5 ms·
Math That Takes Newton into the Quantum World
- m12k 7y agoThis was an interesting read - reminded me of another article [1] I read in 2013 about using a high-dimensional 'jewel' to describe reality, which then turned out to be an extremely efficient way to do the calculations from a Feynman Diagram. I'm still holding out hope that a unified theory will be found within my lifetime, and that these kinds of math will hold the key. [1] https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917/ https://www.quantamagazine.org/physicists-discover-geometry-...
- _Microft 7y agoYou might also like https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/ https://www.quantamagazine.org/the-octonion-math-that-could-...
- jacknews 7y agoI believe this is somewhat controversial
- m12k 7y agoThat was an interesting read! Interestingly, John Baez, author of the originally posted link is also quoted in it.
- vankessel 7y agoI personally think that the split-octonions[1] hold promise for physics. The subset of the split-octonions where the i, j, k, and l components are 0 have a metric that is similar to that of Minkowski space[2]. (t + xli + ylj + zlk) * (t - xli - ylj - zlk) = t^2 - x^2 - y^2 - z^2 [1] https://en.wikipedia.org/wiki/Split-octonion https://en.wikipedia.org/wiki/Split-octonion [2] https://en.wikipedia.org/wiki/Minkowski_space https://en.wikipedia.org/wiki/Minkowski_space
- deleted 7y ago[deleted]
- danbruc 7y agoIf you are interested in this, there are quite a few lectures by Nima Arkani-Hamed available on YouTube. From some aimed at the general public about the big picture of fundamental physics and the unresolved issues in it to pretty technical discussions of the amplituhedron and the related physics.
- deleted 7y ago[deleted]
- Koshkin 7y ago> Newton into the Quantum Simply put, "the first quantization." (I am amazed how difficult popularizers of science often make it to understand what the hell they are talking about.)
- soVeryTired 7y agoIf you don't already know what quantization is, that's just jargon though.
- gus_massa 7y agoThe problem in the title is that "Newton" just means "Classic Mechanics". Newton has a lot of results, like in gravity, light, mechanics, ... Replacing "Classic Mechanic" with "Newton" looks like the weird replacement tables in some xkcd comics. (Inside the article, the idea is clear, the problem is in the title.)
- JJMcJ 7y agoSimilar to personalizing all General Relativity advances and issues as being about "Einstein". Nobody does that for Quantum Mechanics.
- gus_massa 7y agoFor what it's worth, I hate the articles with title "Einstein is wrong/right". (Extra bonus hate point for "Scientist say Einstein is wrong/right") The case of Quantum Mechanics is strange, there is no clear name to choose. I guess Heisenberg an Schrödinger are the best candidates, but their names are associated in popular culture with some specific effect instead of the whole theory.
- danbruc 7y agoWhy should our universe be so readily governed by mathematical laws? As he put it, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” This is something that gets repeated again and again but I don't find this puzzling at all. Mathematics is an extremely general tool for modeling all kinds of things, so if something follows some sort of rules, you most certainly can use mathematics to describe, model, and analyze it. While I am not aware of any specific results or hypotheses, I would still guess that mathematics - or even some small subset like set theory - is in some sense universal for modeling things in a way similar to universal models of computation like Turing machines or lambda calculus. I can not even imagine a universe with laws of physics that could not be tackled with mathematics. Even if the universe was pure chaos, everything happening totally randomly without any recognizable rules, we still could try throwing statistics at it, at least ignoring the fact that such an universe would probably not be a place for life to flourish. Finally mathematics does not exist in a vacuum, we invented large parts of it specifically to deal with real world phenomenons. And then of course »some« more that does not describe anything existing in the physical world. Somewhere deep down below there are certainly many puzzling issues, from why there is a universe at all and why it is the way it is to human consciousness and why and how we are able to make sense of the universe, but that mathematics can describe the universe does not seem to be one of those, at least to me.
- dreamcompiler 7y agoI think of it in terms of Kolmogorov complexity: The number of mathematical symbols you have to write down to describe some phenomenon of the universe. Given the apparent complexity of the universe, it still amazes me that that number of symbols is so small. There doesn't seem to be a reason why that should be true. We know from complexity science that complexity can arise from simple rules, but there's still no reason why those rules have to be simple in the first place.
- kaibee 7y agoMy layman's perspective on this: I think there's some hidden complexity at play here also. Yes, the number of symbols required is small. But those symbols are only meaningful to someone with the education to understand them. Namely, usually, a human being with a very complex brain, both in terms of requiring millions of years of evolution and years of training time. Actually, those alone aren't enough, since these people are building on top of hundreds of years of previous work in the field.
- paulpauper 7y agoto say that Cartesian geometry is in any way like algebraic geometry is like saying that a skateboard is like a Ferrari >One reason is that quantum physics is based on algebra, while general relativity involves a lot of topology. But that suggests an avenue of attack: If we can figure out how to reduce topology to algebra, it might help us formulate a theory of quantum gravity. huh? everything boils down to big matrices and hard differential equations in the end >My physics colleagues will let out a howl here, and complain that I am oversimplifying. Yes, I’m oversimplifying: no, you're not making any sense. i stopped reading here
- chunky1994 7y agoI'm in complete agreement. The fact that he entirely glosses over there existing a field like algebraic topology with tremendous application to physics shows the author has little understanding of what he's writing about when it comes to physics.
- gilleain 7y agoThe author is https://en.m.wikipedia.org/wiki/John_C._Baez https://en.m.wikipedia.org/wiki/John_C._Baez who: > He is known for his work on spin foams in loop quantum gravity.[3][4] For some time, his research had focused on applications of higher categories to physics and other things. So he probably has _some_ understanding of physics, no?
- danharaj 7y agoJohn Baez is one of the most qualified people in the world to talk about mathematical physics. Who are you?
- chunky1994 7y agoThat's an appeal to authority if I ever saw one. He may be qualified to talk about it, but he certainly isn't showing that here. The parent comment shows what we're taking issue with.
- Koshkin 7y ago> algebraic geometry Then there's always geometric algebra! https://en.wikipedia.org/wiki/David_Hestenes https://en.wikipedia.org/wiki/David_Hestenes
- Myrmornis 7y agoIn addition to giving some idea about algebraic geometry, I appreciated the insight and honesty it contained regarding how a (high profile) researcher decides to try to learn more about an area, and about how the author was intimidated by it. I appreciated it, but, it is also pretty depressing, in that a professional mathematician of Baez's calibre clearly found it very tough-going just trying to survey the existing knowledge, let alone adding to it.
- DoctorOetker 7y agoCan anyone recommend good course notes, books, ... on algebraic topology? Good reference books? But first and foremost any recommended primers into algebraic topology?