arXiv subjects

Patrick Moylan

Publications and source records attributed to Patrick Moylan.

4 recordsLinked to original sources

arXiv2023

Poincare and Einstein on Mass-Energy Equivalence: A Modern Perspective on their 1900 and 1905 Papers

Both Poincar\'e in his 1900 Festschrift paper \cite{Poincare} and Einstein in his 1905 \textsl{Annalen der Physik} article \cite{Einstein} were led to $E=mc^2$ by considering electromagnetic processes taking place in vacuo. Poincar\'e's treatment is based on a generalization of the law of conservation of momentum to include radiation. Einstein's analysis relies solely on energy conservation and the relativity principle together with certain assumptions, which have served as the source of criticism of the paper beginning with Max Planck in 1907. We show that these objections raised by Planck and others can be traced back to Einstein's failure to make use of momentum considerations. Relevance of our findings to a proper understanding of Ives' criticism of Einstein's paper is pointed out.

physics.hist-ph↗

arXiv2016

Anti de Sitter Holography via Sekiguchi Decomposition

In the present paper we start consideration of anti de Sitter holography in the general case of the (q+1)-dimensional anti de Sitter bulk with boundary q-dimensional Minkowski space-time. We present the group-theoretic foundations that are necessary in our approach. Comparing what is done for q=3 the new element in the present paper is the presentation of the bulk space as the homogeneous space G/H = SO(q,2)/SO(q,1), which homogeneous space was studied by Sekiguchi.

math.RT↗

arXiv2010

Moving Charge Distributions in Classical Electromagnetism and the FitzGerald-Lorentz Contraction

In [Eur. J. Phys. {\bf 25} (2004) 123-126], Dragan V. Red{\v z}ić is led to the FitzGerald-Lorentz contraction by comparing electromagnetic images of a moving point charge and a moving conducting sphere. We wish to point out that much simpler possibilities intrinsic to electromagnetism already exist from which we may get at the FitzGerald-Lorentz contraction hypothesis. In particular we consider an example going back to Poincaré in [{\it Bulletin des Sciences mathématiques}, 28, (1904) pp. 302-324], in which he considers the problem of two moving, parallel line charges in order to get at length contraction. We develop this model of Poincaré and show that it leads not only to the FitzGerald-Lorentz contraction but also to an elementary derivation of the composition of velocities formula in special relativity for collinear velocities. Red{\v z}ić suggests that, by considering such purely electromagnetic examples, the Maxwellians could have been led to the contraction hypothesis much before the time of the Michelson-Morely experiment, and we agree with him that such elementary results as the ones discussed here could not have escaped their attention. Apparently, it took an extremely sensitive experiment, not intrinsic to electromagnetism, such as was the Michelson-Morley experiment, together with the efforts of persons with authority, like Lorentz and Poincaré, trying to uphold the relativity principle before the radical notion of length contraction could seriously be entertained, and making ripe the way for the genius of Einstein.

physics.hist-ph↗

arXiv2004

Tachyons and Representations of SO(2,3)

We describe an embedding of the Poincare Lie algebra into an extension of the Lie field of SO(2,3) (the anti-de Sitter group). We also describe higher dimensional analogs of this embedding, which connect SO(p,q) groups to their associated motion groups (higher dimensional Poincare groups). Further some results on q generalizations of these results are given. We apply our results to certain unitary, continuous series representations of SO(2,3) associated with functions on SO(2,3)/SO(1,3). From the embedding theorem we obtain representations of the Poincare Lie algebra which are associated with unitary, tachyonic representations of the Poincare group, provided these representations are integrable to group representations.

math-ph↗