Christoph
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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