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Dec
15
comment How can the universe be flat and have no center if universal mass-energy content is finite?
eg a torus is a closed manifold (ie compact without boundary) and can be flat
Dec
15
comment Feynman-Stueckelberg interpretation
Let us continue this discussion in chat.
Dec
15
comment Feynman-Stueckelberg interpretation
@CuriousOne: or formulated another way: just because humans only remember the past doesn't necessarily mean that the universe has to operate that way
Dec
15
comment Feynman-Stueckelberg interpretation
@CuriousOne: once you have a Cauchy surface, past and future are fixed; sure, you only can send a positron into the past if your grandmother emitted an electron; but in the Wheeler-Feynman absorber formulation of EM, you also only can send a light ray into the future it it gets absorbed eventually by, say, your unborn granddaughter; hence the transactional interpretation of QM, which is philosophically interesting, but sadly worthless from the point of view of theoretical physics
Dec
15
comment Feynman-Stueckelberg interpretation
@CuriousOne: So you are saying that the positrons in my accelerator can actually meet my dead grandmother some time in the past? Yes, but the process is indistinguishable from (actually identical to) your grandmother emitting an electron.
Dec
15
comment Feynman-Stueckelberg interpretation
@CuriousOne: see physics.stackexchange.com/a/17781/6389
Dec
15
comment How does covariant derivative act on Christoffel Symbols?
that makes more sense - I'm guessing this is supposed to be a step on the way towards evaluating the expression $\nabla_\nu\nabla_\mu R^{\beta\gamma}$ and $\nabla_\nu\nabla_\mu R^{\beta\gamma\delta\epsilon}$...
Dec
14
comment How does covariant derivative act on Christoffel Symbols?
the expression is meaningless as the Christoffel symbols do not form a tensor; however, if you use a more abstract way to define your connection (principal connection on the frame bundle, Ehresmann connections), there is a way to have something like the covariant derivative of it: its curvature
Dec
13
comment Classical Mechanics contradicts Conservation of energy?
My answer is No - Your answer disagrees with experiment
Dec
11
comment How far away must a galaxy be for its light never to reach us due to the expansion of the universe?
I'm a bit uncomfortable with redshift as a generic measure of distance - a priori, it only labels events on the lightcone. But I have no idea what the conventions in the community actually are, so saying the event horizon is currently at $z\approx2$ might be perfectly acceptable - it's just that I always have to think twice when such 'distances' get mentioned
Dec
11
comment How far away must a galaxy be for its light never to reach us due to the expansion of the universe?
@Thriveth: Q: What's the redshift of photons we detect right now that were emitted by the galaxy that arrives at the event horizon at current cosmological time? A: $z\approx2$. Q: Where was the event horizon at that time? A: At $35\mathrm{Gly}$ co-moving distance. Q: What will be the redshift of photons that get emitted by that galaxy at current cosmological time? A: $z=\infty$.
Dec
11
comment How far away must a galaxy be for its light never to reach us due to the expansion of the universe?
This is no duplicate: The answer to the posed question is $60Gly$ in comoving distance, which is not an answer to the question it is supposed to be a duplicate of
Dec
11
comment How far away must a galaxy be for its light never to reach us due to the expansion of the universe?
@Thriveth: we don't know if galaxies exist beyond the event horizon because we cannot see them crossing (redshift goes to infinity); this is why I said it's plausible that galaxies exist beyond the horizon, but if there existed as 'cosmic firewall' that incinerated them (yes, it's obviously a silly notion), we'd never know; the event horizon is not at $z\approx2$ - you have to project the purple curve at time of observation onto the yellow light rays at time of emission to map redshift to events
Dec
10
comment How far away must a galaxy be for its light never to reach us due to the expansion of the universe?
@JonathanBasile: clocks that are deeper within a gravity well will appear to be ticking slower, and as far as a distant observer is concerned, an object falling into a black hole will 'freeze in time' at the event horizon; a similar thing happens at the cosmic event horizon; this is one way to interpret redshift: the light has a lower frequency because the time between emission of consecutive wave fronts has increased
Dec
10
comment From affine space to a manifold?
@Heaviside: the topology of spacetime might be incompatible with $\mathbb R^n$
Dec
10
comment From affine space to a manifold?
for geometric or topological reasons (eg curvature, singularities), distance parallelism and single-valuedness may fail in GR and gauge theories like electromagnetism; see also holonomy and monodromy
Dec
9
comment Does entropy have a physical meaning?
shameless self-promotion: see also physics.stackexchange.com/a/127769/6389
Dec
9
comment Intuition and difference between centrifugal force & Coriolis force?
@DavidHammen: So, should we also correct people that claim to 'feel the force of gravity'? After all, the real force is the normal force of the surface of the earth that prevents us from falling freely...
Dec
8
comment Intuition and difference between centrifugal force & Coriolis force?
@DavidHammen: ??? if you sit on a swing ride, your butt will be pressed into the seat; it feels as if there's a force pushing you into it; sure, if you cut the chain, you'll be in free fall and conclude the force was fictious, but you felt it nonetheless
Dec
8
comment Why is quantum mechancis is not content with symmetric operators, but wants self-adjoint operators?
@ACuriousMind: a small note on terminology: Hermitian can be used either as a synonym for symmetric, or as a name for symmetric operators defined on the whole Hilbert space (ie bounded self-adjoint operators) - see eg math.stackexchange.com/a/38395