Talk:Relativistic angular momentum

To add in time

• tangential velocity bounded by c,
• relations to relativistic angular velocity, moment of inertia, and torque, and all their subtitles/surprises,
• 3d Lorentz transformations of components would be instructive (drafted but need to confirm),
• maybe even more on the Thomas precession and Ehrenfest paradox than just in the see also section (or not, can leave for now without loss of continuity)...
• need to pin down the nature of the mass moment: partially its name(s) and symbol(s) but more importantly it's relativistic 3d definition as a component of the AM tensor. The one I wrote is consistent (aside from typos), but there must by subtleties... It can wait a while.
• some illuminating examples of astrophysical applications would help, especially for planetary motion, neutron stars, galaxies, even black holes...
• mention Komar quantities and the Pauli-Lubanski pseudovector?

M∧Ŝc²ħεИ_τlk 06:48, 5 June 2013 (UTC)

Update: the strikeouts above are redundant.

Now I need to rewrite the section Relativistic angular momentum#Spin, orbital, and total angular momentum in special relativity in more prose and less equations (it was taken out of MTW, the section is useful but not too easy to follow). M∧Ŝc²ħεИ_τlk 00:02, 28 October 2013 (UTC)

Factors of 2?

In a couple places where wedge product definitions are used, there are these factors of two running around that don't seem consistent with the cross product definition (or its corresponding wedge product definition) in 3d. Are these in the source material? Muphrid15 (talk) 13:52, 5 June 2013 (UTC)

Yes they're in Penrose's book, and by definition of antisymmetrization. I don't know why N. Menicucci has missed the factor of two. The wedge product and cross product equations are separate and the products are not interchangeable. M∧Ŝc²ħεИ_τlk 14:21, 5 June 2013 (UTC)

Before pointing to Exterior algebra, I'm aware there is no factor of two. In MTW there is also no factor of two. So the definition should read (in components):

$[\mathbf {x} \wedge \mathbf {p} ]_{ij}=[\mathbf {x} \otimes \mathbf {p} -\mathbf {p} \otimes \mathbf {x} ]_{ij}=x_{i}p_{j}-x_{j}p_{i}$

So it seems the factor is just a convention... I was sticking to Penrose because it was just easier to get things started when writing relativistic quantum mechanics and the AM section in relativistic mechanics. MTW is not easy to read for AM in GR unfortunately. Let's just remove them.

Thank you for feedback on this.

Also - I know, in the GA context it should be the outer product, not exterior product. M∧Ŝc²ħεИ_τlk 14:32, 5 June 2013 (UTC)