Electromagnetism

We address a long-standing debate over whether classical magnetic forces can do work, ultimately answering the question in the affirmative. In detail, we couple a classical particle with intrinsic spin and elementary dipole moments to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle’s dipole moments must be collinear with its spin axis, and argue that the magnetic field does mechanical work on the particle’s elementary magnetic dipole moment. As consistency checks, we calculate (...) the overall system’s energy-momentum and angular momentum, and show that their local conservation equations lead to the same force law and therefore the same conclusions about magnetic forces and work. We also compute the system’s Belinfante–Rosenfeld energy–momentum tensor. (shrink)

Standard lore holds that magnetic forces are incapable of doing mechanical work. More precisely, the claim is that whenever it appears that a magnetic force is doing work, the work is actually being done by another force, with the magnetic force serving only as an indirect mediator. On the other hand, the most familiar instances of magnetic forces acting in everyday life—bar magnets lifting other bar magnets—appear to present manifest evidence of magnetic forces doing work. These sorts of counterexamples are (...) often dismissed as arising from quantum effects that lie outside the classical regime. In this paper, however, we show that quantum theory is not needed to account for these phenomena, and that classical electromagnetism admits a model of elementary magnetic dipoles on which magnetic forces can indeed do work. In order to develop this model, we revisit the foundational principles of the classical theory of electromagnetism, showcase the importance of constraints from relativity, examine the structure of the multipole expansion, and study the connection between the Lorentz force law and conservation of energy and momentum. (shrink)

Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany (...) and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture. (shrink)

The force law of Maxwell’s classical electrodynamics does not agree with Newton’s third law of motion (N3LM), in case of open circuit magnetostatics. Initially, a generalized magnetostatics theory is presented that includes two additional physical fields B_Φ and B_l, defined by scalar functions. The scalar magnetic field B_l mediates a longitudinal Ampère force that balances the transverse Ampère force (aka the magnetic field force), such that the sum of the two forces agrees with N3LM for all stationary current distributions. Secondary (...) field induction laws are derived; a secondary curl free electric field E_l is induced by a time varying scalar magnetic field B_l, which isn’t described by Maxwell’s electrodynamics. The Helmholtz’ decomposition is applied to exclude E_l from the total electric field E, resulting into a more simple Maxwell theory. Decoupled inhomogeneous potential equations and its solutions follow directly from this theory, without having to apply a gauge condition. Field expressions are derived from the potential functions that are simpler and far field consistent with respect to the Jefimenko fields. However, our simple version of Maxwell’s theory does not satisfy N3LM. Therefore we combine the generalized magnetostatics with the simple version of Maxwell’s electrodynamics, via the generalization of Maxwell’s speculative displacement current. The resulting electrodynamics describes three types of vacuum waves: the Φ wave, the longitudinal electromagnetic (LEM) wave and the transverse electromagnetic (TEM) wave, with phase velocities respectively a, b and c. Power- and force theorems are derived, and the force law agrees with Newton’s third law only if the phase velocities satisfy the following condition: a >> b and b = c. The retarded potential functions can be found without gauge conditions, and four retarded field expressions are derived that have three near field terms and six far field terms. All six far field terms are explained as the mutual induction of two free fields. Our theory supports Rutherford’s solution of the 4/3 problem of electromagnetic mass, which requires an extra longitudinal electromagnetic momentum. Our generalized classical electrodynamics might spawn new physics experiments and electrical engineering, such as new photoelectric effects based on Φ- or LEM radiation, and the conversion of natural Φ- or LEM radiation into useful electricity, in the footsteps of dr. N. Tesla and dr. T.H. Moray. (shrink)

In discussions of the Aharonov-Bohm effect, Healey and Lyre have attributed reality to loops $\sigma_0$ (or hoops $[\sigma_0]$), since the electromagnetic potential $A$ is currently unmeasurable and can therefore be transformed. I argue that $[A]=[A+d\lambda]_{\lambda}$ and the hoop $[\sigma_0]$ are related by a meaningful duality, so that however one feels about $[A]$ (or any potential $A\in[A]$), it is no worse than $[\sigma_0]$ (or any loop $\sigma_0\in[\sigma_0]$): no ontological firmness is gained by retreating to the loops, which are just as flimsy (...) as the potentials. And one wonders how the unmeasurability of one entity can invest another with physical reality; would an eventual observation of $A$ dissolve $\sigma_0$, consigning it to a realm of incorporeal mathematical abstractions? The reification of loops rests on the potential's ''gauge dependence''; which in turn rests on its unmeasurability; which is too shaky and arbitrary a notion to carry so much weight. (shrink)

Several decades ago, Wheeler and Misner presented a model of electric charge based on the topological trapping of electric field lines in wormholes. In this paper, which does not argue for or against the "charge without charge" concept, I describe some generalizations of this model which might serve as topological analogs of color charges and electroweak charges.

