joigus

It is the only rank-2 tensor that has identically zero covariant derivative. Einstein wanted something as analogous as is possible to get to Maxwell's equations. I know of piecewise ways to understand its different pieces, but not the thing itself. IOW, if you had a conversation with a pure differential-geometry person and you asked them: "What is this G = Ricci-(1/2)R(metric) tensor to you?" They would probably go, "well, it's the way to obtain a 2-rank tensor from the Riemann tensor that is covariantly constant, if you want to, for some reason." You, "But does it codify anything about the manifold, holes, winding numbers, other topological features? Can I see it coming from something more basic" They, "Well, the R that you mention codifies the genus (number of holes), but not the G. Not that I know of, why you ask?" You, "You don't happen to know of any way to quantise it, do you?" Them, "Our time is up."

Absolutely. Both, of course, are mathematical limits. They indicate, AFAIK, that the interpretation cannot be brought to those limits experimentally and something has to give. Exactly as @MigL says. That's my understanding, anyway.

It can't happen. If a particle is at rest for just the shortest of times, the uncertainty in position becomes zero for just that time, so the uncertainty in momentum goes to infinity in every direction, and the particle immediately flies away. This is kind of a "pictorial" way of talking, of course. One must do the regular Hilbert-space operator procedure. Particles "at rest" like, eg, in an ion trap, are not really at rest. They're twirling around in some kind of stationary-state confined micro-dance.

Of course they are. Sorry, my mind is somewhere else lately. I'll be back soon.

One question then. If all of this is consistent with a more-or-less established field of research in 5D-GR, why not send your work to a peer-reviewed publication so you could get a more specific criticism to your ideas? Maybe by some experts in the field? Ok, so everything are photons in 5D. Only some of them look like photons in 4D, while others look like massive particles due to certain constraints in the loopy dimension? What is an EFE?

Depends very much on the potential energy. Free Schrödinger equation: plane waves, (harmonic)x(plane waves), etc. Schrödinger equation in potential wells, barriers etc: Plane waves with discrete harmonics, reflected and transmitted waves, etc. Schrödinger equation with inverse-square-distance potential: Hydrogen eigenfunctions Schrödinger equation with linear potential: Airy functions Schrödinger equation with harmonic-oscillator potential: Hermite polynomials, etc. So when people talk about "the" Schrödinger equation, they actually mean "the infinitely many" Schrödinger equations associated to infinitely many possible potential energy where the electron can be captured.

Photons have no rest-frame energy because photons have no rest frame.

Before you hit us with those 20+ pages, let's do some preliminary discussion if you will... You seem to posit that the energy of a particle is a static expression (derived from a scalar field) integral of phi(r)xelectrostatic_potential. Are you aware that energies must be frame-dependent and 0-component covariant? Where is the time dependence?

I think I see reasons why what you say cannot be right. I think... So let's see. Mind you, it should always be a good thing people pointing out reasons why what you say cannot be right: Either you unknot a knot, or else you rule out a bad way of reasoning. So let's see. Cheers!

I think it's English with ð=th There's been a 2-year hiatus, so I must I remind myself of what all of this was about...

I can't stress enough how much I agree with this. Give it a couple of years and that letter will come through.

I do. Believe me. Just yesterday a video appeared with the effects of bombing on a Palestinian kid that couldn't be older than 7 or 8 and I couldn't bear to watch it. What worries me most is that this kid (assuming he gets over PTSD, and such) will not join the forces of jihad some day, and a better future than that is in store for him. That, and an immediate stop of rampant antisemitism. And also the future of so-called progressive thinking, with re-examination of basic premises and careful separation of problems. And...

No problem with me. Thank you. Good answers. Some of them anyway. So this scalar field is a part of every other quantum field and comes from the K geometry? I still don't understand why you equate the energy of a point charge to the energy of a photon? What energy of a photon? A photon can have just about any energy.

The EM fine-structure constant is about 1? (!?!?!?) What does a EW-mixing angle --or any other standard-model mixing angle for that matter-- have to do with a coupling constant? If they are related, there should be a pretty convincing argument for it happening. What makes you think electrostatics is relevant when dealing with particles' self-energies? Why does a photon have a self-energy? Why should it equal the self-energy[?] of a point charge?

No, that's no example of either one of them, because: (from oxfordlearnersdictionary.com) At what point did I cross into 'hyperbolic' or 'metaphoric'? I think I was quite literal. Flooding the sentence with adjectives does not constitute by itself any kind of exaggeration or dishonest comparison. Each and every one of those adjectives totally apply to Hamas' way of launching their "liberation war". The part "lest we finally understand somehow what we're really dealing with here" was intended as sarcasm. Demagogues rarely use sarcasm. But I am guilty of sarcasm, that's all. Well, things going on in alleged concentration camp and what kind of reactions, comings and goings --or lack thereof-- take place, have some bearing on judging whether said place is a concentration camp or not. But never mind. I do recognise that as possibly the weakest part of my argument. I'm glad that wasn't intended for me: Unless it's actually me and you think I'm lying and really I don't care about that 99%? I wonder where you got that number from. Of course Gazans are the first victims of most of what's going on there. Never mind that 3/4 of them seem to have applauded the mayhem of 10-7. What do they know? Regular Abdullah or Fatimah in the street is no political analyst. Not to mention the poor kids. And, Never mind it's quite impossible to tell which one is a civilian and which one is not. UNRWA also plays a big role in decreeing that no Palestinian will be relocated, that never mind that Hamas has been documented as stealing supplies, and that the condition of refugee (only for Palestinians) lasts forever and is inherited from parents to children, to grandchildren, to grand grandchildren, and so on for all of eternity, so that they can never ever go to a safe place. Never mind that the UNRWA (a refugee-problem managing organisation that's exclusively for the Palestinian problem) has been found to publish twits incriminating Hamas, only to delete them minutes later. Here's a sequence of "innocent civilians" manhandling a woman that's been identified as Re'im music-festival attendant, Art student Inbar Haiman, after an Israeli air strike, These poor people are in a multi-pronged stranglehold by their own religious creed, some neighbour countries not really giving a f**k about them, Netanyahu making deals with the devil and hard-pressed for expediency, and other neighbour countries pushing their particular agendas. A horrible tragedy for all involved that will go on and on, be in no doubt about it. As it's only too obvious seeing how the roots of the problem are not even being addressed. Two-state solution. Yeah, righ! See you in 10 years to check how that's gone down.

