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joigus

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Everything posted by joigus

  1. It may be interesting to notice that the EM contribution to mass is negligible in most macroscopic cases. If you plug in the values of \( \varepsilon_{0} \), \( c^{2} \) and assume 'typical' values for the field \( \boldsymbol{E} \) the order of Volts/metre, volumes the order of cm3, you get for this charged macroscopic object a correction to mass of its uncharged state the order of one proton mass or thereabouts. This is, of course, due to the high value of the speed of light.
  2. Agreed. Once you have any gauge field, you have mass. It's a package deal. It's a contribution to total mass. The Higgs is different, I think. But that's another topic.
  3. I didn't mention the Higgs. I didn't mean to mention the Higgs. I don't think the Higgs has any bearing on OP. Why the Higgs came up at all is a mystery to me. EM weighs, that's all I meant to say. And that, I said.
  4. OK. I don't know whether you retracted from your question or from a previous point. But keep in mind the Higgs mechanism is an ad hoc mechanism. Brilliantly insightful, to be sure, but ad hoc nonetheless. IOW: We don't really understand where mass comes from. It's nice to have a multiplet of particles that gives mass to everything else. The Higgs floats around while the Goldstone bosons from the multiplet (not the Higgs, this is not faithfully reflected in the literature) provide mass to all fermions and short-range bosons. But where do the completely disparate mass spectrum comes from? I don't think we've developed a picture in the way that the OP seems to suggest, that mass differences could be explained by means of field self-interaction, and self-interaction alone. That's a fair point.
  5. Somebody would think it's a weak confirmation, but here's one: No charged particle with zero rest energy (relativistic mass) has been found. So the EM field has inertia. Always. To which I will add a prediction: No charged particle with zero rest energy (relativistic mass) will ever be found.
  6. Thanks for confirming this. In the case that a classical calculation were valid, you would have to add the EM contribution to the mass as \( \triangle m_{\textrm{EM}}=\frac{\varepsilon_{0}}{2c^{2}}\int_{0}^{\infty}\left(\left\Vert \boldsymbol{E}\right\Vert ^{2}+\left\Vert \boldsymbol{B}\right\Vert ^{2}\right)dV \) Well, it's because it's really when you go down to something as elementary as an electron that the question becomes really intractable classically.
  7. Now that I think about it, @exchemist wasn't necessarily talking about the electron... For some reason, I was thinking about the electron.
  8. This calculation cannot be done classically. You've hit the same wall that a generation of physicists (Abraham, Einstein, Lorentz) and a notorious mathematician (Poincaré) hit a century ago*. If the electron is point-like and static (static cannot be, we know this from QM), then the Poynting-vector approach (that @Markus Hanke referred to) gives you infinity, as the integral of \( \frac{\varepsilon_{0}}{2}\int_{0}^{\infty}\left\Vert \boldsymbol{E}\left(r\right)\right\Vert ^{2}dV \) is divergent. So the classical calculation is nonsense. The possibility that the electron is a little sphere of charge is even worse, as it is impossible to make it relativistically consistent. The pedestrian way of seeing it is that discontinuous charge densities in space-time do not bode well for relativistic invariance. You need fields that are smooth everywhere. The modern way of dealing with it is using QED (the fully-relativistic, quantum-mechanical version) and attribute part of the energy to self interaction of the electron. We could phrase it as 'the electron tries to move, emits a quantum of radiation, and suffers radiation reaction.' These virtual processes contribute to the energy. Unfortunately, for all I know, nobody has come up with a way of plugging in the fields (involving the electron's charge), and deriving from there the mass of the electron. The mass of the electron has to be plugged in by hand. This, I think, is an outstandingly-good question. By no means just a good question. Edit: * A century-odd, which was also an odd century.
  9. Not a lot, to me at least. For example, as a definition of 'energy': Energy doesn't always result in translation. OTOH, not an operational definition. As to 'action': Yes, good physicists are in that habit, because they have good reasons to think space is finite, and action in a confined space leads to quantised energy, for the simple reason that space-time confinement leads to a periodicity. Continuous energy is probably just a theoretical extrapolation. Same reason why angular momentum cannot be even conceived of but as quantised, because it's the conjugate momentum to an angle, which always restricted to a confined space \( \left[0,2\pi\right] \). Action again: Time, mass, and length are not derived from action. It's the other way around. As to the conclusion: This doesn't even make a smidgen of sense to me. I'm sorry. But I do have a sense of what the problem is with this kind of definitions/'derivations': They lack the operational point of view, on which all of physics rests, they engage in a loose runaway of concepts and statements, and consequently they lead to whatever preconfigured picture was already in the author's mind.
  10. I know du Sautoy from the documentaries. 'The Self-Made Tapestry' does ring a bell, perhaps you mentioned it before. I have no idea about cement mixer patterns, but sounds interesting.
  11. That seems to be the trend. The discontinuity of the fossil record is very important to keep in mind. I think we're in for more surprises. Dmanisi was another big big surprise in a different direction. Thanks for the link to Jebel Irhoud.
