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Posts posted by ajb
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If you have some questions I might be able to help. But for sure M-theory is not my area of speciality.
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It is certailny a lot easier to read for me. Would that be acceptable ?
So you want to discuss some English and not science?
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"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.
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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.
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...due to the lack of commas.
I doubt that is the main issue here. Not that I want to write an introduction to string theory, M-theory and string dualities ;-)
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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.
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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.
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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/
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What Strange has said...
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They're virtual. Really we don't know enough about gravitons to answer firmly but assuming they are similar to virtual photons their virtual existence is between interacting particles.
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.
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The question of if we could ever have a table top experiment that could detect quantum effects of the gravitational force is another issue.
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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.
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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.
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We are talking about the distinction between simple and advanced mathematics. The question was about advanced maths and maybe I should have been clearer in my post.
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.
I'm suggesting that more simple maths evolved.
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.
Advanced maths has only existed for a very small number of generations (much of it only in the current generation I assume) so evolution has had no time have any effect. Therefore it must be a learned and communicated behaviour.
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.
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I am not sure.
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?
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Mathematics is only a field of human thinking.
Sure, but still this has to be part of our evolution.
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Maybe it didn't evolve. Since it's happened in such a short time it seems unlikely to me.
If our capacity for mathematics is not tied to the evolution of our species, then where did it come from? Some supernatural source?
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In real life, most work is not only physically demanding, but also boring. For a lot of people, sitting at the desk thinking about something is a lot more attractive than actually doing something useful, like ploughing or weeding.
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
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That doesn't seem to add much evolutionary advantage.
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.
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Electromagnetism is very enteresting because it is complex and yet holds certain symmetries, making it also simple.
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)
Not as simple as gravitation, which is basically large objects pulling each other towards each other.
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.
... and I think it also deserves some kind of simple explanation to go with it.
You might have to except that simple explanations are not particularly useful and may not be easy to find.
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You need to differentiate between the math and the explanation in words of the system in hand. A good theory needs both, like general relativity.
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.
My idea isn't about light it is about how the electric force works.
Okay, but the light and the electromagnetic force are not really separate things - Maxwell's equations tell us this.
And vice versa maxwell's theories do not directly explain how the electric force works, they explain how light "works", which is neat on it's own, using electromagnetism.
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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...I think a simple explanation that can be used in words with no math is also needed,
This is called an interpretation - some 'wordy' description of a mathematical framework or calculation.
for example if you want to explain it to kids in school.
This is a different question.
I am not a mathematician, and do not yet know the math involved in my theory, it could also be correct.
This is backwards. A theory is a mathematical model and then one can build interpretations.
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You asking about benchtop gravitational experiments? I know that people do think about such things - but I can not recall who right now!
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ajb says ,"there already exists usage of >3D in engineering". but I could not see any reference yet. so ,it is illogical now.
I have given you a whole area of study - classical mechanics - that is used widely in engineering. You would like me to find a paper that uses classical mechanics? There are lots that use the notions to different degrees - see what you can find.
Anyway, classical mechanics is used in the study of robotics, air craft, space craft etc. Basic notions of statics are used in the analysis of stability and equilibrium of structures.
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M theory/string theory limits dimensions to 11?
in Modern and Theoretical Physics
Posted
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.