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joigus

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joigus last won the day on March 5

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About joigus

  • Birthday 05/04/1965

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    Biology, Chemistry, Physics
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    Physics
  • Favorite Area of Science
    Theoretical Physics
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    I was born, then I started learning. I'm still learning.
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    teacher

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  1. Picture an inflating balloon. Now suppress the space around and inside the balloon, as there is no such thing as "inside" or outside the balloon. There would be only whatever stuff makes up the balloon. Now make the balloon itself 3-dimensional, with time providing for the "history" aspect of it. Spaces don't have to be embedded in higher-dimensional spaces. IOW, the only existing directions are those tangential to the balloon's rubber if you will.
  2. How about StPD at the root of many, if not all, of these reports? https://en.wikipedia.org/wiki/Schizotypal_personality_disorder Religious types could, after all, be not much more than socially-accepted schizotipicals, that have somehow met the medium, and the way, to make their illness socially palatable.
  3. Indeed. I --and others, you among them-- have said it before elsewhere on the forums, actually. It's the energy-momentum that sources the gravitational field. I also agree with the absence, of necessity, of any causal connection between the Einstein tensor and the energy-momentum tensor.
  4. There is no such thing. Thermodynamics defines temperature based on thermal equilibrium. Statistical mechanics relates it to average kinetic energy per degree of freedom. For statistical mechanics to make the connection between both concepts through the partition function and the Maxwell distribution, we need approximations on really big numbers of molecules.
  5. The group of symmetry of electromagnetism is U(1) (complex numbers of length 1), and electrical charges are at the centre of it. From the POV of symmetries, conservation laws, and irreducible representations of groups (particle multiplets) QFT of electromagnetism and its brethren --weak interaction, strong interaction-- is more user-friendly by orders of magnitude. Things kinda "fall into boxes." GR is not like that. Not by a long shot. The group of symmetry of GR is basically just any differentiable transformation of the coordinates. Once there, after one picks a set of coordinates that locally make a lot of sense (they solve the equations easy, yay!), they could go terribly wrong globally, so that one must introduce singular coordinate maps to fix the blunder. Because the symmetry group of GR is this unholy mess, group theory doesn't help much, if at all. The equations are non-linear, so: Are there any solutions that might help clarify divergences, and so on, that we might have missed entirely? Who knows. In my opinion, the very fact that the set of coordinates that, locally, happens to be the most reasonable one could (and sometimes does) totally obscure the meaning of the coordinates far away from the local choice, and thereby their predictive power out there, makes the status of any parameters that the theory suggests (mass in particular) much less helpful than charge is in EM. Mass to GR is nowhere near anything like charge is to Yang-Mills theory (our paradigm of an honest-to-goodness QFT field theory).
  6. Yes! It's like a tinkertoy assembly for logically compressed inflexions[?]. Whatever I mean by that... For some reason, phonetics, syllables and their frequencies, it seems to be very friendly to the forming of composite words. The end result doesn't sound awkward.
  7. Is this (admittedly rough) understanding that I've acquired through the years correct?: The currency of red-ox reactions is electrons The currency of acid-base reactions is protons Now, in a manner of speaking, Both oxydisers and reductors can be understood in terms of "soaking up" and "giving off" electrons Both bases and acids can be understood in terms of "soaking up" and "giving off" protons That's the reason why so much of chemistry hinges around these two dual concepts Other cations, even the smallest ones, like Li+, are "monsters" in comparison to H+. Orders of magnitude so much so. So even though the mean free path of a proton is sizeably higher than that of an electron, it's bound to be gigantic as compared to that of even such a small thing as Li+. That would qualitatively account for an extraordinarily high mobility of protons, thereby the reactiveness of anything that either gives them off or soaks them up. That's the key to the concept of Lewis acids. Is it not? Then, for something to be a base, in its most general sense, it must be able to soak up protons. But for it to display this character, there must be some protons around to soak up. Wouldn't something like this be at the root of NH3 not "behaving as a base" just by itself, or in the presence of chemicals that cannot give off protons? Wouldn't it behave as a base in the absence of water, but in the presence of acids (neutralisation) like, NH3+A --->NH4++A- with A being any acid?
  8. German scientific terms are generally very precise. They feel no embarrassment in making long composite words tagging essential characteristics of the thing. Bremsstrahlung in Spanish is radiación de frenado, which is exactly 'braking radiation', but requires three words. Pronounced as in English, I assume.
  9. For a while I felt nervous about zitterbewegung and bremsstrahlung, but it grows on you.
  10. Spatially flat and space-time flat are often conflated in the literature. I would have to review the Riemann coefficients with 0t pairings of indices (a space cannot warp in just one dimension). I'm not sure nor do I have the time (nor the energy) now to review these notions. Maybe someone can do it for all of us. Most likely @Markus Hanke. I'm sure DS space-time is often characterised as having constant curvature*. We're kind of mixing it all together as if the scalar curvature were "the thing" that says whether a manifold is flat or nor. It's more involved. If just one Rijkl is non-zero, the manifold is just not flat. Calabi-Yau manifolds are another example which are Ricci-flat (R=0), but not flat. Yes. Thank you. Read my comments to @MigL on flat vs spatially flat, Ricci-flat, and so on. They're very much in the direction you're pointing. Right now I'm beat, but I promise to follow up on this. Yes, of course you're right. This theorem due to Birkhoff[?] that the external solution is unique as long as it's static and spherically symmetric. Schwarzschild's solution was just an unfortunate example. I know very little about exact solutions in GR. I just figure there must be solutions with not all curvatures zero with no clearly identifiable matter distribution giving rise to them. *
  11. Infinite at one point. Zero everywhere else. But you're right. It's not a good example. De Sitter is more what I was thinking about.
  12. It's a bit more subtle than this, I think. You can have vacuum solutions with curvature. If you think about it, the Schwarzschild solution is a vacuum solution. De Sitter and anti-De Sitter are too. OTOH, the Einstein field equations are nonlinear, so I wouldn't rule out other exotic vacuum solutions with curvature.
  13. Right. A scalar provides a particular type of covariance. Rank zero. L'(x')=L(x) That's what one must prove in this case.
  14. LOL forgot x106 didn't I? Coming from me lately, how could it be otherwise? fortunately more than 4000 and more than 6000 could also be more than 4.7x109 yo. Thanks
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