Are muon neutrinos faster-than-light particles?☆

It is now well known that Maxwell equations admit of wavelet-type solutions endowed with arbitrary group velocities $(0l{v}_{\mathrm{g}}l\ensuremath{\infty}).$ Some of them, which are rigidly moving and have been called localized solutions, attracted large attention. In particular, much work has been done with regard to the superluminal localized solutions (SLSs), the most interesting of which are the ``X-shaped'' ones. The SLSs have been actually produced in a number of experiments, always by suitable interference of ordinary-speed waves. In this paper we show, by contrast, that even a superluminal charge creates an electromagnetic X-shaped wave: namely, on the basis of Maxwell equations, we are able to evaluate the field associated with a superluminal charge (under the approximation of pointlikeness): It results in constituting a very simple example of a true X wave.

Localized X-shaped field generated by a superluminal electric charge.

Localized waves (LW) are nondiffracting (“soliton-like”) solutions to the wave equations and are known to exist with subluminal, luminal, and superluminal peak velocities V. For mathematical and experimental reasons, those that have attracted more attention are the “X-shaped” superluminal waves. Such waves are associated with a cone, so that one may be tempted—let us confine ourselves to electromagnetism—to look [Phys. Rev. Lett.99, 244802 (2007)] for links between them and the Cherenkov radiation. However, the X-shaped waves belong to a very different realm: For instance, they can be shown to exist, independently of any media, even in vacuum, as localized non-diffracting pulses propagating rigidly with a peak-velocity V>c [Hernandez et al., eds., Localized Waves (Wiley, 2008)]. We dissect the whole question on the basis of a rigorous formalism and clear physical considerations.

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E. Recami

Papers

Erratum to: Classical theory of tachyons (special relativity extended to superluminal frames and objects)