sol {lorentz}

Speed of light and Minkowski metric

Description

Getting and setting the speed of light

Usage

sol(c)
eta(downstairs=TRUE)
ptm(to_natural=TRUE, change_time=TRUE)

Arguments

c

Scalar, speed of light. If missing, return the speed of light

downstairs

Boolean, with default TRUE meaning to return the covariant metric tensor g_{ij} with two downstairs indices, and FALSE meaning to return the contravariant version g^{ij} with two upstairs indices

to_natural, change_time

Boolean, specifying the nature of the passive transform matrix

Details

In the context of an R package, the symbol “c” presents particular problems. In the lorentz package, the speed of light is denoted “sol”, for ‘speed of light’. You can set the speed of light with sol(x), and query it with sol(); see the examples. An infinite speed of light is sometimes useful for Galilean transforms.

The speed of light is a global variable, governed by options("c"). If NULL, define c=1. Setting showSOL to TRUE makes sol() change the prompt to display the speed of light which might be useful.

Function eta() returns the Minkowski flat-space metric

\mathrm{diag}\left(-c^2,1,1,1\right).

Note that the top-left element of eta() is -c^2, not -1.

Function ptm() returns a passive transformation matrix that converts displacement vectors to natural units (to_natural=TRUE) or from natural units (to_natural=FALSE). Argument change_time specifies whether to change the unit of time (if TRUE) or the unit of length (if FALSE).

Note

Typing “sol(299792458)” is a lot easier than typing “options("c"=299792458)”, which is why the package uses the idiom that it does.

In a R-devel discussion about options for printing, Martin Maechler makes the following observation: “Good programming style for functions according to my book is to have them depend only on their arguments, and if a global option really (really? think twice!) should influence behavior, there should be arguments of the function which have a default determined by the global option”

I think he is right in general, but offer the observation that the speed of light depends on the units chosen, and typically one fixes one's units once and for all, and does not subsequently change them. This would indicate (to me at least) that a global option would be appropriate. Further, there is a default, c=1, which is returned by sol() if the option is unset. This is not just a “default”, though: it is used in the overwhelming majority of cases. Indeed, pedagogically speaking, one learning objective from the package is that units in which c\neq 1 are difficult, awkward, and unnatural. In the package R code, the only place the speed of light option is accessed is via sol(). Similar arguments are presented in the clifford package at signature.Rd.

Author(s)

Robin K. S. Hankin

Examples

sol()                          # returns current speed of light
sol(299792458)                 # use SI units
sol()                          # speed of light now SI value

eta()                          # note [t,t] term
u <- as.3vel(c(100,200,300))   # fast terrestrial speed, but not relativistic
boost(u)                       # boost matrix practically Galilean
is.consistent.boost(boost(u))  # should be TRUE
sol(1)                         # revert to relativistic units