Let F be the set of functions from an infinite set, S, to an ordered ring, R.

We develop some ideas about gauge symmetry in the context of Maxwell’s theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and configurational degrees of freedom, so that a decomposition of one side into subsets can be translated into a decomposition of the other. In the case of electromagnetism, this enables us to pair degrees of freedom of the electric field with degrees of freedom of the vector potential. Another benefit is (...) that the formalism algorithmically identifies subsets of the equations of motion that represent time-dependent symmetries. For electromagnetism, these two benefits allow us to define gauge-fixing in parallel to special decompositions of the electric field. More specifically, we apply the Helmholtz decomposition theorem to split the electric field into its Coulombic and radiative parts, and show how this gives a special role to the Coulomb gauge = 0\)). We relate this argument to Maudlin’s discussion, which advocated the Coulomb gauge. (shrink)

Although physical theories routinely posit absolute quantities, such as absolute position or intrinsic mass, it seems that only comparative quantities such as distance and mass ratio are observable. But even if there are in fact only distances and mass ratios, the success of absolutist theories means that the world looks just as if there are absolute positions and intrinsic masses. If comparativism is nevertheless true, there is a sense in which it is a cosmic conspiracy that the world looks just (...) as if there are absolute quantities: the comparative quantities satisfy certain relations that only absolutism can explain. I show that such cosmic conspiracies are a pervasive feature of comparativist theories. The argument is structurally similar to the well-known No Miracles Argument for scientific realism. Just as anti-realism cannot explain the empirical adequacy of our theories in general, so comparativism cannot explain the empirical adequacy of absolutist theories in particular. (shrink)

The recent debate about whether gauge symmetries can be empirically significant has focused on the possibility of 'Galileo's ship' types of scenarios, where the symmetries effect relational differences between a subsystem and the environment. However, it has gone largely unremarked that apart from such Galileo's ship scenarios, Greaves and Wallace (2014) proposed that gauge transformations can also be empirically significant in a 'non-relational' manner that is analogous to a Faraday-cage scenario, where the subsystem symmetry is related to a change in (...) a charged boundary state. In this paper, we investigate the question of whether such non-relational scenarios are possible for gauge theories. Remarkably, the answer to this question turns out to be closely related to a foundational puzzle that has driven a host of recent developments at the frontiers of theoretical physics. By drawing on these recent developments, we show that a very natural way of elaborating on Greaves and Wallace's claim of non-relational empirical significance for gauge symmetry is incoherent. However, we also argue that much of what they suggest is correct in spirit: one can indeed construct non-relational models of the kind they sketch, albeit ones where the empirical significance is not witnessed by a gauge symmetry but instead by a superficially similar boundary symmetry. Furthermore, the latter casts doubt on whether one really abandons Galileo's ship in such scenarios. (shrink)

We present an epistemological schema of natural sciences inspired by Peirce's pragmaticist view, stressing the role of the \emph{phenomenological map}, that connects reality and our ideas about it. The schema has a recognisable mathematical/logical structure which allows to explore some of its consequences. We show that seemingly independent principles as the requirement of reproducibility of experiments and the Principle of Sufficient Reason are both implied by the schema, as well as Popper's concept of falsifiability. We show that the schema has (...) some power in demarcating science by first comparing with an alternative schema advanced during the first part of the 20th century which has its roots in Hertz and has been developed by Einstein and Popper. Further, the identified differences allow us to focus in the construction of Special Relativity, showing that it uses an intuited concept of velocity that does not satisfy the requirements of reality in Peirce. While the main mathematical observation connected with this issue has been known for more than a century, it has not been investigated from an epistemological point of view. A probable reason could be that the socially dominating epistemology in physics does not encourage such line of work. We briefly discuss the relation of the abduction process presented in this work with discussions regarding ``abduction'' in the literature and its relation with ``analogy''. (shrink)

We argue that the asymmetry between diverging and converging electromagnetic waves is just one of many asymmetries in observed phenomena that can be explained by a past hypothesis and statistical postulate (together assigning probabilities to different states of matter and field in the early universe). The arrow of electromagnetic radiation is thus absorbed into a broader account of temporal asymmetries in nature. We give an accessible introduction to the problem of explaining the arrow of radiation and compare our preferred strategy (...) for explaining the arrow to three alternatives: (i) modifying the laws of electromagnetism by adding a radiation condition requiring that electromagnetic fields always be attributable to past sources, (ii) removing electromagnetic fields and having particles interact directly with one another through retarded action-at-a-distance, (iii) adopting the Wheeler-Feynman approach and having particles interact directly through half-retarded half-advanced action-at-a-distance. In addition to the asymmetry between diverging and converging waves, we also consider the related asymmetry of radiation reaction. (shrink)

