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arXiv:1110.1790

Apparent Superluminal Muon-neutrino Velocity as a Manifestation of Weak Value

Shogo Tanimura

Published Oct 9, 2011• 2 citations

Abstract

The result of the OPERA experiment revealed that the velocity of muon-neutrinos was larger than the speed of light. We argue that this apparent superluminal velocity can be interpreted as a weak value, which is a new concept recently studied in the context of quantum physics. The OPERA experiment setup forms a scheme that manifests the neutrino velocity as a weak value. The velocity defined in the scheme of weak measurement can exceed the speed of light. The weak velocity is not a concept associated to a single phenomenon but it is a statistical concept defined by accumulating data at separated places and by comparing the data. Neither information nor physical influence is conveyed at the weak velocity. Thus the superluminal velocity in the sense of weak value does not contradict the causality law. We propose also a model for calculating the neutrino velocity with taking neutrino oscillation into account.

DOI: 10.48550/arxiv.1110.1790

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The result of the OPERA experiment revealed that the velocity of muon-neutrinos was larger than the speed of light. We argue that this apparent superluminal velocity can be interpreted as a weak value, which is a new concept recently studied in the context of quantum physics. The OPERA experiment setup forms a scheme that manifests the neutrino velocity as a weak value. The velocity defined in the scheme of weak measurement can exceed the speed of light. The weak velocity is not a concept associated to a single phenomenon but it is a statistical concept defined by accumulating data at separated places and by comparing the data. Neither information nor physical influence is conveyed at the weak velocity. Thus the superluminal velocity in the sense of weak value does not contradict the causality law. We propose also a model for calculating the neutrino velocity with taking neutrino oscillation into account.

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We theoretically explore the possibility of observing the quantum decoherence of neutrino oscillation due to the vacuum dispersion, that the wave-packet of neutrino spatially splits according to the different velocities of two mass eigenstates. We find that if this decoherence could be observed and the range of values of the mixing angle is known, then the superluminal neutrino phenomena could occur for some mixing angles as the consequence of a weak measurement about flavor mixing in the neutrino propagation. Our calculation gives the explicit dependence of group velocity shift to the decoherence factor and the weak value of neutrino's pre and post-selected states. We also study the related problems for the neutrino oscillation with three generations.

Non-dispersive wave packet for massless fermions is formulated on the basis of squeezed coherent states that are put in a form of common eigenfunction for the Hamiltonian and the helicity operator, starting from the Dirac equation. The wave packet thus constructed is demonstrated to propagate at a constant velocity as that of light. This explicit expression of wave packet for the massless fermions can facilitate theoretical analysis of problems where a wave packet is of formal significance. Furthermore, extensive wave packet may result in a superluminal velocity statistics if determined from the time-of-flight measurement, as recently done on muon neutrinos, when a threshold particle flux or energy transfer, which is eventually referred to the propagation of wave packet, to invoke a detection event is assumed.

We present an easy way of observing superluminal group velocities using a birefringent optical fiber and other standard devices. In the theoretical analysis, we show that the optical properties of the setup can be described using the notion of "weak value." The experiment shows that the group velocity can indeed exceed c in the fiber; and we report the first direct observation of the so-called "signal velocity," the speed at which information propagates and that cannot exceed c.