joigus

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'.

Not exactly. You might be made up of an even number of fermions and thereby operate as a boson. But this is a very interesting point, that I've thought about many times. Let's assume for the sake of argument that you're made up of an odd number of fermions. Your wave function, after being rotated 360º (which for just one point in space looks like a sequence of two reflections) would be minus your original wave function. This has nothing to do with ordinary space. 'You' haven't been reflected at all. This all happens in the space of states (quantum amplitudes). So how do we know your wave function has changed its phase to produce a global minus sign? The only way to do it is to prepare a high number of indistinguisable Eises with the same number of fermions, and make that number be odd by design. Then make sure this number doesn't change. And lastly conceive of a way to make all these Eises interfere with each other (like for example throwing them through a double-slit screen). Something like that. Forgive me if the details of the experiment are not watertight.

First of all, as @Mordred pointed out, this is from Quanta Magazine, which is not a peer-reviewed scientific publication. Second of all, if that were true, it doesn't mean it validates the numerology of paper under discussion. Third of all, you chose to ignore morsels of language that are very relevant: [...] may be [...] [...] hints that [...] [...] If true, it would be [...] [...] It's possible we're seeing [...] And, above all, (from provided source; my emphasis.) All of that you interpret as "actually, vacuum dilutes [...]" I'm kinda old. I've seen many, many 'earth-shattering' discoveries come and go: Antigravity, cold fusion, superluminal neutrinos, and what not.

Thanks.

OMG. This thread should be renamed to "The whittling down of Kihara" . Anyway... You guys got the holographic principle wrong. It's actually more general than what I said. I referred to the inspirational idea which was the AdS/CFT duality, or gauge-gravity duality, etc. Anyway, the holographic principle refers to relating field in the bulk with field on the boundary of that bulk. I don't see how the crazy SU(3) background relates to that. @MigL and @Mordred seem to agree. But that's not the worst, this is a matter background, not a vacuum. A vacuum does not dilute with the expansion of the universe. A background does. (reprise)

Yes, exactly. Those are the cyclic rings, or discrete... They go under several names.

Ahem... No. Although weird or not is in the eyes of the beholder. I'm not giving an answer. I'm pointing out a mistake. Nothing should be weird about that. If you have a better understanding of what 'holographic' means in the context of field theory, and why it's relevant here, I'm all ears. Holographic in this context would mean that a particular gauge theory, presumably SU(3) being the gauge group on the surface of the cosmic horizon, is dual in a precise mathematical sense to a gravitational vacuum in the bulk (inside the cosmic horizon). In particular it must have the same degrees of freedom. I'm no expert on holographic field theory, but presumably the gauge theory would have to be highly constrained: Hamiltonian constraints, plenty of Lagrange multipliers, quantisation rules on the constraint surface in phase space. BRST quantisation perhaps. You know the drill... This should be so, I'm only guessing, so that the dual version is a simple scalar (actually a number) on the inside, which is what the vacuum looks like from the point of view of GR. That's not what our friends are telling us here. They're telling us the cosmic volume is filled with these SU(3) 'atoms', and that their volumetric count gives the energy content of the universe given by the cosmological constant. So no, it's not a surface-to-volume correspondence (so non-holographic), and no, I'm not giving an answer; and again no, I don't think it's weird what I'm saying.

Interesting. I wasn't aware of differences between us and them. Now that you mention it I seem to remember notes from some professor pointing out that one could either demand the existence of an non-zero identity or leave it out. And then rings with an identity would be 'ring with identity'. Like Zp with p prime. (Please correct me if I'm wrong, I'm not checking anything I'm saying here). The turn-around way that @Eise suggested, or the mirror way, or @StringJunky's yes-no, or @MigL's even/odd rule, or anything that's ultimately an involution (leaving fermions aside) would be perhaps the most intuitive way. Something like this: Ok, kids. Multiplying by 1 is: Nothing changes Multiplying by -1, on the other hand, is some kind of a 'switch'. When you switch the switching, it doesn't switch more. It just unswitches! It may sound silly, but kids generally get it when you give them examples like these. Semigroups and the like are for geezers like myself.

Good point. I was thinking of using reflections too, until I remembered fermions. I don't think children would care too much about fermions tho... I agree. Any other choice would give you problems with the distributive property and/or other equally fundamental properties though. After all, there must be a reason why we've been choosing that option and no other one has resulted in an interesting algebraic framing.

Nothing holographic going on on this thread, believe me. Don't get confused. 'Holographic' means a gauge theory on the boundary of a region can be seen as isomorphic in some sense to a gravitational theory in said region. I don't see where any of this is 'holographic'.

Nah, I wouldn't say that, although I see how you can think that. As I understand it, the main focus of this website is on discussion. There are sections that are particularly focused on education. I'd say this website's focus is quite good for setting you straight. Anyway. Welcome to the forums. So true. I tend to be very mathematical, always referring to the formalism, which scares people off sometimes. Not you.

I've always found it interesting that these dreams are recurring. Seems like the brain is bumping into morsels of code for unresolved issues... No wonder people have been trying to interpret dreams for millenia.

Yeah. Clearly the brain can't handle the narrative of the ongoing events. It's clear to me that his mind must have re-edited his immediate experience, so to speak. He was startled for some reason that could not be retrieved by the senses, and had this automatic reaction of removing the tubes, but not because of the scene repeating itself. Only later, when that nurse or doctor came in asking what's the matter, he "re-edited" his immediate memory as if it had been the looping had been the cause of his disturbance... His brain must have filled in the details of this illusion that the whole thing was happening because he was experiencing the looping. Why am I startled? Because the scene is repeating itself. Something like that. Weird. The OP's experience reminds me a lot of that, but without the 'parallel universes' version of it.