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As documented by textbooks, the teaching of electromagnetic induction in university and high school courses is primarily based on what Feynman labeled as the ``flux rule'', downgrading it from the status of physical law. However, Maxwell derived a ``general law of electromagnetic induction'' in which the vector potential plays a fundamental role. A modern reformulation of Maxwell's law can be easily obtained by defining the induced electromotive force as $\oint_l (\vec E +\vec v_c\times \vec B)\cdot\vec{dl}$, where $\vec v_c$ is the velocity of the positive charges which, by convention, are the current carriers. Maxwell did not possess a model for the electric current. Therefore, in his law, he took $\vec v_c$ to be the velocity of the circuit element containing the charges. This paper aims to show that the modern reformulation of Maxwell's law governs electromagnetic induction and that the ``flux rule'' is not a physical law but only a calculation shortcut that does not always yield the correct predictions. The paper also tries to understand why Maxwell's law has been ignored, and how the ``flux rule'' has taken root. Finally, a section is dedicated to teaching this modern reformulation of Maxwell's law in high schools and elementary physics courses., Comment: Accepted for publication in the American Journal of Physics. 28 pages, 3 figures. arXiv admin note: text overlap with arXiv:2102.11036

The discovery of Electromagnetism by Oersted (1820) started an 'extraordinary decennium' ended by the discovery of electromagnetic induction by Faraday (1831). During this decennium, in several experiments, the electromagnetic induction was there, but it was not seen or recognized. Faraday built up a local theory of electromagnetic induction based on the idea that there is an induced current when there is an intersection between lines of magnetic force and a conductor in relative motion. In 1873, Maxwell, within a Lagrangian description of electric currents, wrote down a 'general law of electromagnetic induction' in which a fundamental role is played by the vector potential. A modern reformulation of Maxwell's general law is based on the definition of the induced emf as the line integral of the Lorentz force on a unit positive charge and the use of the equation that relates the electric field to the potentials. Maxwell's general law has been rapidly forgotten; instead, the "flux rule" has deeply taken root. The "flux rule" not always yields the correct prediction, it does not say where the induced emf is localized, it requires ad hoc choices of the integration paths. It is not a physical law but only a calculation tool. To understand why Maxwell's `general law' has been forgotten, also a sample of representative textbooks, distributed over about a century, has been analyzed. In this framework, a part of the paper deals with the idea of rotating lines of magnetic force, falsified by Faraday, but common in the first decades of the Twentieth century and astonishingly resumed recently. It is shown that this hypothesis is incompatible with Maxwell - Lorentz - Einstein electromagnetism and that it is falsified also by recent experiments. Finally, the electromagnetic induction in some recent research papers is briefly discussed., Comment: 55 pages, 7 figures

A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the statistical independence between two measurements space - like separated. This assumption is valid only with the additional one that statistical dependence between two measurements requires a causal connection between them. This additional assumption rules out the possibility that statistical dependence may due to an intrinsic property of the physical system under study. Therefore, hidden variables theories are built up with a restriction which leads them to be disproved by experiment. Quantum mechanical non - locality, invoked for describing EPR - type experiments, is strictly connected to the hypothesis (NDV hypothesis) according to which the twin photons of entangled pairs do not have a definite polarization before measurements. Both hypotheses are used only for describing EPR experiments and not for making predictions. Therefore, they can be dropped without reducing the predictive power of quantum mechanics concerning entangled photons pairs. Furthermore, both hypotheses can be experimentally tested by a modification of a standard experimental apparatus designed for studying entangled photons pairs., Comment: 25 pages, 2 figures

In 1907, Einstein suggested an experiment with flying atoms for corroborating time dilation. In that paper, the flying atom was conceived as a flying clock: the reference to the Doppler effect was only indirect (the experiments by Stark to the first order of $v/c$). In 1922, Schr\"odinger showed that the emission of a light quantum by a (flying) atom is regulated by the conservation laws of energy and linear momentum. Therefore, the Doppler effect for photons is the consequence of the energy and momentum exchange between the atom and the photon: a central role is played by the quantum energy jump $\Delta E$ of the transition (a relativistic invariant). The first realization of the experiment devised by Einstein is due to Ives and Stilwell (1938). Since then till nowadays experiments of this kind have been repeated in search of better precision and/or a deviation from the predictions of special relativity. The striking feature is that all the papers dealing with these experiments completely neglect Schr\"odinger's dynamical treatment. The origins of this omission are of different kind: pragmatic (agreement between formulas, wherever coming from, and experiments), historical (deep rooting of the wave theory of light) and epistemological (neglect of basic epistemological rules).

The analysis of the Doppler effect for photons in rotating systems, studied using the M\"ossbauer effect, confirms the general conclusions of a previous paper dedicated to experiments with photons emitted/absorbed by atoms/nuclei in inertial flight. The wave theory of light is so deeply rooted that it has been--and currently is--applied to describe phenomena in which the fundamental entities at work are discrete (photons). The fact that the wave theory of light can describe one aspect of these phenomena can not overshadow two issues: the corpuscular theory of light, firstly applied to the Doppler effect for photons by Schr\"odinger in 1922, is by far more complete since it describes all the features of the studied phenomena; the wave theory can be used only when the number of photons at work is statistically significant. The disregard of basic methodological criteria may appear as a minor fault. However, the historical development of quantum physics shows that the predominance of the wave theory of radiation, beyond its natural application domain, has hampered the reorientation toward the photon description of the underlying phenomena.

