joigus

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.

Not so fast. He says "abandon local realism." Abandoning faithful Stalinism does not imply abandoning faithfulness, does it? NOT (A AND B) = NOT(A) OR NOT(B) As quantum mechanics abandons realism from the start, abandoning locality is not necessary. In fact, it would be quite silly to do so. The Kochen-Specker theorem is more ontological. It does not say anything about locality. It goes to the heart of the matter, which is indeterminism, of course. The background of it is V. Neumann's theorem. Gleason's theorem is, so to speak, a basic version of it. But these theorems were proven insufficient by John Bell, who also contributed to the theorem, providing a proof. When the dimension of the Hilbert space is at least 3, you can build observables that cannot even be represented consistently by hidden variables, so to speak. Here's a sketch of the argument: https://plato.stanford.edu/entries/kochen-specker/ There's a much more complete account of it in, Incompleteness, Non-locality, and Realism, by Michael Redhead. But it's dealt with by means of the heavy machinery of spectral analysis. It's been a long time since I spent any time reading or thinking about the "ontological" versions of the impossibility theorems for hidden variables. I don't think there's any interesting physics behind them, TBH. Producing noiseless quantum signals, that's another matter. That opens up wonderful technological possibilites. But Star Trek? Forget about it!

🤣🤣🤣 (quoting Zeilinger) Here's where I think Zeilinger is talking about superdeterminism. Again, a bad name. Psychodeterminism? Volition-driven determinism? Anyway. I have to admit I don't know a great deal about models based on that option. I find it unpalatable. That's all I can say. But to me it does sound like Zeilinger does believe in some kind of non-locality, or at the very least in ambivalent about it. @bangstrom may be right on that one. If that's the case, I have no doubt that he is old-school and thinks the projection postulate is physical, not a convention. In any case, that's very old-school. I remember the days in the mid-90's when, if you even dared to suggest the projection postulate was just an artifact, not likely to represent the actual dynamics of the fields, you were considered a heretic. Most people today are convinced that the projection postulate is bollocks, and we have either misunderstood something or not accounted for everything that's relevant.

Very interesting comments. And superb work in documenting. +1 At this point I will commit to clarifying the discussion to the best of my abilities. If, at any point, I have sounded derisive to @bangstrom, I'm sorry. I apologise. That's not what I meant. Discussion with Bangstrom has proved to be frustrating in what I perceive as an "argument from gullibility" or, perhaps better, "argument from hurried interpretations of what actually is more subtle." The question at stake is certainly obscure at some points. I'll recognise that. But I do intend for this discussion to be leading to some kind of common ground that we can all agree upon, and faithfully represents what most working physicists see as standard wisdom. From there, a landscape of possible interpretations opens up, which is unfortunate. I'm even willing to admit that a brilliant experimentalist such as Zeilinger differs in posture from what others --important ones-- have expressed. I'm not 100% sure about that. Another very respectful physicist, arguably one of the most brilliant theoretical minds of his generation, Gerard 't Hooft, has been looking for a model based on the idea of cellular automata, in order to save what I would call "a minimally assuming version of determinism that's still compatible with quantum mechanics." I think his attempt falls under the category of superdeterminism. Maybe you can help me with that, @Eise. Why would anyone like 't Hooft pursue such a thing? Why did Weinberg too look for alternatives to the projection postulate? Does not Bell's theorem and the experimental proof of its violation exclude that?* * Exclude determinism, that is.

(Zeilinger) This is correct, but because of the "realism" bit of it, not because of the "local." The Schrödinger equation is 100% local. (Zeilinger again, with my boldface.) This is not correct. I think I've proved it. People who don't (or didn't) think quantum mechanics forces you to give up on locality: Feynman, Gell-Mann, Coleman, Susskind, Hossenfelder... It's a long list. It's perhaps interesting to point out that most of them are (or were) field theorists. I could add more. Do you want me to? Yeah. It seems eerie, because that's not what happens. You also quote my quote. I will quote your quote of my quote (with your underline) now. Pay attention, please, because this is somewhat subtle: This is from Wikipedia. It seems to assume "a quantum state is being transferred." Now, here's an interesting question that I would like you to answer: A pure quantum state cannot be measured. It's not an observable of the theory. In particular, its global phase cannot be measured, and gauge invariance tells us that infinitely-many local prescriptions of it cannot be measured either. How can anybody tell they have teleported something that cannot be measured, and according to many people, it could represent a human idea? If you happen to know Zeilinger, you can pass that question to him, if you wish. Please, do. This cannot be addressed by scavenging for quotes in pop-sci books, declaring yourself to be the proud owner of a T-shirt, or any of the like. You keep repeating this and proving that you don't understand the first thing about QM. There is no such thing as "the quantum identity." Identical particles are fundamentally indistinguishable. This doesn't mean they're perfect lookalikes. It's deeper. It means they're rather more like instantiations of one thing. Or they are multi-represented. Find your own language to say it, if you will. But please don't misunderstand and misrepresent QM any longer. Good! We're getting somewhere. At least you admit that now. Unfortunately, your sentence ends badly: Well. It seems you're implying that there are two channels; one classical, and one quantum. It's the classical one that's under the strictures of sub-luminal propagation. But the quantum is not. Again: How do you know, if a pure quantum state cannot be measured? All those quantum changes can be measured on the mixed quantum state, which implies a considerable fewer degrees of freedom than the pure quantum state, and a lot more measurements. As a matter of fact, infinitely many experiments. How do you know it's FTL if you need infinitely-many measurements to measure it? Oh, I'm sorry. It does. It has everything to do with it. This is the generally accepted protocol for quantum teleportation (with my emphasis in boldface): Mmmm. "both qubits at location A are then discarded." Don't look now, but that's the projection postulate in disguise. Because measurements are involved, there is an extraction of classical data from a quantum state, in order to package this output in the whole signal. This measurement always implies the choice of a basis. In the case of spin, you must decide which polarisation direction you're going to use for the signal. Is it x, is it y, or is it 45º in between? Or is it any other from the infinitely-many possibilities? Once you do that, if you express your density matrix in the corresponding representation you've chosen for the qubit, you will see, very transparently I might add, that it now corresponds to a mixed state. Nothing has travelled anywhere. You've dropped infinitely many components that were initially packaged in the Bell state. You've performed an einselection (one selection.) Zurek's work is about measurement. And so-called quantum teleportation is a particular example. Epilogue: You should be very careful when/if trying to extract hard conclusions by the very iffy method of scavenging for quotes by famous physicists. Some of them prefer to stick to the old-school Copenhagen prescription of the projection postulate which, as I told you, is good for all practical purposes, but incompatible with the Schrödinger equation and formally non-local.* Zeilinger seems to be one of them. People working in field theory, cosmology, etc., of course, know it is hopeless. It works in a quantum-information laboratory at extremely low temperatures, but you cannot make sense of it anywhere else, particularly in cosmology. If you want to go there, you need Zurek's analysis: It works in the laboratory and also for dissipative systems. Even though it's not completely free of problems. Representing the pointer states --in a way that's general enough-- being the real conundrum. Oh, I've just remembered another (Nobel Prize) who disagrees with Zeilinger: https://en.wikipedia.org/wiki/Gerard_'t_Hooft#Fundamental_aspects_of_quantum_mechanics Cheers. *Not only non-local. It's non-unitary, and non-linear. Why? I would agree that behind it there's no argument at all, but I find it very interesting to hear your reasons, when you have the time.

