joigus

Yes, according to Hossenfelder. http://backreaction.blogspot.com/2021/09/the-physics-anomaly-no-one-talks-about.html Thinking about neutrinos again... Could it be that very heavy leptons corresponding to an extended family of flavours were copiously produced in early stages of the universe, but decayed so long ago there are no traces of them to be found? Being very massive, they could be out of reach in laboratories. But their flavours would still be there, potentially explaining the anomaly, and their slight masses accounting for dark matter.

Hello. Is there any way to look up for content started by a particular user? Thanks in advance.

Not exactly. It has to do with an expansion of the classical EM field away from the sources that are not point-like (charges and currents.) Look, eg, at the field from a dipole antenna: https://en.wikipedia.org/wiki/Dipole_antenna It falls off as 1/r with the distance. Neutrinos are a completely different matter. There is no way that you can study neutrinos with a classical approximation, as you can do with EM field. They have spin 1/2. They are always highly relativistic. They're always left-handed. They change flavour ever so slightly. So, as you get away from their source, an electron neutrino mutates into a muon neutrino, and so on... They're very quirky on a series of levels. Anomalous deviations from predictions of the standard model being one of them. Here's a quick but high-quality low-down of the whole thing: And there certainly isn't a multipolar expansion for the neutrino field, as it has no sources. It sources itself, so to speak. You can have quantum wave functions --I suppose-- serve as analogues of radiation from a source point by, eg, having them diffract from a narrow window... Non-linearity may be very important in many, many contexts. GR is certainly non-linear. It's important from the start in the strong interactions. Even in QED you have non-linear effects of sorts, because at very high energies, photons can scatter off each other. But one has to be very careful stating in what precise sense one's talking about non-linear effects.

Referring to, (My emphasis on both.) Thank you: It's so nice to have such attentive and deep-thinking readers on this thread. I'll let @Eise, @swansont and yourself (+1) do all the conceptual clearing up from now on, as long as the point gets across. My word, you folks really are no-nonsense thinkers. I'll gladly accept the humble role of "finessing up" the points to make them more and more obscure, which is my thing, from the looks of it.

Multipolar expansions of the field: 1/r: radiation, as wide-range as you can get, without getting into GR. 1/r2: monopolar, narrower-range 1/r3: dipolar, even narrower ... Van der Waals (Casimir effect,) etc. You said "spin." Don't look now, but that's quantum, in a way that cannot even be thought of as classical.

Hold that thought, please. That is the heart and soul of the problem. I'm hoping by Hannukah/Christmas we will all be able to agree on a common ground. Where do classical data come from in the formalism of QM? Bell's theorem --and its extensions-- tell us that if you want some "internal classical data, mutually-commuting hidden variables" to be able to hold the information that corresponds to the eigenvalues we later measure, all along, while the quantum state is propagating, they would have to implement that non-locally. So what happens when we actually perform a measurement? The environment-chosen, einselected in Zurek's parlance, data have to be implemented in the quantum state in a way that's nothing to do with QM (the Schrödinger equation.) That would be non-local. That's what quantum-teleportation people call "classical data." So, when you say, You got it backwards. It's the components of the quantum state that have been experimentally discarded that must die now => They non-locally disappear. They must magically slip out of existence. Schematically: Because you can never measure anything concerning something that --following Copenhagen's old-school-- slipped out of existence, and because your fancy-schmancy quantum state was never an observable in the first place. How can you tell? This cross-out red scribble is all there is to your "non-local interaction." Of course, there's presumably nothing of the kind. I must acknoledge I'm confused by the word "contextual" in KS-theorem. I will have to take a deeper look at that, and your help will be much appreciated. What I know about it is that, for dim > 2 in space of quantum systems, you can actually build 3 mutually commuting operators --thereby compatible observables--, such that their expected values constitute an algebra closed under addition and multiplication: <ABC> = <A><B><C> <A+B+C> = <A>+<B>+<C> From this critical dimension of 3 upwards, you cannot obtain these averages over commuting (classical, sharply-defined, yes-no, etc) hidden variables: A(v), B(v), C(v). How that tells you something about the context, your guess is as good as mine. I tend to see it as "ontological." You cannot obtain them except for certain judicious choices of A, B, C, that is. Bell's flavour all over it.