Recently, Dewar (2019) has suggested that one can apply the strategy of 'sophistication' - as exemplified by sophisticated substantivalism as a response to the diffeomorphism invariance of General Relativity - to gauge theories such as electrodynamics. This requires a shift to the formalism of fibre bundles. In this paper, I develop and defend this suggestion. Where my approach differs from previous discussions is that I focus on the metaphysical picture underlying the fibre bundle formalism. In particular, I aim to affirm (...) the physical reality of gauge properties. I argue that this allows for a local and separable explanation of the Aharonov-Bohm effect. Its puzzling features are explained by a form of holism inherent to fibre bundles. (shrink)

This is the BJPS Short Read version of the article When Fields Are Not Degrees of Freedom. In our article, Vera Hartenstein and I show that the world of classical electromagnetism might differ radically from the one we see in physics textbooks and experience day-to-day. First, light may not exist; second, the laws of electromagnetism are either incomplete or completely different; and, third, the mathematics needed to make exact calculations with these novel laws is in early development and not part (...) of the general mathematics curriculum at colleges and universities. (shrink)

According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g., commutative ring) of scalar-valued functions, which can be interpreted as representing a scalar field, and deriving other structures from it. In this work, we point out that this leads to the unjustified primacy of an undetermined scalar field. Instead, we propose to consider algebraic structures in which all (and only) physical fields are (...) primitive. We explain how the theory of natural operations in differential geometry—the modern formalism behind classifying diffeomorphism-invariant constructions—can be used to obtain concrete implementations of this idea for any given collection of fields. For concrete examples, we illustrate how our approach applies to a number of particular physical fields, including electrodynamics coupled to a Weyl spinor. (shrink)

We show that in the Maxwell–Lorentz theory of classical electrodynamics most initial values for fields and particles lead to an ill-defined dynamics, as they exhibit singularities or discontinuities along light-cones. This phenomenon suggests that the Maxwell equations and the Lorentz force law ought rather to be read as a system of delay differential equations, that is, differential equations that relate a function and its derivatives at different times. This mathematical reformulation, however, leads to physical and philosophical consequences for the ontological (...) status of the electromagnetic field. In particular, fields cannot be taken as independent degrees of freedom, which suggests that one should not add them to the ontology. (shrink)

The goal of this work is to compile the basic components for the construction of an electromagnetic field theory of consciousness that meets the standards of a fundamental theory. An essential cornerstone of the conceptual framework is the vacuum state of quantum electrodynamics which, contrary to the classical notion of the vacuum, can be viewed as a vibrant ocean of energy, termed zero-point field (ZPF). Being the fundamental substrate mediating the electromagnetic force, the ubiquitous ZPF constitutes the ultimate bedrock of (...) all electromagnetic phenomena. In particular, resonant interaction with the ZPF is critical for understanding rapidly forming, long-range coherent activity patterns that are characteristic of brain dynamics. Assuming that the entire phenomenal color palette is rooted in the vibrational spectrum of the ZPF and that each normal mode of the ZPF is associated with an elementary shade of consciousness, it stands to reason that conscious states are caused by the coupling of the brain to a particular set of normal modes selectively filtered from the full frequency spectrum of the ZPF. From this perspective, the brain is postulated to function as a resonant oscillator that couples to a specific range of ZPF modes, using these modes as a keyboard for the composition of an enormous variety of phenomenal states. Theoretical considerations suggest that the brain-ZPF interface is controlled by altering the concentrations of neurotransmitters, placing the detailed study of the neurotransmitter-ZPF interaction at the center of future research activities. (shrink)

I address the view that the classical electromagnetic potentials are shown by the Aharonov–Bohm effect to be physically real. I give a historico-philosophical presentation of this view and assess its prospects, more precisely than has so far been done in the literature. Taking the potential as physically real runs prima facie into ‘gauge-underdetermination’: different gauge choices represent different physical states of affairs and hence different theories. This fact is usually not acknowledged in the literature, neither by proponents nor by opponents (...) of the potentials view. I then illustrate this theme by what I take to be the basic insight of the AB effect for the potentials view, namely that the gauge equivalence class that directly corresponds to the electric and magnetic fields is too wide, i.e., the Narrow Equivalence Class encodes additional physical degrees of freedom: these only play a distinct role in a multiply-connected space. There is a trade-off between explanatory power and gauge symmetries. On the one hand, this narrower equivalence class gives a local explanation of the AB effect in the sense that the phase is incrementally picked up along the path of the electron. On the other hand, locality is not satisfied in the sense of signal locality, viz. the finite speed of propagation exhibited by electric and magnetic fields. It is therefore intellectually mandatory to seek desiderata that will distinguish even within these narrower equivalence classes, i.e. will prefer some elements of such an equivalence class over others. I consider various formulations of locality, such as Bell locality, local interaction Hamiltonians, and signal locality. I show that Bell locality can only be evaluated if one fixes the gauge freedom completely. Yet, an explanation in terms of signal locality can be accommodated by the Lorenz gauge: the potentials propagate in waves at finite speed. I therefore suggest the Lorenz gauge potentials theory—an even narrower gauge equivalence relation—as the ontology of electrodynamics. (shrink)

