Physical Laws and the Theory of Special Relativity

this paper to its present form. Special thanks are due to him for bringing the theorem of Van Dam-Wigner to my attentio

The "Aarau Question" and the de Broglie Wave

Introduction A strange similarity between the embryonic ideas from which special theory of relativity theory (STR) and wave mechanics (WM) originated might have escaped general attention. The similarity concerns the fuzzy and hitherto unexplained picture of some periodic phenomenon seen by an imaginary observer "riding" on a photon and on an electron, respectively. We begin by considering the "Aarau Question" posed by Einstein when he was a young man (Einstein 1956, 1949): During that year (sometime between October 1895 and the early fall of 1896) in Aarau the question came to me: If one runs after a light wave with (a velocity equal to the) light velocity, then one would encounter a time-independent wavefield. However, something like that does not seem to exist! This was the first juvenile thought experiment which has to do with the special theory of relativity. Further, in his more extensive autobiographical notes, published in 1949, Einstein remarked that "after ten yea

The Uncertainty Principle Revisited

where F, G, and A are Hermitian operators. Then, for the mean-square deviations from the average, or "variances" DF and DG: D Y Y F F F G G G U V | | W | (2) it follows that D D Y Y F G A 2 (3a) or, less rigorously: D D Y Y F G A (3b) where F and G are termed "the uncertainty" in F and G, respectively. For the special choice F p x = (linear momentum) and G = x ("position"), eq. (1) reduces to: p x xp i I x x - = - (4) with I the identity operator. The inequality : D D p x x (5) is the most frequently quoted form of the UP. The joint measurement of the x and y spin components bears a formal analogy with the positionmomentum case. Indeed, the commutation relation for the spin numbers: S S iS x y , = (6) together with the matrix elements: d S z = (7) where , = 2 , lead to the inequality D D S S x y 2 (8) This result is (rightly) questioned by Sanchez-Ruiz (1993) since S x and S y are discrete observables in a finite dimensional Hilbert space

VALENCE INSTABILITIES IN MAGNETITE DOWN TO 15 K

Nous discuterons les instabilités de la valence des ions du fer dans la magnétite sur la base d'un mécanisme de nucléation de la charge électrique en cascade de 15 K jusqu'à 151 K. Les fluctuations de la valence sont étudiées en détail vers 15 K par effet Mössbauer. Les températures d'instabilité de la valence, calculées par le modèle proposé, sont en bon accord avec les températures déterminées par les minima du facteur Debye-Waller.Valence instabilities in magnetite are discussed in terms of a multi-stage charge-nucleation mechanism which starts at 15 K and continues till 151 K. The formation of fluctuating valence states near 15 K is followed in detail by the Mössbauer effect. The valence-instability temperatures obtained by this model agree well with the temperatures at which minima in the Debye-Waller factor were observed

Farewell Minkowski Space?

3-4, p.121) invite physicists to bid farewell to Minkowski space in favour of Poincaré’s (3+1)D model. They ignore that neither, on purely mathematical grounds, is applicable in physics and that this is the reason why the mathematical untenability of special relativity (SR), independent of its obvious inapplicability in dynamics, has not been seen. In consequence, oblivious of the warning, by many mathematicians including Lakatos and Kline, that modern methods are instruments of mystagoguery, they present their argument in terms of an esoteric mathematical jargon which serves to obscure the simple logic of the case they purport to describe. They thus fail to see, for instance, that the isotropy claimed by J.-P. Vigier can also easily be shown to be a phantom. Minkowski proclaimed that “henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality ” (I restrict references to essentials). This was a strange claim coming from a mathematician, for in the mathematics of motion, as is to date evident in textbooks at all levels, time, as a so-called parameter, has always been intrinsic to space measurement, in that distances are exclusively quantified in terms of parametric expressions like vt or ct. Poincaré cannot escape blame for the havoc caused by dissolving the union, and Minkowski’s noumenal ict renders ct, the resultant of the space vectors, orthogonal to itself. Einstein’s exquisitely simple original description of moving points is preferred by physicists precisely because the conventional parametric rendition is still clearly present if unacknowledged; only uncritical acceptance of the group concept, not applicable to parameters, may have led such a distinguished author as Silberstein to complain that “Einstein’s method of reasoning, as given in his original paper may be mathematically interesting, but does not seem the fittest when a clear discussion of the physical aspect of the [case] is aimed at. ” To my knowledge, only Cullwick (1959) distances himself from “the four-dimensional analysis so attractive to mathematicians ” and presents diagrams in accordance with parametric convention. Leaving Minkowski space for the (3+1) mathematics of Poincaré, irrespective of the argument from dynamics, is therefore no solution for physics