![]() |
The observer, abandoned by the rocket. |
Uμ = (1 , 0 , 0 , 0)
and the four-velocity of the rocket is
Vμ =(γ , γv , 0 , 0)
where v is the three-velocity and
γ = 1 / (√(1 - v2 ) )
so that
v = √(1 - γ-2)
"
It is easy enough to understand the first and last equations but the two middle ones were not so easy.
His (2.51) itself starts
that seems to come out of nowhere and had me thinking.
It all ends well with the gloriously tensorial equation
which allows me to proceed to section 2.6 on An Expanding Universe!
His (2.51) itself starts
γ = -ημν UμVν
"since η00 = -1"that seems to come out of nowhere and had me thinking.
It all ends well with the gloriously tensorial equation
v = √(1 - (Uν Vν)2 )
which allows me to proceed to section 2.6 on An Expanding Universe!
Details are in Commentary 2.5 Metric Rocket 4-velocity.pdf.
I reviewed this June 2021 and realised that this is really an example of Riemann normal coordinates which is super useful! Details in the pdf, I have not modified this very old, rather quaint post.
No comments:
Post a Comment