Building upon work by Mary Hesse (1974), this paper aims to show that a single method of investigation lies behind Maxwell’s use of physical analogies in his major scientific works before the Treatise on Electricity and Magnetism. Key to understanding the operation of this method is to recognize that Maxwell’s physical analogies are intended to possess an ‘inductive’ function in addition to an ‘illustrative’ one. That is to say, they not only serve to clarify the equations proposed for an unfamiliar (...) domain with a working interpretation drawn from a more familiar science, but can also be sources of defeasible yet relatively strong arguments from features of the more familiar domain to features of the less. Compared with the reconstructions by Achinstein (1991), Siegel (1991), Harman (1998) and others, which postulate a discontinuity in Maxwell’s approach to physical analogy, the account defended in this paper i) makes sense of the continuity in Maxwell’s remarks on scientific methodology, ii) explains his quest for a “mathematical classification of physical quantities” and iii) offers a new and more plausible interpretation of the debated episode of the introduction of the displacement current in Maxwell’s “On Physical Lines of Forces”. (shrink)

In the present book the author shows how electromagnetism connects classical with post-classical thought, creating new structures, and impacting materialism and dialectics. Please note: T&F does not sell or distribute the Hardback in South Asia.

Reflectance physicalists define reflectance as the intrinsic disposition of a surface to reflect finite-duration light pulses at a given efficiency per wavelength. I criticize the received view of dispositional reflectance (David R. Hilbert’s) for failing to account for what I call “harmonic dispersion,” the inverse relationship of a light pulse's duration to its bandwidth. I argue that harmonic dispersion renders reflectance defined in terms of light pulses an extrinsic disposition. Reflectance defined as the per-wavelength efficiency to reflect the superimposed, infinite-duration, (...) Fourier harmonics of pulses can be an intrinsic disposition of surfaces. This conclusion raises questions about mathematical realism, about which I nevertheless remain neutral. (shrink)

Elay Shech and John Earman have recently argued that the common topological interpretation of the Aharonov–Bohm (AB) effect is unsatisfactory because it fails to justify idealizations that it presupposes. In particular, they argue that an adequate account of the AB effect must address the role of boundary conditions in certain ideal cases of the effect. In this paper I defend the topological interpretation against their criticisms. I consider three types of idealization that might arise in treatments of the effect. First, (...) Shech takes the AB effect to involve an idealization in the form of a singular limit, analogous to the thermodynamic limit in statistical mechanics. But, I argue, the AB effect itself features no singular limits, so it doesn’t involve idealizations in this sense. Second, I argue that Shech and Earman’s emphasis on the role of boundary conditions in the AB effect is misplaced. The idealizations that are useful in connecting the theoretical description of the AB effect to experiment do interact with facts about boundary conditions, but none of these idealizations are presupposed by the topological interpretation of the effect. Indeed, the boundary conditions for which Shech and demands justification are incompatible with some instances of the AB effect, so the topological interpretation ought not justify them. Finally, I address the role of the non-relativistic approximation usually presumed in discussions of the AB effect. This approximation is essential if—as the topological interpretation supposes—the AB effect constrains and justifies a relativistic theory of the electromagnetic interaction. In this case the ends justify the means. So the topological view presupposes no unjustified idealizations. (shrink)

The paper considers the absorber theory of radiation by (Wheeler and Feynman 1945) and (Wheeler and Feynman 1949) and advances the idea that the theory is grounded on the philosophical intuition of overall processes. Such intuition consists of having to consider advanced and retarded radiation as well as the interaction between absorbers and emitter. I discuss the discrepancy between microdynamic time-symmetry and the asymmetry of the experimental evidences. In doing so, I consider (Price, 1991)'s reformulation of the theory and argue (...) that it overlooks the philosophical intuition. I then compare the overall process idea with some accounts of holism and ultimately suggest that it also played an important role in Feynman's later works. (shrink)

This monograph examines James Clerk Maxwell's contributions to electromagnetism to gain insight into the practice of science by focusing on scientific methodology as applied by scientists. First and foremost, this study is concerned with practices that are reflected in scientific texts and the ways scientists frame their research. The book is therefore about means and not ends.

