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While the eigenvalues are somewhat unavoidably tricky, this new result shows that the eigenvectors can be written down in a simple, compact and easy-to-remember form once the eigenvalues are calculated. For this reason, the trio called the eigenvalues “the Rosetta Stone” for neutrino oscillations in their original publication: “Once you have them, you know everything you want to know.”
Experts fully expected this formula to exist somewhere in the literature for centuries, but the team couldn’t find any evidence for it online or in textbooks. The trio of theorists were eventually directed to a similar result by UCLA mathematics professor Terence Tao, who has a Fields Medal and Breakthrough Prize to his name. When they presented Tao with their result, he cheerfully declared that it was, in fact, the discovery of a new identity, and he provided several mathematical proofs, which were recently published online. (Tao also discussed the new identity in his math blog.)
“I couldn’t believe it at first, because linear algebra has been studied for centuries,” Zhang said. “But Prof. Tao’s proofs show that our method, which was created to calculate neutrino oscillations quickly and with better precision, can also be expressed as a very elegant math formula.”
originally posted by: frenchfries
a reply to: bastion
ok , we have a diference of opinion. Riemann hmmm ? 1850 . Riemann spheres , read about it in a book from penrose.
Basically math can do anything I agree with that. Also there are infinite mathematical ways to describe the universe. But a description is not 'reality'.
There is reality without descriptions. But descriptions don't generate 'reality' . also imaginary time in a complex plane is it real ?
Point here is that math is a superset and the laws of physic is a subset. But that superset cannot operate in that subset. Operations in that subset of 'reality' are always done in a realm that lies beyond math... e.g. one needs matter energy , space , time and taxes to generate reality...
Then again thanks for clearing things out.... new insights won !
originally posted by: Arbitrageur
I am not sure if I understand what you mean here, but we all have access to the pre-prints on arxiv.org, just click on the "pdf" link in the download section (other formats is another option if you want to pursue that but the pdfs work great for me).
originally posted by: bastion
If you have access to the papers on arxiv.org I'm really interested in reading both the Eigen Vectors from Eigen Values paper (my specialism) and highly intruiged by the Eigenvalues: the Rosetta Stone for Neutrino Oscillations in Matter paper, I wouldn't understand a lot of it but interested to see what paticular technique differs from what we had to self derive at Uni.
originally posted by: TEOTWAWKIAIFF
a reply to: Specimen88
Thou are ignorant and prove that Freemasons need to keep secrets from the profane like yourself!
As far as the laws of mathematicsrefer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” Einstein