Define proper acceleration in the obvious way: a) Find α0 and α in terms of u...

Define proper acceleration in the obvious way:

a) Find α⁰ and α in terms of u and a (the ordinary acceleration).

(b) Express α _μ α ^μ in terms of u and a.

(c) Show that η ^μ α _μ = 0.

(d) Write the Minkowski version of Newton’s second law, Eq. 12.68, in terms of

α ^μ. Evaluate the invariant product K ^μ η _μ.

Reference equation 12.68