Ah, what part of theoretical Condensed Matter are you specialising in?

Cheesenium/BlueWind: M-theory is simply a unified version of 5 (iirc) different string theories [yes there are plenty of variants of string theories]. String theory is currently an approach to unify general relativity (not Newton's Laws) with quantum physics, but well, there are some philosophical issues surrounding it right now, let's say

edit: note the plural, theories. yes string theories. plenty of them around.

There are also other candidate theories, but to be honest everyone's (I am massively exaggerating - but yes the community seems, from my quite distant perspective) now simply waiting for the results from the LHC (CERN) [the big bang machine, machine that will end the world, blah blah blah] to start culling down on the theories available to give some new direction of study I guess. Because frankly, any crazy/non-crazy idea is possible. They just await the test of experimentation [the truth test in science], which the LHC will do [but the LHC won't be able to do much though, it's energy reach is too low to see effects of supersymmetry and stuff which is afaik, a feature of most string theories, believe it or not, for all the talk in the media about how powerful it is and stuff - but they hope to be able to see hints of supersymmetry at the upper end of the energy reach of the LHC. don't expect much till 2012 and beyond though, the LHC will slowly ramp up from this september onwards to the 7 TeV beam hopefully sometime early - middle of next year]

This post has been edited by bgeh: Jun 14 2009, 08:17 PM

Don't know what I'm doing yet to be honest. Gravitating towards mathematics/quantum field theory.

But frankly, haven't a clue.

This post has been edited by bgeh: Jun 14 2009, 07:44 PM

Trust me, if only we all knew the answer. String theory has plenty of brilliant minds working on it (and I mean damn damn brilliant)

Plenty of brilliant people finding that the last 30 - 40 years of research into string theory came to nought, plenty of depressed theoretical physics departments specialising in string theory I'd imagine

But if that ever occurs, well at least it did bring in a lot of beautiful mathematics

beatlesalbum: There exists an alternative reformulation of classical mechanics in a variational setting, and this is what we call Lagrangian/Hamiltonian mechanics, and they're very useful, and beautiful refomulation, because of the following reasons:

1) The form of the formulas is independent of the coordinate system, i.e. take Newton's laws, and apply it to a cylindrical coordinate/spherical polar coordinate system. You'll find out that the equations change when you change the coordinates. These don't.

2) It incorporates in symmetries very well (Noether's Theorem), and conservation laws are incorporated into the Lagrangian/Hamiltonian. e.g. if the Lagrangian is independent of some coordinate, then you get a corresponding conservation law, or symmetry.

They're widely used in quantum mechanics, where the Hamiltonian is the governing equation, and in quantum field theory, where the Lagrangian is employed heavily.

edit: and no, wiki can be very detailed too, it's just that the maths without an introduction would probably confuse most people.

edit: to add, Lagrange's formulation in the Lagrangian involves a minimisation problem of minimising some quantity called the action. Just think of it as a more complicated version of taking some curve, and using dy/dx to find the minimum of that curve - it's something like that, and Lagrange's formulation allows you to take all the classical mechanics problems we're used to seeing, and then solving for the 'true' trajectory (the trajectory that is actually taken by the particle) by finding the trajectory that minimises this action quantity.

This interpretation (Lagrange's) doesn't really work in quantum mechanics, because we're considering the probabalistic nature of quantum physics. It was a Richard Feynman, which is probably feynman's namesake, that formulated the quantum mechanical equivalent of Lagrangian classical mechanics, or the action principle to something called the path integral formulation, where the particle goes through all possible intermediate states between some initial state A and final state B, weighted by the probability of each intermediate state. feynman's avatar can then be seen as one of the possible paths for some particle interaction [actually to be more precise, it's a 2nd order diagram describing an annihilation and pair production of a particle and a antiparticle], and his avatar is called a Feynman diagram after the man that invented it himself. These Feynman diagrams are used a lot by particle physicists.

I've probably said too much now, but yeah it should give you an idea of what it is, and perhaps I might've also explained feynman's nickname and his avatar

probably final edit: What exactly is the classical calculus proof of Newton's Laws? I think they're taken to be axioms instead.

This post has been edited by bgeh: Jun 16 2009, 06:57 AM

No the Eulerian and the Lagrangian approach in fluid dynamics (they're essentially points of view, one an outside observer, the other, an observer following a single fluid particle) is very different from the Lagrangian (a quantity that you have to compute) in mechanics

You do. Newton's 2nd law says: Resultant force = rate of change of momentum of the object

So it's actually upwards thrust - weight = dp/dt (rate of change of momentum)

I'd argue that SPM level physics has too much of practical physics instead of theoretical ones

What background are you coming from, a more mathematical background or a physics background? What kinds of applications are you interested in? I could recommend some but knowing this would make it much easier for me to recommend books

Edit: Are you in grad school or doing an undergrad thesis? If so, where are you? Am just interested. PM me if you don't want this to be known to the public

This post has been edited by bgeh: Mar 6 2011, 12:41 AM