This is not true. I think I was the first to mention the no-communication theorem. It deals with quantum-mechanical states. Period. In the mathematical formalism of quantum mechanics, how do finite sums and products introduce non-locality? IOW, how would the continuity equation be violated, how would the Lagrangian contain an unbounded order of spatial derivatives? IOW, how would any coupling of any form relating \( \varphi_{1}\left( x \right) \) and \( \varphi_{2}\left( x+a \right) \) be justified in the Lagrangian, or the Hamiltonian?

Exactly. They've experimentally proven the completely local non-reality of quantum mechanics.

Yes, it's come up on that thread. Thank you. We're now discussing how this does not imply that there's no locality, as you say. There's only one die-hard non-localist, I believe.

Don't forget the Monty Python version, which is sermon on the mount + noise. Blessed be the cheesemakers. And why not?

Wrong! Did you read what I wrote? I hate to write the same thing 100 times. Sorry. Your comment was previous to my comments.

I already have, plus I have accepted @Eise's definition as good enough, as a sacrifice in order to reach a minimal common entendre here. For better or worse --for worse is more like it-- I will have to avoid resorting to mathematics. I will use pictures, plus reference to mathematical symbols. Are you OK with that? Careful here, because an equation can be perfectly local, while violate relativistic causality. Non-local => Relativistic causality is violated But, Relativistic causality is violated =/=> Non-local In words: "relativistic causality being violated does not imply non-locality. Non-locality would be much, much, much, incommensurably much worse. And I'm telling you this knowing full well that relativistic causality is considered sacred by most physicists post-Einstein. It would imply that --in certain simple contexts-- you could make "something" instantly disappear "here," and at the same time appear "there." If you accept this standard, we can go on. If not... Well, the best I can do is recommend you to go back to intermediate physics books and learn about it: Local conservation of charge density, angular-momentum density, probability density (QM), energy, etc. You may well ask: Is it the probability amplitude that's disappearing "here" and appearing "there" instantly? We can tackle that question if you want.

More comments: You can't solve the dynamics, energy splittings, etc. of internal electrons with the non-relativistic Schrödinger equation. You have to use the Dirac equation and do an expansion series with different relativistic corrections, like the Darwin term, mass-velocity term, etc. If it has many electrons, you really have to go to a whole different level, with the Slater method, etc. So it's more complicated than you want it to be.

What do you mean "more canonical"? Something is either canonical or it isn't. You can't be more presidential than being a president. Here it is. I seem to be right about this: https://physics.stackexchange.com/questions/20187/how-fast-do-electrons-travel-in-an-atomic-orbital According to Andrew Steane, Oxford Physics professor.

The KG equation does not represent electron clouds. It represents the dynamics of creation/annihilation of charged/neutral, as the case may be, spin-zero particles, as @Markus Hanke told you. Very internal electrons might. I'm not sure about that now, but I'd expect them to have a sizable fraction of the speed of light as expected value.

Equations are not prone to anything. Microscopic version of Maxwell's equations can be expressed either in terms of \( \boldsymbol{B} \), \( \boldsymbol{E} \), or in terms of \( \varphi \) and \( \boldsymbol{A} \) --the scalar and vector potentials. Macroscopic version of Maxwell's equations can be expressed in terms of \( \boldsymbol{E} \), \( \boldsymbol{B} \), \( \boldsymbol{D} \), \( \boldsymbol{H} \), which in turn can be expressed in terms of \( \boldsymbol{E} \), \( \boldsymbol{B} \), \( \mu \), \( \epsilon \), which in turn can be expressed in terms of \( \varphi \) and \( \boldsymbol{A} \), \( \mu \), \( \epsilon \). Mu and epsilon carry the properties of materials.

The Schrödinger equation with Coulomb potential also assumes that the motions of the electron are much slower than the speed of light.

No. The KG equation is local. Relativistic theories arose from the demand of complying with Lorentz symmetries, and there's nothing long-range about that. AAMOF, relativistic theories are far-better locality-compliant than Newtonian ones, and you can see that in the fact that exact dynamic solutions are expressed in terms of potentials that take account of the delay. Eg, the Liénard-Wiechert potential. In fact, the standard solutions of the Schrödinger equation for hydrogen-like atoms assumes an instantaneous action, not because it's non-local, but because the proton is considered as having infinite mass, so the CoM coincides with the position of the proton, which plays the role of a classical object for all intents and purposes. As you know the reduced mass of a pair of objects, when one of them is enormous in comparison, reduces to the smaller one, while the position of the smaller one with respect to the big one reduces to the position of the smaller one with respect to the CoM. Relativity is useful for muons, rockets, and most everything else. It's the real deal. Schrödinger's equation works for an infinite chain of paramagnetic atoms, for just one atom, or for an electron moving in a constant electric field.

