Calling all theorists

[homology]

:beer:The situation: I need a master\'s thesis topic (my advisor has given me some freedom in choosing) completable in 2-3 years that could bring together the following areas of physics

1)quantum
2) relativity
3)topology (this is a must, as my advisor is a topologist)

and I\'m certainly not opposed to pinches of

a) Mechanics
b) Electrodynamics

I\'d like to use my master\'s thesis as an excuse to study quantum stuff and relativity stuff with topological stuff for three years.

Most importantly is time, I could certainly keep myself busy for three years, but I need to ahve some sort of plan to win over the love of my advisor! :D

Any and all ideas are welcome and appreciated. If necessary assume I have a BA in mathematics and physics.

[Sir_Zerp]

That\'s a rough mix. The topology I mainly think of is gravity wells in space. That takes care relativity, but quantum doesn\'t mix well with gravity.

Shape of something in 6D? That\'s topo.

Shape of gravity wells in 5D. That could work.

Still stumped on the quantum part.

[keebler_giant]

For combining relativity and quantum mechanics, maybe you might want to look at quantitizing maxwell\'s equations and then rederiving special relativity. I say this because QM and SR both seem to have certain roots in Maxwell\'s equations.

[keebler_giant]

And of course for topology and relativity, you might want to try to formulate GR in terms of relationships (I\'ve heard it\'s been done before), and then giving the relationships a topological basis by showing the relationships in terms of a graph (the node-vertice type graph, not the function type graph), although this seems sort of like cheating

[homology]

:coffee:Nice folks! Keep \'em coming. If it turns out that Mr. Homology here isn\'t going to be able to mix topology quantum and relativity then: oh well, however I\'d like to try.

What about: I have heard (though really no nothing about) how gravity is at odds with quantum. How much work is it to find out why they haven\'t been \'merged\' and is there any topology in that? Furthermore could such knowledge be obtained in 2-3 years?

Thanks again folks!

Kevin

[Larne]

Originally posted by homology
How much work is it to find out why they haven\'t been \'merged\'

I\'m pretty sure the short answer is \"a lot.\" This is an area of very active research, with the two major approaches being string theory and loop quantum gravity.

and is there any topology in that?

Topological considerations seem to come up a lot in discussions of both approaches, although I\'m far from being able to understand what, exactly, people are talking about. Searches on google or the arxiv (http://arxiv.org/) for combinations of topology, string theory and/or loop quantum gravity turn up a whole bunch of things that sound juicy.

There are also topological quantum field theories, although I gather these haven\'t be particularly successful beyond toy models in 2+1 dimensions, and I haven\'t heard anything about a TQFT of gravity.

You could also approach this via gauge theory. Not to sound like a Baez fanboy (even though I am), but start with Gauge Field, Knots and Gravity (http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?isbn=9810220340&) which begins with electromagnetism and has some coverage of both quantum and topological issues. It builds to a parallel treatment of gravity developed by Abhay Ashketar (http://en.wikipedia.org/wiki/Abhay_Ashtekar) (I\'m only about a fifth of the way through, but so far I\'ve found it very readable and immensely fun).

Have fun! And I envy you, this is exactly the topic I want to specialize in as well, but I\'m still several years from being able to start.

[homology]

There are also topological quantum field theories, although I gather these haven\'t be particularly successful beyond toy models in 2+1 dimensions, and I haven\'t heard anything about a TQFT of gravity.

You could also approach this via gauge theory. Not to sound like a Baez fanboy (even though I am), but start with Gauge Field, Knots and Gravity which begins with electromagnetism and has some coverage of both quantum and topological issues. It builds to a parallel treatment of gravity developed by Abhay Ashketar (I\'m only about a fifth of the way through, but so far I\'ve found it very readable and immensely fun).

I\'ll check it out, thanks!

[homology]

Hmmm, the state of Maine doesn\'t seem to have this book,Gauge Field, Knots and Gravity, (at least in a library), could you recommend a runner-up or two?

Kevin

[Larne]

Originally posted by homology
Hmmm, the state of Maine doesn\'t seem to have this book,Gauge Field, Knots and Gravity, (at least in a library), could you recommend a runner-up or two?

From memory I think Chris Isham\'s Modern Differential Geometry for Physicists (http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?isbn=9810235623) and Bernard Schutz\'
Geometrical Methods of Mathematical Physics (http://search.barnesandnoble.com/textbooks/booksearch/isbnInquiry.asp?isbn=0521232716) cover a lot of the same mathematical background at about the same level of readability. I don\'t know how deeply, if at all, they go into quantum gravity issues, but one of these, plus some general relativity, might be enough background to follow Ashketar\'s paper (http://prola.aps.org/abstract/PRL/v57/i18/p2244_1).

[Larne]

Oh, and to be fair I should say that everything I\'ve mentioned so far goes down the loop quantum gravity road. If you\'re more interested in string theory there\'s A first course in String Theory (http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?isbn=0521831431). I hear it\'s really good, although I don\'t know how much it covers gravity or topology. If nothing else it should be sufficient preparation for more advanced treatments though.

Or if you\'re looking for some well-written popularizations to start off with, there\'s Three Roads to Quantum Gravity (http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?isbn=0465078362) and The Elegant Universe (http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?isbn=0375708111).

[Xerxes314]

For instant satiation of your LQG hunger, try Rovelli\'s LQG Book (http://www.cpt.univ-mrs.fr/~rovelli/book.pdf).

Xerxes

[Sir_Zerp]

http://www.advancedphysics.org/viewthread.php?tid=856&page=1#pid3843

You asked for it.

1)quantum
2)relativity
3)topology

Just give me a footnote when you are finished :wink:

[ket]

Originally posted by keebler_giant
For combining relativity and quantum mechanics, maybe you might want to look at quantitizing maxwell\'s equations and then rederiving special relativity. I say this because QM and SR both seem to have certain roots in Maxwell\'s equations.

This has been done with Special Relativity, hasn\'t it? Isn\'t this what Dirac\'s equation is about?

[keebler_giant]

No, Dirac derived his equation by allowing Einstein\'s equation E=sqrt(m^2c^4+p^2c^2) is an eigenvalue to the equation i*hbar*dw/dt=Ew, for a wave function w.