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16h
comment Link between a topological space and a manifold
@Roopam: they don't exhaust the topology, but generate it
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
awarded  Critic
Apr
10
comment Name this Mulltivariable Calculus Theorem
-1: you're looking for the Jacobian matrix, which is basically the differential; however, $H_\mu$ is not given by the differential - it just agrees with it at point $a$
Apr
9
awarded  Nice Answer
Apr
9
comment Singular wave function
@user119264: it's a valid space, but it won't help - the Lebesgue integral doesn't change if you just remove individual points (or any set of measure 0)
Apr
9
revised Trace in non-orthogonal basis?
use algebraic dual
Apr
9
answered Trace in non-orthogonal basis?
Apr
6
comment What are the spaces over spacetime points in which a field takes its values? Is it always the same?
slight correction: while the typical fiber of the principal bundle is the Lie group, the connection form (aka gauge field) as well its curvature form (aka field strength) take their values in the Lie algebra
Apr
5
comment Dark energy and conservation of energy
@Jim: we do not need global time translation symmetry in GR - the time-like vector field of your choice basically becomes a gauge parameter