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seen Aug 26 at 8:22

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
Jun
19
revised Is the edge of our Hubble Sphere within our Cosmic Event Horizon and why?
clarification
Jun
19
answered Is the edge of our Hubble Sphere within our Cosmic Event Horizon and why?
Jun
18
answered Higher order derivatives - Equation of motion
Jun
15
comment A Subtle Connection Between Time Dilation in SR and GR - Why is this so?
that would be my understanding as well
Jun
15
comment A Subtle Connection Between Time Dilation in SR and GR - Why is this so?
related: arxiv.org/abs/gr-qc/0411060
Jun
14
comment If we say the universe is expanding, shouldn't it be expanding relative to something?
note that instead of expanding space, there's a perfectly valid dual description that shrinks atoms - including rulers; you'll also have to do stuff like speed up clocks, make things more massive and weaken gravity to make it work, but on the plus side, you can get rid of the big bang singularity this way...
Jun
13
revised Conservative Forces & Conservation of Energy?
added 1 character in body
Jun
13
answered Conservative Forces & Conservation of Energy?
Jun
11
comment Euler Lagrange equation in different frames
@user139981: it's independent of parametrization, but not independent of geometry: the derivation of the EL equations assumes coordinates that respect the bundle structure, and if you do a transformation that doesn't, you'll get nonsense
Jun
7
comment Didn't anybody see an apple falling before Isaac Newton?
Newton himself apparently claimed to be inspired by falling apples (see eg newscientist.com/blogs/culturelab/2010/01/…); also note that Ibn al-Haytham might have figured out a lot of the story centuries before Newton
Jun
5
comment Can the Berry Connection be derived from a metric?
Also, I think for every connection, there exists a metric for which the connection is a Levi-Civita connection. This is not the case; see eg mathoverflow.net/questions/54434/…
Jun
5
revised Minkowski metric and definition of coordinate differentials?
added 48 characters in body