joigus

But I didn't mention the Coulomb. I mentioned the Franklin (Fr, AKA statCoulomb or statC). Many, many people wrongly believe the so-called electric permitivity of the vacuum \[ \varepsilon_{0} \] to be an actual physical property. It's rather a part of the definition of electrostatic charge. I'm sorry that I'm not familiar with Faraday's (independent?) convention. But it sounds to me very much like it is made to depend on current rather than on electrostatic charge. Fair enough. This of course is always possible. Don't forget Maxwell's equations contain the term \( \mu_{0}j \) with \( \mu_{0} \) being the magnetic permeability of the vacuum. One could define the "permitivity of the vacuum" to be anything one wants. And then the "magnetic part of the overall EM machinery" react to varying electric fields with much more "inertia" (bigger \( \mu_{0} \) ). Every game you want to play with E and M definitions is OK as long as, \[ \varepsilon_{0} \mu_{0} = \varepsilon_{0}\mu_{0}=\frac{1}{c^{2}}\] It's not the first time that the French have made other people disagree. 😅 In matters of units, and just this once if you will, we should all have stuck with British units (Heaviside's). Much more sensible.

Gladly. We do need to step back a bit to before quantum mechanics was invented. The reason is once you introduce Planck's constant, electric charge becomes dimensionless, as you know very well and I've read you talk about in these forums several times. Before one knows anything about quantum mechanics, one can use Coulomb's law to define units of charge by, \[ F=\frac{q²}{r²} \] where electric charge is expressed in statCoulombs or, Franklins. Also, \[ F=\frac{1}{4\pi}\frac{q²}{r²} \] In Heaviside-Lorentz units. As dimensions of force are, \[ [F]=MLT^{-2} \] \[ \left[Q\right]^{2}=MLT^{-2}L^{2} \] and therefore, \[ \left[Q\right]=M^{1/2}L^{3/2}T^{-1} \] Now, the question is, does this have any significance at all by way of the physical laws? Let me state clearly: I'm totally clueless about this. The closest one can get to this purely dimensional fact having any significance at all is what I mentioned about the KG and Dirac equations. As, once we introduce Planck's constant, electric charge becomes dimensionless, that means mass can be made dimensionless too and, at least in principle, a function of charge and perhaps other (dimensionless) quantum numbers. Or maybe just as an artifice. As I've remarked over and over to other people in countless discussions, there is the possibility that physics units might be ultimately be overdetermined. Why not? Edit: I've removed one comment as it's just too speculative and not really necessary. I striked it through to keep it visible.

CGS with rationalised units for charge (Heaviside-Lorentz) are my favourite. I once won a bet that you could reduce units of charge to mass-length-time units (something which should be obvious) against a student of electronics. The MKS system introduces the crazy fiction that units of charge are (for some mysterious reason) independent of mass, length, and time. They aren't. IMO, there are foggy hints of this in the Klein-Gordon equation and the Dirac equation. (statCoulombs are proportional to the square root of grams). The KG equation is the square of the Dirac equation. And in the KG eq. mass occurs naturally, while in the Dirac eq. it has to be forced into it. I'm still waiting for that person to pay me.

"A very faint amount of light" is described as relatively few photons, rather than one photon. Intensity is related to the number of photons as well as energy of each photon. Photons in the double-slit experiment are not "pointed at" one slit or the other; they are just let go off in every direction or a range of directions. Some of them hit the screen, others go through. For those that go through, it's really not possible to say "they go through this or that slit". When photons interact with matter, I'm not sure it makes much sense to speak of this or that individual photon anymore. It is actually an essential part of the Young experiment that photons not be very high-energy, otherwise difraction would be harder to notice. Lower-energy photons diffract better, and therefore are not "being pointed" at all. High-photons point better than low-energy ones. But this has nothing to do with the faintness of the beam. A spherical wave does have momentum, only it is not precisely determined. It has a lot of dispersion. You could say the photon is an observable of that spherical wave. These "waves" do not have a little thing inside that you can picture as the individual photon going certain way. Much of it is making peace with the fact that you cannot say what you want to say, as, eg, it doesn't make sense to say that the electron has a smile.

