Table of contents

Figure 1. J J Thomson giving lecture demonstration of Braun e/m tube in the 1890s. (Photograph courtesy of the Cavendish Laboratory, Cambridge.)

In spite of some competitors, Joseph John Thomson, second successor to James Clerk Maxwell in the Cavendish Chair at Cambridge, is generally accepted to be the discoverer of the electron; and although subatomic electrically charged particles were floating throughout the entire history of 19th Century physics, the 30th April 1897, when Thomson gave his lecture on `Cathode rays' at the Royal Institution of Great Britain in London, is being celebrated as the particle's official birthday. The reason is that, after a detailed overview with some demonstrations of facts in cathode-ray physics, Thomson expounded an interesting hypothesis, namely that `atoms of the elements are aggregations of very small particles, all similar to each other; we shall call such particles corpuscles, so that the atoms of ordinary elements are made of corpuscles and holes, the holes being predominant', and that the cathode rays must be identified with these corpuscles [1].

Clearly, this hypothesis combined elements of former knowledge with the speaker's new convictions, notably that all corpuscles had the same mass. He reported on his own method for measuring the ratio of mass m to charge e by magnetic deflection; the value obtained, 1.6 × 10^-7, `was small compared with the value 10<sup>-4</sup> for the ratio of the mass of an atom of hydrogen to the charge carried by it', and hence it favoured together with other results `the hypothesis that the carriers of the charges are smaller than the atoms of hydrogen'. [2] Thomson concluded finally: `It is interesting to notice that the value of e/m, which we have found from the cathode rays, is of the same order as the value 10^-7 deduced by Zeeman from his experiments on the effect of a magnetic field on the period of sodium light.' [2]

Thomson's pioneering work of 1897, together with the Dutch investigations of the Zeeman effect and the German studies by Emil Wiechert and Willy Wien (also on cathode rays) established the electron as a constituent of matter. Thus began the electron's great role in science.

This issue of European Journal of Physics celebrates the centenary of this occasion, certainly one of the most influential events in the history of physics, with five contributions provided by physicists and historians of science. The first two articles, those of N Robotti and A Kox, describe the discovery of the electron, a veritable double-birth of what soon turned out to be the same child. A condensed (and very selected) chronology of the successful deeds of the electron in the physics of almost the past century by H Rechenberg is followed by a more lengthy narrative of decisive episodes between 1900 and 1930 through which the electron revolutionized the foundations of modern chemistry, presented by T Arabatzis and K Gavroglu. The last paper, by R Penrose, provides a glimpse of the mathematical elegance in the now standard description of the electron by Paul Dirac's famous relativistic equation.

Much more can and will be written in many papers devoted this year to the electron's anniversary. It will be argued that: firstly, the electron is (still) a fundamental constituent of all matter; secondly, it is a driving force in many different natural phenomena (or fields of physics); and, thirdly, it exhibits unique properties (such as spin or the particle - antiparticle property) which provide the key to solving the profoundest riddles of Nature and its evolution. That these properties are far from being easily `visualizable' can be derived from the paper of Arabatzis and Gavroglu: at the beginning of this century, chemists endowed the electron with so many abstruse properties that physicists were ultimately happy to have available `non-visualizable' quantum mechanics, allowing the non-classical features of the electron and its behaviour to be described so perfectly. Let us finally recall what Arthur Eddington states in 1926 in the introduction to his The Internal Constitution of Stars: he did not know who was the hero of his story, the big star or the small electron. Today we do know the answer: the electron is the star, both in micro and macro physics.

References

[1] Thomson J J 1896 - 98 Cathode rays Not. Proc. Meetings R. Instn Great Britain (with abstracts of the discussions of the discourses delivered at the evening meetings) vol 15, pp 419 - 32 (see, especially, pp 431 - 2)

[2] Thomson J J 1896 - 98 Cathode rays Not. Proc. Meetings R. Instn Great Britain (with abstracts of the discussions of the discourses delivered at the evening meetings) vol 15, p 432

Helmut RechenbergMunich

This paper describes the process by which the first studies on discharges in rarefied gases led to the discovery of the electron in 1897. Particular emphasis is laid on the debate between the so-called `aetherial' and `material' theories regarding the nature of `cathode rays'. The paper goes on to demonstrate how the debate was resolved by J J Thomson with his proposal of a third hypothesis - the `corpuscle' (or `electron' as it became called). The paper closes with an analysis of the first measurement of the charge of the electron by J J Thomson in 1899.

