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Jul
8
comment Why does a flat universe imply an infinite universe?
For example the surface of a torus is flat but finite slight correction: the surface of a torus can be flat, but the generic 2-dimensional torus embedded in $\mathbb R^3$ isn't; Wikipedia informs me that it cannot be flat if the embedding is at least $\mathcal C^2$, but an explicit $\mathcal C^1$ embedding has been found rather recently (April 2012); see eg gipsa-lab.fr/~francis.lazarus/Hevea/Presse/index-en.html for some pictures
Jul
5
comment Equivalence between Hamiltonian and Lagrangian Mechanics
so we just vary $v,p$ independently and do the integration by parts on $\delta\dot q$ as usual to end up with $\delta S = \int(\dot q-v)\delta p + (\partial L/\partial q - \mathrm dp/\mathrm dt)\delta q + (\partial L/\partial v - p)\delta v + \text{boundary terms}$; I'll have to meditate on that for a bit...
Jul
5
comment Equivalence between Hamiltonian and Lagrangian Mechanics
note that due to its dependence on $\dot q^i$, $L_E$ is not a function on some (extended) phase space, but a functional(?!)
Jul
5
answered What predictions can a quantum gravity theory make?
Jul
4
comment What predictions can a quantum gravity theory make?
Why no mention of BICEP2 - or do you expect their discovery to turn to dust?
Jul
4
comment What are the alternative theories of dark energy? ($w \neq -1$)
Hajdukovic tries to explain dark matter and energy both by gravitational vacuum polarization due to repulsion between virtual matter and anti-matter particles; in arXiv:1201.4594, he calculates a current $w_\text{eff}\approx -0.99$, which will eventually approach $w_\text{eff}=-1/3$
Jul
3
comment Inflation in a closed universe or a stage 1 multiverse?
Just having edited the question, perhaps going with ininite and finite instead of open/non-compact and closed/compact would be even clearer?
Jul
3
revised Inflation in a closed universe or a stage 1 multiverse?
better link, improve terminology: flat -> open
Jul
3
comment Inflation in a closed universe or a stage 1 multiverse?
the difference between infinite and finite but very large is extremely marked as far as Tegmark's musings go: if I remember the one talk I watched about his stuff correctly, he thinks about identifying Everett's (or rather DeWitt's) many worlds with causally disconnected parts of an inflationary universe, which only works if the multiverse is big enough to realize all branches of the (no-longer-quite universal) wavefunction
Jul
3
comment E&M and geometry - a historical perspective
@gn0m0n: sure, no need for gauge theory just to use differential forms; but the question (or at least its title) was concerned with EM and geometry - and geometrically, vector potential and field strength are not just some arbitrary forms, but principal connection and corresponding curvature
Jul
3
answered E&M and geometry - a historical perspective
Jul
2
revised Global vs. local gauge group in mathematical sense - physics examples?
added 58 characters in body
Jul
2
answered Global vs. local gauge group in mathematical sense - physics examples?
Jul
1
comment Difference in calculated and simulated ellipsies
drawEllipse() contains the line b=a * Math.sqrt(1 - o.e) that looks suspicious...
Jun
27
revised Understanding and deriving ellipsoidal coordinates geometrically
fix coordinate trafos
Jun
25
comment Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity?
shouldn't we use $a_c = (r-r_e)\omega^2=GM(r-r_e)/r^3$ to account for the different orbital velocity of black and white dot?
Jun
25
revised Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity?
more details
Jun
25
answered Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity?
Jun
25
comment Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity?
@JohnRennie: is this really correct? the center of gravity is in free fall, but we are not: if we were, we'd drift apart
Jun
25
comment Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity?
you can also lose (or gain) weight by travelling around the world