3,573 reputation
1614
bio website
location
age
visits member for 2 years, 4 months
seen 44 mins ago

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
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
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
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
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
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
Apr
5
comment Dark energy and conservation of energy
@JohnRennie: you can read more of Philip and Luboš in the comments of Philip's blog posts on energy conservation in GR ( blog.vixra.org/2010/08/06/energy-is-conserved blog.vixra.org/2010/08/08/energy-is-conserved-the-maths blog.vixra.org/2010/08/17/energy-is-conserved-in-cosmology )
Apr
5
comment Dark energy and conservation of energy
@JohnRennie: I disagree with energy not being conserved in FLRW cosmology; the relevant papers are linked from this comment
Apr
5
comment Dark energy and conservation of energy
Friedmann-type universes have zero total energy - the positive contributions by matter and dark energy are cancelled by the negative contribution due to gravitational energy
Apr
4
comment How can water evaporate at room temperature?
@JohnRennie: I expanded the answer and made it community wiki - feel free to improve upon it as yous ee fit...
Apr
2
comment Is the universe flat?
@user12262: see en.wikipedia.org/wiki/Torus#Flat_torus
Mar
24
comment What is the intepretation of the electromagnetic tensor?
geometrically, it's a Lie-algebra valued 2-form representing the curvature of a principal connection and thus describes the obstruction to integrability of the horizontal subbundle; depending on your mathematical background, I suspect this comment is rather unhelpful...
Mar
24
comment Many times speed of light
@AlanSE: no, I do mean that they had recession velocities $> c$ at time of emission; basically, the Hubble sphere is arbitrary - as long as we don't move beyond the event horizon, we're good to go
Feb
24
comment How far could the LHC “fire” a particle
@Zephyr: the value I was getting at was at solar system galactic radius; you're right that the relevant quantity is actually the root of the sum of the appropriate escape velocities (earth from surface, sun from earth orbit, milky way from solar system) squared, but the first two are negligible
Feb
24
comment How far could the LHC “fire” a particle
LHC protons are ultrarelativistic and should basically be able to escape anything that's not a black hole; as to the escape velocity of the Milky Way, according to Wikipedia it's less than that of the sun and thus well below the speed of light (though I cannot confirm right now as it's nightime where I'm sitting ;)).