Ultra high energetic neutrinos in their rest frame: can their time of arrival be determined?

Abstract

In the light of the recent observation by the KM3NeT collaboration of an ultrahigh energetic neutrino, we analyse it in its rest frame, where shortly after creation of the neutrino a muon arrives and interacts. Since the neutrino is at rest we use (in this first analysis) a non relativistic Gaussian wave function, and consider its spread. Due to the finite size of the packet, the time of the interaction of the muon will have an uncertainty. This uncertainty is small in the neutrino rest frame, but boosted to our frame, increases 18 orders of magnitude, making it extremely large. This effectively prevents the possibility of the observation of bursts, or the correlation with other events. A similar analysis for less energetic neutrinos show that the uncertainty is smaller than the duration of the observed bursts.

Comments: There are serious flaws in the treatment of the relativistic transformations. I thank Drs. Troitsky, Libanov and Naumov for making me aware of the mistake. A correct treatment of the behaviour of wave packets in the relativistic case can be found in D. V. Naumov, On the theory of wave packets in quantum field theory, Phys. Part. Nucl. Lett. 10, 642-650 (2013), arXiv:1309.1717 [quant-ph]