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Dec
10
revised How far away must a galaxy be for its light never to reach us due to the expansion of the universe?
added 331 characters in body
Dec
10
answered How far away must a galaxy be for its light never to reach us due to the expansion of the universe?
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
revised Origin of momentum. Noether's theorem
deleted 2 characters in body
Dec
9
answered Origin of momentum. Noether's theorem
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
answered Why is quantum mechancis is not content with symmetric operators, but wants self-adjoint operators?
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
Dec
7
comment Interpretation of a singular metric
to quote a comment I made yeterday: a GR singularity is not necessarily topological: possibly, it's 'just' a metric degeneracy; @CristiStoica probably has something to say about that...; the gist: the FLRW singularity is 'quasi-regular', the densitized stress-energy-momentum tensor remains smooth and the Weyl curvature hypothesis holds
Dec
7
comment Gravity is curved geometry: A fact of nature or model-dependent interpretation?
@MBN: the name 'teleparallel equivalent of GR' was probably chosen for 2 reasons: first, to distinguish it from Einstein's attempt at a unified theory; second, because it looks that way if you only take the local equations of motion derived from an action principle into account
Dec
7
comment Gravity is curved geometry: A fact of nature or model-dependent interpretation?
@MBN: they are locally equivalent, where this particular notion of 'local' is big enough to cover the observable universe, so it's 'good enough' in practice; btw, if the manifold is not simply connected, a flat connection doesn't necessarily mean the manifold is parallizable - but you're right that the claims of 'equivalence' are perhaps a bit too enthusiastic (the physics literature I have read is a bit light on such details); in case of bi-metric theories, you need not necessarily choose Minkowski space as your background - de Sitter space would probably be a convenient choice as well
Dec
6
awarded  Enlightened
Dec
6
awarded  Nice Answer
Dec
6
comment Integration and Differentiation of Proper Time
if $P:[a,b] \to M$, then $\tau = \int_a^b \sqrt{\sum_{\mu,\nu}g_{\mu\nu}(P(\lambda)) \cdot \mathrm dx^\mu(\dot P(\lambda)) \cdot \mathrm dx^\nu(\dot P(\lambda))} \,\mathrm d\lambda$
Dec
6
comment Symplectic Structure without predefined Hamiltonian
note that because you chose to consider the problem in velocity phase space instead of momentum phase space, the symplectic form depends on mass; in momentum phase space, the symplectic form is what you end up with if you forget about the geometry of the cotangent bundle and just keep the bare minimum you need to transform forms to vector fields, enabling the derivation of evolution equations from potentials; it's less about physics and more about geometry
Dec
6
comment Gravity is curved geometry: A fact of nature or model-dependent interpretation?
@Sofia: is unifying gravity and electromagnetism really more unreasonable than electroweak unification? anyway, I was talking about the teleparallel equivalent of GR, which does not include electromagnetism; see the preprint (PDF) of this book for details on teleparallel gravity and this article for a different perspective
Dec
6
answered Gravity is curved geometry: A fact of nature or model-dependent interpretation?