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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
Jun
23
comment Curvilinear Coordinates and basis vectors
for each $t$, $\mathbf r=\varphi_t(\mathbf q)$; as $\varphi_t$ is bijective, so is the Jacobi matrix $J_{\varphi_t}$ (this follows from differentiating $\varphi_t\circ\varphi_t^{-1}=\mathrm{id}$); the vectors $\frac{\partial\mathbf r}{\partial q_i}$ are just the columns of $J_{\varphi_t}$
Jun
20
comment Why do we need a metric to define gradient?
@joshphysics: your comment is misleading: if we want to define a vector field dual to the differential (which is what the gradient is), we need to specify an isomorphism between the tangent and cotangent spaces because there's no canonical one; a metric (or more generally, any non-degenerate bilinear form) does just that; covariant derivatives do not enter the picture: the covariant derivative of a function is the plain old differential