I Relativity of Simultaneity and Length Contraction

[Orodruin]

I was brought up to use $\sin^{-1}$ etc. I think that might be a U.K. vs U.S. thing.

My "beef" with that is the risk of confusion between csc and asin. After all, we write $\sin^2(x)$ implying the square of the sine so interpreting $\sin^{-1}(x)$ as $1/\sin(x) = \csc(x)$ is not a long shot.

 

[DrGreg]

My "beef" with that is the risk of confusion between csc and asin. After all, we write $\sin^2(x)$ implying the square of the sine so interpreting $\sin^{-1}(x)$ as $1/\sin(x) = \csc(x)$ is not a long shot.

I agree, there is an inconsistency in the notation.

 

[robphy]

In discussions with physics teachers, rapidity is (sadly) sometimes considered an advanced topic.
(See https://www.physicsforums.com/threa...etime-physics-by-wheeler.1004722/post-6513631 )

In typical problems, one doesn't need the value of the rapidity.
One can get by with ratios:
"$\beta=\tanh\theta=\frac{OPP}{ADJ}=\rm (slope)$" and
"$\gamma=\cosh\theta=\frac{ADJ}{HYP}$" and
"$\beta\gamma=\sinh\theta=\frac{OPP}{HYP}$".
One just needs to know how to recognize Minkowski-right-triangles in a spacetime diagram,
then generalize the familiar formulas for "trig-functions as ratios of right-triangle-legs".

 

[Orodruin]

In discussions with physics teachers, rapidity is (sadly) sometimes considered an advanced topic.

Some people have little respect for properly using an additive parameter for their continuous one-parameter groups … sigh

 

[robphy]

Some people have little respect for properly using an additive parameter for their continuous one-parameter groups … sigh

$\xi$ ?

Some people prefer to use a parameter, which is actually non-additive,
but treat it as additive [due to inappropriate extrapolation].

$v$