Maths and Physics #5: To Present Day

It is one thing for patterns of overlap and relevance to emerge between physics and maths. But to make the actors in the two fields actively work with the belief that work in one can yield insights into the other, that is a different thing altogether. For the latter to happen, you need someone very charismatic, very persuasive, someone “inclined to whip up enthusiasm for wild ideas”. The mathematician, Michael Atiyah, was just that guy.

 

He convinced (math) geometers and (physics) gauge theorists that they were working on the same subject, just from different perspectives. Subatomic physicists were surprised that a very hard problem in their field could be solved using a maths theorem that connected topology and calculus. So much was the overlap that the Wu-Yang dictionary was created to enable physicists and topologists to talk to each other! In fact, repeatedly, both sides found advances or a new theory in the other field gave insights into questions on their side.

“The effectiveness of mathematics in physics is no less remarkable than the effectiveness of physics in mathematics.”

 

But there is also tension between the two fields. Maths needs iron-clad proofs. Physics, on the other hand, is not interested in “perfect rigour” and will instead settle for whatever increases their understanding of the universe.

 

The idea of supersymmetry began to be taken seriously by physicists because:

“Supersymmetry is the only possible way to extend the symmetry between space and time… (to also be) quantum mechanical.”

It was, to the mathematicians, “too beautiful to be wrong”. But where was the experimental proof for it, countered the physicists?

 

This love of maths irritated experimental physicists at times:

“The theorists are inventing particle after particle… and of course, we are supposed to find them.”

 

String theory. It is highly controversial because it doesn’t make any new predictions that can be verified. At least, not yet. And yet, its maths is appealing to many. It unifies quantum mechanics and general relativity, without throwing up any annoying infinities. Plus, it needs gravity to exist, unlike most other theories that find gravity messing up the theory. Was mathematical beauty a sign of “truth” about the universe? Or was this a case of maths going too far?

 

The maths-physics story will continue to evolve in the future.

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