The paper gives an account of the discovery, in the fall of 1896, of the Zeeman effect and of the developments in the months that followed. It is to a large extent based on previously unknown archival material.

Sammenvatting. In dit artikel, dat is voor een groot deel is gebaseerd op onbekend archiefmateriaal, wordt een historisch overzicht gegeven van de ontdekking van het Zeeman effect in het najaar van 1896 en van de ontwikkelingen in de maanden na de ontdekking.

The crucial role of the electron in the history of physics over the past hundred years is documented in a selected, four-part chronology: 1. The early electron - conductivity, -rays and relativity theory; 2. The electron and the old quantum theory of atomic structure; 3. The electron in quantum and wave mechanics; 4. The electron in nuclear and elementary particle physics.

Zusammenfassung. Die beherrschende Rolle des Elektrons in der Physikgeschichte der letzten hundert Jahre wird anhand einer vierteiligen Chronologie (1. Das frühe Elektron - Leitfähigkeit, -Strahlen und Relativitätstheorie; 2. Das Elektron und die ältere Quantentheorie des Atombaues; 3. Das Elektron in der Quanten- und Wellenmechanik; 4. Das Elektron in der Elementarteilchenphysik) aufgezeigt.

This paper narrates the way chemists have been using the electron to account for one of the most intriguing problems, namely the bonding of two neutral atoms to form a molecule. The chemists' attempts to account for the mechanism of the homopolar bond, first in the context of the old quantum theory and after 1926 in the context of wave mechanics, brought the specter of reductionism to physics. We argue that the chemists' successful appropriation of the electron strengthened, first, the autonomy of physical chemistry and, then, of quantum chemistry with respect to physics.

The Dirac equation for the electron is central to a considerable body of mathematics. Its essential mathematical ingredients, namely Clifford algebras and the theory of spinors in n dimensions have wide applications in numerous fields. A taste of all this is supplied here.

In the middle of the 18th century around 30 different temperature scales with various fixed points existed, but only the scales by Fahrenheit, Réaumur and Celsius have survived to the present time. Anders Celsius realized the need for well defined fixed points and he was exceptional in his careful measurements of these temperatures, the freezing and boiling points of water, thus creating a true international temperature scale. His determination of the change in the boiling point with barometric pressure shows a very high degree of accuracy. The development towards modern scientific scales is briefly reviewed up to the resolution of 1990, according to which the Celsius scale is regarded as no longer formally being a true centigrade scale.

Cyclists - particularly in flat areas - will have noticed that wind increases their total time to traverse a circuit, whichever way the wind is blowing. Here we present a simple aerodynamic model to explain this effect, and give some quantitative predictions. The results indicate that the total journey time depends strongly on the wind speed, the sensitivity increasing with wind speed.

A simple result about the failure of determinism of classical particle dynamics is presented. This result is much more accessible than similar ones in the usual literature.

Resumen. Se muestra un sencillo ejemplo de las limitaciones al determinismo de la dinámica clásica de partículas. Dicho ejemplo es mucho más accesible desde el punto de vista técnico que otros similares en la literatura usual.

We present a computer simulation designed to serve as an educational tool for insight into the microscopic nature of spontaneous magnetization, using the spin- Ising model at low temperatures. The transition of a crystalline substance consisting of magnetic and non-magnetic atoms to the ferromagnetic state and the surface effect on the said transition are studied using this simulation. Within the framework of percolation theory, the strength and the fractal structure of the infinite cluster and the correlation length are further aspects that can be analysed by means of this computational application.

Resumen. Presentamos una simulación por ordenador diseñada para servir como herramienta didáctica para la comprensión de la naturaleza microscópica de la magnetización espontánea, utilizando el modelo de Ising con spin a bajas temperaturas. La transición al estado ferromagnético de una sustancia cristalina formada por atomos magnéticos y no magnéticos y el efecto de las superficies en dicha transición, son estudiados mediante esta simulación. Dentro del marco de la teoría de la percolación, la magnitud y la estructura fractal del racimo infinito y la longitud de correlación, son aspectos que pueden ser también analizados mediante esta aplicación informática.