I was going to drop out of this discussion, but I can't leave it at this: Well, you can compare it if you want. If it is, it's a very peculiar concentration camp, where the "inmates" apparently spend billions of dollars in weapons to make their life more... bearable? One of the borders is also sealed (by Egypt) but for some magical reason that border does not contribute to making it a concentration camp? And when Egypt occupied the land in the past, that was no occupation. No, no, no. But when Israeli settlers build irrigation systems, that's an occupation. And even after they pack their bags and go, they were still occupying the land!!! (According to this Albanese person from the UN.) With their minds, I suppose. In other words, it's simply a metaphor, and a very bad one at that. Metaphors, comparisons, and hyperbole are the favourite rhetorical tricks of demagogues. And they use them to great effect. You just remove the word "like" and it works its magic. "That thing" becomes "the other thing". It's not that reminds you of the other thing, which seems to invite lots of questions. It just is the other thing. And critical thinking just shuts down. And sure, let's not mention that big, scary, monstrous, barbaric, medieval, inhumane, irrational, unmentionable thing that we don't want to mention, lest we finally understand somehow what we're really dealing with here. I'm sorry that you feel that way. From where I stand, it looks like a thankless task to study for years and years and years, without getting anywhere, and thinking all that study time could have been spent in something more productive, more constructive, more beautiful. It feels like Sysyphus.

I think we're losing the patient.

"Differentiation" is frequently used as synonymous of "taking the derivative". Interpreted in that sense, it is an operation which, given a function of the right class (differentiable functions) produces its derivative, which is another function. Example: \[ x^{3}\overset{\frac{d}{dx}}{\mapsto}3x^{2} \] We say that we have "differentiated" \( x^{3} \) to obtain \( 3x^{2} \), its "derivative". 3xerivative". Mathematicians sometimes talk about a function being "differentiable" when you can express little increments of it as a linear function of the increment in its variable. This linear function of the increment is what they (the mathematicians) call "the differential". With our previous example, the difference between the values of \( x^{3} \) evaluated at \( x+h \) and the same function evaluated at \( x \) is, \[ x^{3}+3x^{2}h+3xh^{2}+h^{3}-x^{3}=\left(3x^{2}\right)h+\left(3x+h\right)h^{2} \] Now, the idea is that, when \( h \), the increment in the independent variable, is very small, the increment in the dependent function is a linear function plus something "very small". And indeed, \[ \left(x+h\right)^{3}-x^{3}=\left(3x^{2}\right)h+o\left(h^{2}\right) \] where, \( o\left(h^{2}\right)=\left(3x+h\right)h^{2} \) really is "something very small" when \( h \) itself is small. This is what physicists write as, That's why physicists like to write, \[ y=x^{3} \] \[ dy=\frac{dy}{dx}dx=3x^{2}dx \] when rigorous mathematicians would rather have us write something like, \[ \triangle y=3x^{2}\triangle x+o\left(\left(\triangle x\right)^{2}\right) \] Now, a function has a derivative at \( x \) if and only if there increments of it can be expressed as a linear function of the increment plus a little correction that goes to zero as the increment goes to zero. Did that help at all? If not, please just ignore it.

That was very interesting, thank you.

No, I said "Copernican revolution" meaning "humans are not at the centre". You always take scientific discussions to an anthropocentric frame. And people naturally call you out on that. In this particular thread I think it was @Sensei who first pointed out, it's a matter of perspective. The first Copernican revolutionary was arguably that unknown genius from prehistory who invented the grammatical mode "3rd person plural"

Two words: Copernican revolution.

I think what Seth means is QM allows for the final state in a complex multi-step reaction being "there" as a potentiality, so to speak, in the form of a quantum amplitude driving the process. Classical thinking, OTOH, seems to require first one step, then another, then another. Something like that?

I really don't want to butt in on the very interesting discussion you were having with Seth. But here's an interesting point: It is precisely because microscopic variables are so extremely sensitive to initial conditions, these systems (called ergodic) become highly indifferent to initial conditions (reach thermal equilibrium quite efficiently) macroscopically. How about that for pointing out that nothing is as simple as it might seem in physics?

x-posted with @Genady

Outcome of what? Thermodynamics of system can be predicted under certain circumstances. Where molecule X is going to be, no. Absolute certainty doesn't exist.