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seen Mar 14 at 14:18

Apr
25
awarded  Enlightened
Apr
25
awarded  Nice Answer
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Mar
27
awarded  Nice Answer
Mar
2
comment Relation between Vector space $V$ and its dual $V^{*}$
@Ben: well, if you do not make the distinction between row- and column vectors, you can do that, but I'd advise against it (vectors are traditionally represented as column vectors, and covectors as row vectors, ie $n\times 1$ and $1\times n$ matrices)
Mar
2
comment Relation between Vector space $V$ and its dual $V^{*}$
@Ben: personally, I thinks this is misleading, in particular the Riemannian case, both in terms of differential geometry (vectors are equivalence classes of curves $\mathbb R\to M$, whereas covectors are equivalence classes of functions $M\to \mathbb R$) and physics (velocities vs momenta)
Mar
2
comment Relation between Vector space $V$ and its dual $V^{*}$
@Ben: it's abuse of notation, and I do not believe I've seen any literature going quite that far; the basic idea is that given a non-degenerate bilinear form (resp. a metric tensor in case of (pseudo-)Riemannian geometry), $V$ and $V^*$ become canonically isomorphic and can be 'identified'; if you prefer, you could introduce a new space $V^\blacktriangle$ isomorphic to both, and a single geometric object from $V^\blacktriangle$ can be represented by elements of $V$ and $V^*$ both; the culmination of that idea is that there are only (4-)vectors with co- and contravariant components
Mar
1
awarded  Nice Answer
Feb
27
revised Is the accelerated expansion of the universe consistent with conservation of energy?
stop mixing densities and totals
Feb
26
revised Is the accelerated expansion of the universe consistent with conservation of energy?
photon energy, not energy density
Feb
26
comment Is the accelerated expansion of the universe consistent with conservation of energy?
quoting said article: “energy is conserved in general relativity, it’s just that you have to include the energy of the gravitational field along with the energy of matter and radiation and so on.” [...] There’s nothing incorrect about that way of thinking about it
Feb
26
revised Is the accelerated expansion of the universe consistent with conservation of energy?
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Feb
26
revised Is the accelerated expansion of the universe consistent with conservation of energy?
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Feb
26
answered Is the accelerated expansion of the universe consistent with conservation of energy?
Feb
25
comment Is it valid to apply Einstein's Relativity to scenarios involving expansion of space?
another relevant paper I just googled: arXiv:0804.3595
Feb
25
comment Is it valid to apply Einstein's Relativity to scenarios involving expansion of space?
@СимонТыран: ultimately, Einstein ;) I do not have any convenient links lying around that make exactly the point I was trying to make, but you could look at arXiv:0808.1081 and meditate over the beautiful graphic in this answer by Pulsar
Feb
25
comment Is it valid to apply Einstein's Relativity to scenarios involving expansion of space?
@СимонТыран: the same thing it does when you cross a black hole's event horizon
Feb
25
comment Is it valid to apply Einstein's Relativity to scenarios involving expansion of space?
@СимонТыран: time will stand still - but not at the Hubble sphere, but the cosmological event horizon
Feb
25
revised Is it valid to apply Einstein's Relativity to scenarios involving expansion of space?
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