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joigus

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Everything posted by joigus

  1. Update QAnon believers are in disarray: https://www.bbc.com/news/blogs-trending-55746304 I don't know what it means when a group of numb nuts are "in disarray". Was there any array, to start with? They seem to imply that a shockwave of disbelief is going through their ranks.
  2. Another possibility is that someone has been messing around with alternative histories. Parallel-universe plumbing if you will.
  3. There is no such thing as "absolute values of the metric coefficients" with an invariant meaning. Also, I don't think there's an invariant meaning to the concept of "relative sizes of the coordinate intervals". Another methodological comment on my part. If you're serious about relativity, try not to build up your arguments from coordinate patches. You're going to make mistakes. The literature is full of similar arguments, in the years before intrinsic formalisms were developed, which were proved to be wrong. The technique in GR today is: You use intrinsic formalism --vectors, forms, and tensors formed from them-- to establish the general results, and then go to a coordinate patch for a particular calculation with a particular distribution of energy-momentum. Allowed coordinate transformations in GR are diffeomorphisms, which means they're infinitely differenciable and never change the invariants of the metric --because their inverses are also differentiable--, so it's possible that you're going to a mathematical no-man's land. Nobody would bother to check due to your always working in coordinates.
  4. Stands for either "original poster" or "original post".
  5. Sorry, Markus. I hadn't seen this. But reading my comments you'll see I understood what you meant.
  6. No "recalculation" requested this time, I suppose. He will probably be proud of it.
  7. One of the girls in the last cover looks strangely familiar...
  8. That would be the Lorenz gauge --different Loren*s --. https://en.wikipedia.org/wiki/Ludvig_Lorenz It's first order. It becomes second order when substituted in Maxwell's equations, which I think is probably what you meant, Markus. ----- Maybe a split is in order? I agree with @studiot and @MigL. Although I find the discussion with @Markus Hanke very interesting. It's OK. If somebody had to be in charge of the Inquisition I'd rather it be 21st-Century Canadians. Much more humane, I'm sure. Nobody expects... that joke. 😆
  9. http://www.folksong.org.nz/soon_may_the_wellerman/index.html
  10. Let me get back to you when I get more time to think about this and review some literature. It's correct that radiation is generally described as having "2 DOF" in the sense of having two polarisation states. But the term "degrees of freedom" is a bit ambiguous. Some people use it in the sense of counting spin states. But there are also space-time variables, according to, \[\left|\boldsymbol{k},s\right\rangle\] The \( k_x \), \( k_x \), \( k_x \), and \( s \) would be four variables, more in the sense that I was talking about (DOF as number of variables necessary to describe the states). As I said, let me get back to you. Also, I think you can do the counting on the E's and B's, which are gauge invariant. You can do it on the A's, but AFAIR there's just one gauge fixing condition, because you're in \( U\left(1\right) \)... Still thinking. Apparently I'm outside my comfort zone too. LOL
  11. Ok. There's a couple of things that you're seeing there that are already taken care of in the mainstream formalism. And have been mentioned repeatedly. One of them is that for any physical 4-vector the pseudo-norm with signature (+,-,-,-) must be positive --causality. The other one that I at least forgot to mention --it's possible that either @Ghideon and/or @Markus Hanke have mentioned it and I've missed it--, is that the naught component must be positive. Those are called orthochronous 4-vectors. So you cannot add two arbitrary 4-vectors and hope that that has any physical meaning. When you add two orthochronous 4-vectors, you obtain another orthochronous 4-vector. Also, the orthochronous character ( \( v^0 > 0 \) ) is split in mutually disconnected subsets of the Minkowski space, so the idea that you suggest that there is a "perforated" structure is actually a misguided intuition. The reason is that both the sign of the Minkowski pseudometric and the zero component are continuous and differentiable function of their arguments: \[ f\left(\alpha^{0},\alpha^{1},\alpha^{2},\alpha^{3},\beta^{0},\beta^{1},\beta^{2},\beta^{3}\right)=\alpha\cdot\beta \] \[g\left(\alpha\right)=\alpha^0\] So you can't have either changes in sign of the product, nor changes in the sign of any component for arbitrarily close 4-velocities, as you posit.
  12. (My emphasis.) Your tangents are always very interesting. Of course, you're right. I meant "in a sense" in the sense that it is an object that only has 6 non-zero components in general, which can be relevant when there is charged matter around, although in that case the new degrees of freedom can be attributed to matter densities --see below. Let me check the counting. Pure EM field must have identically null Lagrangian,* \[\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}=\frac{1}{2}\left(E^{2}-B^{2}\right)\] as in the vacuum \( \left|\boldsymbol{E}\right|=\left|\boldsymbol{B}\right| \), so the Lagrangian is identically null on solutions, as corresponds to massless particles. That leaves 5. If we now throw in the transversality, \[\boldsymbol{E}\cdot\boldsymbol{B}=0\] that leaves 4 DOF, which are the ones you're talking about. Correct me if I'm wrong. When light goes through matter, we no longer have the \( \boldsymbol{E} \) and the \( \boldsymbol{B} \), but also the \( \boldsymbol{D} \) and the \( \boldsymbol{H} \), so that, \[\mathcal{L}=\frac{1}{2}\left(\boldsymbol{E}\cdot\boldsymbol{D}-\boldsymbol{B}\cdot\boldsymbol{H}\right)\neq0\] with, \[\boldsymbol{D}=\varepsilon\left(x\right)\boldsymbol{E}\] \[\boldsymbol{B}=\mu\left(x\right)\boldsymbol{H}\] so we have two "additional" DOFs, the matter medium, characterised by \( \varepsilon\left(x\right) \) and \( \mu\left(x\right) \) that take us back to 6. But it's a fictional 6. *Edit: \( c=1 \) throughout.
  13. Your premises are wrong, precisely for the reasons that Swansont has pointed out. A proton exerts a force on all the other electrons in the universe, and all the other protons, as well as on any other charged particles. On any charged particle, the electrostatic force is the sum of all the forces exerted on it by all the other charged particles in the universe, according to the superposition principle. You could say that the electric force is 6 dimensional in some sense, if you include the magnetic effects. But 1-dimensional? That certainly is not the case. You also seem to be confusing the number of particles on which a charged particle can act with the number of dimensions. Neither of them is one.
  14. Virtual particles indeed appear in QFT always as a result of perturbative calculations. It could make sense to ask "are they really there?" They're really there in the sense that you must take them into account if you want to calculate the renormalised quantities, like mass, charge, etc. They're also "there" in the sense that, whenever you put in the required energy, they "leap into reality" and new real, detectable particles appear. In the decades after the glorious years of perturbative QFT around the 50s, towards the 80s and 90s, new non-perturbative methods were developed, by people like 't Hooft and Polyakov. Topological field theories are also non-perturbative, but I think we're still not there. I could be wrong, but I don't think we completely understand QFT from a non-perturbative POV. There are new games in town, but it may well be the case that a new synthesis of the formalisms is necessary.
  15. Perturbation techniques is a different idea. It applies to both classical as well as quantum theories. It has to do with studying an interaction that you cannot solve exactly as one that you can solve exactly plus a small deviation from it, or "perturbation," and then expanding the perturbed states as a power series of the small perturbation parameter, and the states of the exactly solvable theory. The closest to what you're saying is what @Halc has explained, AFAIK.
  16. joigus