Did I get this wrong? Denying locality implies that actions to the past are possible. Would that be 2yes => 5yes instead? I think that's right. I think I did get that one wrong. Somebody help me here. I got confused with the mix of "denying" and "accepting." The possibility of combining "sufficiency" and "necessity," (directional arrows) or even neither one nor the other would turn this into a logical maze.

Oh, boy. This is SOOOO exciting. For some reason I'm not allowed to react to your post. I'm not cajoling you, honest. I'm just thankful that you're here. I think @bangstrom is half-way there. Swansont has been there all the time, because he takes no bullshit. Let me just repeat your points (echoing Zeilinger): Just one observation: What about a combination of some of them? Eg, it could be: 1yes, 2no, 3no, 4no, 5no. (yes-denying/accepting, no-denying/accepting; that's my take.) Careful everybody, because some are "deny" and others are "accept." The logical tree becomes more complicated when you consider more and more possibilities. 3 is important, but obscure. That's what I think is the case. I think it's a "no." And I also think there's experimental case for it. I'd be very interesting to learn about Zeilinger's take on it. 5no because 5no <= 2yes We're getting there, we're getting there... It's such a pleasure to have you here, @Eise. We may have to agree on terms of what 3 actually means.

Let me do this à la Deep Throat: Woodward (you): But all these guys have proven that quantum mechanics is non-local! Deep Throat (me): Oh, all those guys in the pop-sci media. They're not very bright. Things got out of hand. Follow the concept of realism. Woodward: But these guys, Clauser, Zeilinger, they've come in from the cold. Supposedly they've got a superluminal interaction signal with an n-times FTL tag in it. Deep Throat: Follow the concept of realism. Woodward: But you could tell me what your criterion of locality is... Deep Throat: No, I have to do this my way. You tell me what you know, and I'll confirm. I'll keep you in the right direction if I can, but that's all. Just... follow the concept of realism.

For a recent work on knotted topologic solutions of Maxwell equations: https://arxiv.org/pdf/1502.01382.pdf The biblio will take you back to the origins of this extensive body of work. My --recently deceased-- and dearest professor Antonio Fernández Rañada* was one of the pioneers, along with José L. Trueba. Both of them I knew personally, and I can attest to the fact that they have done very interesting work in the field. * I will never forget Rañada. I got my paper on quantum theory of measurement peer-review-published thanks to him, in the face of staunch opposition of other members of the Faculty.

Take a long hard look at this sentence you wrote. Why would anyone believe any of that? What do you mean "very wide range"? What do you mean "in general"? What do you mean "likely"? How do you know "statistically inclined"? What do you mean "simplest geometric shapes"? What do you mean "minimum number"? Does any of your reasoning depend on this statement? Also, you seem to be looking for topological solutions of Maxwell equations. Do you know there's an extensive field of work on that already? Also, you're implying "classical" all the time, but you're saying "spin." Are you aware that spin is fundamentally non-classical?

I mean "quantum amplitude for either annihilating a particle or producing an antiparticle at x=\( \left( t, \boldsymbol{x} \right) \). I prefer the rather less theology-laden terms appearing and disappearing, rather than "creating" and "annihilating." But that's me. I find God-fearing Pauli suspect of having introduced these semi-religious terms, but who knows. I'm a stickler for clean, minimally-assuming language that really tells you what's going on, and nothing more.

As Markus says (+1), the KG equation is not controversial at all today, because we understand it in terms of field operators, not in terms of the probability amplitude of just one relativistic particle. When the kinematics enters the relativistic regime, you no longer are dealing with one particle, and enter the realm of particle-antiparticle pairs, so your field variables are not interpreted in terms of localisation amplitudes for one particle. The KG equation was in fact hypothesized by Schrödinger, but he originally ruled it out on account of producing "negative probabilities." In quantum field theory, the φ(x) field variable does not represent a probability amplitude at spacetime point x, but annihilating a particle --or producing an antiparticle-- at x.