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In a world overabundant in information, a subject is defined by its iconography. Physics is the falling apple, the planetary atom, the laser, the mushroom cloud and the image of the later Einstein - images that represent, respectively, gravity, atomic theory, quantum theory, mass-energy and the scientist who had a hand in all four. It is therefore appropriate that World Year of Physics is called Einstein Year in the UK.

Of course one can argue that progress in science depends on the contributions of many people; that there are other geniuses in physics, even some colourful personalities. Nevertheless there are fundamental reasons why Einstein's early achievements stand out even in their company.

When at last the thought came to him that 'time itself was suspect', Einstein had found a new insight into the nature of the physical universe. It is this: that the universal properties of material objects tell us about the nature of space and time, and it is through these properties, not philosophical logic or common sense, that we discover the structure of spacetime. The later Einstein turned this successful formula on its head and sought to use the properties of spacetime to define those of material objects, thereby seeking to abolish matter entirely in favour of geometry.

Before I introduce this special feature of European Journal of Physics I will say a few words about what is not here. Like all great geniuses Einstein can be seen as the climax of what went before him and the initiation of what was to follow. Looking back we can see the influence of Mach's positivism, according to which the role of science is to relate observations to other observations; hence only observations can tell us what is 'real'. But Einstein also grew up with the family electromechanical businesses, which testifies to the reality of the Maxwellian electromagnetic fields: thus only theory can tell us what is real!

As is well known, Einstein himself refused to accept the full consequences of this pivotal insight into the role of theory when it came to quantum mechanics. Much has been written about this and we do not add to it in this collection. Quantum theory is a consistent description of nature whatever Einstein may think of 'god' for making it so. Many of us would side with Einstein in hoping it will yet turn out not to be a complete description. This will not happen, as Einstein hoped throughout his later work, from a return to classical field theory. But quantum behaviour is a universal property of matter and may therefore be expected, according to Einstein's way of thought, to have a geometrical origin. The advent of non-commutative quantum geometries may turn out to be a step in this direction.

My own introduction to Einstein's physics was through what has come to be known as Mach's principle. My research supervisor, Dennis Sciama, in what he always claimed was probably Einstein's last significant scientific conversation, talked with him on this subject, during which Einstein explained that he had abandoned the idea of Mach's principle. This principle had been a guiding thought in the development of general relativity, but superfluous to its final exposition. It can be interpreted variously as the determination of the local compass of inertia by the distant stars, the non-rotation of the Universe or, more restrictedly, as requiring a critical density universe (to generate the right amount of inertia). This last formulation amounts to Gρτ² ≈ 1, where ρ is the density of the Universe at time τ. This appears to be a classical expression, which would probably be sufficient to relegate Mach's principle to mere historical interest along with the classical unified field theories. It is also usually considered to be accounted for by inflation, which drives the Universe to Ω=1. However, we can also think of the expression as saying that the Universe has a Planck mass in a Planck volume at the Planck time:

G=(hc / G)^1/2(c³ / Gh)^3/2(Gh / c⁵)=1.

This suggests that Mach's principle may yet have a surprising role in expressing the fact that the Universe contains sufficient matter to exist as a classical system: that is, that it contains sufficient material degrees of freedom to allow quantum decoherence to occur. It would at least be a nice irony if Mach's principle turned out to be a necessary quantum condition for the existence of a classical universe!

Coming now to the papers in this special feature, these include several that treat historical aspects of relativity. Brown offers us a novel insight into Einstein's ambivalence about the status of special relativity in providing a mechanism for the contraction hypothesis. Trainer looks at the way in which Einstein presented a brief account of relativity in a lecture that he gave in Glasgow in 1933. Galvangno and Giribet look at Einstein's approach to the representation of particles within general relativity, or variants thereof, while Battimelli provides an account of attempts at unification of electromagnetism and relativity from the point of view of the origin of mass.

In their contribution, Guerra and de Abreu look again at the relationship between the constancy of the speed of light and the nature of time that was central to Einstein's thinking.