Homeric! 🤣 I understand your concern. But you can always cut the bread twofold or threefold to suit your caloric needs. Anyway, in my defence, I burn a lot of calories cycling every week.

Right! I correct my humble contribution to less than a minute microwaving. The whole thing should take about a minute, or little over a minute. And packed with essential nutrients.

I'm surprised by this, as ever since 1918, we know energy to be a derived quantity, not a defined one, and it's based on the Lagrangian. If the dynamical system is amenable to a Lagrangian formulation, and if that Lagrangian does not explicitly depend on time, then there is an energy, and the different expressions can be obtained with a precise recipe. So it's been a while since we know all these "mainstream definitions" are nothing but the corollaries of a master theorem.

Focaccia with a bed of tomato sauce, scraps of sliced black olive and tuna, mozzarella, oregano or basil. A minute to melt the cheese in the mw oven. You can use other kinds of bread, but focaccia is best. Very similar to the coca valenciana = the Spanish version of a pizza. Very substantial. Nice thread. I'm hungry!

I think @TheVat was referring to repetition of your principle of insisting on understanding the underlying concepts. I favour the use of repetition too, to hammer home some particular ideas, or even just sequences of words (like the title of an influential work, name of the author, dates etc) that's central to the development of the topic. The reason I say this is because all of us also have this automaton inside of us, the hippocampus, that does things for us without us ever thinking about them. In fact, I favour a two-pronged system: 1) Synthesising the main ideas ("filtering", as the Vat was saying --> writing an outline of the topic at hand, which requires understanding) and 2) Automation of some items (memorising names, dates, difficult-to-spell-and-remember new words. The use of AI (or AGI) should come later, and should be presented from the start as a dialogue. With questions such as, "how do you know what the machine told you is actually correct?" etc.

Agreed. And a safe rule of thumb might be that it only works efficiently in simulating when it follows well-trodden paths, which would make it suitable for education if used properly. I know exactly what you mean. I remember being taught to use tables of logarithms... yuck! Some contact with these old tools might be interesting. Knowing what they are and how the craft got underway. But dwelling on such thechniques is a bit like insisting on learning to cook by using bifaces and grinding stones. Getting intuitions for what numbers are is what's important, but when you learn about p-adic numbers, just to take one example, you realise numbers are not the sequences of digits yout teachers taught you about, but something much more abstract.

Let me concentrate on this point, because somehow it's the closest to my heart. An important aspect of scientific endeavour consists of (or at least implies) interacting with other minds. I think putting AI to good use would entail facing the student with interacting with other working minds. It is conceivable (and very understandable) that educators need to develop the necessary criteria to extract pedagogical benefits from this. IOW: I want to see your interaction with the automaton mind. A. N. Whitehead (as reflected in my signature) once wrote: "Civilisation advances by extending the number of important operations which we can perform without thinking about them". This goes to show that the problem in a general context is not new. The question we face now is a new one: What about the important operation being thinking itself? Can we perform thinking without thinking about thinking? I think we can't. We must think about this new machine thinking, and refine the criteria. That's all. And nobody says it's easy.

I cannot stress how important this is in what concerns both pedagogy and scientific methodology. There are very interesting comments on societal and economic derivations, but I'll make no comment on that because I don't feel competent enough. AI should, and will, be included at some point in education. It's simply a matter of time. New standards for exams will have to be put in place. The further forward the field will develop (and it will), the truer the previous two statements will become. Taking up on suggestions from others, one (among many) possibilities would be something like, a) Verbal (oral or written) examination merely to probe the student's mind in order to simply see if they've gained a reasonable grasp of the subject b) Exploration with the AI tool to see that they actually are able to formulate significant questions, clarify context, and highlight nuances, as well as follow up answers, by refining the prompt c) Presentation of results again in a verbal (oral or written format) Needless to say, the worst-case scenario would be to start using AI as some kind of oracle, which too many have been doing for some time now.

Yes.

For that particular observable. But it is in a probability distribution for any other observable that doesn't commute with what's just been measured.

It is. The rules to combine probabilities for different events are different in QM and CM. Most spectacularly so for systems of spins. Also, classical probabilities have nothing in the way of amplitudes. But none of that means that consciousness plays any role in QM. Classicality, as we understand it today, has more to do with massive loss of quantum coherence.

