Re: [Phys-L] another DIY relativity experiment

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding JD's comments:

> ...
> Here's an example:  Suppose we write a particle's energy and
> momentum as
>    E = m cosh v                               [1]
>    p = m sinh v

and later:

> ...
> -- it unifies the ideas of slope and velocity:
>    slope    = tan θ     in the xy plane
>     velocity = tanh  -- it unifies the ideas of slope and velocity:
    slope    = tan θ     in the xy plane
    velocity = tanh θ    in the xt plane    in the xt plane

These two quotes are inconsistent with each other.  In the first quote v seems to be claimed to be a velocity/speed, but is actually the rapidity of the boost from rest for the particle.  In the latter quote that quantity is now designated as θ and its tanh is called the slope = velocity in the more conventional nomenclature.  I fully agree with the overall thrust of JD's comments, but I don't think we should be conflating an (imaginary) angle with its (imaginary) slope.

David Bowman