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Do it exactly as doG suggests. write down the forumla for the volume, surface area and sum of the sides. You now have 3 simultaneous equations and 3 unknowns which you can solve.

I was told that most of the lattice field theory work on QCD is trying to explain experimental results form many years ago. On the theoretical side twistor string theory and MHV (maximally helicity violating ) tree amplitudes in (super) QCD, has become a big thing.

I have a signed copy that I picked up in Oxford. I would agree with bascule, it is not an easy book and does contain a lot of modern mathematics. Pick it up and see what you can get out of it.

People are also interested in quark matter, which may be in the centre of neutron stars. Have a look at this short introduction http://en.wikipedia.org/wiki/QCD_matter

I wrote down [math]\circ [/math] just to represent some abstract linear, associative binary operation. When we pick a representation for the elements of this algebra we also pick a representation of this operation. So, if we think about matrices, this binary operation is simply matrix multiplication. (And then the multiplication of a matrix with a vector). When we represent this algebra by differential operators the binary operation is composition of the operators, e.g. [math](x \circ p)(f) = x(p(f))[/math] where [math]f[/math] is a function of [math]x[/math] i.e a state vector.

It is just the product in the algebra. It would be matrix multiplication if we used matrices as a representation. I did hear that Heisnburg did not know that he was using matrices. It was only later that someone pointed that out to him.

I watched the first few minutes of the program. What is evident is that that there is a lot of money and effort going into spreading the word against evolution. From what I can gather not watching the full program is that they have taken our gaps in the understanding of evolution and used them to completley debunk the theory. Not exactly a balanced view, as the presenter suggested. I think it is good that people question and examine scientific theory, it is the only way to develope science. But done in this way it can be very damaging. On a slightly different topic, what do these kinds of people think about cosmology, theoretical physics and mathematics?

In my experience the answer is "no". Just about all of what you will learn in a typical degree in physics is well tested and understood. The only exception is cosmology and particle physics, as you pointed out. With improved observational cosmology many unexpected things have been discovered. I remember when I studied cosmology as an undergraduate it was just after the current inflation was discovered. It was mentioned in the course, but was held as being speculative. Today, most people beleive in the current acceleration of the expansion. We were also taught about cosmic strings as a possible alternative to inflation as a method of galaxy seeding. Today most people do not expect this. Also, my undergraduate particle physics course talked about neutrino mixing and neutrino mass. These things at the time were speculative although the data from Japan was there. Even so, the fundamentals behind cosmology and the standard model of particle physics remain intact and so remain on the course.

Tannin is right, differential and bracket geometry is the modern way of thinking. The book by Arnold is cited in many papers, but I must confess that I have never read it. At some point I will get it out from the library.

Just about all the equations of physics can be generalised to any dimension. However, "special" things may happen in certian dimensions.

I assume you are talking about length contraction of spherical objects, such as ions in a collider. They do indeed become rugby ball shaped when travelling at high velocities. The basic reason for this is that length contraction only applies to the direction of motion. Any book on speical relativity will talk about this. For a start look at these links http://en.wikipedia.org/wiki/Length_contraction http://www.spacetimetravel.org/fussball/fussball1.html http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/specrel/lc.html

you talking about length contraction? any book on special relativity will talk about that.

Serviant and 5614 make good points. Quantum mechanics stems from a rather simple looking equation [math] [x,p] = x\circ p - p \circ x = i \: \hbar [/math] where {x,p} are the quantum anologue of the position and momentum. Quantum mechanics is basically the study of representations of this equation. It is known as the canonical commutator relations CCR. It was Heisenburg who realised that matrices could be use as a reprsentation of this and Schrodinger who realised that differential operators could be used. von Newmann showed that these two different repesentations are in fact equivalent. (techincal point: this is true provided we only have finite degrees of freedom). I beleive he showed that any representation of the CCR is equivalent to either Heisenburg's matrix representation or Schrodinger's differential operator representation and hence all equivalent.

Doesn't classical probability theory require that you can in principle know all the possible outcomes? Without knowing the ratio of statble to unstable chemicals you don't have enough information to continue. So I think your original question cannot be tackled using classical probability theory. Maybe you would need to use topos theory? It is not something I know much about, but I know it can be applied to situations where classical probability theory fails. Maybe Matt Grimes, knows more about this....

I learnt some particle physics in my 3rd and 4th year, but no QFT formally untill my MSc. However, I did start to look into some basic QFT before that.

The basic reason we need to consider matrices is beacuse they can be used to represent linear operators on vector spaces. In quantum mechanics we have the (usually) infinite dimensional space of states, which is technically a Hilbert space. Observables are represented by linear operators on this space, which in turn have the mathematical representation as infinite dimensional matrices.

Vacuum polarisation effects for quantum fields on curved space-times are very interesting. They lead to violations of various energy conditions. Also the work of I.T. Drummond & S.J. Hathrell and later G. M. Shore on QED vacuum polarisation on curved space-times is interesting. Vacuum polarisation effects can allow for a photon to propagate at a speed greater than c! I'm not sure if any of thsi is related to what you have written Norman?

You should be aware that no-one knows exactly what M-theory is!

This paper might be of interest http://arxiv.org/abs/quant-ph/0607124 The "Unromantic Pictures" of Quantum Theory Authors: Roderich Tumulka Comments: 37 pages LaTeX, no figures; written for special volume of J. Phys. A in honor of G.C. Ghirardi I am concerned with two views of quantum mechanics that John S. Bell called ``unromantic'': spontaneous wave function collapse and Bohmian mechanics. I discuss some of their merits and report about recent progress concerning extensions to quantum field theory and relativity. In the last section, I speculate about an extension of Bohmian mechanics to quantum gravity.

Mathematica will give you the answer that I gave. I tried it!

I agree with Matt and Woelen, I have given you the "final" answer. I have given you a well defined function that for you can eveluate for any x. It is however, as I stated originally not in terms of elementary functions like polynomials, trigs etc..

What is true is that the intagral of [math] \sqrt{\sin x} [/math] cannot be written in terms of elementary functions. It can be written in terms of the elliptic integral of the second kind [math]E(\phi,m) = \int^{\phi}_{0}(1-m \sin ^{2}\theta)^{1/2}d \theta[/math] with [math] -\pi/2 < \phi < \pi/2 [/math] The integral can be expressed as [math] \sqrt{\sin x}= -2 E(\frac{1}{2}(\frac{\pi}{2} -x),2) [/math]

I'm from the Uk and have no idea what AP calculus is or what how the grading system works. Anyone care to explain it?

This is a new one on me. Phantom energy (responsable for present day inflation) could support worm holes and lead to our universe being engulfed in a huge wormhole, before exiting the present inflationary phase. When the universe is engulfed it could be taken on a trip through space-time! Have a look at these papers. http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+t+big+trip&FORMAT=www&SEQUENCE= Any comments?

I think it does take something like 8 to 10 years to become anything like an working mathematician, 3 or 4 for the undergraduate training, another 3 or 4 postgrad (MSc + PhD) and then a few years working as a post doc. It is a long time, loads of work and little financial gain.