A high-precision numerical solution of the tunnelling problem for three different one-dimensional potentials is performed in order to verify the accuracy and the range of validity of the recently proposed general expressions for the phase of the transmission amplitude and the total delay time of a quantum particle tunnelling through smooth potential barriers. The results show those expressions, as well as Kemble's formula for the transmission rate, to be of high quality in wide ranges of the particle's energy that include the top of the barrier but not its base.

Zusammenfassung. Eine hochpräzise Zahlenlösung des quanten-mechanischen Tunnelproblems ist für drei verschiedene eindimensionale Potentiale durchgeführt worden, die zum Zweck hatte, die Genauigkeit und den Gültigkeitsbereich der vor kurzem abgeleiteten grundlegenden Formeln für die Phase der Übertragungsamplitude und die gesamte Verzögerungszeit eines Teilchens zu überprüfen, das im Tunnelprozeß durch glatte Potentialsperren einbegriffen ist. Die Ergebnisse der ausgeführten Zahlenanalyse bestätigen die hohe Qualität dieser Fromeln, sowie auch die der Formel von Kemble für die Übertragungswahrscheinlichkeit, im breiten Bereich der Energie des Teilchens, einschließlich des Scheitels der Potentialsperre doch nicht des Sperrenfußes.

The well known master equation which describes the decay of a field in a single mode cavity is derived from a simple physical argument. This is achieved by applying the correspondence principle to obtain the master equation describing the decay of a field in an arbitrary quantum state from the knowledge of the decay mechanism for a classical field.

Resumo. A bem conhecida equação Mestra que descreve o decaimento de um campo em uma cavidade monomodo é derivada através de um argumento físico símples. Isto é feito aplicando-se o princípio da correspondência para obter a equação Mestra que descreve o decaimento de um campo em um estado quântico qualquer através do conhecimento do mecanismo de decaimento de um campo clássico.

The JWKB approximation is extensively used in tunnelling probability calculations. We apply the JWKB formula to a triangular potential barrier and test its accuracy.

Zusammenfassung. Die JWKB-Methode wird extensiv benutzt bein Berechnungen von Tunnel-Wahrscheinlichkeiten. Wir wenden die JWKB-Formel auf eine dreieckige Potentialschwelle an und testen ihre Genauigkeit.

The phenomenon of particle tunnelling through a modified cubic potential is studied by focusing on the transition amplitude instead of the wavefunction, as is done in the usual WKB approach. The Green function, decay width and transmission probability for the tunnelling of localized wavepackets are computed within this framework.

Resumen. La horadacion de una particula por media de una potencial de forma cubica es estuadiada por enfocando al amplitud de transicion en vez de function de onda como en el motodo de WKB. La function de Green, anchura de decaer y probabilidad de transmision estan computadas dentro de esta armazon.

We study the possibility of localization of the front present in a one-dimensional ballistically controlled annihilation model in which the two annihilating species are initially spatially separated. We show that the front can be localized by taking as initial condition an inhomogeneous Poisson-type distribution.

A Kater pendulum has been automated, using a symmetric differential capacitive (SDC) sensor connected to a personal computer through an analogue-to-digital (A/D) converter. Adjustments of the instrument, to measure the acceleration of gravity, are assisted by Lissajous figures referenced to a computer generated signal.

Zusammenfassung. Anhand eines mit einem Komputer durch einen A/D-Konverter verbundenen symmetrischen Differentialkapazitivsensors ist ein Katersches Pendel automatisiert worden. Lissajous-Figuren, die man aus der Mischung der experimentellen Daten mit einem vom Komputer erzeugten Bezugssignal entstehen lässt, helfen bei der Justierung des Gerts, das zur Messung der Schwerkraftsbescheunigung dienen soll.