According to the standard realistic interpretation of classical electrodynamics, the electromagnetic field is conceived as a real physical entity existing in space and time. The problem we address in this paper is how to understand this spatiotemporal existence, that is, how to describe the persistence of a field-like physical entity like electromagnetic field. First, we provide a formal description of the notion of persistence: we derive an “equation of persistence” constituting a necessary condition that the spatiotemporal distributions of the fundamental (...) attributes of a persisting physical entity must satisfy. We then prove a theorem according to which the vast majority of the solutions of Maxwell’s equations, describing possible spatiotemporal distributions of the fundamental attributes of the electromagnetic field, violate the equation of persistence. Finally, we discuss the consequences of this result for the ontology of the electromagnetic field. (shrink)

Computational neuroscience attributes coloured areas and other perceptual qualia to calculations that are realizable in multiple cellular forms. This faces serious issues in explaining how the various qualia arise and how they bind to form overall perceptions. Qualia may instead be neuroelectrical. Growing evidence indicates that perceptions correlate with neuroelectrical activity spotted by locally activated EEGs, the different qualia correlate with the different electrochemistries of unique detector cells, a unified neural-electromagnetic field binds this activity to form overall perceptions, and this (...) field interacts with sensory circuits to help attentively guide perception. The coloured areas in images may thus be seated in the electrochemistry of unique cells, while constancy mechanisms and other multiply realizable computations just help refine these images behind the scenes. This theory is ultimately testable. (shrink)

This article re-examines Schrödinger’s charge density hypothesis, according to which the charge of an electron is distributed in the whole space, and the charge density in each position is proportional to the modulus squared of the wave function of the electron there. It is shown that the charge distribution of a quantum system can be measured by protective measurements as expectation values of certain observables, and the results as predicted by quantum mechanics confirm Schrödinger’s original hypothesis. Moreover, the physical origin (...) of the charge distribution is also investigated. It is argued that the charge distribution of a quantum system is effective, that is, it is formed by the ergodic motion of a localized particle with the charge of the system. (shrink)

