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Failure of commutativity and associativity using visual plots

comm_fail.Rd

Relativistic addition of three-velocities is neither commutative nor associative, and the functions documented here show this visually.

Usage

comm_fail1(u, v, bold=5, r=1)
comm_fail2(u, v, bold=5, r=1)
ass_fail(u, v, w, bold=5,r=1)
my_seg(u,start=as.3vel(0), bold=5, ...)

Arguments

u,v,w,start

Three velocities. Arguments u and w are single-element three velocities, argument v is a vector. See the examples

bold

Integer specifying which vector element to be drawn in bold

r

Radius of dotted green circle, defaulting to 1 (corresponding to \(c=1\)). Use NA to suppress plotting of circle

...

Further arguments, passed to arrows()

Value

These functions are called for their side-effect of plotting a diagram.

Note

The vignette lorentz gives more details and interpretation of the diagrams.

Function my_seg() is an internal helper function.

Author

Robin K. S. Hankin

Examples


u <- as.3vel(c(0.4,0,0))
v <- seq(as.3vel(c(0.4,-0.2,0)), as.3vel(c(-0.3,0.9,0)),len=20)
w <- as.3vel(c(0.8,-0.4,0))

comm_fail1(u=u, v=v)

comm_fail2(u=u, v=v)

  ass_fail(u=u, v=v, w=w, bold=10)