joigus

The SM's Lagrangian is full of so-called gamma-5 matrices all over the place, just to make it explicitly and unambiguously break CP symmetry maximally. It's not just broken, it's broken by design. All leptons and quarks are lefties in the SM. So... I, for one, am sure about that. It better be, cause maximal parity violation has been shown to hold in EW decays in the laboratory ad nauseam.

Do you consider Ebonics, English-based creoles and pidgins, like Walpiri, as English? They all have different degrees of English features.

Denisovans, Neanderthals and maybe other post-Heidelbergensis are a fascinating topic, but I think the original OP's intention was to make a point about possibility of implausible hybrids, more common, to say the least, in species that spawn, rather than mate the way mammals do. Because the topic is fascinating nonetheless, I suggest splitting in a friendly and dispassionate way, or creating a new topic.

That sounds to me like sympatric speciation. In plants it's common, but in animals it seems to be not so common and to have more to do with sexual conflict than with adaptation. Allopatric speciation is far more likely. But I'm sure even that is not the whole story. In species like humans, which are very successful across different environments, and have been for several hundreds of thousands of years, hybridization has very likely played an important part. But this drifts us apart from the topic.

In the framework of concepts that I've grown up with, it would be neither of them. For me, for anything, (differential manifold, analytic manifold, space of solutions to a differential eq., etc.) for this space to be local, non local, or have global properties, it should have at least correlations from one point to another. If there are no correlations at all, well. I can see no meaningful way in which I (or anybody) can define any reasonable concept of locality. But I would be interested to know if anybody should put forward a sensible one. Edit: On second thought, maybe you could come up with a sensible definition based on correlation functions... I don't know. The concept is a bit alien to me, but maybe it's possible. Edit 2: The more I think about it, the more I think it's an interesting idea. +1. Whenever I hear of an idea that I haven't heard before and I can see no reason why it doesn't make sense, it becomes automatically interesting to me. So you would have a random angle at every point x: \[\theta_{x}\] And then you would have a density for these thetas: \[\rho\left(\theta\right)\] And yet you could have the thetas at distant points having well-defined, well-behaved, smooth correlations functions, even satisfying PDEs, if you want them to. Why not?: \[\left\langle \theta_{x},\theta_{x'}\right\rangle =f\left(x,x'\right)\] If anybody can think of any reason why this is not possible, please tell me. It's a bit late. I'm going to bed.

I couldn't resist quoting this: Lee Siegel Net of Magic, Wonders and Deceptions in India. (my emphasis and my additions in square brackets) I once went to a conference by James Randi, and it was very interesting. He's the guy who debunked Uri Geller when even professional scientists had failed to do so. Ask any professional magician and they will tell you that all magic is real (meaning based on deception, and not supernatural). The reason is very simple: it can actually be done.

https://en.wikipedia.org/wiki/Multipole_radiation

Then your "photons" are not elementary particles, because sure as hell they would radiate. Either that or Maxwell's equations don't hold for your charges. Which one is it? Edit: Sorry, what did you say, elementary particles do not radiate?

I don't know others, but for all I care you could either be a street musician or a Nobel Prize winner in Physics and I would still tell you that your dipoles will radiate. In fact, there is no way for me to know who you are, or the other way around. I could be a gorilla who's learnt how to type and studied physics, or the Sultan of Brunei. That shouldn't worry you in the least.

I particularly like the example of the soldier who uses the F word in one sentence like seven times, except to refer to the sexual act!

Part of it is geographic isolation, there are also environmental pressures conditioned by different circumstances in the different "cells of isolation", but there's a very important factor which is genetic drift: https://en.wikipedia.org/wiki/Genetic_drift

This is actually a bit more complicated than I first thought, but my intuition seemed to be correct. The monopolar field would go like 1/r2. The force between two magnetic dipoles goes like 1/r4. At larger separations, the monopolar term would dominate, as I said first. You can find more details here: https://en.wikipedia.org/wiki/Force_between_magnets In any case, the placing of the circuits is unstable, and be in no doubt that it would radiate.

