*v*in an inertial frame

*S*, what is the speed

*v'*measured in an inertial frame

*S'*moving at speed

*u*relative to

*S*?

In frame

*S*:

v = \frac{x}{t}

In

*S'*:

v^\prime = \frac{x^\prime}{t^\prime}

= \frac{\gamma(x-ut)}{\gamma(t-\frac{ux}{c^2})}

= \frac{vt-ut}{t-\frac{uvt}{c^2}}

v^\prime = \frac{v-u}{1-\frac{uv}{c^2}}

It is possible, from here, to prove that the speed of light is constant under velocity transformations (and thus that c is a limiting speed). Setting

*v*= c:

v^\prime = \frac{c - u}{1-\frac{u}{c}} = c\frac{c-u}{c-u} = c

Cool, huh?

## No comments:

## Post a Comment