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Nov
20
comment Why is the value of the action integral in general relativity the same on all regions that are homologous?
He's just using the residue theorem: en.wikipedia.org/wiki/Residue_theorem
Nov
20
comment “Falling upward” - how far you have to be from Earth to start falling to the Moon?
To add to what the others are saying, ~300,000 km is about 85%, or 17/20, of the distance from Earth to the Moon. Just to put that big number into perspective :).
Nov
20
comment Root of $i$, which one to take?
@Jiang-minZhang He means that, by convention, the $\sqrt{}$ symbol means only the positive root. Even though there is a positive and negative solution to $z^2=i$, just as there is with $z^2=n$, by definition we take $\sqrt{i}$ to mean the positive root, just like $\sqrt{n}$ is the positive root.
Nov
20
comment Abstract concept of wave propagating on a string
You've actually come very close to recognizing the Heisenberg uncertainty principle. If a wave packet is very localized (i.e. near definite position) then properties like frequency and wavelength don't make much sense. In the reverse case, when the wave packet is very spread out over space, the wave will have a well-defined wavelength but undefined position. In quantum mechanics the momentum of a particle is inversely proportional to its wavelength, which is only defined if the packet is spread out over space. (I.e. the more you know about momentum, the less you know about position.)
Nov
20
comment Energy of a charge inside spherical conducting shell
The potential energy while it's inside the sphere is $qV_0$. At infinity the potential vanishes. By conservation of energy the work done in bringing the charge to infinity must be $W=qV_0$. (Otherwise where did the energy go?)
Nov
20
comment Problem in deducing the equations of motion using indefinite integral
As for the first part of your question, $f = \int df$ for the same reason that $x = \int dx$.
Nov
20
comment Why we don't integrate intital velocity in body cast equation?
$\int V_0 sin(\alpha) dt = V_0 sin(\alpha) t$
Nov
19
comment The virtual particles are only a fictive tool in equations? DO they exist or DON'T? And if they exist, why do we call them VIRTUAL?
@Sofia Why the downvote? Nothing I said is inaccurate.
Nov
18
comment Questions after watching the movie Interstellar
For a body in orbit the factor just becomes $\sqrt{1-3r_s/2r}$ because $v^2=GM/r$.
Nov
18
revised Movie Interstellar - Question about Escape Velocity
added 6 characters in body
Nov
18
comment Advantage and disadvantage of weak field approximation
Linearized gravity is basically just electrodynamics with a tensor field instead of a vector field (i.e. $h_{\mu \nu}$ instead of $A_\mu$). With appropriate gauge choice the field equations reduce to a wave equation similar to Maxwell's equations for the four-potential.
Nov
18
revised Movie Interstellar - Question about Escape Velocity
added 77 characters in body
Nov
18
comment Movie Interstellar - Question about Escape Velocity
@CarlWitthoft His question is perfectly fine, and the physics here is perfectly well-defined. I don't understand your objection.
Nov
18
answered Movie Interstellar - Question about Escape Velocity
Nov
18
comment Most general second-rank symmetric tensor in Einstein theory
You could also include higher-order terms, i.e. terms like $g_{\mu \nu} R^2$, $g_{\mu \nu} R^{\alpha \beta} R_{\alpha \beta}$, etc. But once you include those you aren't talking about GR anymore.
Nov
18
comment What Would Negative Mass Do To Spacetime?
Newton's inverse-square law is equivalent to general relativity in the limit where everything is moving slowly and the gravitational field is weak. So, the first (and easiest) thing to check would be to see what happens if you plug a negative mass into Newton's gravity law. The answer, of course, is repulsive gravity. I.e. a negative mass would be repelled by ordinary matter.
Nov
17
comment Derivation of correction to canonical stress energy tensor due to addition of total divergence to Lagrangian
How about these: research.physics.illinois.edu/Publications/theses/copies/… research.physics.illinois.edu/Publications/theses/copies/…
Nov
17
comment How is strong time dilation consistent with weak tidal forces?
No problem. Don't worry about the points, they don't particularly matter to me.
Nov
17
comment How is strong time dilation consistent with weak tidal forces?
Actually (axial) tidal forces fall off as $1/r^3$ to leading order. But that just highlights your point further.
Nov
17
comment How is strong time dilation consistent with weak tidal forces?
A body in orbit doesn't feel the force of gravity, save tidal forces. That's why astronauts in the ISS are weightless! :)