General Relativity Stuff · 6:39pm Nov 26th, 2015
Vectors by Pangbot, awesomeluna, Dipi11, CutsieArt
This week is the 100th anniversary of Einstein’s theory of General Relativity. At least according to some science news outlets. Others say the centenary was earlier this year, and some will mark it next year depending on which particular Einstein moment you consider the birth of the theory. Time is relative.
So what is General Relativity? Let’s hear it from a panel of pony experts:
General relativity is a beautiful theory which describes gravity using geometry. In classical physics, gravity is a force between two massive objects. But in GR it is the shape of space. Massive objects like the sun warp space so objects fall towards them as they move along the path of least resistance in a curved space.
This means gravity can bend the path of light. We see this when the light from distant stars is distorted by an intervening galaxy.
Space and time are intrinsically connected. Where spacetime is warped, time will run slower. So a clock on the summit of Canterlot mountain will run very slightly faster than one in Ponyville. Time being a big ball of wibbly-wobbly timey-wimey stuff.
The universe is a great big expanding mass of jelly which we can squash and stretch and twist and make into black holes and wormholes and stuff!
Further explanation by David Tennant:
Related blog post: It's About Time Dilation
That video is pretty good. I have such a Tennant fetish (again) after watching Jessica Jones. He's also my favorite Doctor, so forgive my bias.
Trying to understand Gravity without Quantum Mechanics, is like trying to understand water without water molecules, although there have been recent advancements in understanding the flow, and solidification of macroparticles such as sugar and grain, using simple functions, that have words such as chaotic flow in occasionally.
It also doesnt help that asking how water molecules flow is actually the wrong question, as the motion of induvidual molecules isnt flow, it heat. Which can behave as a fluid, when nothing actually moves but energy and varying motions.
One experiment so far suggests that the mass energy of the graviton is about 700 Hz. This is such a tiny mass energy, that if the graviton weighed 1 kg, a bag of sugar, the next most massive particle, the neutrino, would weigh the mass of the sun.
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Trying to understand gravity without quantum mechanics is what we have been doing since the first theories of gravity were invented. And GR has done remarkably well. We presume there is a theory of quantum gravity, but no attempts to find it have been successful and, from an experimental point of view, it is still in the realm of fairy tales.
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Its like trying to measure a rubber sheet with a rubber ruler. You cant see the gaps in spacetime, because you cant see the gaps in the ruler.
Also, if gravitational waves cause distortions in spacetime, and we can measure the Bending of light around the sun, why does LIGO etc use time of flight, where the speed of light is Always a constant, instead of a deviation of geometrical angles, that is the sum of the triangular light path is greater or less than 180 degrees? If they made the pathlength exactly one half wavelength longer, alternate loops would cancel out, which means any remaining signal is noise? I also personally like beat frequency analysis, given sound cards are cheap, are sensitive to parts per hundred million and sample rates to hundreds kilohertz. sum over periods of time for low frequency and you get even better S/N.
Seen the recent news about the pair of Gallileo navigation satelites launch fault, going into eliiptical orbit? the variation makes the overall system even more sensitive to GR variations. you would think something would vary in nonlinear spacetime at parts per million. km/s variations?
I like that video's graphic of an object's gravity curving of spacetime in 3d as opposed to the usual ball on a sheet visual normally used.
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imgs.xkcd.com/comics/teaching_physics.png
Pinkie Pie is is bending timespace? Seems legit.
I wonder whether the quantum foam is more dense near the surface of planets. Or in the center of planets/stars, since there's plenty of empty space within the atoms.
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Given that we never observed any difference between travel time of neutrinos and light, the Lawrence-Contraction of neutrinos must be in the millions, so their rest-mass must be minuscule. Gravitons must have unbelievably low masses.
It is interesting to model different numbers of spatial and temporal dimensions:
0 temporal dimensions, and nothing happens or everything happens at once.
> 1 temporal dimension, and one ends up with an acausal mess (for timetravellers, it is useful to distinguish the time of chronometer on the timetraveler from the time of the spacetime coordinates of the spacetime the timetraveler currently visits).
With < 3 spatial dimensions one has no escape (all orbits are closed). With > 3 spatial dimensions, all orbits either escape to infinity or lead to collisions, with no closed orbits. Only with 3 spatial dimensions do we have orbits which escape to infinity, orbits which are closed, and collisions.
We also have a nice pattern about the interior of n-spheres:
(τ(d-1)/d))r^d
Where d is the number of spatial dimensions.
2D:
(τ/2)r^2
3D:
(2τ/3)r^3
4D:
(3τ/4)r^4
5D:
(4τ/5)r^5
6D:
(5τ/6)r^6
7D:
(8τ/7)r^7
8D:
(7τ/8)r^8
9D:
(8τ/9)r^9
Some ponies would prefer to write this out in terms of half Tau, but the sometimes cancelling and sometimes not cancelling powers of 2 obscure the pattern in the series:
(2π(d-1/d))r^d
2D:
πr^2
3D:
(4π/3)r^3
4D:
(3π/2)R^4
5D:
(8π/5)r^5
6D:
(5π/3)r^6
The Half-Tau Notation obscures the underlying pattern.