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"Exploring the Mirror Link Between Two Geometric Worlds" Topic


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Tango0116 Apr 2018 10:06 p.m. PST

"TWENTY-SEVEN YEARS AGO, a group of physicists made an accidental discovery that flipped mathematics on its head. The physicists were trying to work out the details of string theory when they observed a strange correspondence: Numbers emerging from one kind of geometric world matched exactly with very different kinds of numbers from a very different kind of geometric world.

To physicists, the correspondence was interesting. To mathematicians, it was preposterous. They'd been studying these two geometric settings in isolation from each other for decades. To claim that they were intimately related seemed as unlikely as asserting that at the moment an astronaut jumps on the moon, some hidden connection causes his sister to jump back on earth…"
Main page
link

Amicalement
Armand

Bowman17 Apr 2018 6:37 a.m. PST

From the link:

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

From that aspect I'm not sure how successful the article is. I don't think I'm stupid but I'm having a hard time figuring out the purpose of what the people are doing and what they are hoping to solve. Perhaps the author assumes some understanding of the reader. Until then writing such as:

"Another major open line of research seeks to establish that, assuming you have a torus fibration, which gives you mirror spaces, then all the most important relationships of mirror symmetry fall out from there."

….seems just like "word salad".

gladue17 Apr 2018 7:52 a.m. PST

If I'm remembering correctly, mirror symmetry ends up being important for quantum mechanics because they allow you to choose the space which you make proofs in. Basically, the conditions of one of the mirror spaces may make a particular mathematical proof impossible (or very difficult) where it is very *easy* in the mirror space. Since they are mirror images, if you can prove something in one of the spaces it must apply to both. It's just that the mathematical conditions of one will allow some proofs to be easier than in the other (and vice versa).

Bowman18 Apr 2018 12:04 p.m. PST

That doesn't totally clear things up, but your explanations are better than the authors.

mandt224 Apr 2018 9:49 a.m. PST

I was reading about twin particles that match each other's behavior even when they are far apart, faster than the speed of light. Perhaps this sheds some light on that…

link

…or maybe that sheds some light on this.

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