Luis Gonzalez-Mestres, Sheldon Glashow, Lee Smolin and Lorentz symmetry violation (I)

Nuclear Physics Proceedings has just published (Nuclear Physics B - Proceedings Supplements Volumes 212-213, March-April 2011, Pages 26-33), in the Proceedings of the Cosmic Ray International Seminars, CRIS 2010 - 100 years of Cosmic Ray Physics : from pioneering experiments to physics in space, the article by the CNRS researcher Luis Gonzalez-Mestres « Cosmic rays and tests of fundamental principles », also available at the electronic archive. One of the basic principles now being tested at ultra-high energy cosmic-ray (UHECR) experiments is the validity of special relativity, following a suggestion made by Gonzalez-Mestres in April 1997 and in subsequent papers. Gonzalez-Mestres met some skepticism when he started considering unconventional patterns of Lorentz symmetry violation in his 1995-96 papers. But when he showed that it was possible to check some of his original ideas in UHECR experiments, he was confronted to attempts to present similar results without citing his work. In his book The Trouble with Physics, Lee Smolin, a former doctoral student of Sidney Coleman at Harvard, wrongly attributes to Sidney Coleman and to the Nobel Prize Sheldon Glashow the Gonzalez-Mestres idea that a violation of special relativity at Planck scale may lead to the suppression of the Greisen - Zatsepin - Kuzmin cutoff in the flux of ultra-high energy cosmic rays. This idea was explicitly formulated by Luis Gonzalez-Mestres in several articles during the spring 1997, well before Coleman and Glashow. As the relevant information seems to be systematically censored by some Wikipedia administrators, we shall devote to the affair a few notes in this blog.


The Greisen - Zatsepin - Kuzmin (GZK) cutoff on the UHECR flux predicts a fall of this flux at energies above ~ 5x1019 electron-volts (eV), due to collisions of the ultra-high energy cosmic rays with cosmic background radiation photons.

(Kenneth Greisen, « End to the Cosmic-Ray Spectrum ? », Physical Review Letters 16 (17), 748–750, 1966 ; G.T. Zatsepin et V.A. Kuz'min, « Upper Limit of the Spectrum of Cosmic Rays », Journal of Experimental and Theoretical Physics Letters 4, 78–80, 1966)

Such an effect becomes possible beacause of a specific property of relativistic kinematics at high energy : as momentum increases, the contribution of the mass term to the total energy decreases like the inverse of momentum. Thus, inelastic reactions become possible at very high energy with a lower and lower energy cost. At energies between 1019 and 1020 eV, collisions with microwave background radiation photons start playing a crucial role in cosmic-ray propagation.

In April 1997, Luis Gonzalez-Mestres pointed out that if an absolute inertial frame exists in our Universe leading to a violation of special relativity, even very small, the deformation of relativistic kinematics can lead to a suppression of GZK cutoff.

Luis Gonzalez-Mestres also predicted in April 1997 that, by a similar mechanism, particles usually unstable such as the neutron may become stable at ultra-high energy.

These results were presented for the first time in the article by Gonzalez-Mestres « Vacuum Structure, Lorentz Symmetry and Superluminal Particles » made public on April 14, 1997, by the electronic archive :

The abstract of this paper explicitly states, concerning Lorentz symmetry for "conventional" particles :

(...) The sectorial Lorentz symmetry may be only a low-energy limit, in the same way as the relation $omega $ (frequency) = $c_s$ (speed of sound) $k$ (wave vector) holds for low-energy phonons in a crystal. We study the consequences of such a scenario, using an ansatz inspired by the Bravais lattice as a model for some vacuum properties. It then turns out that: a) the Greisen-Zatsepin-Kuzmin cutoff on high-energy cosmic protons and nuclei does no longer apply; b) high-momentum unstable particles have longer lifetimes than expected with exact Lorentz invariance, and may even become stable at the highest observed cosmic ray energies or slightly above. (...)

(end of quote)

The calculation presented in this article has a very general validity, the only ingredient being the deformation of relativistic kinematics for ordinary particles in a Universe where a preferred local rest frame exists.

Gonzalez-Mestres subsequently wrote several articles on this sujet and presented his work at the main international events in the field, clearly showing that the existence of a fundamental length, of a privileged inertial frame (the « vacuum rest frame ») and of a very small deformation of relativistic kinematics was enough to produce such effects.

More than a year later, Sheldon Glashow and Sidney Coleman published similar results without quoting the work by Luis Gonzalez-Mestres.


In his book The Trouble with Physics (Penguin Books, 2006) :

Lee Smolin erroneously cites Coleman et Glashow as follows (page 221) :


These events may be a signal that special relativity is breaking down at extreme energies. Sidney Coleman and Sheldon Glashow proposed in the late 1990s that a breakdown of special relativity could raise the energy required to make pions, thus raising the GZK cutoff energy and allowing protons of much higher energy to reach our detectors on earth 11.


(end of quote, reference 11 being : S. Coleman et S. L. Glashow, « Cosmic Ray and Neutrino Tests of Special Relativity », Phys. Lett. B, 405, 1997, p. 249-252 ; Coleman et Glashow, « Evading the GZK Cosmic-Ray Cutoff », hep-ph/9808446.)

The first of these two articles by Coleman and Glashow (a misprint by Smolin has been corrected in the reference) explicitly cites Gonzalez-Mestres and does not contain any suggestion on a possible suppression of the GZK cutoff. See the April 30, 1997, version of this article at :

Furthermore, it is somehow surprising that Lee Smolin cites in this context an article by Coleman et Glashow whose physical conclusion stated in the abstract :

The existence of high-energy cosmic rays places strong constraints on Lorentz non-invariance.

(end of quote)

is deeply erroneous and clearly whows that, by the end of April 1997, Sidney Coleman and Sheldon Glashow were actually following a philosophy opposite to that of the paper by Luis Gonzalez-Mestres that had appeared two weeks before and already contained the ideas put forward by Coleman et Glashow much later without citing Gonzalez-Mestres.

Precisely, Gonzalez-Mestres had shown in April 1997 that Lorentz symmetry violation can strengthen the stability of ultra-high energy particles and favour their propagation as cosmic rays.

The second article by Coleman et Glashow quoted in Smolin's book appeared in August 1998, more than a year after the April 1997 original proposal by Gonzalez-Mestres and after several other papers by the same author.

A regrettable affair, that we shall further discuss in forthcoming notes on this blog.

A note in French on the same subject, « Gonzalez-Mestres, Glashow, Smolin, relativité... (I) », can be found at this address:


See also our articles :

Luis Gonzalez-Mestres

Gonzalez-Mestres, Glashow, Smolin, relativité... (I)

Lee Smolin, CNRS, crise et critique des institutions (I)

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