joigus

I'd be very surprised that only very light element and iron (which has never been involved in superconduction of any type) were the only ingredients of no less than superconductivity at room temperature. That's a very tall order. Your extraordinary claim truly deservers extraordinary evidence. No problem. I tried to react quickly.

No.

Of course. I tried to imply it: This sounds a tad more complicated than what I mean by an "interface" in IT. As I understand, an interface is barely a computer version of a translator. A piece of software/hardware that speaks both languages. But then again, I'm not an expert on AI by any means. I do remember having studied simple code widgets to generate neural networks many years ago (back in the '90s). As soon as I learned you had to reassure the system, in a manner of speaking, of what is right and wrong as an answer, my initial interest lost considerable momentum. This code was supposedly good at recognizing letters in different typographies. The world has changed a lot since then.

That's a fair point. If you just dropped a solar system somewhere in the universe at random (equal probability of dropping it anywhere), I suppose there would be instances (like, eg, if you do it close to the rim of a big cosmic void) where the mass, radiation, etc distribution would not look isotropic, nor would it look homogeneous. In fact, it would look highly "non-so". In that sense, that vantage-point factor in it cannot be overlooked. We might have been fortunate (or unfortunate, as the case may be) that things look more or less uniform from here.

The word I'm having problems with is "indeed"... 🙂

Why would it do any of those things? There is a good rationale at present to ascribe DE to the energy of the vacuum in QFT. The cosmological constant in Einstein's field equations is independent of the distribution of matter in the universe, and does not depend on time or place --thereby the name: cosmological constant. AKA dark energy.

I was wondering the same thing. Given the modular nature of these technologies (from what I gather), an important challenge that comes to mind is whether and/or to what extent, and efficient interfacing between the language-handling and the maths-handling modules can be achieved. Fatal mistakes can happen at any level, and you wouldn't want your maths module to carry out a calculation to perfection, only to find the LLM operating with the outputs failing to see the significance of a particular result. That's what human minds achieve to almost perfection, given the necessary conditions.

Agreed. It's perhaps worth nothing that whenever you have a "bulk" behaviour in physics that's complicated (or in fact non-solvable), a first-order approximation that manages to qualitatively describe things reasonably well is some kind of coarse graining that averages over any local features. One example is mean-field approximation in magnetism.

No, you're not learning. You're not learning anything at all this way. At least from this particular discussion. In a manner of speaking, you're trying to learn Chinese poetry without having studied Chinese first. If you persist, you're doomed to failure. I think most of us have kinda taken to you because you're so nice and respectful, as well as passionate about science. If you want to write Chinese poetry, you first: 1) Learn simple sentences and instructions in Chinese, like: "Hello", "can I have a bowl of rice?", 2) Then learn Chinese nuances, idioms, double-meaning, collocations of words, and so on. 3) Once you have all that mastered, the universe is the limit, and you can now aspire to create new tropes, alliteration, humour. Does it make more sense this way? Last time I told you something like this it felt like I was shooting you with neutrinos.

Please, don't answer with edits to a previous post, as it would produce a ripple in the causal fabric of space-time. ;) I didn't say it was... And more than likely it isn't.

At least this isn't another AI-generated manifesto.

Elementary operations between transcendental numbers will likely produce at least an irrational. But it's a case study.

And \( \pi^{\pi} \) is likely irrational, but we don't know...

No, no, no. You're fudging big time. And you need to understand dimensional analysis. Energy doesn't couple to curvature in GR. Energy sources curvature, by way of Einstein's field equations: \[ R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c⁴}T_{\mu\nu} \] Well... only those components of curvature contained in the Einstein gravitational tensor. Yes, you're trying to fudge, because --as @swansont told you--, for any pair of numbers p and q, you can always fix r so that p = rq. So you're doing the fudging of all fudges. Of course, saying that \( G=\frac{c⁴}{8\pi\rho} \) is wrong in almost every way. For starters, it's dimensionally incorrect. The dimensions of Newton's constant are, \[ \left[G\right]=MLT⁻²M⁻²L²=M⁻¹L³T⁻² \] This you can get from Newton's universal law of gravitation. OTOH, the dimensions of your RHS are, \[ \left[\frac{c⁴}{8\pi\rho}\right]=L⁴T⁻⁴M⁻¹L³=M⁻¹L⁷T⁻⁴ \] So you have a mismatch. Einstein's field equations tell you, \[ R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c⁴}T_{\mu\nu} \] Now, the LHS has dimensions of curvature (although it's not the whole story about curvature; it leaves out the Weyl components). But sure enough it has dimensions \( L^{-1} \). And indeed: \[ \left[\frac{8\pi G}{c⁴}T_{\mu\nu}\right]=M⁻¹L³T⁻²L⁻⁴T⁴ML²T⁻²L⁻³=L⁻² \] Please stop trying to dive before you've learned to swim, or else you'll sink. @studiot , @KJW , @swansont , @MigL , @Phi for All , @Markus Hanke , and myself, are just trying to help you. You should be diving into dimensional analysis, balancing chemical equations, proving trigonometric identities, learning vector algebra and the like. PS: Please refresh the page for LateX display

I see. But massive objects that are at rest relative to each other also experience gravity. Furthermore, gravity satisfies the equivalence principle, so all objects experience the same acceleration, irrespective of their state of motion (relative velocity with respect to anything). It seems difficult to explain these features with a theory that puts relative velocity with respect to some "ripples" at the source of forces. Besides, we already know that the only way (consistent with the principles of either classical mechanics or quantum mechanics) that a fundamental force of Nature can depend on a relative velocity (known as magnetic) is: \[ F=k\boldsymbol{v}\times\boldsymbol{B} \] where \( k \) is a constant and \( \boldsymbol{B} \) is a vector function of position and time. This is known popularly (and a little bit incorrectly perhaps) as "Feynman's proof of Maxwell's equations", as divulged by Freeman Dyson, and revisited by others. See, eg, https://arxiv.org/pdf/hep-ph/0106235 for a later review. It is entirely possible that I misunderstood something in the key idea, of course. PS: Please refresh the page for the maths to display correctly.

