General Relativity.

Unfortunately, I doubt this really brings him any further along. As long as he is thinking of gravity having to be a force, he isn't thinking in the language of curved spacetime. There isn't any force which is curving spacetime -- the curvature of spacetime is a different language in which one expresses one's gravitational theory, as an alternative to a language of gravitational "fields" and "forces." Well, not exactly. If you have a static solution to Einstein's field equations (i.e., the ten equations represented by G=8(pi)T), then there are no gravitational waves. Without gravitational waves, there is no gravitational energy being transmitted. No gravitational energy means no addition to the stress-energy tensor T. Honestly, analogies might be nice, but beyond a certain point, I would recommend picking up the math. General Relativity is a little tough as it is expressed in the language of pseudo-Riemannian geometry. But if one can pick up differentiation, partial differentials, and matrice mathematics, then one can pick up the tensor mathematics of General Relativity (although I am not sure how many people are able to follow through Einstein's derivation of his "field" equations). However, Special Relativity (essentially what corresponds to classical mechanics without gravitation) can be understood without the aid of anything more than algebra and matrices.

Hi Tim, thanks for the comments.I haven't got time to address the points here at the moment but I'll get back later.BTW, I try not to be into credentials, but just to save time and awkwardness I'll just say I used to be a member of a leading relativity group This message has been edited by cavediver, 12-16-2005 05:15 AM

You are quite correct, and it is hard to accept just how much I am forgetting these days! You are describing the mathematics of Newton-Cartan theory. I haven't read or even considered this in well over a decade. You won't see it in physics approaches to GR, but it is the undelying mathematical apparatus. Try Geometrical Methods of Mathematical Physics by Bernard Schutz... it emphasises applications to GR and SR. Or Nakahara is an awesome book, with far more physical basis and depth, but with an equivalent (initially scary) depth to the mathematics Look! It assumes some familiarity with GR and QFT concepts (3rd yr undergrad/intro grad) No, I'm not describing Twistor theory although it too depends totally upon the mathematics of bundles. You can check this out in the two volume Penrose and Rindler... not that I would be so mean as to advise this

Beautiful!Another physics geek like myself. In my case, I taught myself calculus a little early just so that I could follow through the derivation of the Schwartzchild solution. Didn't get much further than that, though, then turned my attention to Quantum Mechanics, but it has been a long time for me as well. In college I ended up into philosophy, and now I am a computer programmer. Currently getting into evolution as much as I can in my offtime, though.Anyway, I will have to check out the geometric approaches. Not sure how far I will get, or when I will be able to get to them, but they do sound interesting.

Yeah, I didn't think that describing it as curved could suffice. Thank god the difficult version wasn't explained... And to think I blamed it on my teacher. But of course!To any of you who didn't catch the sarcasm of my previous statements, I no longer have any idea what's going on. In actuality, my brain exploded (true story) when I read that first line. Still, I'm a little jealous of the genius level of physics knowledge displayed here, so I'm hoping that either of you might be able to recommend a few sources so that I might be able to better understand these concepts in the future (however distant).

Given your comments, I would probably recommend Einstein's Universe by Nigel Calder. There's bound to be a million similar books by now, but check Amazon out on this title and look at the similar offerings. His book will give a good grounding in the concepts of Special and General Relativity. It won't swamp you with stuff outside of these two theories, which will keep you focussed and you should learn something.Once you've got through that you can go two ways (well, a third would be to stop, but that's boring). You can broaden yourself into the full arena of modern fundemental physics with stuiff like Hawking's Universe in a Nutshell. This should be ok after Calder's book.Or you can delve deeper into SR and GR but it will require mathematics and lots of patience. I'm tempted to suggest Gravitation (:eek in this case, but SG may tell me to get a grip, in which case it would be his favourite: Schutz, or mine: D'Inverno.

Hi Tim, Ok, curvature as a source of curvature doesn't involve T and doesn't require dynamic solutions. All of my favourite solutions are vacuum: T=0. So G=8(pi)T reduces to just R=0... so much nicer and gets rid of all that nasty physics side of the equation. You're just left with maths Pure Schwarzschild is a vacuum solution and is static but as you know has considerable curvature. What is the source of this curavture? Itself. That is just a result of the non-linearity of the equations. (of course you can generate a non-vacuum Schwarzschild with a non-zero T... As you know, it is the solution outside an uncharged, non-rotating spherical mass)If we move to quantum gravity, this means the graviton self-interacts, like the gluons and the Weak bosons. The photon is the quantum of the LINEAR Maxwell equations, so photons don't self-interact. It's a good job as otherwise there would be such thing as sight!The Linearity relates to EM being an Abelian gauge theory, where-as Gravity, Strong and Weak are non-Abelian gauge theories.This message has been edited by cavediver, 12-17-2005 05:51 PM

The stress-energy (or in the case of the Schwartzchild solution, the mass) is the source of the curvature. Just as the electric charge is not the same thing as the electromagnetic field, but is the source of the electromagnetic field, the stress-energy/mass is not the curvature, but is the source of the curvature.As for myself, I kind of like the Friedman solutions. Yet the strong and the weak forces have been integrated, whereas we have yet been unable to cancel out the infinities in the case of gravity. I forget exactly what the difference is.However, gravitational waves are generated only in the case of dynamic solutions. For example, the Kerr solution is the solution for a black hole with angular momentum, but in the Kerr solution, nothing actually changes, therefore no gravitational waves are produced, whereas with two neutron stars revolving around one-another, gravitational waves are produced, and therefore energy is lost from the system in the form of gravitational waves, resulting in the death spiral where they will ultimately collide.See the following:Binary pulsar PSR B1913+16
compiled by Wm. Robert Johnston
last updated 30 August 2004
Binary pulsar PSR B1913+16No gravitons are emitted in the case of the non-dynamic solution, but when the solution is dynamic, gravitational waves are produced, in which case gravitons are produced which result in the loss of energy. The gravitons are the energy, just as photons are energy, and the energy will be equivilent to mass, resulting in additional spacetime curvature.

Can you then explain the vacuum solution Schwarzschild solution where T=0? Or any other non-flat vacuum solution? Schwarzschild does not require mass... This is what I was trying to explain: they are VERY different theories. Maxwell is linear, where-as GR is non-linear. In Maxwell, the field is charge-less and hence does not self-interact. In non-linear theories, the fields also carry charge: gluons have colour, W and Z carry Hypercharge... and gravity gravitates. True, but you have to understand that curvature is also a source of curvature. You do not need stress-energy to get curvature. True, you need a quadrupole moment to generate gravitational waves. But that is irrelevant to the discussion regarding curvature generating curavture. The Kerr solution is another vacuum solution.Also, gravitons are not only related to dynamic solutions and gravitational waves. They are also the quantum element of static solutions.