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seen Aug 26 at 8:22

May
25
answered How do I find the generalized coordinates in a certain system?
May
25
answered Tensor algebra doubt
May
24
comment Linear independence of the Covariant Derivative
@V.Moretti: mixed-rank tensors are perfectly fine elements of the tensor algebra - it's just that they are rarely used (and are of course not relevant to the question at hand)...
May
23
comment Is the universe expanding faster than we could catch up with it?
also note that light we emit right now will eventually reach galaxies that currently recede with $v_{\mathrm{rec}}=c$; while there are regions of space that we no langer can "catch up" to, these aren't simply the ones with recession velocities above $c$!
May
15
comment Which is the most fundamental constant between the Planck constant $h$ and the reduced Planck constant $\hbar$?
just to be clear: $\hbar$ converts between energy and angular frequency - for regular frequence, you need regular $h$
May
14
comment Choices within the many-worlds interpretation
universes split on quantum 'measurement', supposedly a decoherence effect that occurs when a sufficiently isolated quantum system interacts (and becomes entangled with) the messy (and thus essentially classical) environment; if quantum effects are relevant for decision-making processes in the brain, 'conscious' choice (which would actually be random) is correlated with splittings; if the process is largely classical, choice would only be affected through macroscopic effects (eg different memories), and these would probably go with further differences between the universes
May
14
answered What is the relation between General Relativity and Newtonian Mechanics?
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