joigus

Oh, that's so Italian! No, com'on, those recollections I'll keep to myself. But you sent me down memory lane now.

Thanks for the very interesting historical note. I didn't know it went by the name of 'hexagonal aether'. I do remember Feynman's Lectures on Physics mentioning it along the lines of 'Maxwell conceived of an aether made up of gears' or something like that.

Friends fairly sharing pizza has always worked for me. I seem to remember some explanation with pie when I was a kid. It's possible my brain has edited my memories and it was all more formal than I care or dare to remember. Pies work because rational fractions make immediate intuitive sense, IMO. I lost my innocence when I had a teacher at university who said something like 'definitions are not to be understood; definitions are definitions!' which, let me say, I think is completely wrong. Definitions should be motivated. For this man definitions were like a thunderbolt from mathematical heaven. Marcus du Sautoy explains Egyptian, Babilonian, Indian and Chinese mathematics with beans, and peas, and eggs, and things like that, in a wonderful documentary about the history of mathematics.

Exactly. And it would share cosmological equation of state with ordinary matter. It would be another garden-variety type of matter to be detected in scattering experiments. Why bother with superconductivity if the idea doesn't even leave the ground?

Yeah, we got it. To boldly think what no one has ever thought.

One problem with this configuration is that it is anisotropic. And what keeps the spheres from collapsing due to electrostatic attraction? You need a constraint, like rigidities in mechanical problems. Or guess what... quantum mechanics. Dislocations, or kinks, or twists in this grid would not propagate equally in every direction, I think. You should also be aware that field theory does all of this much more simply and elegantly. Plus it gives the right predictions. And that people have tried for ages to build something in the way of a mechanical model, without success...

has a better chance? Yes, it seems to go in the direction of helping kids understand positive integer multiples of (-1) as sequential subtractions. It's very much in the spirit of what @John Cuthber said.

Blah. Ahem: What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? What would make you conclude that the cosmological constant problem has been solved? As in 'I would be happy if you answered any of my concerns' (2nd conditional). From Oxford Dictionary: (my emphasis) If 1) an idea like SUSY were confirmed, and 2) the symmetry were broken slightly enough that it allowed for a small value of vacuum energy, that would make us conclude that the problem has been solved. Has it? No.

You're right about that. Those go under the name of selection rules for photon absorption/emission. The one that rings a bell to me is \( \Delta S = 0 \) for angular momentum. As magnetic dipole moment is proportional to spin angular momentum, there you go. Here's an interesting Q/A dialogue on the topic, that explains more: https://physics.stackexchange.com/questions/174719/selection-rule-delta-s-0-why-does-a-photon-not-interact-with-an-electrons-sp

1st: Find the reason for the monumental overcount in QFT Example: The exactly supersymmetric Hamiltonian gives zero for the expectation value of energy of the vacuum. 2nd: Find the reason why the actual energy is not exactly zero, but a little positive correction to that Example: Postulate a mechanism to break SUSY ever so slightly that the expectation value of vacuum energy is slightly above zero. Then solve for the values of symmetry-breaking parameters for different models. Then go to the lab. Something like that.

Relativistic conservation of momentum would be violated. It's a common exercise for students to prove. Only virtual photons can be absorbed by an electron. They must be off-shell is another way to say it. Somewhere on these forums I included a proof of the converse theorem. Namely; that a free electron cannot emit a 'proper' photon (one that satisfies Einstein's mass-shell condition). The alluded result can be found here: https://physics.stackexchange.com/questions/225522/free-electron-cant-absorb-a-photon Sorry, @Genady. I hadn't noticed you'd already answered that.

The sorriest part of this is they don't even realise how big a number 10123 actually is. There's nothing that we can see or grasp, or intuit, the counting of which is 10123 in the observable universe. You must get into combinatorics of countable things in the universe to get to (and surpass) a number like this. Even the number of photons is ridiculously small in comparison. So coldly stating that there are 10123 Helium-like things among us and nobody has ever noticed takes some gall.

Absolutely. Once they posit those things are there. How can we prove they're not there? By as many ways as we can. If you think something is right, you try to prove it's wrong! "Why do we want to attack the argument?", our interlocutors may think. Because that is the heartbeat of science: Attack the argument from as many directions as you can. If it survives the attacks, you got yourself a theory or a principle.

They certainly are the Methuselahs of the strongly-interacting matter. Everything else decays in a tiny fraction of a blink or in the time it takes to sip out a coffee. But I agree. It's probably a green[?]-swan kind of issue. With every year that Super Kamiokande keeps running, it becomes increasingly unlikely that we will see any single proton decay. Looks like stars will die long before protons do. Yes, that's funny. One is related with the speed of light and the age of the universe. The other with the strong coupling. I wouldn't say it's impossible for them to be related, but it's not very compelling, to say the least. This idea of dividing the size of the universe by the size of a proton is not new, btw. Dirac thought of it many years ago. This hypothesis has fallen out of favour for a series of reasons. 1040 seemed to be the central scaling factor. Some of these ratios had to be fixed with a root, like (1040)9/4=1090 which is the number of photons, or the entropy of the observable universe. The whole 'theory' reeked of numerical mysticism, aka numerology.

This whole question reminds me of fractals, and the problem of measuring the coastline. Nice comment, Dim. The point being that you can make a lot of convolutions fit even inside the width of an atom.