Thanks for the detailed explanation. I've sometimes thought that (even) religious issues should be discussed under the light of scientific evidence (archaeology, literary criticism, history, etc.) But I understand the difficulty of reaching a compromise here.

I just learnt. Rest in peace, Loretta Lynn: And patron of motocross too.

This should go in the Speculations section, @universeteory. Welcome to the forums. Also, religion has never helped science, it's always stood in its way, as far as I know.

From: https://en.wikipedia.org/wiki/Quantum_teleportation With my additional emphasis for the parts where you are embarrassing yourself the most. For quantum teleportation you need to select an observable --a measurement always implies a selection of basis--, so you have loss of quantum coherence. Plus you need to supplement the output: "Because classical information needs to be sent, teleportation can not occur faster than the speed of light." Not even Zeilinger's Nobel Prize --very well deserved, as I said-- can change that fact. Zurek's work is about any kind of measurement, your "teleportation" --which is not the superluminal teleportation of anything-- included. If you go back to the previous posts, you will see I already said or implied that. Abundantly. You're a bad, bad, very very bad reader. Or just the observable that you have measured. The particular einselection. In this case, it's the environment (the experimentalist and her experimental equipment) that selects the observable ("one selection")=einselection. Totally Zurek. Understand?

How do you propose to reduce the effect of gravity? Why change a theory that already works? Why we never see anything going faster than light?

"teleselection," "telefiltering," or even better perhaps "Q-teleselection," "Q-telefiltering," to further insist that these cannot be replicated by dice, gloves, or boots, would be far more honest-to-goodness terms than "teleportation." The reason, of course, being that correlations after measurement involve selecting a basis which wasn't implied in the initial preparation of the state. I know by now that the reasons for this will fly right over your head. It's no insult to your intelligence, which I assume perfectly sufficient in order to understand any of this. It's because of your very limited attention span. Maybe you're busy and have no time to read anything... Who knows. I must honour the possibility that you may be having some impediment I can't see. Here. This may be helpful: https://arxiv.org/abs/quant-ph/0105127 Wojciech Zurek was the one who coined the term einselection. The famous "teleportation" (tele-einselection?) is a particular case. Exactly. I like to put it in a (hopefully) intuitive way I've used before: The speed at which 1-1=0 is infinity

I made no mistake or omission, therefore no excuse is needed on my part. Read back. @Eise gave a quite economic, quite satisfactory one I agreed to. I gave at least two more mathematical ones and referred to them later when asked. But because mine are perhaps too technical --although perfectly mainstream--, I'm OK with Eise's. All are equivalent and it can be shown mathematically in terms of a so-called Cauchy problem. I can do my best to help people understand or clarify possibly obscure points, but I do not condone laziness.

Of course, you don't. How could you? Sabine Hossenfelder http://backreaction.blogspot.com/2020/05/understanding-quantum-mechanics-3-non.html You're welcome. I disagree with Hossenfelder that it's difficult or "complicated." I think it's obvious if you pay attention to some arguments people have presented here. Are you familiar with Ctrl+F? There are 153 comments. I hope you're not looking for it by skimming through the text! It's not. Believe me.

http://backreaction.blogspot.com/2020/05/understanding-quantum-mechanics-3-non.html There. It took me a couple of seconds. That's what it takes when you actually read what people are telling you.

Very good post, Eise. +1 You certainly bring clarity into the question, and perfectly understand the logical points. You say you're not totally familiar with the formalism, but still. And thanks for the reference to Hossenfelder's blog. And that Nobel Prize is well deserved for Clauser, Aspect, and Zeilinger. Oh, be in no doubt!