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‘Alien calculus’ could save particle physics from infinities

quantamagazine.org

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Re: ‘Alien calculus’ could save particle physics from infinities

#31

Post by eloff »

d--b wrote: post #25
axilmar wrote: post #12

Sincere question: could it be that the underlying structure of the universe is really simple but since we have no idea what it is we have to use exotic mathematics for it?

This is Stephen Wolfram’s bet. He thinks the universe is based on simple computation rules. The emergence of complex traits from simple rules still requires exotic mathematics to describe macroscopically.

I’m just a computer guy, but I also see that as likely. When it comes down to it there’s less than 100 elements, made of a handful of forces and subatomic particles that make up the incredible universe that we live in. It seems somehow to get simpler as you go down.

Until you hit all the quantum weirdness and then it’s all wave functions and probabilities. That maybe comes out of something simple as well.

Re: ‘Alien calculus’ could save particle physics from infinities

#33

Post by staunton »

est wrote: post #7

> Tunneling is one of many nonperturbative phenomena in quantum physics, but nonperturbative effects are everywhere: The branching growth of snowflakes, the flow of a liquid through a pipe with holes, the orbits of planets in a solar system, the rippling of waves trapped between round islands, and countless other physical phenomena are nonperturbative. This is beautiful. Any examples of using Écalle's method to solve…

The three-body problem is solved nowadays (the existence and structure of possible solutions is known). It can also be simulated very precisely using numerics. There is no need for perturbation theory.

Re: ‘Alien calculus’ could save particle physics from infinities

#34

Post by pmontra »

omeysalvi wrote: post #9

I really appreciate how writers at Quanta turn extremely complex and dry topics into a pleasurable read by mixing simple analogies with history. I really admire the skill it takes to break down these topics and make them fascinating for someone with no understanding of them, such as me.

I like those articles too but I wish they include a short version with the major takeaways. In another industry that would be an executive summary. I don't always have the time to read all the story, so I end up fast reading it trying to find the important points and I'm never sure I really found them. In this case they seem to be the paragraphs after "Here’s an extremely rough cartoon version of the approach:"

Re: ‘Alien calculus’ could save particle physics from infinities

#35

Post by simonh »

esperent wrote: post #30
simonh wrote: post #18

Earlier quoted context omitted.

That’s quite possible. A lot of what we think of as fundamental physics might turn out to be emergent behaviour. In fact that’s pretty much the story of the development of physics. It turns out Newtonian mechanics is emergent from Relativity. Maxwells equations are emergent from quantum mechanics. The behaviour of bosons is emergent from the behaviour of quarks. As I understand it there are theoretical reasons to sus…

> It turns out Newtonian mechanics is emergent from Relativity. However relativity is far more complex than Newtonian physics.

That’s an interesting point, but I don’t think the complexity gradient from underlying causes to macroscopic effects always goes the same way. The macroscopic dynamic effects of an earthquake on a building can be modelled fairly easily. Trying to model the earthquake’s dynamics through the earth at the molecular level is a lost cause though.

Re: ‘Alien calculus’ could save particle physics from infinities

#36

Post by evanb »

sesm wrote: post #29

The way I read this: this method of finding non-pertrubative terms requires calculating perturbative terms first, that’s why it can’t be applied to QED and other more-or-less realistic theories. But of course string theorists can use this method to write more papers.

People can calculate perturbative processes in QED. Some observables are known to 7 loops (!), last I paid attention.

Re: ‘Alien calculus’ could save particle physics from infinities

#37

Post by staunton »

eloff wrote: post #31
d--b wrote: post #25

Earlier quoted context omitted.

This is Stephen Wolfram’s bet. He thinks the universe is based on simple computation rules. The emergence of complex traits from simple rules still requires exotic mathematics to describe macroscopically.

