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ajb

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Everything posted by ajb

  1. 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.
  2. 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 space-time 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..
  3. There are several possible ways of compactification in string theory - look up G2-manifolds, 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.
  4. If you have some questions I might be able to help. But for sure M-theory is not my area of speciality.
  5. "M-theory which is formulated in 10+1 dimensions has as certain low energy limits a supergravity theory in 10+1 dimensions" Okay, so no-one really knows how to formulate the full theory of M-theory, 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.
  6. Well, M-theory 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 M-theory and these live in 9+1 dimensions. Another limit is a 10+1 dimensional supergravity theory.
  7. I doubt that is the main issue here. Not that I want to write an introduction to string theory, M-theory and string dualities ;-)
  8. The quantum theory of a single superstring only works properly in 9+1 dimensions. M-theory 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.
  9. A masters student wants to work on a project with me - something to do with Riemannian supergeometry is going to be the topic - first masters student I will look after.

    1. StringJunky

      StringJunky

      I'm sure you will be a useful resource and mentor for them.

    2. ajb

      ajb

      Yoda voice - "Maths learn from me they will"

    3. imatfaal

      imatfaal

      If you are half as patient and kind with your time as you are here then your students will be very very lucky.

  10. 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.
  11. 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/no-cuts-no-confidence-at-university-of-leicester/
  12. 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 2-loops. 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.
  13. Given the length and time scales, and masses involved here you can model gravity accurately using Newton's theory. Observing these plates will not reveal anything further about gravity.
  14. 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.
  15. 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.
  16. If mankind's ability to think abstractly, form complex communication systems and develop mathematics is not tied to the evolution of our brains, then what? Are you suggesting some supernatural element here?
  17. If our capacity for mathematics is not tied to the evolution of our species, then where did it come from? Some supernatural source?
  18. Sure, bit I am think of our biological ancestors and early groups of humans. The planning and communications skills in hunting laid the foundations for farming and then economics, mathematics and science. Our in built curiosity has just grow and grown
  19. Basic mathematics and science skills are an advantage for our species. The more advanced mathematics and physics seems less so, directly at least. I suspect that our love for science and mathematics comes from our early ancestors need to develop hunting methods, and then farming methods and so on.
  20. 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.
  21. Again, you are confusing the notion of a theory and a pedagogical interpretation. Just saying that 'space-time 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 space-time. 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.
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