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Still special

Nature volume 450, pages 801803 (06 December 2007) | Download Citation

Is special relativity a clapped-out classical theory, to be replaced by a shiny new quantum model as soon as possible? On the contrary, it would seem: the theory still has a youthful ability to surprise us.

Since Albert Einstein introduced it to the world in 1905, the special theory of relativity has embodied the journey of modern physics from an 'intuitive' description of the world to a deeper level of understanding — an understanding at first profoundly baffling to established ways of thinking. Concepts such as the equivalence of mass and energy, embodied by the formula E = mc2; the existence of an unbreakable speed barrier, the speed of light in vacuo, c; and the paradox of two twins who, by dint of experiencing different accelerations through space, can age by different amounts, have all stamped themselves on the public's consciousness (Fig. 1). At the same time, special relativity has provided a reliable description for an ever-growing list of physical phenomena.

Figure 1: Einstein equals most celebrated, squared.
Figure 1

The equation embodying mass–energy equivalence has become, along with its creator, the most recognizable symbol of modern physics — here on a German stamp to commemorate the 2005 'Year of Physics', the 100th birthday of special relativity.

Writing in Physical Review Letters, Cubero et al.1 add to that list, establishing how special relativity affects certain equilibrium properties of a gas of idealized particles. The work is symbolic of special relativity's odd position in the pantheon of modern physics theories: continuously tested and always successful; yet also disparaged as not really 'belonging' in the grander scheme of things. To physicists, special relativity was only really ever a fundamental theory for 11 years: in 1916, it ceded that title to Einstein's general theory of relativity. General relativity incorporates special relativity's maximum-speed principle into a comprehensive theory of gravitational phenomena, and through that arrives at a description of gravitational acceleration as a consequence of the curvature of space-time.

Special relativity is thus a humble 'effective theory', valid only as an approximation under certain conditions — specifically, that gravitational effects such as the curvature of space-time can be ignored. But, as luck would have it, physicists have devoted most of the century since Einstein first dreamt up his relativity to studying the quantum properties of particles in just such cases. The particle physicist at a laboratory such as CERN does not need to worry about the local topology of space-time when smashing particles together: particle physics' ultra-successful 'standard model' is built on the special, not the general, theory of relativity.

Since the end of the 1990s, however, the blanket application of special relativity in these instances has come under renewed attack. The reason for this is that gravity, in its general-relativistic description, is the only one of the four fundamental forces of nature that is still described using the rules of classical mechanics. Pursuing the hypothesis of a 'quantum gravity', one encounters the possibility of small, but non-negligible quantum-curvature effects, even where the average curvature is zero.

This could have practical implications for, say, the observation of objects in the distant Universe. The particles that we observe from so far away (mainly photons of light) propagate for billions of years, and quantum-curvature effects, although individually tiny, could accumulate to an appreciable effect that might, for example, affect our estimates of the objects' distance. But in all the astrophysical tests so far performed to test this hypothesis, special relativity comes out tops, with no evidence of deviations from its predictions. A more definite picture will emerge only after other crucial tests are performed, such as γ-ray observations soon to be conducted with NASA's GLAST space telescope. But at present even I — a researcher deeply involved in all the quantum-curvature speculation — must admit that special relativity seems in remarkably rude health.

In fact, rather than discovering regimes to which special relativity does not apply, we are actually learning how to use it to describe even more areas of physics. Cubero and colleagues' analysis1 of the special-relativistic equilibrium properties of a gas of particles is a case in point. Although Einstein's original formulation provided straightforward prescriptions for attributing special-relativistic properties to each particle in such a multi-particle system, it has not always been easy (and has sometimes been terribly hard) to derive from these properties a macroscopic, statistically valid description of the system.

The authors find a clever and reliable way to simulate numerically a dilute, one-dimensional gas consisting of two species of particle, and study macroscopic properties such as temperature and the velocity distribution of the particles. The statistical distribution of the particle velocities in the gas that emerges clearly favours a description proposed2 on the basis of a maximum-entropy principle that has been criticized for lacking explicit compatibility with relativity. The authors also succeed in introducing a concept of 'proper' temperature such that, in agreement with the principles of special relativity, observers moving differently with respect to the gas will agree on the temperature's value.

As so often happens in the development of young theories — at 100 years old, special relativity is still looking remarkably youthful — these results clarify some issues, but also present new challenges. In particular, the authors' analysis must be generalized from one to three spatial dimensions, the number we really care about. This will require getting rid of the simplification introduced by the authors that the point particles in the gas interact only when they actually touch. In one dimension, touching collisions are rather frequent, and this approximation is appropriate; but in three dimensions, contact collisions would not be frequent enough to allow the establishment of a definite temperature. For a complete description, interactions at a distance must also be considered.

Such caveats do not detract from the success, exemplified by Cubero and colleagues' work1, of special relativity in characterizing the properties of complex systems. Even those of us speculating about a quantum version of the theory, and at present concentrating on very simple systems, might do well to take a lesson from that — this theory's retirement might be some time coming yet.


  1. 1.

    , , , & Phys. Rev. Lett. 99, 170601 (2007).

  2. 2.

    Ann. Phys. 34, 856–882 (1911).

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  1. Giovanni Amelino-Camelia is in the Department of Physics, Università di Roma La Sapienza, and the Sezione Roma 1, INFN, Piazzale Moro 2, Rome 00185, Italy.

    • Giovanni Amelino-Camelia


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