Very powerful argument! Absolutely right, in connection with Riemannian and pseudo-Riemannian geometries the word "intrinsic" means exactly that.

Yeah. To tell you the truth, I found the wikipedia article a tad ambiguous about whether it's "standalone" or it's "contributes to". @swansont had a similar point to make, besides the weakness of an only-spin source. But AFAIK too, you're right. Spinors cannot be represented by 4-vectors. After looking through the provided papers, it seems clear that none of the authors (related to such idea by the Wikipedia article) mean to say that spin be the one and only source of gravitation. Rather, they set out to find subtle effects of gravity on spin systems safely above the Plankian scale.

As said, suggested, implied: Angular momentum has energy. Energy sources gravity. Ergo, Angular momentum sources gravity. At the moment, we don't know whether the words "quantum gravity" are akin to what people once used to say: "elastic properties of the luminiferous ether". It could well be the case that these words finally have to be abandoned. There is also a spin formalism for general relativity. So, in a way, all of GR is about spin. This is because spinors are more basic objects than space-time 4-vectors (for every 4-vector, or event, there are two spinors representing it).

Aaah... This sounds more like it. Although I wouldn't call the various equations coming from the Schrödinger equation "constitutive equations". Constitutive equations in physics implement properties of the medium, while the Bohmian wave implements properties of the system under study in reaction to that medium. After all, they come from a simple change of variables in the Schrödinger equation. But maybe that's just a matter of words. I'm not surprised that the theory in its form of particle + wave does not work. That point-like particles are inconsistent with relativity has been known for a long time. So long a time that the scientific community as a whole seems to have forgotten, as the whole business painfully ground to a halt during the first decades of the 20th century. A topological scalar field consistent with local gauge invariance might do the required jobs. A point particle is hopeless.

In the De Broglie-Bohm theory the pilot wave is source of a so-called quantum potential, that must be added to all other potentials acting on the particle. This quantum potential produces infinite repulsion in places where \( R=\left|\psi\right|^{2} = 0 \) (interference), as its form is proportional to \( \frac{\nabla²R}{R} \). You are using "configuration space" in a sense that is not familiar to me. "Configuration space" in mechanics usually refers to the set of all accessible positions. I don't know what you mean by "a real constraint structure". Constraints in mechanics are obstructions to how the system can move (holonomic constraints), like a particle being forced to be at the tip of a rigid rod, etc. Your vocabulary is a bit weird, and I at least do not understand what you mean. The theory has its virtues, but makes calculations extremely awkward, not least the ones pointed out by @Mordred . Besides Pauli's objections, Einstein also seems to have said that it goes against every physical intuition to conceive of something that acts on other physical entities, but cannot be acted upon. John Bell was one of its most notorious advocates. He didn't say it must be correct. He said it must be studied. </my two cents> IMO there is the possibility that it's but a version of a more elegant idea that we haven't been able to fathom so far. Among other things, point particles cannot carry irreducible representations of the relevant space-time groups, so it could be the case that there's a generalisation of it having to do with scalars, rather than point-like densities. That seems healthier in the context of field theory. </>

For me it's number 3. I can't recall how many times I've listened to it. Especially the 3rd movement. I have no words to describe the experience. But it's all of the Brandenburg concertos really. And it's Bach. Always Bach. The cello suites, the Goldberg variations, Magnificat... There's something about Bach that makes it seem as if all of music were already in it. Haven't we had an exchange about Bach before? I've noticed exactly the same feature. I must say I lack a criterion to judge so-called generative AI. How "generative" generative AI actually is? I don't know. I've skimmed through news about some generative AI packages genuinely doing seminal work in mathematics, for example. I can't significantly commit an opinion on that, TBH.

Today I learned that "Today I Learned" can also be used to discuss whether I actually learned something or not. 🫠 Cheers! Very interesting, and impossible to watch from where I stand. Thank you.

I propose to remove the "work" bit from anything speculative coming from AI. It would be just a "frame". That is, the "framework" without the "work". "I've been given a frame to talk about this" would be at least honest.

Ditto.