Nothing stands still. Motion is relative. Galileo knew this already.

I was reading some angry comments by a member whose thread has been closed hours ago. This person wrote a saying in a language other than English. A language spoken by quite a number of people in the world that I couldn't understand. While using Google Translate in order to ascertain any possible precise nuances of the sentence, I've been led to ponder on how much of what we say might be lost in translation when we use such tools. Here's the result of my experiment taking a sentence in vernacular English as a seed and Hawaiian (how vernacular, I don't know) as target language in the first part of an obvious loop: Input in English: "Shut up, bitch!" Translation to Hawaiian: "E noho mālie, e ka wahine!" Input in Hawaiian: "E noho mālie, e ka wahine!" Translation to English: "Be quiet, woman!" I somehow find hard to believe that GT would produce anything like the inverse loop here. This is mostly an observation, but any reflections are welcome.

Your ignorance of physics is Mariana-Trench deep. Perhaps only comparable to your hubris. "Virtual particles" is just a fancy name for fluctuations of quantum relativistic fields that can go off-shell for fleeting times. The number operator in QFT for virtual particles gives zero for the expectation value, as it should. Suggesting there are something in the ballpark of 1034 virtual particles (per what?, per unit volume?, in the whole universe?) just because the value of Planck's constant suggests you so strikes me as a feverish hallucination. Oh, and Planck's constant can be said to to go to 0 in a certain sense (although that's not exactly what we mean when we say that)*. But it makes absolutely no sense to say that it tends to 1. You see, it's not a variable: IT'S A CONSTANT!!! Never mind. You might not read a lot from me on any of your threads from now on. And please do correct your syntax and spelling, it seriously interferes with your clarity. Good luck. *What we mean when we say that is that every characteristic quantity with the dimensions of action in the problem under consideration is huge in comparison to \( \hbar \).

I meant thermal DOF, not geometric DOF. IOW, what are the microstates? To this day, nobody knows for sure what the microstates of a BH are. There are proposals, but not a mainstream explanation, AFAIK.

Then edit your post and correct it, as I do. Members shouldn't be striving to understand what you're trying to say. Also, don't put my words in your mouth, and use the quote function correctly. It wasn't you who made that comment about similar quantities at infinitesimally close point and different quantities at the same point. I was. Your physics doesn't make sense either. You don't understand the difference between the configuration space and the phase space. It's obvious you don't even understand the meaning of Planck's constant. Besides, it's not 1.054571817...×1034, but 1.054571817...×10-34. And it has dimensions of (energy)x(time), or equivalently, (momentum)x(distance), or equivalently, (angular momentum). Therefore, it wouldn't, shouldn't, and can't represent a cardinal (number of objects). I'll say it again: Jeez!

You start with a coarse-grained version of space, and explicitly introduce a preferred time, but you deny there is space-time in your model, although we can all see there is. You implicitly introduce gravity fields, because you illegitimately use G, thereby making room for fields with the dimensions required by gravity, but you call them "photons". The LLM you're using, instead of correcting your mistakes, helps perpetuate in your mind the false impression that you've come up with a novel idea. The lack of testable predictions should be a powerful clue that there's nothing there. When I say "testable predictions" I mean real ones, not things like, Didn't we agree this "photon collapse" was not gravitational? By the way, there is no reason in GR not to consider BH formation from just photons. Some models actually do that for the sake of simplicity, although that's not the way it happens in actual collapsing stars. Or, Redefining something with nice-sounding words is not a prediction. What are the degrees of freedom of the curvature field? A smooth curvature field does not have anything in the way of thermality. It doesn't look like you've explained that. This is getting almost painful to watch. I couldn't agree more with @Ghideon that you're engaging in ontological (or at least conceptual) bootstrapping.

I should have said "On the left hand side, we have the average perpendicular component of the electric field per unit volume with respect to..." You see, it's not easy to condense the meaning of Gauss' law into a handful of words.

I will say it again (apparently I need to say things three or four times before they get through): You have a fundamental confusion between non-commutativity in (pseudo)Riemannian geometry (non-commutativity of similar quantities at different but infinitesimally close points) and non-commutativity in QM (non-commutativity of essentially different quantities at the same point). Geometric quantisation is about commutation of dynamical functions (= phase-space functions = functions of x and p) evaluated at the same point (x,p) of phase space. Lie brackets, connections, curvature, etc, are about commutation of local functions in infinitesimally close points of space. I'm not saying there couldn't be a bridge between both notions. I'm saying both things are different and you haven't built that bridge AFAICS. Then there's the small business of connecting all that to the free parameters of the standard model.

Ah, but it's secretly the speed of light what's at play. If, mysteriously, the speed of light changed overnight. The day after that, antenna designers everywhere would say, "holy Molly, the impedance of the vacuum must have changed!".

I should have said "per unit volume" throughout that sentence. Never mind.