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?
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 suspect that quarks do not have any decomposition though. We’ll see.
> The behaviour of _bosons_ is emergent from the behaviour of quarks.
I think you mean
> The behaviour of _hadrons_ is emergent from the behaviour of quarks.
--
Anyway, back to your main idea, the problem is that most of the times the new underlaying theory is even worse than the original one
> Newtonian mechanics is emergent from Relativity
For Newtonian Mechanics you need only basic calculus. For General Relativity you need curvature, tensors, two definitions of derivatives and other nasty stuff. [I never saw the details, but it's in my todo list.]
> Maxwells equations are emergent from quantum mechanics
Well, electromagnetism is just the local gauge invariance of the U(1) group. The idea is very simple but each word in that sentence needs like one semester to be decoded. [I saw the calculations a long time ago. I don't remember the details, but I remember the general idea. I wrote a comment with a oversimplified version https://news.ycombinator.com/item?id=8189346 )
> there are theoretical reasons to suspect that quarks do not have any decomposition though.
My favorite reason is that for a classic small ball, the ratio of the magnetic moment to the inertia moment is 1 (once you fix some nasty details about units), but for an elementary quantum particle it is 2. For composite particles, there is no theoretical value. https://en.wikipedia.org/wiki/G-factor_(physics)
The experimental value for protons is 5.5 and for Neutrons is 3.8, that is not surprising because we are sure they are composed particles.
For Electrons and Muons it's slightly more than 2, but we understand that difference quite well (but not perfectly, and that is related to the main point of the article here).
I don't think it has been measured directly for Quarks, but my guess is that it's used in some parts of the calculation of some Feynman diagrams, and if it were very different from 2 someone would have noticed.
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.
Everything is simple, given the right notation (and the concepts underlying it).
The original Maxwell theory of electromagnetism is about 10 rather involved equations. Maxwell-Heaviside form is 4 simpler equations. A formulation using differential 3-forms is 2 simple equations. A formulation using geometric algebra / Clifford algebra is one utterly simple equation.
I think this ends up being a question that is the cousin of Bertrand's paradox. In that case, the English words in the original question, despite feeling concrete in what they ask for, leave enough vagueness to give different ways to solve the problem that all seem to satisfy the query but give incompatible answers. I say this because I see two similar phrases in your query that seem to carry equal levels of assumptions.
First is the idea of simple. If something has a few very well defined rules that are understood in isolation, but whose emergent behavior is beyond our ability to define, is it simple? Conway's Game of Life is somewhat the default example. 2 very simple rules (or perhaps more, depending upon specifically how you count them), but it gives rise to a Turing complete system. Math itself is another example, as mathematicians seek to find simple rules from which math arises, yet even for the subsets of math that are limited to such rules, is it really fair to call it simple?
The second idea is that of an underlying structure. Does the universe have an underlying structure, and even if it does, does that exist in side of some more foreign concept? What happens before the big bang? Why did the big bang happen when it did? Are there other universes, both from the many worlds interpretation of quantum mechanics, and universes that entirely separate from our own. These seem questions that feel almost entirely in the realm of science fiction, not physics, but there are plenty of theoretical physicists who dive into this field even though it currently doesn't produce testable hypothesis and is thus outside the scope of proper science.
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 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 rhyme or reason I think we’d be in big trouble.
I’m not totally unsympathetic to the view that maths is fundamental though. It’s an interesting way to think about it.
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).
The universe could be simpler than the current models suggest, but that would require taking a step back too far for the comfort of today’s STEM-oriented mind. For as long as natural sciences consider philosophy a load of hand-wavy abstract inapplicable hogwash they will be stuck iterating on existing physical models towards local maximum.
simonh|2 years ago
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 suspect that quarks do not have any decomposition though. We’ll see.
gus_massa|2 years ago
I think you mean
> The behaviour of _hadrons_ is emergent from the behaviour of quarks.
--
Anyway, back to your main idea, the problem is that most of the times the new underlaying theory is even worse than the original one
> Newtonian mechanics is emergent from Relativity
For Newtonian Mechanics you need only basic calculus. For General Relativity you need curvature, tensors, two definitions of derivatives and other nasty stuff. [I never saw the details, but it's in my todo list.]
> Maxwells equations are emergent from quantum mechanics
Well, electromagnetism is just the local gauge invariance of the U(1) group. The idea is very simple but each word in that sentence needs like one semester to be decoded. [I saw the calculations a long time ago. I don't remember the details, but I remember the general idea. I wrote a comment with a oversimplified version https://news.ycombinator.com/item?id=8189346 )
> there are theoretical reasons to suspect that quarks do not have any decomposition though.
My favorite reason is that for a classic small ball, the ratio of the magnetic moment to the inertia moment is 1 (once you fix some nasty details about units), but for an elementary quantum particle it is 2. For composite particles, there is no theoretical value. https://en.wikipedia.org/wiki/G-factor_(physics)
The experimental value for protons is 5.5 and for Neutrons is 3.8, that is not surprising because we are sure they are composed particles.
For Electrons and Muons it's slightly more than 2, but we understand that difference quite well (but not perfectly, and that is related to the main point of the article here).
I don't think it has been measured directly for Quarks, but my guess is that it's used in some parts of the calculation of some Feynman diagrams, and if it were very different from 2 someone would have noticed.
esperent|2 years ago
However relativity is far more complex than Newtonian physics.
d--b|2 years ago
The emergence of complex traits from simple rules still requires exotic mathematics to describe macroscopically.
eloff|2 years ago
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.
nine_k|2 years ago
The original Maxwell theory of electromagnetism is about 10 rather involved equations. Maxwell-Heaviside form is 4 simpler equations. A formulation using differential 3-forms is 2 simple equations. A formulation using geometric algebra / Clifford algebra is one utterly simple equation.
staunton|2 years ago
WindyLakeReturn|2 years ago
First is the idea of simple. If something has a few very well defined rules that are understood in isolation, but whose emergent behavior is beyond our ability to define, is it simple? Conway's Game of Life is somewhat the default example. 2 very simple rules (or perhaps more, depending upon specifically how you count them), but it gives rise to a Turing complete system. Math itself is another example, as mathematicians seek to find simple rules from which math arises, yet even for the subsets of math that are limited to such rules, is it really fair to call it simple?
The second idea is that of an underlying structure. Does the universe have an underlying structure, and even if it does, does that exist in side of some more foreign concept? What happens before the big bang? Why did the big bang happen when it did? Are there other universes, both from the many worlds interpretation of quantum mechanics, and universes that entirely separate from our own. These seem questions that feel almost entirely in the realm of science fiction, not physics, but there are plenty of theoretical physicists who dive into this field even though it currently doesn't produce testable hypothesis and is thus outside the scope of proper science.
criddell|2 years ago
simonh|2 years ago
Well, I hope so. If reality was inconsistent and things happened arbitrarily with no rhyme or reason I think we’d be in big trouble.
I’m not totally unsympathetic to the view that maths is fundamental though. It’s an interesting way to think about it.
Xcelerate|2 years ago
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).
tourgen|2 years ago
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strogonoff|2 years ago
CyberDildonics|2 years ago