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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
Jun
20
comment If and how are the Coriolis force and gravitation related?
it is indeed true that general relativity doesn't really differentiate between inertia and gravity
Jun
20
revised Why do we need a metric to define gradient?
added 48 characters in body
Jun
20
answered Why do we need a metric to define gradient?
Jun
19
revised Is the edge of our Hubble Sphere within our Cosmic Event Horizon and why?
fix redshift
Jun
19
comment Is the edge of our Hubble Sphere within our Cosmic Event Horizon and why?
damn - I forgot that in Pulsar's figure, redshifts need to be projected onto the light rays to associate them with events - the actual redshift is not $3$, but somewhere between $1\dots3$
Jun
19
comment Is the edge of our Hubble Sphere within our Cosmic Event Horizon and why?
next item on the list: figure out if and why any sphere of constant $v_\text{rec}\gt c$ will intersect the event horizon
Jun
19
comment Is the edge of our Hubble Sphere within our Cosmic Event Horizon and why?
@ChrisWhite: see edit - it might be a bit more clear now