Lorentz transformations from the first postulate

Abstract-Light scattering from small spherical particles has applications in a vast number of disciplines including astrophysics, meteorology optics and particle sizing. Mie theory provides an exact analytical characterization of plane wave scattering from spherical dielectric objects. There exist many variants of the Mie theory where fundamental assumptions of the theory has been relaxed to make generalizations. Notable such extensions are generalized Mie theory where plane waves are replaced by optical beams, scattering from lossy particles, scattering from layered particles or shells and scattering of partially coherent (non-classical) light. However, no work has yet been reported in the literature on modifications required to account for scattering when the particle or the source is in motion relative to each other. This is an important problem where many applications can be found in disciplines involving moving particle size characterization. In this paper we propose a novel approach, using special relativity, to address this problem by extending the standard Mie theory for scattering by a particle in motion with a constant speed, which may be very low, moderate or comparable to the speed of light. The proposed Received 29 October 2010, Accepted 13 January 2011, Scheduled 24 January 2011. 350Handapangoda, Premaratne, and Pathirana technique involves transforming the scattering problem to a reference frame co-moving with the particle, then applying the Mie theory in that frame and transforming the scattered field back to the reference frame of the observer.

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“…Using the Lorentz transformations [17,18] (1) can be written in the coordinates of inertial frame S as,…”

Section: Stationary Source and Moving Particlementioning

confidence: 99%

Plane Wave Scattering by a Spherical Dielectric Particle in Motion: A Relativistic Extension of the Mie Theory

Handapangoda¹,

Premaratne²,

Pathirana³

2011

PIER

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“…This principle may be applied to the co-ordinate transform, from inertial frame S to frame S 0 at velocity v in S, which must take the same form as the back transform from S 0 to S with velocity Kv (Lee & Kalotas 1975;Lévy-Leblond 1976). The transform must be linear if linear equations in one frame are to transform into linear equations in the other frame.…”

Section: Principle Of Relativitymentioning

confidence: 99%

Derivation of special relativity from Maxwell and Newton

Dunstan

2008

Phil. Trans. R. Soc. A.

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Special relativity derives directly from the principle of relativity and from Newton's laws of motion with a single undetermined parameter, which is found from Faraday's and Ampère's experimental work and from Maxwell's own introduction of the displacement current to be the − c −2 term in the Lorentz transformations. The axiom of the constancy of the speed of light is quite unnecessary. The behaviour and the mechanism of the propagation of light are not at the foundations of special relativity.

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“…This problem can be addressed using spacetime algebra with just a few lines of simple algebraic calculations without loosing the physical and geometrical interpretation as in dry formalisms [21]. Furthermore, spacetime algebra can be also used to put in evidence that Einstein's second postulate on the speed of light is not necessary to special relativity [21,22] -a very important physical and epistemological issue, already shown by several authors although using different approaches [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Doppler Shift from a Composition of Boosts with Thomas Rotation: a Spacetime Algebra Approach

Paiva¹,

Ribeiro²

2006

Journal of Electromagnetic Waves and Applications

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Abstract-As is well-known, Lorentz boosts do not form a group: the composite of two boosts is, in general, equivalent to the composite of a rotation -the so-called Thomas (or Wigner) rotation -and a single boost. Using spacetime algebra, the geometric algebra for Minkowski spacetime, we show in this paper how to relate the Thomas rotation to the Doppler shift experienced between two observers in relative motion. Both observers are moving away from a third observer, set in the laboratory, with relative non-parallel velocities.

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Lorentz transformations from the first postulate

Cited by 108 publications

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Plane Wave Scattering by a Spherical Dielectric Particle in Motion: A Relativistic Extension of the Mie Theory

Plane Wave Scattering by a Spherical Dielectric Particle in Motion: A Relativistic Extension of the Mie Theory

Derivation of special relativity from Maxwell and Newton

Doppler Shift from a Composition of Boosts with Thomas Rotation: a Spacetime Algebra Approach

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