Previzualizare carte -/- O introducere în fenomenologia opticii geometrice (reflexia, refracția, principiul lui Fermat, oglinzi, miraje, dispersia, lentile), opticii fizice (undele luminoase, principiul Huygens–Fresnel, difracția, interferența, polarizarea, vederea tridimensională, holografia), opticii cuantice (fotoni, efectul fotoelectric, dualitatea undă-particulă, principiul incertitudinii, complementaritatea) și culorilor (transparența, translucența, amestecul culorilor, culori complementare, pigmenți), în conexiune cu teoriile fundamentale ale luminii. Despre proprietățile luminii (unde electromagnetice, spectrul electromagnetic, materiale transparente și opace, umbra, sistemul vizual uman, lumina Soarelui) și emisia luminii (stări excitate, spectrele de emisie (...) și absorbție, incandescența, fluorescența, fosforescența, LED, laser). Cartea explică bazele fizice pentru înțelegerea fenomenelor optice, cu accent pe fenomenele naturale și aplicațiile specifice. -/- CUPRINS: -/- Lumina - Optica fenomenologică Proprietățile luminii - Unde electromagnetice - - Viteza undelor electromagnetice - - - Viteza luminii - Spectrul electromagnetic - - Intervalul spectrului - - Argumentare pentru denumirile regionale ale spectrului - Materiale transparente - - Ceramica transparentă - - Transparența în izolatori - - Camuflaje - Materiale opace (Opacitatea) - - Radioopacitatea - - Definiție cantitativă - Umbra - - Surse de lumină punctuale și non-punctuală - - Astronomie - - Variația în timpul zilei - - Viteza de propagare - - Culoare - - Umbre tridimensionale - - În fotografie - Sistemul vizual uman (Ochiul) - - Ochiul uman - - Retina - - Vedere binoculară - De ce este apusul de Soare roșu? - De ce sunt norii colorați? - Ce culoare are apa? - - Culoarea intrinsecă - - Culoarea lacurilor și a oceanelor - - Culoarea ghețarilor - - Culoarea probelor de apă Culori - Reflexia selectivă (Culoarea unui obiect) - - Culoarea obiectelor - - Difuzia culorilor - Transmiterea selectivă (Transparența și translucența) - - Împrăștierea luminii în solide - - Absorbția luminii în solide - Amestecul luminii colorate (Amestecul culorilor) - - Amestecul aditiv - - Amestecul subtractiv - Culori complementare - - Culori complementare - - În diferite modele de culori - - - Model tradițional de culoare - - Culorile produse de lumină - - Imprimarea culorilor - - Persistența imaginii - - Aplicații practice - Amestecul pigmenților colorați (Pigmenți) - - RYB - - Procese de imprimare CMY și CMYK - - Amestecarea subtractivă a straturilor de cerneală - - Amestecarea vopselelor în palete limitate - De ce e cerul albastru? - - Radiația difuză a cerului - - Împrăștierea Rayleigh - - De ce e cerul albastru Reflexia și refracția (Optica geometrică) - Istorie - Reflexia - - Reflexia luminii - Principiul timpului cel mai scurt (Principiul lui Fermat) - - Derivare - - Istorie - Legea reflexiei - - Formula vectorială - - Reflectivitate - - Consecințe - - - Reflecția internă - - - Polarizare - - - Imagini reflectate - - Exemple - Oglinzi plane (Oglinzi) - - Efecte - - - Forma suprafeței unei oglinzi - - - Imagine în oglindă - - Oglinzi plane - - - Preparare - - - Relația cu oglinzile curbate - Reflexia difuză - - Mecanism - - Obiecte colorate - - Importanța pentru vedere - - Interreflexia - Refracția - - Explicaţie - Mirajul - - Mirajul inferior - - - Încețoșarea - - Mirajul superior - - - Fata Morgana - - Miraje de noapte - - - Miraje ale obiectelor astronomice - Dispersia - - Exemple - - Dispersia materialelor - Curcubeul - - Prezentare generală - - Numărul de culori în spectru sau curcubeu - - Explicaţie - Reflexia internă totală - - Explicația optică - - Unghiul critic - - Reflexia internă totală eșuată - - Schimbarea de fază la reflexia internă totală - Lentile - - Construcția lentilelor simple - - - Tipuri de lentile simple - - Ecuația lui Lensmaker - - - Convenția de semn pentru razele de curbură R1 și R2 - - - Aproximarea lentilelor subțiri - - Lentile compuse - Formarea imaginilor prin lentile - - Mărirea - Defecte ale lentilelor - - Aberații sferice - - Coma - - Aberația cromatică - - Alte tipuri de aberații - - Difracția diafragmei Undele luminoase (Optica fizică) - Principiul Huygens–Fresnel - - Istorie - - Teoria lui Huygens și funcția de undă fotonică modernă - - Principiul lui Huygens și teoria câmpului cuantic - - În alte dimensiuni spațiale - Difracția luminii - - Exemple - - Mecanism - - Difracția luminii - - - Difracția printr-o singură fantă - Interferența optică - - Cerințele sursei de lumină - - Dispozitive optice - - Interferometria optică - Interferența pe straturi subțiri - - Teorie - - Sursă monocromatică - - Sursa de bandă largă - - Interacțiunea de fază - - Aplicații - Polarizarea - - Propagarea și polarizarea undelor - - - Unde electromagnetice transversale - - - Unde netransversale - - Starea de polarizare - - - Elipsa de polarizare - - Polarizarea fotonilor - Vederea tridimensională (Percepția în adâncime) - - Indicii monoculare - - Indici binoculare - - Percepția tridimensională în artă - Holografia - - Cum funcționează - - - Laser - - - Aparatura - - - Procesul - - - Vs. fotografie - - Fizica holografiei - - - Fronturile de undă plane - - - Surse punctuale - - - Obiecte complexe Emisia luminii (Surse de lumină) - Excitarea (Stări excitate) - Spectrul de emisie al luminii - - Emisie - - Origini - - Radiații din molecule - Incandescența - - Observații și utilizare - Spectrul de absorbție (Spectroscopia de absorbție) - - Teorie - - Relația cu spectrul de transmisie - - Relația cu spectrul de emisie - - Relația cu spectrul de dispersie și reflecție - - Spectroscopia de absorbție - Fluorescența - - Principii fizice - - - Fotochimie - - - Randament cuantic - - - Durata de viață - - - Diagrama Jablonski - - Anizotropia fluorescenței - - - Fluorența - - Reguli - - - Regula lui Kasha - - - Regula imaginii în oglindă - - - Deplasarea Stokes - Lămpi fluorescente - - Principiile de funcționare - - - Construcție - - - Aspecte electrice ale funcționării - - - Efectul temperaturii - - Fosforul și spectrul luminii emise - Fosforescența - - Explicaţii - - - Mecanica cuantică - - - Ecuaţia - - Chimiluminescență - - Materiale - LED - - Istorie - - Principiul de funcționare - - Tehnologie - - Fizica - - - Indicele de refracție - Lămpi cu LED - - Istorie - - Tehnologia - - Eficiența - Laser - - Concepte de bază - - - Terminologie - - Construcţia unui laser - - Fizica laserilor - - Aplicaţii - - - Științifice - - - Spectroscopie - - - Tratament termic - - - Reflector lunar cu laser - - - Fotochimie - - - Scanere de coduri de bare laser - - - Răcire cu laser - - - Fuziunea nucleară - - - Microscopie - Extreme Light Infrastructure - - Istorie - - Centrul de cercetare ELI NP Cuanta de lumină (Fotoni) - Proprietăți fizice - Optica cuantică - Nașterea teoriei cuantice (Optica cuantică) - - Istoria opticii cuantice - - Concepte ale opticii cuantice - - Electronica cuantică - Cuantificarea și constanta lui Planck - - Metode de cuantificare - - - Cuantificarea canonică - - Constanta lui Planck - - - Valoare - - - Semnificația valorii - Efectul fotoelectric - - Mecanismul de emisie - - Observații experimentale ale emisiei fotoelectrice - - Descrierea matematică - - Utilizări și efecte - - - Fotomultiplicatori - - - Senzori de imagine - - - Electroscop cu frunză de aur - - - Spectroscopie fotoelectronică - - - Nave spațiale - - - Praful lunar - - - Dispozitive de vedere pe timp de noapte - Dualitatea undă-particulă - - Tratamentul în mecanica cuantică modernă - - Vizualizare - - Aplicarea la modelul Bohr - Experimentul celor două fante - - Prezentare generală - - Interpretările experimentului - - - Interpretarea de la Copenhaga - - - Formularea integrală a căii - - - Interpretarea relațională - - - Interpretarea multiplelor-lumi - Difracția electronilor - - Proprietăți cuantice - - Difracția electronilor - - Interacțiunea electronilor cu materia - - Microscop cu electroni de transmisie - Principiul incertitudinii - - Definire - - Utilizare - Complementaritatea - - Conceptul - - Natura - - Considerații suplimentare - - Experimente Referințe Despre autor - Nicolae Sfetcu - - De același autor - - Contact Editura - MultiMedia Publishing. 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We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for (...) specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry of spacetime. (shrink)