I don't see that's stable. The minutest fluctuation would bring the poles of +/- pairs on top of each other until they cancel each other out, if you don't introduce some restrictive 'force' that impedes negative charges fall into the positives (and viceversa) like quantum mechanics does with position-momentum quantum uncertainty (dispersion). So much of the stability of the world we see depends on quantum fuzziness... Why do you need electric charge to generate space? Just curious.

So these atoms are there. They're not a vacuum. They're a background. Why is it high-precission tests of the standard model haven't found them yet? Hadrons of all kinds, from high-energy beams and jets would certainly scatter off SU(3) bound states, with a very sizable cross section. On top of that, they are 1043 times more abundant than ordinary neutrons, so the luminosities would be over the roof. Why haven't we seen the littlest inkling that they're there? Don't think for a moment I haven't noticed you aren't answering any of this. This thread is starting to smell with a really foul stink.

Is that why they're called 'progressive conservatives'? What are they trying to progress in the conservation of? I like that. I'm very eclectic. I like to discuss problems one by one. One of the things that make me nervous about many political movements is that you must accept their whole agenda. It's either that, or you're a fascist, or a Bolshevik.

I don't know what to say, Seth. I would try not to look for paralellism between -1/1 and i/-1. I think they're different couples. But I'm guessing you're thinking about something having to do with the square root... Am I right? My usual approach for these properties (that try to explore the limits of what we (as students) previously knew about the numbers) is to try to find an intuitive hookup first, and then try to convince the students that it's a good thing to try to extend the idea so that one doesn't have to change the rules. (Mind you, I've used the word 'try' 5 times in the same paragraph). Example: Why is n0=1 for n>0 or n<0? Because we wish to preserve the property nk+j=nknj. So pick k=0, and j=anything, and there you are.

Ah. Ok. You wrote T2(-1)=-1 So I understood something like (i)x(i)(-1)=-1, which didn't seem right.

Ad hominem, IMO. I've given you two the negative reputation points you deserve for judging people on a thread about physical ideas. What people? How do you know what my intention is? What kind of people do you think we are? Irrelevant, of course.

You're right. There's nothing a priori that says what (-1)2 should be. I suppose it's rather a question of how far you can go with a definition like this and not find that it's inconvenient for certain purposes. As you well know, multiplication by complex numbers is better suited to represent rotations. Spatial reflections are a better embodiment of complex conjugation really. At least in 2D. Ultimately, I don't think one can prove that (-1)*(-1)=1, and one must decide what the suitable definition for the purposes of extending the system in a useful way. How many times have we been told something like 'you will understand later'? Btw, I think your example for i would be the first one rather. Wouldn't it?

I would never harm a senior member on purpose. But I'm not to be trusted with experimental equipment. I wouldn't harm any member, actually.

That's (more than likely) because you feed into the Maldacena conjecture theories that are related by S-duality in superstring theory, not because (or not necessarily so) of the correspondence itself (take good notice of the word 'when' in your quote). The correspondence itself seems to be something equally deep and perhaps not totally understood yet, although the holographic principle could well be a unifying / synthetic principle explaining it. Those are difficult ideas with considerable conjectural stretching at the seams. Wikipedia articles are accessible to all, full of references, valuable for many reasons. But clarity is not always one of them. That's part of the reason why I try to avoid using Wikipedia articles in order to argue anything, but just in order to attach a working definition for a term I have to mention. I don't like it so much (although I sure use it) because it's sometimes (or can be) rather obscure. I remember a seminar by Neil Turok in which he practically ended up dissuading his students from reading the Wikipedia article on Noether's theorem, because after many paragraphs the simple idea that off-shell symmetries imply on-shell conservation laws was not displayed at all in the article, while the reader ended up probably confused by the inordinate amount of side tracks and embelishments. I haven't seen anyone in the thread claiming that. The paper about antigravity is from the '80s and largely forgotten. I seem to remember an Eötvös-like kind of experiment. But I wouldn't blame anyone for not remembering... As to cold fusion's infamous Fleishmann-Pons experiment, or the Gran Sasso neutrino fiasco, where have you been all these years? There you are. Feast your eyes. I've even included a Wikipedia article. The way you like it. Are you scared by one two three 123 in 10^123. Are you being silly on purpose? It's not a scary number; it's an embarrassing one. Any physicists worth their salt would be embarrassed by this mismatch. Aren't you? And it's not 123. It could be 122, or 120. Nobody knows exactly. It's a very rough estimate. Correction: I would believe it.

Not necessarily. SU(3) is just SU(3), a continuous group characterised in several ways: Its structure constants (commutation relations between generators), fundamental definition: 3x3 complex unitary matrices with det=1, etc. Strong force, OTOH, implies a coupling constant. There could be two copies of SU(3), both locally gauged (not global gauge group, like, eg, baryon number, but local, like EM), and each with a different coupling constant. One strong, and the other one very, very feeble. Almost undetectable. Why not? There is no such thing if by 'duality' you mean Maldacena duality. There is a strong-coupling to weak-coupling duality in superstring theory. Sharks can be fish, and they can be dishonest money loaners too. The word in itself doesn't clarify the situation. As @Mordred says, 'Moving the goalposts' does not even start to describe what's going on here. You have an SU(3) every time three complex wave functions get shuffled into each other in a continuous and unitary way, like u, d, and s quarks in the primitive eightfold way. It doesn't imply 'strong'.