A stack of transparent plates with randomly varying thicknesses (e.g. viewgraphs) reflects light perfectly, as a result of the accumulation of reflections from interfaces at the air gaps separating the plates. Two theories of this effect are discordant. The naive ray theory assumes that the random phases associated with the thickness variations make all the reflections incoherent, and predicts that the transmitted intensity decays as 1/N. This theory is wrong because some distinct multiply reflected waves have identical path lengths and so superpose coherently. The true decay is exponential: exact averaging of the logarithm of the transmitted intensity over the random phases, assuming these are uniformly distributed modulo , gives the transmitted intensity as , where is the intensity transmittance of a single interface. Transparent mirrors are naked-eye examples of the localization of light, for which the localization length (inverse decay exponent) can be calculated exactly. Experiments confirm the exponential decay.

Zusammenfassung. Ein Stapel von transparenten Platten mit beliebig variierender Dicke (z.B.Overhead-Folien) reflektiert Licht perfekt. Diese perfekte Reflexion ist das Ergebnis der Akkumulation von Reflexionen an den Grenzflächen der Luftspalte zwischen den Platten. Die zwei Theorien dieses Effektes stimmen nicht überein. Die naive Strahlen-Theorie nimmt an, daß die beliebigen Phasen, die mit den Variationen der Plattendicke verknüpft sind, zu absolut inkoherenten Reflexionen führen und sagt einen 1/N Verlauf für die durchgelassene Intensität voraus. Diese Theorie ist falsch, da einige der mehrfach reflektierten Wellen identische Weglängen haben und daher koherent überlagern. Der wahre Verlauf ist exponential: exakte Mittelung des Logarithmus der durchgelassenen Intensität über die beliebigen Phasen, unter der Annahme sie seien gleichmässig verteilt modulo , führt zur durchgelassenen Intensität , wo die durchgelassene Intensität einer einzelnen Grenzfläche ist. Durchsichtige Spiegel sind Beispiele der Lokalisation des Lichtes für das unbewaffenete Auge, für die die Lokalisationslänge (inverser Exponentialkoeffizient) exakt berechnet werden kann. Experimente bestätigen den exponentialen Verlauf.

A classical problem is revisited using boundary diffraction wave theory as an alternative viewpoint to the Fourier optics treatment. Advantages and limitations of both treatments are discussed.

Riassunto. Un problema classico della diffrazione è riesaminato sulla base della teoria dell'onda di bordo come punto di vista alternativo alla trattazione con i metodi dell'ottica di Fourier. Sono discussi i vantaggi e le limitazioni di entrambe le trattazioni.

The usual textbook derivation of the thermal expansion of solids based on the Taylor expansion of the interatomic potential is re-examined. It is shown that the simple theory presented in textbooks not only fails at low temperatures, but that the seemingly reasonable high-temperature result is fortuitous. An alternative classical model is presented, which is based on calculating the time-averaged interatomic distance as a function of temperature. The model is applied to the case of solid argon, as an example, to show the excellent agreement with experiment. Since simple numerical computations form an integral part of the undergraduate physics curriculum, this model presents an attractive alternative to the current treatments in the elementary textbooks.

Abstrakt. Vi har undersökt den i läroböckerna vanliga derivationen av termisk expansion av ämnen i fast form som är grundad på Taylors serieexpansion av den interatomiska potensen. Vi vill visa att denna enkla teori inte bara är felaktig vid låga temperatur men dessutom att resultatet vid höga temperaturer har framkommit genom en slump. Här presenteras alltså en ny klassisk modell vilken grundats på beräkningen av medelvärdet av den interatomiska distansen över tid som en funktion av temperatur. Modellen använder argon i fast form som ett exempel för att påvisa den tydliga överensstämmelsen i experimenten. Eftersom enkla numeriska beräkningar är en väsentlig dal av studieplanen så innebär den nya modellen en klar förbättring av textboksinnehållet.

We present a derivation of the equation describing the current flow in a circuit with self-inductance based on Newton's second law plus the Weber force or, alternatively, plus the Lorentz or Liénard - Schwarzschild force. In Weber's approach the self-inductance can be treated as a measure of the effective average inertial mass of the conduction electrons.

Resumo. Apresentamos uma derivação da equação descrevendo o fluxo de corrente num circuito contendo auto-indutância a partir da segunda lei de Newton mais a força de Weber ou, alternativamente, mais a força de Lorentz ou de Liénard - Schwarzschild. No enfoque de Weber a auto-indutância pode ser tratada como uma medida da massa inercial média efetiva dos elétrons de condução.