    math test

    It interacts badly with the round brackets also when you want to show the inline maths tags. It may interact badly with other tags too. I think the safest thing when you want to show code is the code button on the toolbar.
  17. Meanwhile in Nepal... Here's some people paying good money to get a dose of harmful radiation, compounded with hypoxia, frostbite, and perhaps more, all compounded by stress from overcrowding. https://www.bbc.com/news/world-asia-48401491 It is not inconceivable that some of the same people would gladly buy those stickers.
  18. @Anamitra Palit, Maybe you can try some LateX editor, like, https://www.google.com/search?q=wysiwyg+latex+editor+online&oq=wysiwyg+LateX+editor+online and then nest your equations with braces, like this: \[ \textrm{ \[ <LateX code here> \] } \] or with round brackets for inline maths. This would considerably improve the communication of mathematical arguments.
  19. That one's easy, and much less convoluted than the story about the CC. It was Maxwell's equations for electromagnetism. He actually didn't think in terms of 4-dimensional non-Euclidean space for quite a while, until Minkowski came up with his formalism of time as a fourth dimension. For Einstein it was always Maxwell's great unification of electricity and magnetism what was the inspiration, and the experimental corroboration by Hertz. From then on, he always thought the equations must be correct, and must be telling us something very deep about Nature. The equations say the speed of light doesn't depend on the observer, so I'll take it to heart and see what the consequences are. Space and time must be changed to comply with these field equations? It must be it. AAMOF, he conjectured gravitational field equations as kind of an analogue of EM --Maxwell's equations-- for curved spaces. But two corrections about the currently accepted formalism --: Light is not ether. In fact there is no ether, as has been proven to death. There is no lack of an appropriate term: Space-time is the accepted term. It has symmetry properties that explain a great deal of how light behaves. The non-Euclidean character is not a property of the field, but of the space-time continuum. Fields are defined on it, so they inherit this structure.
  20. AKA "overcoming the curse of knowledge." I like to think about it in terms of tying the knot, and untying the knot.
  21. joigus

    math test

    That's nice. Only thing is that you're forced to leave out the braces, which maybe you want to make explicit. But you gave me an idea. Let's see if it works: \[ \textrm{ \[ \frac{a}{b} \] } \] \[ \text{ \[ \frac{a}{b} \] } \] Look at that. It does... You only have to escape the math mode inside the LateX with the \textrm{} or \text{} commands.
  22. Oops! Mmmm. Ok. I have nothing to oppose to that. But, as Swansont has pointed out, I misunderstood. I thought you were talking about arguments in the direction that "something can come from nothing", when you were talking about the argument "anything must come from something". These kind of arguments always give me a headache. Please, carry on.
  23. It must have been Lawrence Krauss: https://en.wikipedia.org/wiki/A_Universe_from_Nothing But it's not a postulate. I would call it a philosophical argument on the periphery of physics.
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