reflect {lorentz}

Mirrors

Description

Plane mirrors in special relativity

Usage

reflect(P,m,ref=1)

Arguments

P

Vector of four-momenta

m

Orientation of mirror, expressed as a three-vector

ref

Coefficient of reflectivity of the mirror

Value

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

Note

All four-momenta are measured in the rest frame of the mirror, but it is easy to reflect from moving mirrors; see examples.

However, note that the ref argument is designed to work with photons only, where it is conceptually the percentage of photons reflected and not absorbed by the mirror. If ref is less than unity, odd results are given for four momenta of nonzero restmass objects.

Author(s)

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))