Mermin's (Special) Relativity without Light

[uby]

I am not mathematically inclined. However, I would love to be able to follow Mermin's treatment deriving an invariant velocity between reference frames (Am. J. Phys, 52(2) 1984 p. 119-124).

Unfortunately, I cannot follow his initial setup regarding the form of the function relating multiple inertial frames. He shows a shorthand notation for partial derivative which I am familar with, but later shows the same notation using a zero in place of a variable which makes no sense to me but upon which further work depends.

For example, he writes: f₂(x,y) = df(x,y)/dy as shorthand for partial derivative by the second variable of the function f. Then, later, uses the notation f₂(y,0). This becomes jibberish to me unless it perhaps indicates derivative by the 'hidden' variable followed by evaluation of that variable for the value shown? He doesn't say.

Can anyone familiar with this paper help clarify what is meant by his notation? Or, alternatively, point me to either extended discussions on this paper or derivations by other authors?

Thanks!

 

[bcrowell]

For example, he writes: f₂(x,y) = df(x,y)/dy as shorthand for partial derivative by the second variable of the function f. Then, later, uses the notation f₂(y,0).

If he wrote f₂(x,0) I would assume that this meant $\left.\frac{\partial f}{\partial y}\right|_{y=0}$. Placing the y first does seem a little strange.

I don't have access to the paper, but Mermin has posted various presentations of SR online. Is either of these similar? --
http://people.ccmr.cornell.edu/~mermin/homepage/ndm.html
http://www.ccmr.cornell.edu/~mermin/homepage/minkowski.pdf

 

[uby]

Thanks for your reply, bcrowell.

Unfortunately, I do not think our interpretation of the implied notation is correct. For example, he also states that it is "evident from the definition of f" that f(y,0) = y.

This, of course, makes no sense to me given that the function is general and could be anything. I should have some time on Friday to type out all of the equations in question (there aren't too many) and where my trouble lies more precisely.

 

[atyy]

I agree with bcrowell's reading of f2(y,0) as the partial derivative of f with respect to the second argument evaluated with the first argument set to y and the second argument set to 0.

He writes f(y,0)=y because he defines vca=f(vcb,vba), where vca is the velocity of c relative to a, so if b=a then vca=f(vca,vaa)=f(vca,0).

 

[ParticleGrl]

Try the paper

A.Sen, "How Galileo could have derived the Special Theory of Relativity", Am. J. Phys. 62 157-162 (1994)

The presentation is very much in the spirit of Mermin, but a bit more algebraic.