The real world observations are the test, not the math. Real world observations can prove a theory wrong, but may not prove it right without further confirmation.
Originally posted by Mary Rose
For a theoretical physicist with an idea that needs testing mathematically
then the actual proof lies in observation in the real world.
Why do you ask?
Are there examples of new maths being invented by theoretical physicists?
I would say more math than physics.
"Unlike in Einstein's time when the relevant mathematics was already in existence, the mathematics we need now hasn't been fully developed yet,& Aganagic says. "This time around, math and physics are being discovered in parallel."
My prediction is that string theory will eventually get moved from the physics department to the math department, until we can actually test it (at energies 10^14 higher than the LHC, perhaps centuries from now, if ever).
String theory as a theory of everything has been criticized as unscientific because it is so difficult to test by experiments. The controversy concerns two properties:
Because the theory is so difficult to test, some theoretical physicists have asked if it can even be called a scientific theory.
There should be heavier copies of all particles corresponding to higher vibrational states of the string. But it is not clear how high these energies are. In the most likely case, they would be 10^14 times higher than those accessible in the newest particle accelerator, the LHC, making this prediction impossible to test with any particle accelerator in the foreseeable future.
Originally posted by Arbitrageur
Why do you ask?
Originally posted by Arbitrageur
The real world observations are the test, not the math.
Originally posted by Arbitrageur
Lisi seems to like the E-8 math and thinks it forms the basis of the theory of everything. I've studied mainstream physics, but not the E-8 An Exceptionally Simple Theory of Everything My first impression is that of a physics theory superimposed on a mathematical E8 Lie algebra model. But does the model make any useful real-world Predictions?
I think it's questionable at best.
Originally posted by Arbitrageur
String theory seems to come up with new math, but it has largely failed to make testable predictions about the real world.
My prediction is that string theory will eventually get moved from the physics department to the math department, until we can actually test it (at energies 10^14 higher than the LHC, perhaps centuries from now, if ever).
So I'd say in his case, it's already in the math department. I've noticed some other string theory professors are also in their respective math departments.
The mathematics department has provided a "supportive atmosphere" he said, speaking highly of his colleagues and their welcoming attitude...
Malmendier is teaching Multivariable Calculus, Differential Equations and Topology this semester. He is also doing independent research concerning the intersection of mathematics and string theory. "You not only solve mathematical problems, you look at them with different perspectives" Malmendier said. These differing perspectives, he explained, make math such an exciting and dynamic field.
So some of these guys are ALREADY in math departments, I expect to see more of that.
Shing-Tung Yau is a force of nature. He is best known for conceiving the math behind string theory...
Yau has held positions at the Institute for Advanced Study, Stanford University, and Harvard (where he currently chairs the math department)
Originally posted by Arbitrageur
discovermagazine.com...
But Yau’s genius runs much deeper and wider: He has also spawned the modern synergy between geometry and physics . . .
Originally posted by Mary Rose
reply to post by fedeykin
I personally really like the fact that he is self-taught. I think that it is a huge plus. He is self-directed and an original thinker. It isn't that he's "making things up." I think he has studied the information that is taught in universities and has evaluated it independently.
Originally posted by buddhasystem
What about pions?
Originally posted by Bobathon
Originally posted by buddhasystem
What about pions?
...physicists think of as leptons but which are actually holographic Grassman-invariant Lagrange points in a non-Hausdorff multidimensional fibre bundle. Obv.
Originally posted by buddhasystem
Sheesh man, and I thought you knew physics! Why do you have to drag Hausdorff formalism into that? It's irrelevant. It's just a perverted way of saying this is a two-dimensional complex manifold, and you must know these were proven to not exist. About Grassman invariance, here I can agree. But in that case the leptons would be massless, and we know they are not.
Originally posted by Bobathon
Originally posted by buddhasystem
Sheesh man, and I thought you knew physics! Why do you have to drag Hausdorff formalism into that? It's irrelevant. It's just a perverted way of saying this is a two-dimensional complex manifold, and you must know these were proven to not exist. About Grassman invariance, here I can agree. But in that case the leptons would be massless, and we know they are not.
I was just stringing together a random bunch of words because I thought it was funny. Sorry. I tried to make the sentence as meaningless as I could.
Originally posted by buddhasystem
Haha, got you.
Originally posted by Bobathon
Originally posted by buddhasystem
Haha, got you.
Ah! Bugger. You got me.
I thought I might have unwittingly said something that made some sense... how embarrassing. Instead I was thinking I was seeing you thinking you were seeing sense when in fact you were replying meaninglessly to my senselessness, as any sensible person would have realised.
BUT you must realize that the Standard Model implicitly relies on the Tietze extension theorem
Where does that leave your pions now, huh?
Originally posted by buddhasystem
It needs to be connected to real science in demonstrable way.
I think my "manifold" pronouncement just may be correct.
BUT you must realize that the Standard Model implicitly relies on the Tietze extension theorem
It does not Good try. Scratch that -- I need to think about it
Where does that leave your pions now, huh?
There was a Christmas party here so I can't guarantee I'm coherent, but sure as hell pions are pseudo-Goldstone bosons. After all, the Goldstone mechanism explains a lot of things including the non-conformant behavior of certain eschatological entities, even in case of non-causality. So there.
Originally posted by Bobathon
That Hausdorff formalism implies a 2D complex manifold, or that 2D complex manifolds have been proven not to exist?
Now you're talking.
You won't get away with that kind of carelessness if you want to succeed in real research.
Ah, maybe I should be more explicit when I'm joking.
Originally posted by buddhasystem
With a few dozen publications in refereed journals, I think I already succeeded, so what the heck
I hope you do realize that the Goldstone part was NOT Haramein style, i.e. it's for real.
If I remember correctly, after a few years of work one of my friends did find that 2D complex manifolds did not exist. I may be wrong, it was in mid 90s.
Originally posted by Bobathon
... but surely the set of ordered pairs of complex numbers is a trivial example of a 2D one?