The original article discussed the heat generated in a friction device as a consequence of arresting a falling climber. Here we point out that, on the short timescale of such an event, heat generation would occur almost entirely at the interface between the rope surface and the metal friction device, leading to unacceptably high temperatures and possible rope melting.

The ψ(x,t) wavefunction of a Gaussian wavepacket spreading in free space (V(x)≡0) is expressed in a didactic form. The expression found is a product of pure real factors and pure phase factors. This makes it very easy to derive the expression for the probability density from the wavefunction. The physical meaning of each of the factors is analysed.

Zusammenfassen. Die Wellenfunktion ψ(x,t) eines Gaußschen Wellenpaketes, welches sich bei der Ausbreitung im freien Raum (V(x)≡0) verbreitert, wird in einer didaktischen Form ausgedrückt. Der gefundene Ausdruck ist ein Produkt von reellen Faktoren und reinen Phasen-Faktoren. Dies vereinfacht die Herleitung des Ausdruckes für die Wahrscheinlichkeitsdichte aus der Wellenfunktion. Die physikalische Bedeutung von jedem Faktor wird analysiert.

While writing a paper [1] about the time evolution of different wavepackets I wanted to find a didactic expression for the ψ(x,t) wavefunction of a Gaussian initial state. The particular expression that was finally constructed is different from those found in quantum mechanics texts [2 ,3].

Figure 1. x- and t-dependent parts of the wavefunction. (a), (b) and (c) show the time development of the real part of factor 1, factor 2 and of the full ψ(x,t). The x, y scale is the same for all (a), (b) and (c). (d) shows the time development of the probability density ρ(x,t). The x, y scale is the same for all time instants. Atomic units are used. a = 2.5 Bohr = 0.13 nm, nm. The atomic time unit is 2.41 × 10^-17 s. See the text for details.

Figure 2. t-dependent parts of the wavefunction. (a) shows the time dependent prefactor of factor 2 as function of time. (b) and (c) show the time dependence of the terms of factor 3. Their real (full curve) and imaginary (broken curves) parts are plotted against time. The thin dashed horizontal lines in (b) show the asymptotes for t=∞. Atomic units are used. See the text for details.

Initial state

Our initial state is a simple Gaussian wavepacket of the form

This wavepacket is a product of three factors:

A normalization factor that makes the norm of the wavefunction unity.

A plane wave factor that accounts for the non-zero momentum p₀ of the wavepacket.

A bell-shaped localizing function with half width at half maximum .

Time evolution

The time development of the initial ψ₀(x) state is given by [2]:

This Fourier integral can be calculated easily with Gaussian integrals and leads to a wavefunction like

Transformation of into didactic form

Now we want to transform this into something more informative. First note that the centre of the wavepacket is moving with the group velocity. Hence it is worth writing instead of x₀into the first term of the numerator in the exponential. Working this out gives the following result

It is getting clearer already! Now let us get rid of the complex denominators!

Utilizing this we get finally

where arg z is the phase of the complex number z, i.e. . Our ψ(x,t) has three main factors ((7), (8) and (9)). The first factor (7) is a product of two pure real coefficients and a plane wave. This plane wave part of factor 1 and the entire second (8) and third (9) factors are pure phase factors, i.e. their magnitude is one. Hence it is very easy to calculate the probability density ; one has only to calculate the square of the pure real coefficients of factor 1 which gives:

The three terms of ψ(x,t) are as follows.

Factor 1. (Cf (7)) A Gaussian of the form (1). This is an expression having the same form as ψ₀(x) but the centre of gravity of the Gaussian is moving with speed and its width is increased to . The maximum value of the Gaussian is decreasing as its width increases making the area under ρ(x,t) (total probability) constant (one). The time evolution of factor 1 is shown in figure 1(a).

Factor 2. (Cf (8)) An x- and t-dependent phase factor that is quadratic in x. One can see from figure 1(b) that this factor oscillates faster for larger|x| values. This accounts for the fact that the higher momentum components of the initial Gaussian ψ₀(x) move with higher velocities. The function which describes the time-dependent prefactor of the phase is . This function (cf figure 2(a)) is not monotonic in time. Its value is zero for t = 0 and t=∞ and has a maximum at .