Next we come to a group of papers that look at educational issues. Einstein's equation E = mc² is now iconic even if general knowledge quizzes that ask what the c stands for miss the entire point of the equation! Thomas starts from the way in which perceptions of relativity still focus on this equation as the essential ingredient of nuclear power and the need to disabuse even students of physics of this notion. He also looks at how we can in fact demonstrate the significance of the equation to a lay audience. I have added a short note on friction, another topic that confuses teachers and students alike, that throws up problems to which the solutions are contained in Einstein's Brownian motion paper. The Open University in the UK has been teaching relativity to distance-learners for forty years; Lambourne writes about the experience that has been gained.

Finally, I have always been intrigued by the opprobrium that Einstein seems to attract from crank authors. I no longer regularly receive such nonsense to referee, I assume because the internet is now awash with 'publication' opportunities for anti-Einstein articles. I do believe however that the work of these authors throws light on the way science works and I have tried to illustrate this thesis briefly in the final paper of this collection.

When Einstein formulated his 1905 treatment of relativistic kinematics, the template in his mind was thermodynamics. This was because a more desirable 'constructive' account of the behaviour of moving rods and clocks, based on the detailed physics governing their microscopic constitution, was unavailable. The price to be paid was appreciated by Einstein and a handful of others since 1905.

On the 20th June 1933 Professor Einstein addressed a large and enthusiastic audience in the Victorian Gothic Bute Hall of the University of Glasgow. Einstein spoke 'About the Origins of the General Theory of Relativity'. In 1905 Einstein had changed the face of physics forever with the publication of his radical new ideas on special relativity. His general theory of relativity was introduced to the world in 1915. However in 1933, Einstein faced another challenge—survival in a world of change. This paper explores Einstein's fascinating address to the Glasgow audience in that year.

This historical note is mainly based on a relatively unknown paper published by Albert Einstein in Revista de la Universidad Nacional de Tucumán in 1941. Taking the ideas of this work as a leitmotiv, we review the discussions about the particle problem in the theory of gravitation within the historical context by means of the study of seminal works on the subject. The revision shows how the digressions regarding the structure of matter and the concise problem of finding regular solutions of the pure field equations turned out to be intrinsically unified in the beginning of the programme towards a final theory of fields. The paper mentioned (Einstein 1941a Rev. Univ. Nac. Tucumán A 2 11) represents the basis of the one written by Einstein in collaboration with Wolfgang Pauli in 1943, in which, following analogous lines, the proof of the non-existence of regular particle-type solutions was generalized to the case of cylindrical geometries in Kaluza–Klein theory (Einstein and Pauli 1943 Ann. Math. 44 131). Besides, other generalizations were subsequently presented. The (non-)existence of such solutions in classical unified field theory was undoubtedly an important criterion leading Einstein's investigations. This aspect was investigated with expertness by Jeroen van Dongen in a recent work, though restricting the scope to the particular case of Kaluza–Klein theory (van Dongen 2002 Stud. Hist. Phil. Mod. Phys. 33 185). Here, we discuss the particle problem within a more general context, presenting in this way a complement to previous reviews.

At the end of the 19th century, efforts were made by several researchers to build up a unified foundation for the whole of physics, grounded solely on electromagnetism. Some of the concepts usually associated with relativity were actually born in this context, before 1905. The main features of these pre-Einsteinian theories are briefly presented, and their interaction with relativity is discussed, by virtue of which ideas originated in a largely different frame were adapted and somehow incorporated into the new theory.

In this work, we show that the null result of the Michelson–Morley experiment in vacuum is deeply connected with the notion of time. It can be deduced, without any mathematics, from the assumption only that all good clocks can be used to measure time with the same results, independently of the machinery involved in their manufacturing. A second important assumption, intrinsic to the very notion of time, is that clocks measure time in the same way in different frames, i.e., the notion of time is the same in all inertial frames. Under this assumption, we point out that the 'postulate' of constancy of the 'two-way' speed of light in vacuum in all frames independently of the state of motion of the emitting body is also strongly related to the concept of time, together with the existence of a limit speed in the 'rest frame'. This postulate simply results from the construction of clocks where 'tic–tacs' are made by objects travelling with the limit speed, taken to be the speed of light.

