Physics and Math

Dec 2017
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Tel Aviv
What terms in math is used in physics?
 

romsek

Math Team
Sep 2015
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1,674
USA
The more physics we observe the more advanced math we find is necessary to model our observations.

Abstract math that seems to have no purpose at all today may well be the backbone of tomorrow's physics.
 
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Aug 2012
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Abstract math that seems to have no purpose at all today may well be the backbone of tomorrow's physics.
Or economy! Since Diophantus, number theory has been the most useless branch of math. Hardy [Jeremy Irons in The Man Who Knew Infinity] said that number theory is the most beautiful branch of math precisely because it's so supremely useless!

And now it's the basis of cryptocurrencies. "Number theory is what puts the crypto in cryptocurrency!" I always wonder what Hardy would say if he came back and learned that number theory was at the heart of the modern global economy.

I wonder what will be the next useless branch of math to become useful. Perhaps the infinite. There's a lot of speculative talk about multiverses. To have a theory of the physically infinite you need to ask yourself if physical infinity follows the rules of mathematical set theory. After all, set theory is a historically contingent idea less than a century old in its modern form. Why should it be true about the world? Nobody's asking these questions but I wonder if the multiverse theorists won't have to grapple with them soon.

How about uncountable sets? Far from the universe being computable, what if noncomputable numbers are the key to the next revolution in physics and/or computing? Or transfinite ordinals and cardinals? What if professor so-and-so from Helsinki proves that the Big Bang can be deduced by assumimg one of the large cardinal axioms along with some laws of physics? That would be a pretty big deal. Set theorists would become overnight rock stars.

I've googled "physics and set theory" from time to time. All that shows up are a handful of academic papers behind paywalls. That tells me that there's more than zero interest in the subject but it's way below anybody's radar.

I think that if the multiverse theorists are serious about making sense, they're going to have to talk about what they mean by infinity.
 
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romsek

Math Team
Sep 2015
2,963
1,674
USA
I've googled "physics and set theory" from time to time. All that shows up are a handful of academic papers behind paywalls. That tells me that there's more than zero interest in the subject but it's way below anybody's radar.
Complexity theory is becoming hugely important as it seems to be the connection between the quantum and general relativity worlds.

I believe what Susskind and others are trying to say is that the strength of gravity between two objects at the quantum level has to do with the complexity of the quantum entanglement network between them. I can't say I even begin to really understand it.
 
Feb 2016
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A nice casual discussion on related topics is given here.

edit: Actually not quite... Still..