EEG signals are records of nonlinear solitary waves in human brains. The waves have several types (e.g., α, β, γ, θ, δ) in response to different levels of consciousness. They are classified into two groups: Group-1 consists of complex storm-like waves (α, β, and γ); Group-2 is composed of simple quasilinear waves (θ and δ). In order to elucidate the mechanism of EEG wave formation and propagation, this paper extends the Vlasov-Maxwell equations of Plasma Brain Dynamics (PBD) to a set (...) of two-fluid, self-similar, nonlinear solitary wave equations. Numerical simulations are performed for different EEG signals. Main results include: (1) The excitation and propagation of the EEG wave packets are dependent of electric and magnetic fields, brain aqua-ions, electron and ion temperatures, masses, and their initial fluid speeds; (2) Group-1 complex waves contain three ingredients: the high-frequency ion-acoustic (IA) mode, the intermediate-frequency lower-hybrid (LH) mode, and, the low-frequency ion-cyclotron (IC) mode; (3) Group-2 simple waves fall within the IA band, featured by one or a combination of the three envelopes: sinusoidal, sawtooth, and spiky/bipolar. The study proposes an alternative model to Quantum Brain Dynamics (QBD) by suggesting that the formation and propagation of the nonlinear solitary EEG waves in the brain have the same mechanism as that of the waves in space plasmas. (shrink)

From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.

