Answer to Question #101065 in Mechanics | Relativity for Kishwer

Question

What is boost parameters by Donald Marolf notes? explain in details

Answer 1

According to Donald Marolf's Notes on Relativity and Cosmology (2003), "The boost parameter is another way to encode the information present in the relative velocity, and in particular it is a very natural way to do so from the viewpoint of Minkowskian geometry."

So what is a "boost"? Refer to the Notes:

"the transformation that changes reference frames is called a ‘boost.’ [...] Boosts are analogous to rotations.”

We simply use vector $r$ and describe its position through the way it is rotated to some axis:

$$x=r\text{ sin}\theta\\ y=r\text{ cos}\theta.$$

The slope is

$$m=x/y=\text{ tan}\theta,$$

and it is similar to

$$v=x/t.$$

Thus, different frames have different θ, which can be shown on any diagram.

"The parameter θ gives some notion of how different the two inertial frames (that of the moving observer and that of the stationary observer) actually are. For θ = 0, event A is at x = 0 and the two frames are the same, while for large θ event A is far up the hyperbola and the two frames are very different."

"$\theta$ is really a measure of the separation of the two reference frames. In this context, we also refer to θ as the boost parameter relating the two frames. The boost parameter is another way to encode the information present in the relative velocity"