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May
12
comment Confusion about Lie derivative on metric
far from the most straight-forward way to prove this, but what the heck ;)
May
12
answered Confusion about Lie derivative on metric
May
11
comment Are intergalactic voids inertial frames?
approximate inertial systems are the only kind there are, and this is true for intergalactic voids in the same way as it's true for any other freely-falling systems; you cannot get rid of the non-uniform gravitational influence of the rest of the universe
May
11
comment Are intergalactic voids inertial frames?
Any freely-falling frame is inertial, and an accelerometer will read 0. For systems of finite size, this is only an approximation because of the non-uniformity of the gravitational field, which you can check by letting several bodies fall besides each other: In general, the distances between them will change, even in the absence of external/non-gravitational forces.
May
11
answered If temperature is average KE per particle, and heat is total KE of all the particles, how can molar heat capacity vary?
May
7
comment Can we divide two vectors?
note that the quaternions are a subalgebra of the geometric algebra, where vector division is essentially (up to scale) the same as (Clifford) multiplication; division of two non-parallel non-orthogonal vectors results in a mixed-grade multi-vector with scalar and pseudo-vector components
May
7
comment Can we divide two vectors?
in the geometric algebra induced by a (positive definite) inner product, all (non-zero) vectors have an inverse; it's just not terribly interesting as it's just the same vector, rescaled...
Apr
25
comment Photon “stuck” on the event horizon of a black hole
@FredericBrünner: I did not talk about arbitrary particles - or do you have a particular process involving on-shell decaying gluons in mind?
Apr
16
comment Intuitively what's the relationship between forces and connections?
the idea of parallel transporting particle properties is just how I tend to think about it; if your fiber bundle isn't trivial, you need a notion of parallel transport to compare stuff 'over here' to stuff 'over there'; thus, connections (basically the infinitesimal version of parallel transport) appear naturally; in the Yang-Mills case, the 'stuff' you want to compare depends on some sort of internal symmetry, and we end up with principal connections
Apr
16
comment Intuitively what's the relationship between forces and connections?
@user1620696: in classical Yang-Mills theory, you get equations of motion for particles from force equations (the generalization of the Lorentz-force law); in the Lagrangian formulation, this is achieved via minimal coupling, which requires a generalized charge (in the general case, a coadjoint orbit instead of just a number); this is not the case for gravity; another way in which gravity is different that the gauge symmetries in YM theory are vertical (leaving space-time alone), wheras in case of gravity, they are not
Apr
15
comment Intuitively what's the relationship between forces and connections?
note that assuming ordinary general relativity, gravity is rather different and shouldn't be lumped together with the other forces (this gets somewhat alleviated in the teleparallel formulation); for a hand-wavy explanation why we care about principal connections: because we need to parallel transport particle properties (which relate to internal symmetries)
Apr
13
comment Can parallel universes constitute the missing mass aka dark matter?
see cdms.berkeley.edu/Education/DMpages/FAQ/question32.html - the assumption is that leakage is short-range
Apr
12
revised Questions on redshift
added 2 characters in body
Apr
12
answered Questions on redshift
Apr
11
comment galaxies fading away after time
Yes. Note that this is a technical limitation - if we could detect light of arbitrary wavelengths and intensity, we'd still be able to see them.
Apr
10
comment Does non-matter energy curve spacetime?
see this picture from wikipedia - anything that's in there has an effect on space-time geometry
Apr
10
revised How Are Galaxies Receding Faster Than Light Visible To Observers?
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Apr
10
answered How Are Galaxies Receding Faster Than Light Visible To Observers?
Apr
10
comment How Are Galaxies Receding Faster Than Light Visible To Observers?
actually, recession velocities may well exceed $c$ at time of emission and we may still be able to observe the galaxy; not the Hubble sphere, but the cosmic event horizon places bounds of the observational universe
Apr
10
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