General Relativity.

Good question. The answer is that not only is mass a warper of space-time, but so is warped space-time! Or as I would put it, both mass and curvature are sources of curvature. The rubber sheet analogy is particularly good in this instance. A mass dropped onto the sheet appears to deform the sheet at all points. In actuality, away from the mass, it is the sheet itself deforming neighbouring points. The deformations are generated locally and there is no action at a distance (no force, attractive or otherwise).

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

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

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.