Superluminal speeds for relativistic random waves

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,...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 45; no. 18; pp. 185308 - 14
Main Author Berry, M V
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 11.05.2012
IOP
Subjects
Computer simulation
Dirac equation
Exact sciences and technology
Group velocity
Intervals
Klein-Gordon equation
Mathematical analysis
Mathematical models
Operators
Particles (of physics)
Physics
Plane waves
weak values
Operator
Space-time
Group velocity
Power spectra
U groups
Digital simulation
Plane waves
Probability
Local group
Massive particle
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/18/185308