Einstein's equation E = mc² has become part of popular culture and an icon of physics. Yet, despite its familiarity, its significance continues to be misrepresented in popular writing: a persistent myth is that it was the key to developing nuclear weapons and that it can explain the source of the Sun's luminosity and of nuclear power. Extracts are quoted from a recent television broadcast and from a recently published book which both propagate this myth. This leaves us with the task of explaining the true status of the equation. We argue that the real importance of the equivalence of mass and energy is that it sanctions interactions in which the creation and annihilation of particles occur.

Einstein's 1905 (Einstein 1905 Ann. Phys.17 549) paper on Brownian motion is his most cited work, yet in terms of the scope of its application, apparently the least understood. In this brief note, I look at some examples of problems involving frictional forces that have puzzled school teachers, university lecturers and students, all of which can be understood from a proper appreciation of the relation between fluctuations and dissipation. For completeness I shall first give a simple derivation of a fluctuation–dissipation theorem, followed by three examples.

This paper examines the challenges and rewards that can arise when the teaching of Einsteinian physics has to be accomplished by means of distance education. The discussion is mainly based on experiences gathered over the past 35 years at the UK Open University, where special and general relativity, relativistic cosmology and other aspects of Einsteinian physics, have been taught at a variety of levels, and using a range of techniques, to students studying at a distance.

I discuss various examples of attempts to disprove relativity, through what is generally agreed to be crank science, in order to illustrate both our view of the nature of science and the role that Einstein played in shaping that view.

We report on a multi-year, multi-institution study to investigate students' reasoning about energy in the context of quantum tunnelling. We use ungraded surveys, graded examination questions, individual clinical interviews and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunnelling through a square barrier are particularly common. Students often state that tunnelling particles lose energy while tunnelling. When sketching wavefunctions, students also show a shift in the axis of oscillation, as if the height of the axis of oscillation indicated the energy of the particle. We find inconsistencies between students' conceptual, mathematical and graphical models of quantum tunnelling. As part of a curriculum in quantum physics, we have developed instructional materials designed to help students develop a more robust and less inconsistent picture of tunnelling, and present data suggesting that we have succeeded in doing so.

We report a study on magnetic levitation by induced ac currents in non-magnetic conductors at low frequencies. Our discussion, based on Faraday's induction law, allows us to distinguish the two components of the current responsible for levitation and heating, respectively. The experimental evaluation of the levitation force in a copper ring revealed the accuracy of our analysis, clearly illustrating its asymptotic behaviour versus frequency, and validating it for the qualitative analysis of magnetic levitation and heating in conductors of different shapes such as tubes and discs, composed of collections of conductive loops. The analysis of the results allows precise values of its electrical conductivity to be found. With the help of a simulation technique, this work also reveals the progressive deformation undergone by magnetic induction lines due to magnetic screening when frequency increases.

The Seebeck and Peltier effects are explored with a commercially available thermoelectric module and a data-acquisition system. Five topics are presented: (i) thermoelectric heating and cooling, (ii) the Seebeck coefficient, (iii) efficiency of a thermoelectric generator, (iv) the maximum temperature difference provided by a thermoelectric cooler and (v) the Peltier coefficient and the coefficient of performance. Using a data-acquisition system, the measurements are carried out in a reasonably short time. It is shown how to deduce quantities important for the theory and applications of thermoelectric devices.

Amateur reception of satellite images gathers a wide number of concepts and technologies which makes it attractive as an educational tool. We here introduce the reception of images emitted from NOAA series low-altitude Earth-orbiting satellites. We tackle various issues including the identification and prediction of the pass time of visible satellites, the building of the radio-frequency receiver and antenna after modelling their radiation pattern, and then the demodulation of the resulting audio signal for finally displaying an image of the Earth as seen from space.

The trajectory, travel time and relative approach velocity of a pursuer tracking a prey along a simple curve of pursuit are deduced using basic principles of two-dimensional kinematics. While such curves are well known in the mathematics literature, little attention has been paid to this problem by the physics educational community, despite the fact that it has abundant physical applications. It also makes an interesting alternative to the traditional problems of introductory kinematics.

Einstein's original Gedankenexperiment leading to the relation between inertial mass and rest energy is analysed in a new perspective, applying the principle of conservation of momentum. The analysis implies both the relativistic momentum and mass–energy relation in a simple way.

