An amplituhedron is a geometric construct that has many attractive properties for constructing a theory of everything that unifies General Relativity and Quantum Field Theory, allowing us to understand how the Universe right down to the Planck scale. https://en.wikipedia.org/wiki/Amplituhedron Presently, it's a "toy model" that doesn't apply to our reality, but a model from which space-time, locality and unitarity are emergent properties seems like it is on the right track to a real theory of everything, as opposed to theories in which these properties are assumed. I wonder what else might be persuaded to drop out of such a theory to do away with some of the extant unsolved problems in Physics such as the vacuum catastrophe and apparent fine tuning of many parameters to support life. https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics Perhaps Plato and Pythagoras were correct, in essence if not detail - mathematics, geometry in particular, is the basis of everything. Plato believed an understanding of geometry was essential to understanding the Cosmos. Above the entrance to his Academy in Athens was a sign that read: “Let no-one ignorant of geometry enter here”. http://www.storyofmathematics.com/greek_plato.html
I was going to say that's extremely interesting, until I realized to just get what this is talking about I have to go at least 3 levels deep into links describing the terminology. I dropped mathematics somewhere around modular forms and number theory, where everything became so abstract it was hard to keep any interest without an external driver. Modern physics is even crazier in that regard, but despite it being more interesting per se, those guys lost me some time after Hamiltonian mechanics (which was in itself fun). That's an amusing to read, though: Why does Star Trek have to come up with nonsensical technobabble, when they can simply quote Wikipedia articles on math? “A quantum affine algebra is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine Lie algebra. They were introduced as a special case of their general construction of a quantum group from a Cartan matrix. One of their principal applications has been to the theory of solvable lattice models in quantum statistical mechanics, where the Yang-Baxter equation occurs with a spectral parameter.” “Ugh, I hate that class, this is so last century. When are we going to study warp theory?” ... On a more serious note, I'm ambivalent about the expectation that a theory of everything will actually ever emerge. Not because I think our present understanding of physics is complete, or accurate, or the most simple model of the universe, or we need to stop looking, or these aren't amazing people who I envy, but because I kind of question the rationale for this expectation. We assume that the current fundamental laws of physics are too complex, patchy, and a convoluted mess with holes in it. So it can't be fundamental, it has to be caused by something else. Which feels like another way of saying we don't like it, so we will be able to further explain it. Looking for further explanation in itself is always a good thing. (You can see me green with envy other people are doing it, and I can barely follow the conversation.) We would have never gotten this far if we thought atoms are really atomic, hairy chemistry is the root of it all, and let's be done with it. But we can't expect to keep finding more explanations. At some point we will hit rock bottom and get to the actual foundation. There is zero reason to expect it will be simple, let alone elegant when we reach it. The current complex, patchy convoluted mess with holes in it that I can't wrap my head around is exactly what I expect the foundation is going to be like. So it might be that we already hit it, we simply haven't figured out all the quirks. Ultimately, our expectation should be that the fundamental laws of physics are the simplest ones that support intelligent life (the day survivor bias cut itself on the Occam's razor). That can be philosophically explained away by invoking infinite universes, and imagining the cosmic equivalent of natural selection. Under such premise, and given how messy the results of biological evolution are, its cosmic evil twin wouldn't yield anything more pleasing. Not to mention that we have literally evolved to enjoy our own messiness (we like sex, for heaven's sake), but we have not evolved to like the universe's. So it might just be as nasty as it was intended to be. Injecting philosophical drivel like multiple universes in itself sounds questionable, but whenever you reach the actual fundamental laws of the universe – which are by their own definition unexplainable (no other other thing causes them, duh), you have to descend into philosophy. I kind of hate the phrase “fine tuning”, as it simply says “it's too complex still”. Well, what's the threshold? It's not like life is something trivial that can just pop anywhere – none of my Game of Life patterns have invented the wheel yet. Sure, the universe makes up for some of that by being gargantuan in size, so if we're the only life anywhere in it, maybe we can expect some simplicity to be found in the rules. It still won't work without some fine tuning, and some might still be a lot. We can't even get planets without fine tuning. Sure, you can have a theory of everything that in itself implies multiple universes in some fashion, so it's no longer philosophical (and sound more sciency). But then where did the multiverse fine tuning that implies this specific set of universes come from? Then you'd have to replace the theory of everything with a theory of anything, and you're back to square one. So it could be that GR and QFT can't really be unified in a single theory, aren't really incompatible e.g. because the insides of black holes don't really exist in our observable universe – you could have two identical universes with a different set of laws governing the insides of black holes, and you wouldn't be able to tell which you're in because of the No Hair Theorem, leaving the conflict zone of GR and QFT untestable (you can even wonder if you're simultaneously in both universes). It's a preposterous suggestion, but only because it's extremely ugly. It could still match observation.
Yeah, I don't understand a lot of the mathematics either. I guess we have to take it on trust that these theorists are extremely clever and not just flim-flamming to obtain research grants. That reality at base might be a mathematical abstraction reminds me of a Heinlein novel I've forgotten the name of where such a realisation leads to the invention of an FTL drive. ETA: The Heinlein novel was one of his junior fiction works "Time for the Stars". ETA2: A long lecture on the subject of the Amplituhedron by Nima Arkani-Hamed: A shorter talk about why unifying GR and QFT is problematic:
Isn't that Melanie Griffith's mother? ...oh, thats Tippi- Hedren https://en.wikipedia.org/wiki/Tippi_Hedren
Every time I see things like this it reminds me of that whole "wave structure of matter" theory from 15 years ago by that french guy. He theorized that elementary particles are basically spherical standing energy waves in the fabric of reality and then used this theory to (partially) reconcile quantum mechanics with general relativity. Taken to its logical conclusion, it even accounts for the predictions of string theory.
It sounds like that particular theory assumes the background of space-time - the amplituhedron generates the background and other properties from twistor space or a form thereof. It would be interesting to know what "french guy"'s theory predicts at the Planck scale - that is at the centre of black holes and at the beginning of the big bang.
Something like an aether, actually, but functionally similar to "space-time" which is already uncomfortably aether-like in its concepts. Actually, though, it was more of an extrapolative model based on wave-particle dynamics and lorentzian relativity. Sort of a crackpot theory, but most of his predictions (before the guy died) actually panned out. So I've reached a point in my life where I actually believe that many theoretical physicists have staked their careers on producing incomprehensible word salads that nobody else has the mathematical background to really question them on for fear of looking unqualified or ignorant. I'm not sure what this sentence is based on, but I suspect this may be an example of this. Crests and peaks between standing wave fronts, if I remember correctly. I think his conclusion was that there's a "standard" wavelength for the structure of any particle (which itself is a spherical standing wave) and that length is basically planck length. Various other energy fields -- gluonic fields, electromagnetic, strong and weak, etc -- are derived from the combinations of many planck-scale wave forms constructively or destructively interfering with each other. The last prediction he made just before he died was based on this, something to do with allotropes formed by combinations of polar atoms because their atomic bonds would always form on predictable angles consistent with the interference patterns of their fields of force.
So, maybe the 19th scientists that came up with that whole aether thing were kind of right? That would be peculiar but, fashions do tend to come back, from time to time...
^ well I would bet that, conceptually, they weren't entirely wrong. At least, the standard model as it now stands has become so convoluted and so packed full of ad hoc explanations that dark matter clusters might as well be epicycles.
Yes - this is true. How about Dark Energy just being this: Space/Time in it's natural state is expansive, so long as there is nothing to anchor it, or cause it to contract?