Time Dilation - Angular Momentum - Mass

kmarinas86
Messages
974
Reaction score
1
Angular momentum must be conserved. Does that mean that if a particle travels at relative velocity to an observer that the decrease in apparent spin rate will be offset by the increase in mass causing the angular momentum to be constant?
 
Physics news on Phys.org
kmarinas86 said:
Angular momentum must be conserved. Does that mean that if a particle travels at relative velocity to an observer that the decrease in apparent spin rate will be offset by the increase in mass causing the angular momentum to be constant?

I think you're confusing the words "conserved" and "invariant". When a quantity is conserved, it maintains the same value at different times in the same reference frame. When a quantity is invariant, it has the same value when measured from different reference frames. Angular momentum is conserved but I don't think it's necessarily invariant. Certainly linear momentum is not invariant, although it is conserved.
 

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 »
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 '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 »

Similar threads

A How to show spin ##= \pm 2/\omega## for a circ-polarized gravity wave
Replies
0
Views
1K
I Do any real macroscopic black holes have a singularity?
Replies
11
Views
2K
I Meaning of the invariants built from the angular momentum tensor
Replies
1
Views
1K
I Effective Potential & Curved Spacetime: Angular Momentum Effects
Replies
13
Views
2K
B Is time an illusion?
Replies
5
Views
2K
A Units of Kerr Understanding Mass & Angular Momentum
Replies
3
Views
1K
I General Relativity: Angular Momentum, Gravity & Questions
Replies
7
Views
2K
I Kinetic vs Gravitational Time Dilation: Perceived Speed
Replies
5
Views
2K
I Measuring Charge & Angular Momentum in Black Holes
Replies
7
Views
2K
I Special Relativity: 3 Objects, Momentum & Time Dilation
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top