipes, I would strongly advise you to buy the CD ROM. The CD ROM contains the programs in all the languages.

When the first edition was published I bought it, and have also bought copies of the other editions as they have appeared. Anyone involved in scientific computing ought to have a copy of at least one version of Numerical Recipes, and there also ought to be copies in every library.

If you already have NR(F), should you buy the NR(C++) and, if not, which version should you buy?

In the preface to Volume 2 of NR(F), the authors say 'C and C++ programmers have not been far from our minds as we have written this volume, and we think that you will find that time spent in absorbing its principal lessons will be amply repaid in the future as C and C++ eventually develop standard parallel extensions'. In the preface and introduction to NR(C++), the authors point out some of the problems in the use of C++ in scientific computing. I have not found any mention of parallel computing in NR(C++).

Fortran has quite a lot going for it. As someone who has used it in most of its versions from Fortran II, I have seen it develop and leave behind other languages promoted by various enthusiasts: who now uses Algol or Pascal? I think it unlikely that C++ will disappear: it was devised as a systems language, and can also be used for other purposes such as scientific computing. It is possible that Fortran will disappear, but Fortran has the strengths that it can develop, that there are extensive Fortran subroutine libraries, and that it has been developed for parallel computing.

To argue with programmers as to which is the best language to use is sterile.

If you wish to use C++, then buy NR(C++), but you should also look at volume 2 of NR(F). If you are a Fortran programmer, then make sure you have NR(F), volumes 1 and 2. But whichever language you use, make sure you have one version or the other, and the CD ROM.

The Example Book provides listings of complete programs to run nearly all the routines in NR, frequently based on cases where an anlytical solution is available. It is helpful when developing a new program incorporating an unfamiliar routine to see that routine actually working, and this is what the programs in the Example Book achieve.

I started teaching computational physics before Numerical Recipes was published. If I were starting again, I would make heavy use of both The Art of Scientific Computing and of the Example Book. Every computational physics teaching laboratory should have both volumes: the programs in the Example Book are included on the CD ROM, but the extra commentary in the book itself is of considerable value.

P Borcherds

In the early 1960s Feynman lectured to physics undergraduates and, with the assistance of his colleagues Leighton and Sands, produced the three-volume classic Feynman Lectures in Physics.

These lectures were delivered in the mornings. In the afternoons Feynman was giving postgraduate lectures on gravitation. This book is based on notes compiled by two students on that course: Morinigo and Wagner. Their notes were checked and approved by Feynman and were available at Caltech. They have now been edited by Brian Hatfield and made more widely available.

The book has a substantial preface by John Preskill and Kip Thorne, and an introduction entitled 'Quantum Gravity' by Brian Hatfield. You should read these before going on to the lectures themselves.

Preskill and Thorne identify three categories of potential readers of this book.

1. Those with a postgraduate training in theoretical physics.

2. 'Readers with a solid undergraduate training in physics'.

3. 'Admirers of Feynman who do not have a strong physics background'.

The title of the book is perhaps misleading: readers in category 2 who think that this book is an extension of the Feynman Lectures in Physics may be disappointed. It is not: it is a book aimed mainly at those in category 1. If you want to get to grips with gravitation (and general relativity) then you need to read an introductory text first e.g. General Relativity by I R Kenyon (Oxford: Oxford University Press) or A Unified Grand Tour of Theoretical Physics by Ian D Lawrie (Bristol: IoP). But there is no Royal Road.

As pointed out in the preface and in the introduction, the book represents Feynman's thinking about gravitation some 40 years ago: the lecture course was part of his attempts to understand the subject himself, and for readers in all three categories it is this that makes the book one of interest: the opportunity to observe how a great physicist attempts to tackle some of the hardest challenges of physics. However, the book was written 40 years ago, and since then there have been many discoveries: black holes and the cosmic microwave background have been observed. There have also been theoretical developments.

Unless you are a category 1 reader, you will find there are substantial passages you will need to skip over. There are also substantial sections throughout the book accessible to all, such as the following excerpt from lecture 13 (there are 16 lectures) in a section entitled 'Disappearing galaxies and energy conservation'.

'Let me also say something that people who worry about mathematical proofs and inconsistencies seem not to know. There is no way of showing mathematically that a physical conclusion is wrong or inconsistent. All that can be shown is that the mathematical assumptions are wrong. If we find that certain mathematical assumptions lead to a logically inconsistent description of Nature, we change the assumptions, not nature.'

If you admire Feynman, then you are likely to enjoy this book. If you want an introduction to gravitation and relativity, there are other more recent and accessible books, but Feynman's insight may help your understanding.

Think about buying it for yourself, but make sure there is a copy in your library.

P Borcherds