The definition of the induced $emf$ as the integral over a closed loop of the Lorentz force acting on a unit positive charge leads immediately to a general law for electromagnetic induction phenomena. The general law is applied to three significant cases: moving bar, Faraday's and Corbino's disc. This last application illustrates the contribution of the drift velocity of the charges to the induced $emf$: the magneto-resistance effect is obtained without using microscopic models of electrical conduction. Maxwell wrote down `general equations of electromotive intensity' that, integrated over a closed loop, yield the general law for electromagnetic induction, if the velocity appearing in them is correctly interpreted. The flux of the magnetic field through an arbitrary surface that have the circuit as contour {\em is not the cause} of the induced $emf$. The flux rule must be considered as a calculation shortcut for predicting the value of the induced $emf$ when the circuit is filiform. Finally, the general law of electromagnetic induction yields the induced $emf$ in both reference frames of a system composed by a magnet and a circuit in relative uniform motion, as required by special relativity., Comment: arXiv admin note: text overlap with arXiv:physics/0008006

The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows to establish the essential features of laser cooling of two levels atoms at low laser intensities. The lowest attainable average kinetic energy of the atoms depends on the ratio $\Gamma/E_R$ between the natural linewidth and the recoil energy and tends to $E_R$ as $\Gamma$ tends to zero. This treatment, as the quantum mechanical ones, is valid for any value of the ratio $\Gamma/E_R$ and contains the semiclassical theory of laser cooling as the limiting case in which $E_R\ll \Gamma$., Comment: The dimensionless parameter $B_D$ have been redefinied as $\Gamma/\Delta E_M$ (instead of $\Gamma/2\Delta E_M$) in order to avoid a factor of two when compared with a similar parameter used in literature. Consequently, some equations have been rewritten and some figures modified accordingly. Of Course, the physics does not change. Some minor changes aimed at improving the clarity of the text

A forgotten experiment by Andr\'e Blondel (1914) proves, as held on the basis of theoretical arguments in a previous paper, that the time variation of the magnetic flux is not the cause of the induced $emf$: the physical agent is instead the vector potential through the term $-\partial\vec A/\partial t$ (when the induced circuit is at rest). The "good electromagnetic potentials" are determined by the Lorenz condition and retarded formulas. Other pairs of potentials derived through appropriate gauge functions are only mathematical devices for calculating the fields: they are not physically related to the sources. The physical meaning of a theoretical term relies, primarily, on theoretical grounds: a theoretical term has physical meaning if it cannot be withdrawn without reducing the predictive power of a theory or, in a weaker sense, if it cannot be withdrawn without reducing the descriptive proficiency of a theory.

A discussion of the quantum mechanical use of superposition or entangled states shows that descriptions containing only statements about state vectors and experiments outputs are the most suitable for Quantum Mechanics. In particular, it is shown that statements about the undefined values of physical quantities before measurement can be dropped without changing the predictions of the theory. If we apply these ideas to EPR issues, we find that the concept of non-locality with its 'instantaneous action at a distance' evaporates. Finally, it is argued that usual treatments of philosophical realist positions end up in the construction of theories whose major role is that of being disproved by experiment. This confutation proves simply that the theories are wrong; no conclusion about realism (or any other philosophical position) can be drawn, since experiments deal always with theories and these are never logical consequences of philosophical positions., Comment: 13 pages. Accepted for publication in Il Nuovo Cimento B

Experimental tests on `time dilation' began in 1938 with Ives and Stilwell's work of the transverse Doppler effect due to atoms in inertial flight. Rossi and Hall (1941) inaugurated the era of fast moving elementary particles that dominated the scene until the discovery of the Mossbauer effect (1957). This discovery suggested the use of photons emitted without recoil in crystalline solids for testing both time dilation and gravitational red shift. Finally, around 1970, Hafele and Keating dealt again with time dilation by sending macroscopic atomic clocks around the Earth. The interpretations of these experiments by experimenters have been characterized by the use of additional hypotheses not necessary for the formal development of the theories under test (the idea that all clocks measure proper time) or hypotheses completely extraneous to the theories themselves (the idea that atoms are clocks). If these assumptions are dropped, it turns out that the only experiments concerning time dilation are those performed with elementary particles in inertial flight. The historical and epistemological implications are discussed., Comment: This paper has been withdrawn by the authors due to wrong treatments of some topics

A general law for electromagnetic induction phenomena is derived from Lorentz force and Maxwell equation connecting electric field and time variation of magnetic field. The derivation provides with a unified mathematical treatment the statement according to which electromagnetic induction is the product of two independent phenomena: time variation of magnetic field and effects of magnetic field on moving charges. The general law deals easily-without ad hoc assumptions-with typical cases usually considered as exceptions to the flux rule and contains the flux rule as a particular case., Comment: 17 pages; 5 figures