Speed of light and Minkowski metric
Getting and setting the speed of light
sol(c) eta(downstairs=TRUE) ptm(to_natural=TRUE, change_time=TRUE)
c |
Scalar, speed of light. If missing, return the speed of light |
downstairs |
Boolean, with default |
to_natural,change_time |
Boolean, specifying the nature of the passive transform matrix |
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
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 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).
Typing “sol(299792458)” is a lot easier than typing
“options("c"=299792458)”, which is why the package uses
the idiom that it does.
Robin K. S. Hankin
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
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