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Everything posted by ajb

M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
Maybe a better analogy is to think of an ant following a line of honey on the floor. A long as the ant just walks along the line the system is effectively 1+1 dimensional. However, the ant could decide to move off this line, the system is then effectively 2+1 dimensional. 
M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
What is the analogy here? I don't know what you mean by this... we usually allow changes of coordinates and so we do in a sense mix dimensions (or directions). Yes, so in this case strings and branes propagate in more that 3+1 dimensions. Anyway, the dimension of spacetime is the number of numbers needed to specify any given point  in standard special or general relativity this is 3 spacial coordinates and 1 temporal coordinate: so 4 numbers in total. In superstring theory we need 9+1.. 
M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
There are several possible ways of compactification in string theory  look up G2manifolds, orbifolds and Calabi–Yau manifolds. This is poor choice of wording... anyway you should think of these extra dimensions as being 'spacial' rather than 'temporal'. Yes. 
M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
If you have some questions I might be able to help. But for sure Mtheory is not my area of speciality. 
M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
So you want to discuss some English and not science? 
M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
"Mtheory which is formulated in 10+1 dimensions has as certain low energy limits a supergravity theory in 10+1 dimensions" Okay, so noone really knows how to formulate the full theory of Mtheory, what we do known is that it should be a theory of M2 and M5 branes.It is also known that these branes can be classically viewed as solitons  so special solutions to the theory  in a supergravity theory in 10+1 dimensions. The string theories can basically be seen as coming from this supergravity theory, in a loose sense. 
M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
Well, Mtheory is a theory of branes (M2 and M5 where the number refers to the dimension) in 10+1 dimensions. Superstring theories can be seen as certain limits of Mtheory and these live in 9+1 dimensions. Another limit is a 10+1 dimensional supergravity theory. 
M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
I doubt that is the main issue here. Not that I want to write an introduction to string theory, Mtheory and string dualities ;) 
M theory/string theory limits dimensions to 11?
ajb replied to Almighty's topic in Modern and Theoretical Physics
The quantum theory of a single superstring only works properly in 9+1 dimensions. Mtheory which is formulated in 10+1 dimensions has as certain low energy limits a supergravity theory in 10+1 dimensions and then superstring theories in 9+1 dimensions. 
First thing to be careful with are any formal rules at the university about this. Check carefully on fonts they allow and do not allow.

Twenty four members of the Department of Mathematics at the University of Leicester  the great majority of the members of the department  have been informed that their post is at risk of redundancy, and will have to reapply for their positions by the end of September. Find out more and sign the petition http://speakout.web.ucu.org.uk/nocutsnoconfidenceatuniversityofleicester/

When people talk about gravitons they are usually thinking in terms of quantum general relativity  that is applying the rules of quantum field theory to general relativity. The method is to linearise Einstein's field equations and then use perturbation theory to get at the quantum theory. The problem is that there is no way to renormalise the theory, so you have to think of the theory as effective, that is we accept that it can only hold reasonably for a small range of energies  we accept that at higher energy some new physics must come into play. However, it is possible to deal with the gravitational force up to 2loops. Thus, we do have some workable handle on what one means by gravitons. But of course we do not have any experimental evidence that they exist, the closest has to be observations of gravitational radiation. The analogy here is that light waves and photons.  The question of if we could ever have a table top experiment that could detect quantum effects of the gravitational force is another issue.

Basic question about particle physics
ajb replied to Artebian's topic in Modern and Theoretical Physics
As swansont says, you should not think of a particle as a tiny spinning ball. The intrinsic spin does not have such a simple interpretation, but it is similar to angular momentum when you take special relativity into account  you could look up the Pauli–Lubanski pseudovector. The usual way to include spin in nonrelativistic quantum mechanics is to simply 'bolt it on' to the theory  you then think of total angular momentum, which is the sum of the orbital angular momentum and the spin. 

I am not sure that we should make too much of a distinction here. Advanced maths could have only been developed on top of more basic notions. The mathematics itself or the ability to comprehend mathematics? It seems that everyone has a natural ability to understand basic number and shape  more advanced ideas take more effort. Sure, modern mathematics has taken a long time to develop and is still developing. Anyway, the fact that our brains are able to cope with mathematics and that we generally have the ability to think mathematically is amazing.

You need to be careful here, I am not sure if you are trying to be technical here or not. In particular, what symmetries are you talking of? (there are several that are very important) Yes, that is what we tell children in infants school. But there is a lot more to gravity that just this statement. Also, we tell children in infants school that electrically charged objects attract or repel. You might have to except that simple explanations are not particularly useful and may not be easy to find.

Again, you are confusing the notion of a theory and a pedagogical interpretation. Just saying that 'spacetime curvature is gravity' is not enough for anyone to calculate with and make predictions. One can try to say something similar with the electromagnetic theory  we have connections and curvature as we do in general relativity, but the geometry is not 'simply' that of spacetime. The mathematical framework for electromagnetism seems a bit less easy to imagine and so the 'rubber sheet' analogy is not used. Okay, but the light and the electromagnetic force are not really separate things  Maxwell's equations tell us this. Maxwell's equations and the Lorentz equation tell us everything about classical electromagnetism  including light and how test particles move in an electromagnetic field.