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What is the paradox? Quantum mechanics is a consistent theory that is well founded mathematically. It is ths interpretation that leads to difficulties. I dont think the person who wrote that article knows much quantum mechanics.

There maybe gravitational waves that originate from the early universe. They are predicted in General Relativity. Here are some experiments trying to detect them http://lisa.jpl.nasa.gov/ http://www.ligo.caltech.edu/ The relativity group at cardiff also do a lot of gravitational wave astronomy http://www.astro.cf.ac.uk/groups/relativity/ Also have a look at the archive http://www-spires.dur.ac.uk/cgi-bin/spiface/hep/www?rawcmd=FIND+T+GRAVITational+waves however, you will see that here is 1637 papers. So it is an active area of research.

Mathematica is generally considered to be superior. I have never used Maple or Mathlab. If you have access to Mathematica you will need to load the following packages; Graphics`PlotField3D` or Graphics`PlotField` If you want to calculate div and grad etc. you can use the package Calculus`VectorAnalysis` All 3 are part of the standard add-ons included with Mathematica.

Mathematica has a package that will draw vector fields for you. Not used it much myself, but I am sure it is good.

I have many books with me in the office. I tend not to read then cover to cover, though sometimes I will. I will flick between books using the chapters/sections that are I need at the time. The books are reseach or postgraduate level mathematics and physics books. I don't think they are intended to be read cover to cover in one go.

Yes, if [math]e_{j}[/math] is a local basis for the tangent vectors then [math]\nabla e_{j} = \Gamma^k_{ij} dx^{i} e_{k}[/math].

[math] \nabla [/math] to me would usually be the Levi-Civita connection on the tangent bundle of a Riemannian manifold. I would also use it to represent a connection on a complex vector bundle, unless I am thinking about it as an an associated bundle. [math] D [/math] would be a connection in a principle bundle or on its associated vector bundle.

Hawking is right. If you gave me a general wave function and a Hamiltonian, I can give you the wave function at a later time EXACTLY. What I could not do is predict the outcome of an experiemnt exactly, but probabilistically. I think this is what Hawking ment.

If you read SIEGEL's book on fields you will see that the guy has a sence of humor! The page you point out swanshot reflects this.

Of course Severian it is comming back to me. I do now remember Dr de Carlos at Sussex saying something about supersymmetry is needed to fix the Higgs mass, I guess this is exactly what she was talking about. Supersymmetry protects the Higgs mass. Right?

I think it is old notation and not in standard use today.

was is it comma for partial derivative and ; for covariant? Something like that. I tend not to use that notation myself. Nabla and D are common, it may depend on the exact context to which you use. I have never seen | or || to refer to a derivative. What branch of mathematics uses this notation?

Ok, sorry, I did not look at the condition at all! From my 30, you could then impose the condition and see what you get.

Taking into account the rotations you have 30 different die. You can see you have 13 axis to rotate about, which gives you 24 turnings. Hence there are 720/24 = 30 different die. Have a look at this website http://www.mathematische-basteleien.de/dice.htm

Isn't the question how may ways can you arrange 6 objects? suppose we have no numbers on the dice. pick a number. how many sides can we attatch this number? The answer is 6. pick another number. This can now only be placed in one of the remaining 5 sides. pick another number. we now only have 4 sides to place it. etc... so we have the number of possible ways os assigning {1,2,3,4,5,6} to the six sides of a dice is 6.5.4.3.2.1 = 6! = 720

relativists use commas.

Isn't it the number of permutations of 6 objects?

I am a physicists and I feel a little uneasy about fine tuning. On a technical note, I always wonder about the renormalisation of fine tuned parameters. Generally you could set it classically to a number and then quantum effects could alter this value. So, Severian what symmetry protects the Higgs mass? As I am no expert at phenomenology, I guess it is gauge symmetry?

abskebabs; Mathematically you can have spaces of any (integer) dimension. [you can also have fractal dimension but that is a different story]. A 26-dimensional space if fine. In fact (bosonic) string theory insists on 26 dimensions. We can talk about that somewhere else if your interested. As for the Rubik cube, the mathematics of the problem is group theory.

Can you explain exactry what you mean by vacuum force? Do you mean somthing like the Casimir effect?

I am having the same problem.

I don't quite understand your question. do some more examples in full.

All I can suggest is that you search the archives http://www-spires.dur.ac.uk/spires/hep/ http://xxx.soton.ac.uk/

My fav has to be maxwells equations written using differential forms. It goes straight to the heart of modern physics; physics does not care about the coordinates.