The discussion revolves around how General Relativity challenges the classical understanding of elliptical orbits as described by Newtonian physics. Participants explore the implications of the curvature of spacetime on the positions of celestial bodies and the bending of light, examining both theoretical and conceptual aspects.
Participants express a range of views, with no clear consensus on the implications of General Relativity versus Newtonian physics. Some agree on the need for further clarification of concepts, while others maintain differing interpretations of the effects of light bending and the positions of celestial bodies.
Participants highlight limitations in understanding the embedding diagrams and the assumptions underlying classical physics versus General Relativity. The discussion remains open-ended regarding the implications of these theories on celestial mechanics.
The horn doesn't depict relative positions in space, rather it is an embedding diagram which shows the curvature of a 2D slice through 3D space. Have you ever heard of the book Flatland? Imagine a species of 2-dimensional beings living on 2D surface which was actually curved, like a trampoline with a depression in it. Since they can only think 2-dimensionally they can't really visualize what a curved 2D surface would look like (just as we can only think 3-dimensionally and can't visualize what curved 3D space would look like, much less curved 4D spacetime), but if you imagine taking a vertical cross-section through the curved trampoline (the intersection of the trampoline's surface and a 2D plane at a right angle to it), you'd get a curved 1-dimensional line which the 2D beings could visualize. The idea of an embedding diagram is like that but with the dimensions raised by one, if we take a 2-dimensional slice through 3D space--which to our 3-dimensional minds would just seem like a flat plane--the embedding diagram would show the true curvature of that slice.luckis11 said:Seeing the horn (which is like a water vortex) of General Relativity, it seems that the position of the Sun is at the bottom of the horn and the planets rotating somewhere above. Doesn't that disaggre with Newton's ellipses on almost the same plane? Any link explaining this?
If it was just a matter of the bending of light, and the Sun was literally at a lower position in ordinary Euclidean 3D space rather than at the center of a well in curved space, then wouldn't that mean probes sent to go into close orbits around the Sun would miss it or something? Anyway if you rejected relativity I don't see what reason you would have to accept any version of the "horn" picture, wouldn't you just accept that the Sun and the planets (aside from Pluto) lie in pretty much the same plane?luckis11 said:Could it mean that (e.g. rejecting Relativity and accepting only the bending of light), that the Sun is positioned at the bottom of the horn and because of the bending of light it seems to be at the mouth of the horn at the same plane as the other planets?
Well, here's some good introductory discussions:luckis11 said:First of all, I cannot reject something (General Relativity) that makes no sense to me. If it did, I wouldn't had made such elementary questions. I do understand quite a bit Special Relativity, but General relativity, I do not.
In what specific way does classical physics reject it? Even Newtonian gravity predicts bending of light, just by a different amount than general relativity, for example.luckis11 said:Classical physics alone reject it, so it doesn't really matter whether I reject it or not, regarding getting answers.
Why do you think I meant that? Aside from Pluto the planet's orbits do lie in nearly the same plane in classical Newtonian physics, which is why I said "if you rejected relativity ... wouldn't you just accept that the Sun and the planets (aside from Pluto) lie in pretty much the same plane?"luckis11 said:I guess you mean "rather than at the same plane".
In general relativity we aren't deluded as to where the Sun is either, as I said it is not any "lower" than the planets in regular 3-dimensional space, positions in an embedding diagram don't correspond to positions in 3D space (did you understand my explanation about embedding diagrams showing the curvature of a 2D cross-section of 3D space? Did you look at the discussion of embedding diagrams in the page I linked to?)luckis11 said:It seems you are saying that, in non-relativistic physics, the bending of light is not so great as to dillude us regarding where the Sun is. Then how is General Relativity prooved?
luckis11 said:The horn at the 4-d diagram has something to do with the bending of light, correct?
Some light from where about the Sun iis, bends till it reaches the Earth. Then the light of the Sun itself does not bend? If it bends then how can the Sun be positioned where it seems to be positioned? It would be positioned where it seems to be positioned if its light does not bend at all but travels in a straight line.
Light coming directly from the Sun doesn't bend in ordinary 3D space, no. It's coming out in a straight line from the Sun, why would it bend left/right or up/down relative to that path when neither would take it any closer to the Sun? Instead of light think of some solid body like a comet in Newtonian gravity, if it was traveling through deep space in a straight line that didn't pass through the center of the Sun then as it approached the Sun its path would be bent in the direction of the Sun due to gravity, but on the other hand if it was falling directly towards the Sun then the gravity would just accelerate it in the same direction but it wouldn't change the direction of its path through space.luckis11 said:The horn at the 4-d diagram has something to do with the bending of light, correct?
Some light from where about the Sun iis, bends till it reaches the Earth. Then the light of the Sun itself does not bend? If it bends then how can the Sun be positioned where it seems to be positioned? It would be positioned where it seems to be positioned if its light does not bend at all but travels in a straight line.
JesseM said:Well, here's some good introductory discussions:
http://www.einstein-online.info/elementary and http://www.einstein-online.info/spotlights
http://www.upscale.utoronto.ca/PVB/Relativity.html
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/index.html
He says on the page that this derivation is for the special case where the object is already moving at very close to light speed so the force "cannot appreciably change the speed of the body because it is going just about as fast as it can. So all the increase of momentum = mass x velocity of the body is manifest as an increase of mass." Then at the end he says "This derivation is for the special case at hand and further argumentation is needed to show that in all cases a mass m and energy E are related by Einstein's equation."Neandethal00 said:Your last site proves E=mc2 this way. Do you really want us to take him seriously?