I’m just a computer guy, but I also see that as likely. When it comes down to it there’s less than 100 elements, made of a handful of forces and subatomic particles that make up the incredible universe that we live in. It seems somehow to get simpler as you go down. Until you hit all the quantum weirdness and then it’s all wave functions and probabilities. That maybe comes out of something simple as well.

The first fundamental step in any physics model (or theory) is to separate the easily describable "laws" from the almost impossible to describe "state". The perhaps surprising question is why anything at all can be separated but if that wasn't the case, we wouldn't be having this conversation.

"Going down" simply means identifying laws that are more universal in that they can underly models of different systems, ideally "any known system". Quantum weirdness isn't significantly harder mathematically than what came before (we don't have an objective measure of how "hard" some piece of math is), it's just harder to relate to everyday experience. It's similar to how we got used to "masses attract each other" or "things just keep moving in a straight line", which seemed ridiculous to most of Newton's contemporaries.

Re: ‘Alien calculus’ could save particle physics from infinities

#38

Post by temp512345 »

criddell wrote: post #23
simonh wrote: post #22

Earlier quoted context omitted.

I see mathematics as a rigorous highly consistent descriptive language. Physics theories expressed mathematically are very precise descriptions of observed behaviour, but calling them laws is deceptive. The fact that they align precisely to observed behaviour just indicates that the behaviour of physical systems is highly consistent. Well, I hope so. If reality was inconsistent and things happened arbitrarily with no…

I wish I understood it better, but you don’t have to go much below classical mechanics before I’m lost. But from what I’ve read, the deeper you go, the more it’s difficult to find something other than mathematics. When you ask what is a particle you find out it’s probably an excitation of a quantum field. So what is a quantum field if not a mathematical structure? Is there a physical reality to wave function collapse…

What do you mean something other than mathematics? It's just a language problem nothing else. Just because the English language lacks the descriptive power it does not mean those objects are "mathematical", just as a round ball is not "English" in it's nature just because you can describe it's properties and behavior using that language. A quantum field is just that, a field, it exists just as much as a magnetic field exists and that you can observe directly. It is an area of space where a specific "force" you might say has impact on objects that enter that area of space. It's properties are measurable and they produce consequences in the world and it has a precise description using the language of mathematics

Re: ‘Alien calculus’ could save particle physics from infinities

#39

Post by evanb »

esperent wrote: post #30
simonh wrote: post #18

Earlier quoted context omitted.

That’s quite possible. A lot of what we think of as fundamental physics might turn out to be emergent behaviour. In fact that’s pretty much the story of the development of physics. It turns out Newtonian mechanics is emergent from Relativity. Maxwells equations are emergent from quantum mechanics. The behaviour of bosons is emergent from the behaviour of quarks. As I understand it there are theoretical reasons to sus…

> It turns out Newtonian mechanics is emergent from Relativity. However relativity is far more complex than Newtonian physics.

The kinds of physical influences that are allowed in Newtonian physics are more general than those allowed in relativity. Relativity requires physics to satisfy constraints.

Which is more complex depends on what you mean. There are fewer laws in the possibility space of generally-relativistic physics than Newtonian physics. So, which metric is more important? Less pleasant calculations or a larger search space?

Your comment suggests you weigh the calculational simplicity more heavily, but most physicists would come down on the other side of the issue.

Re: ‘Alien calculus’ could save particle physics from infinities

#40

Post by Xcelerate »

criddell wrote: post #19
axilmar wrote: post #12

Sincere question: could it be that the underlying structure of the universe is really simple but since we have no idea what it is we have to use exotic mathematics for it?

Some think the underlying structure of the universe is mathematics. That is, the universe isn’t merely describe by mathematics, but it is a mathematical structure.

I’ve wondered that before. The question would be how to differentiate the two possibilities. I suppose if you could somehow prove that our universe is the only one capable of existing while still meeting certain consistency requirements, then it might be fair to call that a “mathematical structure”.

On the other hand, if our universe is one of many arbitrary possible universes, I’d say it’s not a mathematical structure (although it could still be the only universe that exists, hypothetically).

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