The radon indicator is an efficient instrument for measuring the radon daughter concentrations in a house or dwelling. Physics or environmental science students could build a radon indicator as a student project. Another possibility would be to use a radon indicator in a student investigation of radon levels in different houses. Finally the radon indicator is an excellent device for producing a radioactive source, free of charge, for the study of α-, β- and γ-radiation. The half-life of the activity collected is approximately 40 min. The radon indicator makes use of an electrostatic method by which charged particles are drawn to a small aluminium plate with a high negative voltage (−5 kV), thus creating a strong electric field between the plate and a surrounding copper wire. The radioactivity on the plate is subsequently measured by a GM-counter and the result calculated in Bq m⁻³. The collecting time is just 5.5 min and therefore the instrument is only suitable for use in a short-time method for indicating the radon concentration. An improved diagram, ground-radon and/or wall-radon in houses, is presented on the basis of the author's measurements recorded with the radon indicator over many years. This diagram is very useful when discussing how to reduce radiation levels in homes.

The nonlinear dynamics of automobile braking are investigated. Nonlinearity arises because of the manner in which the friction coefficient between vehicle tyres and road surface depends upon vehicle speed and wheel angular speed. We show how antilock brake systems approach optimum braking performance.

The importance of fluid mechanics is often underrated. Besides studying the mechanisms governing static and dynamic fluids, this discipline could have a great role in the understanding of many principles, topics and concepts of general mechanics. When approached in a proper way, fluid mechanics provides numerous 'case studies' apt to clarify the physical content of several mechanical laws. Unfortunately, fluid mechanics, in physics classes, is generally viewed as a 'lower branch' of mechanics. Its rules and laws too often are regarded as too particular, or even as special cases, to deserve the same attention paid to other arguments. The help that fluid mechanics could return in the learning process can be proved by some easy considerations. In this frame, the so-called hydrostatic paradoxes could provide a tremendous contribution to the learning processes.

The problem of the optimum throw in the shot-put discipline is analysed by relaxing the assumption that the height H, from which the athlete releases the shot, does not depend on the angle θ which the arm of the putter makes with the horizontal axis. In this context, the kinematics of the shot-put is studied and results are compared with the traditional analysis, which considers the height H, the angle θ and the modulus V₀ of the initial velocity of the metal sphere as independent parameters.

We analyse the one-dimensional motion of a uniform thin fibre which is pulled upwards from a horizontal plane by a constant vertical force exerted against the homogeneous gravitational field. The solution of the equation of motion which describes this variable mass problem is discussed and the character of the resulting damped oscillations is described.

A systematic account of the use of alpha particles up to the 1930s for promoting the disintegration of atoms is here provided. As will be shown, a number of different radium family alpha sources were used in the experiments that led to the discoveries of the proton (Rutherford E 1919 Phil. Mag.37 581–7) and neutron (Chadwick J 1932 Nature129 312). The reasons leading to the employment of a particular alpha particle source, as well as the relationship between these sources and the available methods of recording, will be closely addressed.

We discuss two alternative methods, based on the Lindstedt–Poincaré technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant. We believe that present discussion and comparison may be a suitable exercise for teaching perturbation theory in advanced undergraduate courses on classical mechanics.

What is the relationship between the propagation of a light wave in a Kerr medium in the presence of a magnetic field and the oscillation of a spherical pendulum on a rotating platform? We apply the general formalism of amplitude equations in order to explore both the nonlinear and the rotation-induced precession of these optical and mechanical experiments. Then, we explain the surprising analogies between the two physical phenomena.

An apparatus was devised using the Traube Stalagmometer for the determination of the surface tension of the alcohols methanol, ethanol, propan-1-ol and butan-1-ol. Measurements were made under atmospheric pressure at temperatures between 288.15 K and 313.15 K. The surface tension values were correlated with temperature and surface thermodynamic parameters, namely surface entropy and surface enthalpy, were also calculated. The results obtained are in agreement with the literature and they are promising for the use of this low cost arrangement for accurate measurement of surface tension. Surface tension values were obtained with a maximum error of 0.5 mN m⁻¹ and a maximum standard deviation of 0.8 mN m⁻¹. We recommend this arrangement for students in advanced university courses and it can also be used for research work.