In this article, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Sec.2), “it is shown that certain mathematical forms of fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms”; (...) where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to fundamental laws of nature is as follows. First based on the assumption of rationality of D-momentum, by linearization (along with a parameterization procedure) of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford, and symmetric algebras) is derived. Then by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of these determined systems of linear equations, a set of two classes of general covariant massive (tensor) field equations (with matrix formalisms compatible with certain Clifford, and Weyl algebras) is derived uniquely as well. Each class of the derived general covariant field equations also includes a definite form of torsion field appeared as generator of the corresponding field’ invariant mass. In addition, it is shown that the (1+3)-dimensional cases of two classes of derived field equations represent a new general covariant massive formalism of bispinor fields of spin-2, and spin-1 particles, respectively. In fact, these uniquely determined bispinor fields represent a unique set of new generalized massive forms of the laws governing the fundamental forces of nature, including the Einstein (gravitational), Maxwell (electromagnetic) and Yang-Mills (nuclear) field equations. Moreover, it is also shown that the (1+2)-dimensional cases of two classes of these field equations represent (asymptotically) a new general covariant massive formalism of bispinor fields of spin-3/2 and spin-1/2 particles, corresponding to the Dirac and Rarita–Schwinger equations. -/- As a particular consequence, it is shown that a certain massive formalism of general relativity – with a definite form of torsion field appeared originally as the generator of gravitational field’s invariant mass – is obtained only by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of a certain set of special relativistic algebraic matrix equations. It has been also proved that Lagrangian densities specified for the originally derived new massive forms of the Maxwell, Yang-Mills and Dirac field equations, are also gauge invariant, where the invariant mass of each field is generated solely by the corresponding torsion field. In addition, in agreement with recent astronomical data, a new form of massive boson is identified (corresponding to U(1) gauge group) with invariant mass: m_γ ≈ 1.47069×10^-41 kg, generated by a coupled torsion field of the background space-time geometry. -/- Moreover, based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented basically by the corresponding quantum operators) of the fundamentally derived field equations, it has been concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times (where this conclusion, in particular, is based on the T-symmetry of these equations). It is shown that CPT is the only combined form of C, P, and T symmetries of interacting fields. In addition, on the basis of these discrete symmetries of derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Furthermore, it has been shown that the metric of background space-time is diagonalized for the uniquely derived fermion field equations (defined and expressed solely in (1+2)-dimensional space-time), where this property generates a certain set of additional symmetries corresponding uniquely to the "SU(2)_L x U(2)_R" symmetry group for spin-1/2 fermion fields (representing “1+3” generations of four fermions, including a group of eight leptons and a group of eight quarks), and also the "SU(2)_L x U(2)_R" and "SU(3)" gauge symmetry groups for spin-1 boson fields coupled to the spin-1/2 fermionic source currents. Hence, along with the known elementary particles, eight new elementary particles, including four new charge-less right-handed spin-1/2 fermions (including two leptons and two quarks), a spin-3/2 fermion, and also three new spin-1 (massive) bosons are predicted uniquely by this axiomatic approach. As a particular result, based on the definite formulation of the derived Maxwell (and Yang-Mills) field equations, it has been also concluded that magnetic monopoles could not exist in nature. -/- Comments: 99 Pages. A summary of a submitted and accepted research project (On "Foundations of Physics"), Ramin Zahedi, Japan, 2012 - 2015. -/- Invited and Presented Research Article at: The 4th International Conference on New Frontiers in Physics ICNFP2015, Europe (CERN), (https://indico.cern.ch/e/icnfp2015); The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, (https://www.siam.org/meetings/ms16/); The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences ( ICMM), Linnaeus University, Sweden, 2016, (https://lnu.se/en/qb/); The 2016 International Conference on Algebraic Geometry and Mathematical Physics (AGMP 2016), University of Tromsø, Norway, (https://site.uit.no/); International Conference on Noncommutative Geometry, Quantum Symmetries and Quantum Gravity (II), XXXVII Max Born International Symposium, Wroclaw University, Poland, 2016, (http://ift.uni.wroc.pl/~mborn37/); 2016 GRavitational-wave Astronomy International Conference (Meeting) in Paris, The Institute d’Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, France, 2016, (Supported by the European Union's Seventh Framework Program: FP7/PEOPLE-2011-CIG); The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016, (http://appc-aip2016.org.au/); The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016, (http://www.gr21.org/). -/- Acknowledgements: Special thanks are extended to Prof. and Academician Vitaly L. Ginzburg (Russia), Prof. and Academician Dmitry V. Shirkov (Russia), Prof. Leonid A . Shelepin (Russia), Prof. Vladimir Ya. Fainberg (Russia), Prof. Wolfgang Rindler (USA), Prof. Roman W. Jackiw (USA), Prof. Roger Penrose (UK), Prof. Steven Weinberg (USA), Prof. Ezra T. Newman (USA), Prof. Graham Jameson (UK), Prof. Sergey A. Reshetnjak (Russia), Prof. Sir Michael Atiyah (UK) (who, in particular, kindly encouraged me to continue this work as a new unorthodox (primary) mathematical approach to fundamental physics), and many others for their support and valuable guidance during my studies and research. -/- External URLs of the Article (Including updated versions): https://inspirehep.net/record/1387680/, https://indico.cern.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahe di--OnDiscretePhysics-Jan.2015-signed.pdf, https://cds.cern.ch/record/1980381/, https://dumas.ccsd.cnrs.fr/TDS-MACS/hal-01476703 , http://eprints.lib.hokudai.ac.jp/dspace/handle/2115/59279/. DOI: https://dx.doi.org/10.17605/OSF.IO/ZCHTP. (shrink)