lorentz (version 1.1-1)

reflect: Mirrors

Description

Plane mirrors in special relativity

Usage

reflect(P,m,ref=1)

Value

Takes a four-momentum and returns the four-momentum after reflection. Will handle objects or photons.

Arguments

P

Vector of four-momenta

m

Orientation of mirror, expressed as a three-vector

ref

Coefficient of reflectivity of the mirror

Author

Robin K. S. Hankin

See Also

photon

Examples

## We will reflect some photons from an oblique mirror moving at half
## the speed of light.

## First create 'A', a bunch of photons all moving roughly along the x-axis:
A <- as.photon(as.3vel(cbind(0.9,runif(10)/1000,runif(10)/1000)))

## Now create 'm', a mirror oriented perpendicular to c(1,1,1):
m <- c(1,1,1)

## Reflect the photons in the mirror:
reflect(A,m)

## Reflect the photons in a series of mirrors:
A |> reflect(m) |> reflect(1:3) |> reflect(3:1) 


## To reflect from a moving mirror we need to transform to a frame in
## which the mirror is at rest, then transform back to the original
## frame.  First create B, a boost representing the mirror's movement
## along the x-axis at speed c/2:

B <- boost(as.3vel(c(0.5,0,0)))


## Transform to the mirror's rest frame:
A %*% t(B)    

## NB: in the above, take a transpose because the *rows* of A are 4-vectors.

## Then reflect the photons in the mirror:
reflect(A %*% t(B),m)


## Now transform back to the original rest frame (NB: active transform):
A |> tcrossprod(B) |> reflect(m) |> tcrossprod(solve(B))