A desktop experiment to demonstrate the linear and quadratic velocity dependence of drag on an object falling in a resistive medium was developed for an undergraduate laboratory. The motion of ball bearings dropped into a cylinder filled with fluid is captured and measured using computer-based imaging. The terminal velocity of falling spheres is measured as a function of size at low and high Reynolds number, and the results are compared to predicted scaling laws for models containing a drag force that is linear or quadratic with velocity.

Albert Einstein used his famous gedanken (thought) experiment of a train struck by two lightning bolts to illustrate the relativity of simultaneity. I discuss foundational and pedagogical aspects of this experiment and of a lesser known but conceptually simpler alternative gedanken experiment.

In various well-known textbooks for undergraduate students of physics, the compound microscope is described as having a standardized 'optical tube length'. On the other hand, in order to fulfil the parfocalization condition required by the human visual system to understand the relation between what is viewed with and without the microscope, the distance between the object and its image through the objective must remain constant as objectives are interchanged. In this paper, we show that these two requirements are not compatible in microscopes containing a revolver with various objectives and that the 'optical tube length' (which differs from the mechanical tube length) cannot be standardized. Moreover, we consider the Deutsche Industrie Norm (DIN) and the Japanese Industry Standards (JIS) norms employed in the microscope industry for standardization of the object-to-intermediate image distance, the parfocal distance and the mechanical tube length.

An exact expression for the currents at any site of a finite discrete open RLC transmission line is obtained. The line is excited at one of its ends by an harmonic current and the other end is kept open. Several regimes are analysed for different values of the components of the line. An effective attenuation factor can be defined for a semi-infinite line. This attenuation factor is evaluated and it is shown that it does not vanish even in the case of a lossless line for a certain range of the exciting frequency.

Reciprocating internal combustion engine models have the antithetical goals of accurately describing complex nonlinear behaviour and being simple enough for such purposes as automatic control and online diagnosis. A one-piston four-stroke engine is modelled here by recursively stating simple physical equations. To do that, the domestic ideas of domination and dependence are called as methodological tools for modelling, since they hand out necessary and sufficient equations with few manoeuvres, allocate simulations with the same characteristic and, hopefully, provide a fine way to understanding. The resulting model reveals both steady cycles and transient behaviour.

One of the few examples of variable mass systems treated in textbooks is the movement of a rope lying on a table, with a part y(t) hanging and falling. In solving this problem what is usually obtained is v(y), but not y(t). In this work, first we obtain y(t) and then show that it is possible to make a canonical formulation of the problem, which in this case also permits an expedite approximation to y(t).

We report on a three-month undergraduate research project to compute energy levels and their corresponding wavefunctions of an electron confined in a tetrahedral-shaped quantum dot heterostructure. A typical example of such a quantum system is an InAs tetrahedral-shaped quantum dot embedded in a cuboid GaAs matrix. For the simulation we used the Schrödinger equation in three-dimensional Cartesian space. After discretizing the Schrödinger equation by using the finite volume method, the resulting large-scale eigenvalue matrix is solved for eigenvalues and eigenvectors.

The applications of the digital video image to the investigation of physical phenomena have increased enormously in recent years. The advances in computer technology and image recognition techniques allow the analysis of more complex problems. In this work, we study the movement of a damped coupled oscillation system. The motion is considered as a linear combination of two normal modes, i.e. the symmetric and antisymmetric modes. The image of the experiment is recorded with a video camera and analysed by means of software developed in our laboratory. The results show a very good agreement with the theory.

We show that one of the problems, considered in Aguirregabiria J M, Hernández A and Rivas M (2004 Eur. J. Phys.25 555–68), contains an error. Namely, under a motion of a point charge near a conducting toroidal solenoid, the effect of the polarization of the solenoid in the electric field of charge should be taken into account. This effect vanishes the electromagnetic linear momentum and recovers the equality of an action and reaction for this problem.

A reply is made to Kholmetskii's comment on the paper 'Linear momentum density in quasistatic electromagnetic systems' (Aguirregabiria et al 2004 Eur. J. Phys.25 555–68).

The PDF file provided contains web links to all articles in this volume.