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joigus

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Everything posted by joigus

  1. Quantum groups are deformations of Lie groups themselves in the space of parameters. They're of concern mainly to mathematicians or very mathematically-minded mathematical physicists. Related to algebraic topology. I don't know what you mean by "classical groups". Finite groups? Lie groups? Groups relevant to classical mechanics only? I don't know what you mean by "quantum algebra". Seems to be some kind of umbrella term for all the tinkering tools somehow related to quantum mechanics, quantum field theory, and the like. For Hopf algebras I would recommend you more specialised forums, like Mathoverflow or MathStackExchange, after you're through with the obvious sources you can find on the internet.
  2. ℵ0 is obviously a symbol used in a definition. The definition involves a bijection. A bijection to the natural numbers. Any set for which a bijection can be constructed to the natural numbers is said to have the cardinality of the natural numbers. We call this cardinality ℵ0. Mind you, we call this abstract concept ℵ0. The question, Proves that you do not understand the definition of ℵ0. Repeat: You do not understand the definition of aleph naught. Nothing becomes anything. It is what it is. Your question is as meaningless as, eg, What is the magic in the natural numbers that makes n(n-1)...2 become n! ? Cardinalities aren't numbers, although sometimes they can be. They are what they are, and what they are is what they are defined to be. They are defined via bijection, therefore no numbers necessarily, but abstract properties of relations between sets that are equivalence relations, and only sometimes happen to "become something" in the sense that you suggest.
  3. True. Last time I was thinking what on earth that (t,x) (y,z) even means, with no metric or interval, or anything else to tell them apart.
  4. I suppose you could say 2D sphere could refer to S2, which is the sphere that can be described with 2 parameters. IOW: The sphere that can be embedded in a flat 3-dimensional space. Mathematicians sometimes talk about: S1: The circle (the 1-sphere) S2: The ordinary sphere (the 2-sphere) S3: The glome or hypersphere (the 3-sphere): https://en.wikipedia.org/wiki/3-sphere Etc. That as to the maths of it. As to the physiscs of it, as @swansont has pointed out, this would be a strange physics with a 2-dimensional time and a 2-dimensional space in which inverse-square law wouldn't hold. So it's a non-starter.
  5. Glad to see you gave speaking in riddles a rest. 👍 +1
  6. What distinguises x to pair up with t? Why does this x go from -infinity to +infinity while y and z are compact? No. But there's worse: What happens to weak interactions and strong force? Are they outside spacetime?
  7. Brilliant. This is my favourite way of talking about discrepacies in measured lengths and times for different observers, and I love that you just used it. Moving is like taking an angle. In fact, that's exactly what it is: Being at an angle with respect to another "mover". Somewhere else I've explained this as just another kind of foreshortening. Consequences of foreshortening are real enough for anybody trying to --eg-- get a large object through a short door by tilting it. Of course, if you change your state of motion, your previous tilting parameter (your velocity) is no longer the same. This is at the core of so many people trying to "point out" to everybody else that "something is wrong" with relativity.
  8. Thanks for the reaction. Yeah, I found out about this guy a couple of days ago on the Rick Beato channel, and I was blown away.
  9. The Bongo Song Author: Safri Duo Drum cover: El Estepario Siberiano Last 1.5 min are promotional material
  10. Neither do I. There are the vacuum solutions that you point out and they correspond to we all know what. There are also interesting possibilities in the so-called topological vacuum solutions which would not be related to source charges. I'm still trying to absorb the impact of "the spirals would be geodesics", or something equally daft.
  11. Your physics is wrong for several reasons that have been pointed out. But here's another one: Logical fallacy implies a bad use of the rules of arguing in order to prove a point; it says nothing about being right or wrong regarding that point. Thus, even a theory based on false assumptions could be correct in the sense that it provides you with the right mathematical model. Ironically, that's what happened with Maxwell's theory of electromagnetism. He pictured mechanical tensions on a medium, which totally was the wrong idea, as later found out. But it gave the right equations, which in turn led to the right ideas that unfurl the amazing generalisation which is relativity, which you don't seem to understand.
  12. For a less intuitive but more encompassing understanding of energy --if somewhat abstract-- one can't do better than this: https://www.feynmanlectures.caltech.edu/I_04.html Or, perhaps, one can. We have Emmy Noether to thank: https://en.wikipedia.org/wiki/Noether's_theorem#Example_1:_Conservation_of_energy When the mathematical dust has settled, the idea is: Energy is an abstract property of systems which they must have if 1) They can be described by a principle of least action, and 2) Physical laws cannot include time explicitly. As we know both to be the case almost universally (cosmology being perhaps a case when things should be discussed more carefully), physical systems must have an energy.
  13. That's not consistent with Maxwell's equations, only too obviously. And I don't know what you mean by "the photon collapses". A localised dipole produces a field that is zero-divergent everywhere. The total charge of a dipole is q-q=0. Any monopolar term cannot be accounted by the photon.
  14. I tried with both German and Chinese. I had to give up on both, but I would recommend studying challenging languages if only to get an idea of the different ways in which information is organised in them. Chinese really was the biggest challenge in the sense that I realised I'd probably never become any fluent in it no matter how hard I tried taking it up that late in my life. 😢
  15. Yes. Now is this difference enough to justify a different symbol? I'm not saying it is. The phonetics of English is very complicated indeed. It's almost as if every word constituted a case study (that's obviously an overstatement, as there are regularities, obviously). But there are clearly many many irregularities, which must have to do with history. I won't pretend I'm an expert on this, of course. I just like to think about these things. And English has taken a lot of my thinking and observing.
  16. The vocal cords are vibrating when you pronounce "rather" while they're not when you pronounce "with" resulting in two very different sounds. Try it, and you'll see. So, in answer to your question: Since the moment you pronounce them. Exactly as in "them" and "bath" (different). I don't care what funny words any linguist uses to describe them. I've done an experiment, and in my book that is sacred.
  17. You could in principle make mass from non-mass. Charge doesn't work that way. For the reasons Swansont is telling you about. You need a divergence. IOW, source field lines to source out of a point. Also, models based on ribbons with kinks and antikinks, and breathers, and many other topological properties have been done to death. I don't see why it's deterministic (Planck's constant is zero?) Probabilities are kicked out of the picture? I don't see how Lorentz's dilation equation could be made more precise either. More precise in what parameter? What does it mean to do an autopsy on an elementary particle? I cannot make sense of anything you say.
  18. Normalisation should come first. What is so suspicious about the motivation that you need an "actual motivation"? Isn't the fact that physical parameters should be expected to depend on the length/energy scale at which you observe them enough motivation?
  19. No. It's based on amplitudes. Probability comes from amplitudes. Amplitudes cannot be explained in terms of probabilities.
  20. I hope you also notice that English doesn't identify a particular sequence of letters with a sound. Eg, (my emphasis) the "th" sound in "rather" is very different from "th" sound in "with."
  21. Sorry, because I was guilty of it. https://en.wikipedia.org/wiki/Scale_invariance https://en.wikipedia.org/wiki/Universality_(dynamical_systems) Universality is frequently mentioned in association to scale invariance, not because it always happens, but because it seems to always happen in connection to critical phenomena.
  22. It rings a bell, yes: https://www.scienceforums.net/search/?q=Alcubierre&quick=1&type=forums_topic&nodes=29 Neither am I. Perhaps translation invariance @grayson? Agreed.
  23. It's a mathematical pattern rather than a process. I'm sure something like that is the reason behind @exchemist's excellent question. Take. eg, principles of extremal time, action, length, etc. They appear everywhere in physics. It's more about a recurring mathematical theme than actually a particular process.
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