Factor 3. (Cf (9)) An x-independent (but still t-dependent) phase factor. This phase factor is a product of two terms. The first term is a monotonic function of time while the second one is oscillating. The phase of the first term is zero for t = 0 (a(t) is pure real) and -π/4 for t=∞ (a(t) is pure imaginary). The second term is where and it accounts for the time development of the plane wave component in factor 1. These two phase factors are plotted in figures 2(b) and 2(c) against time.

Acknowledgment

This work was partially supported by the Hungarian OTKA grant No F 014236.

References

[1] Márk G I Influence of the wavepacket shape to its time development to be published

[2] Cohen-Tannoudji C, Diu B and Laloë F 1977 Quantum Mechanics (New York: Wiley)

[3] Merzbacher E 1970 Quantum Mechanics2nd edn (New York: Wiley)

This third volume of Faraday's Correspondence prints the texts of more than 800 letters, illustrating the wide range of Faraday's activities in the 1840s. While many of the letters are brief and mundane, some are more substantial and informative, and there are some gems to be found. His correspondents range from the luminaries of British science - including John Herschel, Charles Babbage, G B Airey (the Astronomer Royal), William Whewell and the young William Thomson (Kelvin) - to leading European scientists, notably the chemists J B Dumas and C F Schönbein and the physicist Joseph Plücker. An important element of the correspondence is devoted to Faraday's work for various government agencies. His important inquiry, with the geologist Charles Lyell, into the Haswell Colliery explosion in 1844, and other cases where he provided expert advice, attests to his importance in the public arena. The inclusion in this volume of his recently found correspondence with Trinity House shows his role in shaping the lighthouse service, his main involvement in public affairs.

Faraday suffered from ill-health in the early 1840s, and his astonishing scientific productivity fell away. But in 1845 he began a remarkable series of investigations in magnetism, the discovery of the `Faraday' magneto-optic effect and diamagnetism, leading to his introduction of the term `magnetic field'. This work, which features in some of the correspondence in this volume, was to shape his subsequent investigation of field theory, and the course of his later career.

This edition is a documentary compilation, a source book for historians, who will find interest in the detail of 19th century scientific life and will be grateful for the indefatigable industry of the editor. The editorial notes are brief, even parsimonious, but adequate to the texts, and provide scholars with appropriate citations. The browser turning the pages will, however, find points of interest: the correspondence with Whewell, Thomson and Plücker concerns Faraday's major studies in electromagnetism. But the absence of a list of letters, even a list of correspondents, inhibits the accessibility of the book.

Michael Heller (ed)

Tuscon: Pachart 1996 108pp price $37.00 ISBN 0 88126 285 4 (pbk)

Hubble's Cosmology: A Guided Study of Selected Texts. (Pachart History of Astronomy Series Vol 11)

Norriss S Hetherington (ed)

Tuscon: Pachart 1996 218pp price $67.00 ISBN 0 88126 287 0 (pbk)

These two new volumes in the Pachart History of Astronomy Series are different in character. The first one is an integral facsimile reproduction of a 50 page unpublished manuscript by the Belgian cosmologist and priest Georges Lemaître. The manuscript, which was written for a Japanese encyclopaedia, dates from sometime between 1936 and 1940 and summarizes Lemaître's views on the origin of the Universe. In this volume, it is accompanied by an introduction that provides some historical context. Although the manuscript is interesting in itself, its real value will only be apparent for those who are familiar with the development of Lemaître's ideas. This is clearly a volume for the specialist.

Not just for specialists is the other volume, on Edwin Hubble. It contains abbreviated republications of four major papers by Hubble on cosmology, including his paper on the velocity - distance relation (1929). This volume is explicitly intended for a general readership. In his introduction the editor stresses his conviction that the achievements of science should be made accessible to a wider audience, in which liberal arts students should be included. Each paper is preceded by a detailed historical introduction and is accompanied by a large amount of very useful explanatory notes. In fact, the notes to each paper take up as much space as the paper itself. Both the notes and the introductions stress the importance of Hubble's work for our contemporary views of the Universe and cannot fail to capture a wide audience. Hetherington has done an excellent job, and it is to be hoped that his volume will be widely used in science classes for non-science majors.