r3vel {lorentz}

Random relativistic velocities

Description

Generates random three-velocities or four-velocities, optionally specifiying a magnitude

Usage

r3vel(n=7, r = NA)
r4vel(...)
rboost(r = NA)

Arguments

n

Number of three- or four- velocities to generate

r

Absolute value of the three-velocities, with default NA meaning to sample uniformly from the unit ball

...

Arguments passed to r3vel()

Details

Function r3vel() returns a random three-velocity. Function r4vel() is a convenience wrapper for as.4vel(r3vel()).

Function rboost() returns a random 4\times 4 Lorentz boost matrix, drawn from the connected component. If given r=0, then a transform corresponding to a random rotation will be returned.

Value

Returns a vector of three- or four- velocities.

Note

If the speed of light is infinite, these functions require a specified argument for r.

It is not entirely trivial to sample uniformly from the unit ball or unit sphere, but it is not hard either.

Author(s)

Robin K. S. Hankin

Examples

r3vel()

a <- r3vel(10000)
b <- r3vel(1000,0.8)
u <- as.3vel(c(0,0,0.9))

pairs(unclass(u+a),asp=1)
pairs(unclass(a+u),asp=1)

is.consistent.boost(rboost())

sol(299792458)    # switch to SI units
sound <- 343      # speed of sound in metres per second
r3vel(100,343)    # random 3-velocities with speed = 343 m/s

sol(1)   # return to default c=1