B Trying to calculate proper time of worldlines using rotating frames

  • B
  • Thread starter Thread starter Karin Helene Elise
  • Start date Start date
Karin Helene Elise
Messages
1
Reaction score
0
TL;DR Summary
Trying to calculate a proper time of worldlines not using an inertial frame, but a rotating frame.
So, to calculate a proper time of a worldline in SR using an inertial frame is quite easy. But I struggled a bit using a "rotating frame metric" and now I'm not sure whether I'll do it right.

Couls someone point me in the right direction?

"What have you tried?"

Well, trying to help truly absolute layppl with some variation of a "Circular Twin Paradox" not using an inertial frame of reference for whatevere reason.

I thought it would be a bit of a challenge so I made a derivation or approach to do that. But I'm not a 100% sure I did it right.

The point is not some weird umpteenth variation of the twin paradox, but a calculation not using inertial frames.

Thanks in advance,
Well, me.
 
Physics news on Phys.org
Karin Helene Elise said:
Could someone point me in the right direction?
Look up Born Coordinates.
 
Karin Helene Elise said:
I thought it would be a bit of a challenge so I made a derivation or approach to do that. But I'm not a 100% sure I did it right.
The only way for us to evaluate that would be for you to post your calculation. But it might be better for you to look up Born Coordinates first, and then try to do the calculation in those coordinates and see what you get. Then, if you're still not sure, you can post that calculation here.
 

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
View full post »

Thread 'Describing the Big Bang'

I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
View full post »

Similar threads

I Is time dilation a real effect?
2
Replies
54
Views
3K
B My paraphrased explanation of the Twin Paradox
Replies
24
Views
4K
I Understanding Spacetime simultaneity in twin paradox scenarios
Replies
35
Views
3K
I Non-Inertial Relativistic Dynamics
Replies
18
Views
1K
B Metric Line Element Use: Do's & Don'ts for Accelerated Dummies?
Replies
29
Views
2K
I Understand Spacetime Diagrams: Calculating Proper Time
Replies
20
Views
3K
I Are Geometric Points Affected By Forces?
Replies
3
Views
1K
B Time dilation and the reference frame of the vacuum
Replies
17
Views
2K
I Can time run backwards in an accelerating frame?
3
Replies
125
Views
7K
B Time Dilation on Rotating Disk: Clocks on Disk Perspective
Replies
21
Views
3K

Hot Threads

Recent Insights

Back
Top