Status Report, and an Old Review

My paper linked in the previous post was sent back without review by Physics Letters A. This is what the general physics editor said:

Dear Mr. Lush,

I regret that your article is not suitable for publication in Physics Letters A as it does not satisfy our criteria of urgency and timeliness. Please consider submitting your work to a regular journal having a more pedagogical bias.

Thank you for submitting your work to our journal.

Yours sincerely,
(the general physics editor)

I then submitted it to Physica Scripta. Their status shows it sent out to three referees, as of a week ago, with one already having returned a report.

Meanwhile, here is an old review for amusement, of essentially version 3 of my paper about L. H. Thomas' 1927 paper: http://arxiv.org/abs/0905.0927v3

The journal is Studies in the History and Philosophy of Modern Physics.

Referee’s Review about

Regarding Llewellyn Thomas’ Paper of 1927 and the “Hidden Moment” of a Magnetic Dipole in an Electric Field

by David C. Lush

In terms of “mass” and “[relativistic] center of mass”, the author of the paper under review explains his opinion that Thomas precession, as known in the literature on special relativity, is defective. In particular, he claims, the relativistic effect of Thomas precession is in conflict with the relativistic principle of conservation of angular momentum.

However, one has to be careful about the meaning of (i) rest mass, (ii) center of mass, and (iii) momentum conservation in special relativity for the following reasons:
(i) Rest mass in special relativity is not additive; see, for instance, [2] and [10].
(ii) No satisfactory definition of “relativistic center of mass” is available; see, for instance, [3] and [4].
(iii) When momentum conservation involves mass, rather than energy, special care must be taken, owing to items (i) and (ii).

At the end of the paper under review the author justifiably states: “. . . it can be proposed that Thomas with his relativity precession opened a path that has yet to be fully explored.” Indeed, Thomas precession is well-studied in the literature on special relativity, as evidenced from [1]. Furthermore, the contribution of Thomas precession to the hyperbolic geometry that underlies special relativity is explored in [5] – [9].

Thomas precession is determined by the Lorentz transformation group of special relativity as follows:
The application of two successive boosts (a boost being a Lorentz transformation without rotation) is equivalent to the application of a single boost preceded, or followed, by a space rotation. This space rotation turns out to be a Thomas precession. The determination of Thomas precession in terms of Einstein’s velocity addition is well-known; see, for instance, [5] – [9].

Accordingly, the author’s proposal to further explore Thomas precession, since “Thomas with his relativity precession opened a path that has yet to be fully explored”, is welcome. Sadly, however, rather than exploring Thomas precession, the author claims that it is defective and, hence, must be corrected. Unfortunately, any “repair” of the seemingly “defective” Thomas precession is likely to destroy its harmonious interplay between Einstein’s special relativity and the hyperbolic geometry of Bolyai and Lobachevsky.

I therefore recommend against the publication of the paper in the Journal.

Yet, I would like to encourage the author to continue his exploration of the Thomas precession, as he proposed at the very end of his paper.

References
[1] G. B. Malykin. Thomas precession: correct and incorrect solutions. Physics-Uspekhi, 49(8):837–853, 2006.
[2] George Marx. Is the amount of matter additiv? European J. Phys., 12:271–274, 1991.
[3] Luis R. Lehner and Osvaldo M. Moreschi. On the definition of the center of mass for a system of relativistic particles. J. Math. Phys., 36(7):3377–3394, 1995.
[4] M. H. L. Pryce. The mass-centre in the restricted theory of relativity and its connexion with the quantum theory of elementary particles. Proc. Roy. Soc. London. Ser. A., 195:62–81, 1948.
[5] A. A. Ungar. Thomas precession: its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics. Found. Phys., 27(6):881–951, 1997.
[6] A. A. Ungar, Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces. Dordrecht: Kluwer Acad. Publ., 2001.
[7] A. A. Ungar, Analytic Hyperbolic Geometry: Mathematical Foundations and Applications. Singapore: World Scientific, 2005.
[8] A. A. Ungar, Analytic Hyperbolic Geometry and Albert Einstein’s Special Theory of Relativity. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2008.
[9] A. A. Ungar. A gyrovector space approach to hyperbolic geometry. Morgan & Claypool Pub., San Rafael, California, 2009.
[10] A. A. Ungar. On the origin of the dark matter/energy in the universe and the Pioneer anomaly. Prog. Phys., 3:24–29, 2008.

(end of review)

I didn't claim the Thomas precession or relativity is defective, of course. I merely observed that they are inconsistent with the conservation of angular momentum. His suggestion, that this problem will go away if the difference between center of energy and center of mass is respected, is incorrect. The angular momentum nonconservation due to the T.P. is much larger than any that would result from taking the center of mass as the center of energy, as I did. The difference between the two is very very small in the hydrogen atom model employed by Thomas.