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arXiv:quant-ph/0107025 · Physical Review A

Cherenkov radiation of superluminal particles

Daniel Rohrlich, Yakir Aharonov

Published Oct 3, 2002• 54 citations
arXivHTMLPDF

Abstract

Any charged particle moving faster than light through a medium emits Cherenkov radiation. We show that charged particles moving faster than light through the vacuum emit Cherenkov radiation. How can a particle move faster than light? The weak speed of a charged particle can exceed the speed of light. By definition, the weak velocity $〈\mathbf{v}{〉}_{w}$ is $〈{\ensuremath{\Psi}}_{\mathrm{fin}}|\mathbf{v}|{\ensuremath{\Psi}}_{\mathrm{in}}〉/〈{\ensuremath{\Psi}}_{\mathrm{fin}}|{\ensuremath{\Psi}}_{\mathrm{in}}〉,$ where $\mathbf{v}$ is the velocity operator and $|{\ensuremath{\Psi}}_{\mathrm{in}}〉$ and $|{\ensuremath{\Psi}}_{\mathrm{fin}}〉$ are, respectively, the states of a particle before and after a velocity measurement. We discuss the consistency of weak values and show that superluminal weak speed is consistent with relativistic causality.

DOI
10.1103/physreva.66.042102

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Any charged particle moving faster than light through a medium emits Cherenkov radiation. We show that charged particles moving faster than light through the vacuum emit Cherenkov radiation. How can a particle move faster than light? The weak speed of a charged particle can exceed the speed of light. By definition, the weak velocity 〈v〉w〈\mathbf{v}{〉}_{w}〈v〉w​ is 〈\ensuremathΨfin∣v∣\ensuremathΨin〉/〈\ensuremathΨfin∣\ensuremathΨin〉,〈{\ensuremath{\Psi}}_{\mathrm{fin}}|\mathbf{v}|{\ensuremath{\Psi}}_{\mathrm{in}}〉/〈{\ensuremath{\Psi}}_{\mathrm{fin}}|{\ensuremath{\Psi}}_{\mathrm{in}}〉,〈\ensuremathΨfin​∣v∣\ensuremathΨin​〉/〈\ensuremathΨfin​∣\ensuremathΨin​〉, where v\mathbf{v}v is the velocity operator and ∣\ensuremathΨin〉|{\ensuremath{\Psi}}_{\mathrm{in}}〉∣\ensuremathΨin​〉 and ∣\ensuremathΨfin〉|{\ensuremath{\Psi}}_{\mathrm{fin}}〉∣\ensuremathΨfin​〉 are, respectively, the states of a particle before and after a velocity measurement. We discuss the consistency of weak values and show that superluminal weak speed is consistent with relativistic causality.
Cherenkov radiation is one of the problems in light- matter interaction that can be opened new ideas in quantum electrodynamic. A quantum mechanic approach is presented for Cherenkov radiation of a moving atom in uniaxial and biaxial anisotropic medium. A moving particle in a medium emits Cherenkov radiation when its speed be larger than the phase velocity of light in the medium. The electromagnetic field is quantized in the anisotropic media, using maxwell and related constitute equations, phenomenologically. The Cherenkov radiation for an moving charged particle in the anisotropic medium with arbitrary real permittivity tensor is obtained. The dielectric structure can be changed the Cherenkov radiation. For uniaxial media, we give a close form of the Cherenkov radiation for arbitrary dipole alignment. In this manner, the Cherenkove radiation of the biaxial media is calculated.. It is shown the Cherenkov radiation in an isotropic medium can be obtained from the form of an anisotropic medium.
An explanation for superluminal phenomena based on wave-particle duality of photons is suggested. A single photon may be regarded as a wave packet, whose spatial extension is its coherence volume. As a photon propagates as a wave train in vacuum, its velocity is just the speed of light. When it tunnels through a barrier as a particle, its wave function collapses and it will travel faster than light. Superluminal motion can occur only within the coherence length and the time constrained by uncertainty principle. A massive particle cannot be superluminal during the tunneling process. So superluminality does not violate causality. As for the superluminal and negative group velocities in anomalously dispersive medium, they are merely reshaping effect of the pulse, and they will become subluminal at large distances. A couple of experiments are proposed to test the superluminal phenomena.
We exploit the analogy between the transfer of a pulse across a scattering medium and Aharonov's weak measurements to resolve the long standing paradox between the impossibility to exceed the speed of light and the seemingly ``superluminal'' behavior of a tunneling particle in the barrier or a photon in a ``fast-light'' medium. We demonstrate that superluminality occurs when the value of the duration $\ensuremath{\tau}$ spent in the barrier is uncertain, whereas when $\ensuremath{\tau}$ is known accurately, no superluminal behavior is observed. In all cases only subluminal durations contribute to the transmission which precludes faster-than-light information transfer, as observed in a recent experiment.
For Klein?Gordon and Dirac waves representing massive quantum particles, the local group velocity v (weak value of the velocity operator) can exceed c. If the waves consist of superpositions of many plane waves, with different (but subluminal) group velocities u, the superluminal probability Psuper, i.e. that |v| > c for a randomly selected state, can be calculated explicitly. Psuper?depends on two parameters describing the distribution (power spectrum) of u in the superpositions, and lies between 0 and 1/2 for Klein?Gordon waves and 1?1/ and 1/2 for Dirac waves. Numerical simulations display the superluminal intervals in space and regions in spacetime, and support the theoretical predictions for Psuper.
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.
On speed of a photon in a dispersing medium Ogluzdin Valeriy E. Abstract Based on the author of the experimental results and their treatment, a model that demonstrates that the real dispersive medium in spectral regions where the refractive index greater than unity, the velocity of propagation of photons in this environment corresponds to the phase velocity of light. These portions of the spectrum (for example, atomic potassium vapor or other alkali metal) are from low-frequency side of the main lines of the doublet and are available for research using tunable lasers. In the calculations took into account the fact that the atomic vapor of alkali metal used as a dispersing medium, in accordance with the theory of dispersion in the above sections of the spectrum, on the periphery of the cross section of laser beam with Gaussian intensity distribution across the beam - in the shadows refractive index n (ν) is greater than unity, and the axis of the beam, where the radiation intensity is maximum - for radiation following the leading edge of the light pulse, the refractive index is unity, which ensures smooth on the beam axis, without any delay "superluminal "propagation of light with velocity c. This fact causes the appearance of the shadow cone of Vavilov - Cherenkov radiation, indicating a slow propagation of photons from the source of the cone with phase velocity c / n (ν).