□h=-16πT

Apparantly I have handwriting like a doctor's, I don't think it's quite bad as that though, personally.

For a system whose motion is conservative the Hamiltonian gives the total energy of the system. The importance of the Hamiltonian is that it allows one to demonstrate any conservation laws for the system. For example a conservative system has (follows from Hamilton's equations and the "total derivative") dH/dt=0 and so H=constant, i.e. the total energy of the system is conserved. Noether's (sp?) theorem states that for every coordinate the Hamiltonian is independant of there exists a conservation law for it (or at least to give the theorem roughly). From Hamilton's equation one may also derive the equations of motion for the system.

Lagrangian function: L=T(x',y',z') - V(x,y,z) [primes denote time derivatives] Only the kinetic energy is an explicit function of the time derivatives and so partial differentiation of the lagrangian with respect to these is the derivative of the kinetic energy. The kinetic energy of a body under the influence of a conservative force is quadratic in the time derivatives and so upon differentiation we end up with the momentum of the system. For example in Cartesian coordinates 1/2(mx')^2 -differentiate with respect to x'-> mx' which is the equation for momentum. Using a few more examples of coordinates or just a little bit of quick thought it's simple to see how this can be generalised.

I have a GCSE in german.

Bare in mind that that definiton is for manifolds whose connection is torsion free.

Stuff like Incubus, Rage Against the Machine, Jimmy Eat World, Queens of the Stone age, Feeder etc. etc. I like loads of bands from different genres, not dance and shit like that though.

I started getting that the other day.

I am, any particular reason why you wanted to know, Rev?

Yeah, they're all excellent books. I tried to choose those which were the most lucid and informative so that I could learn those subjects of most interest and build up to QFT etc. Anybody know any good texts on QFT and string theory? I assume from the thread title that this thread was aimed at me, Rev. Any particular motive behind your curiosity?

Ok, so I didn't get it written, sorry. How's your revision doing though?

Material I'm reading at the moment: "Classical Mechanics"- TWB Kibble "Geometrical methods of Mathematical Physics"- B. Schutz "A first course in General Relativity"- B. Schutz "Mathematical methods for Physics and Engineering"- Riley et al "Lebesgue Integration and Measure"- Weir "Real and Complex Analysis"- Rudin (I've almost finished the 3rd and 4th books in the list.) I'm also doing some revision of Abstract Algebra; after which I'm going to move onto some advanced Eletromagnetism, Quantum Mechanics (for which the last and first books are principally a requisite) and then advanced GR. So basically I'm teaching myself physics undergrad course with some grad stuff thrown in. Want to know anything else?

I haven't been impressed at all by episodes I or II, but having seen them I'm obligated to go and see the new one. Although episode III does look pretty good.

A link in the science forum on totse.com.

They're reshowing the 80's series on BBC2 on tuesday nights at 11.20 if any one is interested.

"Contact" with Jodie Foster in it. They get contacted by aliens and create a telleporter type thing to go and visit them etc. etc. I quie liked it actually. "Paycheck" Ben Afleck. It's crap but has science in it, very inaccurate science that is.

I'm not going to even bother with your theory. The processes of radiation emission from a blackhole are the Penrose effect and Hawking effect. The two aren't too disimilar. That something you're talking about would probably be a graviton. If you want to know about the maths involved in showing that light is not emitted from a blackhole's horizon look up Schwarzshild geometry for the case of a stationary star or the Kerr metric for a static star. I'm not going to discuss this here, because I'm already talking about GR with you in the relativity forum, so if you want to know anything ask me there.

Yes I have a proof for that. I also have a proof that light has no inertial frame as well. But I can't be bothered to show them right now as I'm rather busy. The sun doesn't have an ergosphere, that is why it doesn't stop light back, or indeed a mass big enough to have a huge surface escape velocity. Light is lensed by gravity, black holes do not allow light to be emitted and, in addition, Kerr black holes can stop light emitted equatorilly.

Light has no inertial mass. Light has no inertial frame. Light does not accelerate. Why the dickens are you using the galilean transformation?

The expansion for exp(x) uses the fact that it is its own derivative. The natural base is "fudged" so that it's its own derivative. Plug it into the definition of the derivative and you end up with mf(x), where m is the gradient at (1,0). So in setting m=1 the only problem remaining is finding the base that has this property, for which you use a Maclurin expansion (a taylor series about a=0) with x=1.

Yes the Pythagorean theorem is supposed to be in there. The gamma factor present in the time dilation and length contraction formulae come from the use of the minkowski interval. This interval is itself a slight variation on the Pythagorean theorem. Look it up. However, not to the extent of your last line, which is wrong.

Ok then. If you want to get into some advanced stuff on geometry get "Geometrical methods of mathematical physics"-B. Schutz. I've recommended it to you before, but it really is excellent and I believe it's very popular with theoretical physicists. It starts at the basics: tensor algebra; discussion of manifolds; fibre bundels etc. It then advances through things such as Lie derivatives and Lie groups; killing vectors; differential forms and their calculus; applications to theoretical physics, all sorts of stuff (I'm not that far into it at the moment). The other book by Schutz that I've recommended omits one or two topics from the above book that aren't of great relevance to a first course in GR. I will do that Riemann tensor thing this weekend by the way.

How's that going?

Yeah, I would have thought so. Just keep going with your linear algebra and continue with tour research into tensor algebra (or even get a book out from a library on it). It's taking me so long because I was busy over the weekend and the exam period is approaching quickly.

It's not a very good discussion. The upside down triangle is the notation for the covariant derivative. Look up parallel transport and geodesics. Then consider the parallel transport of some vector around a closed loop on a general Riemannian manifold and then compute the change in the vector upon traversing fully this loop. Use the equation of geodesic and some of the definitions I gave in my other post. If your up for a challenge that is; if not I'll derive it for you and give a decent discussion of it ASAP.