In section 2.1 on gravitational red shift he says, in the accelerating rockets:

and on the tower in a gravity field

Those are both straight forward.

He then reminds us of the Newtonian potential and that

He then gets

(2.7a) comes straight from (2.5) by integrating the acceleration over time to get Δv.

But I don't see why (2.7b) follows from (2.7a).

However from (2.6) we can get

and on the tower in a gravity field

Those are both straight forward.

He then reminds us of the Newtonian potential and that

*a*= ∇Φ._{g }He then gets

(2.7a) comes straight from (2.5) by integrating the acceleration over time to get Δv.

But I don't see why (2.7b) follows from (2.7a).

However from (2.6) we can get

I don't follow Carroll's logic but I can get the same answer!

Resources.

The above is also in Commentary 2.1 Red Shift.pdf

The above is also in Commentary 2.1 Red Shift.pdf

This needs a picture to make sense if you don't have the book

ReplyDelete