My prediction: Both circuits would keep at a certain (varying distance) due to the monopolar term, which dominates at larger shorter separations, but oscillating because of the unstable 2-dipolar (in total quadrupolar) flipping effect, going like a higher inverse power of the distance, and thereby radiating. How come your photons radiate? Your graph is incorrect. But even if you were right, the attractive branch would have to go upside-down, and the graph that you're showing is that of an unstable equilibrium. Very well put. +1

Well, we've got thermodynamics, SR, GR, algorithms, and QM, off to a good start. Pending some clarification on algorithms. This looks promising.

Well, yes. But (gathering more arguments from above) there would be a monopolar electrostatic term which would be attractive going like 1/r2, and then the attraction/repulsion (depending on the flip) which would go like 1/r and we could assume to oscillate chaotically, because the motion would be unstable, as Swansont pointed out. And it's still by no means clear to me why you can't make higher multipoles of these things.

Exactly, they would surely flip. The whole thing is unstable.

You're quite right. The force would have to be non-local, nonetheless. Plus photons don't have anything that corresponds to a proper length. Edit: And I still can't see why they wouldn't flip.

So, what did you mean when you said, ? Why they don't separate is a key question for me.

As Swansont and Studiot have implied, but in my own re-phrasing: If the charges are separated, you need a non-local interaction to account for them being separated rigidly with no possibility of pulling or pushing one against the other. This exotic force would have to be repulsive and non-local, exactly compensating the mutual attraction between your positrin and negatrin. Charges polarize the space around them, so charged particles always have mass. How does that mass not appear in your photons? I hope it doesn't, as photons are massless. As Ghideon and MigL are implying too, how do you recover known laws of physics? Other examples: Do your photons go through each other at low energies, while scatter at very high energies, which is a known fact of QED? Do they behave as they must when they scatter electrons? Do they contribute to mass and charge renormalization of the electron? Why aren't there 0-spin photons? Why can't they flip? Your model seems to allow for it. Are you considering selection or superselection rules? If so, which are those? Why aren't there multipolar states of those? More selection rules? How do you account for the transversality of photons? The radiating EM field is always perpendicular to the direction of propagation. How do you account for circular, linear, and elliptically polarised photons? More coming. It's 100 years of photonics.

Ah, I think I know what you mean with the Cartan dual. It has g tensors in the definition, doesn't it? Don't worry, I'll take a closer look, ASAP.

LOL. That's a good one. Or two. +1 Sorry, is it meant to be Input = Output + Accumulation or Output = Input + Accumulation?

That reminds me of Matrix. One of those drives you could download all your knowledge from. Even practical knowledge. Tensor calculus in 5 seconds. Helicopter piloting in 3. That would be nice. Thanks. I knew you would appreciate it. Let's see if people can provide some good ideas. Let's see if it arouses some interest. I hope so.

We're all familiar with how certain concepts in science are difficult to grasp, or perhaps to remember. Mottos are these pieces of wisdom that try to capture an idea and make it easier to grasp yourself, or to get across to others through an intuitive verbal formulation. Some of them can be quite unfortunate. They shall not be mentioned here, if possible. So my suggestion is: Let's all share those brief phrasings that have helped us remember an idea, understand it better, keep it closer to our hearts and brains. They can be our own creation or found elsewhere and treasured ever since. One example could be (these are my own): "Velocity is the parameter which tells you what time and space directions you're looking at when you're moving" (special relativity) Or: "A tensor is a product of projections of physical quantities; different observers see different projections; but if they knew the rules of rotation, they would all relate their data and say: 'Oh, we're all seeing the same thing!'" (general relativity, tensor calculus) I invite you all to share brief formulas like these that you've found useful to capture an idea, whether you've devised them yourselves or you've found them somewhere else and retained them as useful conceptual tools. Keep in mind that the more rigorous you try to be, the less memorable the motto. If you don't like mine, feel free to tell me. All science areas welcome.

No. The whole point of relativity, both special and general, is that you can't tell whether you're moving or standing still (special relativity), and whether you're in free space or falling in a gravitational field (general relativity, except tidal forces). So you can never tell by looking at things in terms of your own references. It's other observers (moving differently --SR-- or with different values of the gravitational field --GR--) that see those funny slowing downs, contractions, and the like. In common scientific parlance, those effects are observer-dependent.

Nobody said that.