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We extend the gauge invariance property of the Maxwell΄s equations to the acoustic field equations. We solve the inhomogeneous wave equation for the scalar and vector potentials and obtain the velocity field and the stress field in terms of these potentials. Gauge invariance has symmetry property. We obtain the gauge form for the acoustic scalar potential and the vector potential and demonstrate their invariant property. We apply gauge invariance to negative refraction. Acoustic field equations also possess left hand and right hand symmetry and this gives rise to negative refraction. Here we extend negative refraction to anisotropic materials. [ABSTRACT FROM AUTHOR]

As we have seen, Maxwell took the molecular-vortex model quite seriously – with ontological intent – when he first presented it in 1861–2, and although he later lost confidence in certain aspects of the model and removed it to the periphery of his research program, he continued in his allegiance to the core hypothesis of the model – that is, to the hypothesis of molecular vortices. The centrality of the molecular-vortex model in Maxwell's general thinking about electromagnetic theory and the particular importance of this model in the background of the displacement current and the electromagnetic theory of light together provide motivation for a careful study of this intricate mechanical model of the electromagnetic field. Maxwell's work on the molecular-vortex model was guided, above all, by his desire – his commitment – to fashion a coherent and comprehensive theory unifying the full range of electromagnetic phenomena from the field-primacy point of view. This was required in order to produce a credible alternative to Wilhelm Weber's unification of electromagnetic theory within the charge-interaction framework; comprehensiveness and coherence were required also in connection with the intended realistic status of the theory – Scottish and Cambridge methodologies converged on this requirement. [ABSTRACT FROM AUTHOR]

The first half of the nineteenth century was marked by the discovery of a variety of new phenomena in electricity and magnetism, and the general task to which Maxwell then addressed himself, beginning in the 1850s, was the development of a unified electromagnetic theory that would incorporate all of these phenomena. Section 1 of this chapter explores the broad background in nineteenth-century electromagnetic experiment and theory for Maxwell's work. Section 2 deals with the particular scientific and mathematical education and training that Maxwell brought to his work in electromagnetic theory, including his educational experiences at the universities of Edinburgh and Cambridge, as well as the epistolary tutelage of William Thomson. Finally, Section 3 deals with the methodological approach – growing out of the combined Scottish and Cambridge backgrounds – that Maxwell brought to his work. Electricity and magnetism from Oersted to the 1840s The discovery of the magnetic effects of electric currents, announced by Hans Christian Oersted in July 1820, defined the agenda for the study of electricity and magnetism during the following decades. Viewed in broad terms, Oersted's discovery had implications in two directions: First, Oersted's research had been undertaken in the context of widespread preoccupation – following Alessandro Volta's invention of the voltaic pile in 1800 – with the connections between electric currents and other physical phenomena, including chemical effects, heat, and light. [ABSTRACT FROM AUTHOR]