  12. https://phys.org/news/2022-01-earliest-human-eastern-africa-dated.html?fbclid=IwAR3qOIHmKKO6EsILQUbh6DCngk5MjeQl3pI-ugX_n6yrHc5k-WPp5GhYkEM
  13. But I don't disagree with this. In fact: Let me add another definition of maths that I've heard to Marcus du Sautoy, if I remember correctly: Maths is the study of patterns
  14. Loved the poem. Thank you. Somehow I don't see zero so much as a geometric concept. I think it's more of an algebraic concept. You can do quite a bit of geometry without it (similarity of triangles, Thales theorem, Pythagorean theorem, and so on.) In a curvilinear space you don't really have zero curvature; and in a pseudo Euclidean space there are infinitely many points that have zero "distance" with respect to any one point. I think it's more of an auxiliary concept than really central to geometry. You can do some geometry without mentioning zero. You can't really start doing algebra or analysis without it. I don't disagree with this at all. Maths is a tool. And we'd rather use maths to make a hammer than use hammers to do maths. I even think maths is at the basis of language. Even people who say they hate maths, I think, have a simpler, more basic way of mathematically understanding the world. Perhaps less sophisticated, refined, or whatever.
  15. Today I've learned about the phenomenon of chatoyance or chatoyancy: https://en.wikipedia.org/wiki/Chatoyancy and a beautiful sea snail called Voluta musica that displays this effect. It is an optical effect consisting in certain 2D patterns being perceived as 3D --if I understood it correctly. Thanks to @Genady and @StringJunky. 👍
  16. Ok. I trust you and Euclid. But keep in mind that when Euclid wrote his Elements, there was no distinction analysis/algebra/geometry, so when he wrote that, he didn't make a clear distinction was probably trying to introduce the minimal elements of analysis necessary for doing geometry. Obviously you cannot do anything at all in maths if you don't start out with some elements of algebra and analysis. But zero is the distance between two points only when they're the same point, and as for a coordinate, it doesn't mean anything that its value happens to be zero. So I don't think zero is a relevant part of geometry. There is no 'zero point,' as opposed to the real number zero in analysis, or the element zero in a ring (algebra), etc. That was kind of my point --no pun intended. Edit (addition): On the other hand..., 'that which hath no part.' I don't know what to do with that. I don't think Euclid was in his finest hour when he wrote that.
  17. Ditto. We can only attempt at an explanation when we have a theory (a law), plus its domain of applicability. We can take Newton's law of gravity, or GR, and try to explain planetary motion, or why the Moon is slowly sidling away from us by tidal interactions. To summarise, we can explain relatively complex phenomena in terms of simple laws by means of a mechanism spelled out in terms of that simple law. But fundamental physical laws have no mechanism. Richard Feynman The Feynman Lectures on Physics Vol. II
  18. In geometry, there is no zero. That's either algebra or analysis.
  19. Thank you. https://en.wikipedia.org/wiki/Chatoyancy From 'cat's eye.'
  20. I don't seem to be able to find it now. It must have been a university professor. What I have been able to check though is that many people seem to factually use that dichotomy of mathematics into analysis and algebra, because there are many questions concerning it. It's true that geometry is a completely different animal. I would say that the starting point for the three of them is axioms --that's just what mathematics does. But both analysis and algebra posit them as identities based on definitions, while geometry posits them as giving rise to formulas that claim to state relations in a world of 'visual entities' (Pythagorean theorem, Thales' theorem etc.) Those belong in the realm of perception, or intuitions about space, I would say. From these reasonable intuitions, you are compelled to transform them into algebraic statements that you later use to derive further theorems, and solve problems.
  21. Is there any way that you could identify the species?
  22. I've been pondering this for quite a while. I'm not enamoured of the 'inverse' approach, but I don't think it's impossible. But the way I see it, you would need more 'points' to interpolate. Levels of self-organization appear at different scales --already I know @studiot doesn't find this plausible--. Let's say: cells, multi-cellular organisms, planetary biota, and so on. At stellar level you would reach the point where no longer is there self-organisation. Instead, what you get is qualitatively different systems that, not only don't give rise to self-organisation, but actually erase information from their environment, and give it back to the universe completely thermalised (collapsing stars). I'm not saying it's plausible, I'm just saying the next Boltzmann of this world may be able to outline something like that. Very interesting. Let me keep thinking about this. One difficult aspect about the principle of least action is that, while its application is quite useful and simplifying in many cases, its meaning is obscure at best. It's a very abstract principle of physics.
  23. Yeah, you're right. I forgot about geometry. I kind of think of geometry as a whole different class of its own. In fact geometry went through a process of trying to unify it all of its own, the Erlangen program, by Felix Klein. To me geometry is kind of a bridge between physics and pure (abstract) mathematics. But I don't know really. I think Poincaré tried to base all of maths on the concept of group. I'm not an expert, but I don't think he was successful. Poincaré and I think otherwise. And Euler agrees with us. Now serious. I wish I could remember where I picked up that dichotomy into algebra and analysis. I'll look it up. And this doesn't give me much hope: https://math.stackexchange.com/questions/1392273/algebra-and-analysis
  24. Yes, in fact 'assumptions' or 'concepts' go far beyond the realm of pure mathematics, so these definitions that try to be so broad really don't finish the job of specifying the matter IMO. What I tried to do is to picture the two distinct attitudes that govern all of maths. The idea that everything in maths is either algebra or analysis is not mine AAMOF, but I can't remember where I picked it up. But the feeling, when you're doing maths, of 'I'm doing algebra' or 'I'm doing analysis' is very clear in your mind when you're doing it.
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