# sol: Speed of light and Minkowski metric In RobinHankin/gyrogroup: The Lorentz Transform in Relativistic Physics

## Description

Getting and setting the speed of light

## Usage

 ```1 2 3``` ```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}{g_ij} with two downstairs indices, and `FALSE` meaning to return the contraviariant 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 gyrogroup package, the speed of light is denoted “sol”, for ‘speed of light’.

The speed of light is a global variable, governed by `options("c")`. If `NULL`, define `c=1`.

Function `eta()` returns the Minkowski flat-space metric

omitted

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 (`to_natural=TRUE`) and from (`to_natural=FALSE`) natural units. 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.

## Author(s)

Robin K. S. Hankin

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```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 relativisitic units ```

RobinHankin/gyrogroup documentation built on Feb. 19, 2019, 3:20 a.m.