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elvum brought to my attention a paper called An Exceptionally Simple Theory of Everything by the physicist Garrett1 Lisi. Entertainingly, Lisi appears not to be your typical physicist, spending most of his time surfing in Hawaii. And the title's a pun: he claims to have unified the Standard Model of particle physics and gravity using the "exceptional simple Lie algebra" E8 (about which more later). If true, it looks like very cool stuff; mathematically rather elegant (though I really don't understand most of the mathematics behind it), satisfying some very desirable criteria (as elvum put it, it's like he's reeling off desirable features from the GUT checklist), and likely to make testable predictions.
But the main reason I mention it is so I can link to this slashdot comment, which is just about one of the best bits of pop science writing I've ever seen, and seriously raises the bar for me in my occasional attempts to explain maths and science. It's very light on details, but it explains in non-technical language what's actually going on here, and how symmetry arises in the study of particle physics. I learned a lot from it, and recommend it unreservedly. Edit: just to clarify, I didn't write the slashdot comment! I wish I had, though.
I wrote a somewhat more technical explanation of Lie algebras and the mathematical significance of E8 forelvum, and I might as well ( repost it here )
The highly-regarded mathematical physicist John Baez has written an explanation of some previous attempts at unification here, with some explanation of why exceptional Lie algebras/groups might arise. It mostly goes over my head, though. The physics blog Not Even Wrong has also written about it, somewhat more cautiously: the author thinks that Lisi's probably only shifted old problems into different places. This blog post also looks pretty informative, but I haven't worked through it yet. And the string theorist Luboš Motl thinks it's nonsense, but then Luboš is an unpleasant troll, so I take that as mild positive evidence.
Garrett (or someone) has produced this rather lovely video of E8: it shows a projection of the root system (which is a collection of vectors in some higher-dimensional real space) as it's rotated.
1 Garrett seems to be quite a good name for mathematicians: the only other Garrett I've heard of in any context was the mathematician Garrett Birkhoff, inventor of universal algebra.
2 I prefer to think of them as group objects in the category of manifolds and smooth functions, but that seems like too much of a digression for now :-)
elvum brought to my attention a paper called An Exceptionally Simple Theory of Everything by the physicist Garrett1 Lisi. Entertainingly, Lisi appears not to be your typical physicist, spending most of his time surfing in Hawaii. And the title's a pun: he claims to have unified the Standard Model of particle physics and gravity using the "exceptional simple Lie algebra" E8 (about which more later). If true, it looks like very cool stuff; mathematically rather elegant (though I really don't understand most of the mathematics behind it), satisfying some very desirable criteria (as elvum put it, it's like he's reeling off desirable features from the GUT checklist), and likely to make testable predictions.But the main reason I mention it is so I can link to this slashdot comment, which is just about one of the best bits of pop science writing I've ever seen, and seriously raises the bar for me in my occasional attempts to explain maths and science. It's very light on details, but it explains in non-technical language what's actually going on here, and how symmetry arises in the study of particle physics. I learned a lot from it, and recommend it unreservedly. Edit: just to clarify, I didn't write the slashdot comment! I wish I had, though.
I wrote a somewhat more technical explanation of Lie algebras and the mathematical significance of E8 for
elvum, and I might as well ( repost it here )The highly-regarded mathematical physicist John Baez has written an explanation of some previous attempts at unification here, with some explanation of why exceptional Lie algebras/groups might arise. It mostly goes over my head, though. The physics blog Not Even Wrong has also written about it, somewhat more cautiously: the author thinks that Lisi's probably only shifted old problems into different places. This blog post also looks pretty informative, but I haven't worked through it yet. And the string theorist Luboš Motl thinks it's nonsense, but then Luboš is an unpleasant troll, so I take that as mild positive evidence.
Garrett (or someone) has produced this rather lovely video of E8: it shows a projection of the root system (which is a collection of vectors in some higher-dimensional real space) as it's rotated.
1 Garrett seems to be quite a good name for mathematicians: the only other Garrett I've heard of in any context was the mathematician Garrett Birkhoff, inventor of universal algebra.
2 I prefer to think of them as group objects in the category of manifolds and smooth functions, but that seems like too much of a digression for now :-)