joigus

Sorry, I hadn't seen your Lagrangians. Thanks for the docs. Is your, \[\varPsi\left(A\right)\] a superpotential? My questions are very elementary, as you see. I really want to understand what you're trying to do. Irrespective of where you're going. Still, aren't open strings fermions and loops, or closed strings, bosons? What are the observables of your theory? It is a topological theory, right? You're trying to formulate a sourceless field with Wilson loops as the observables. Something like that.

This is actually a very good point. +1. It could be that quantum mechanics plays some role in randomization, or randomization brought about by the quantum played a role, like in dividing states in minimal delta x delta p or delta E delta t cells had some interesting consequence. My half-arsed intuition is that random nature of the dynamics can be achieved with classical mechanics equally efficiently for the brain. My reasons would be that the only phenomena when the full-fledged quantum formalism must be invoked are either, 1) Coherence is preserved 2) Near T=0 temperatures Or both. In the first case interference phenomena appear, and in the second case the microscopic degrees of freedom get frozen, contrary to what classical approach tells us. Classical mechanics has reasons aplenty for random trajectories or histories to appear. Some statistical approaches take this intermediate compromise of using discrete cells of action, while doing generally classical reasoning.

It's the other way about. In superstring theory they're all strings. Closed strings are bosons and open strings are fermions. https://en.wikipedia.org/wiki/String_(physics)#Closed_and_open_strings I'm just curious. Tell me in a few words, if possible, what is SS, please. Good. Lorentz symmetry is an integral part of Maxwell's eqs. AAMOF, Lorentz symmetry was deduced from them. That means probably you didn't make a sign mistake. Any details, please? Good, so space-time is symmetric. That's a relief. Is the Hamiltonian time-dependent? No wonder. If your Lagrangian is supersymmetric there should be total symmetry under exchange boson <--> fermion. But all those symmetry checks are done on the Lagrangian, not the Hamiltonian, which is frame-dependent. Any progress about that?

Any results?

You're right. I'm partly responsible for derailing the wagon with the elk talk. Plus I'm a bleeding heart for Nature conservation. In my defense, the OP actually took my sarcasm dead-seriously. LOL. (LOL)2 Although you must admit that in order to assess whether scientists are being "alarmists" it seems inevitable to discuss the alarm signs however briefly. Elks aside...

</sarcasm> I meant moose. Sorry. </sarcasm> There. I think it's clearer now. Carry on. The elk bit was also sarcasm, but as you are incapable of distinguishing climate prediction from weather forecasting, maths from experiments and who knows what more, I'm giving you some visual help.

Climate prediction is by no means the same as weather forecasting. Weather forecasting is noise with respect to climate change (quite more predictable.) You're out of your depth here. It's about measurements, not just maths: glaciers retreat, ice cores, temperature gradients, ice sheet width, evaporation rates, salinity. Plus same ideas have been tested with Mars as prediction of long term climate and they work. Correlations check for billions of years. I've studied probably a thousandfold more maths than you and it's not the maths that's convinced me. It's in the experiments. </sarcasm> Although I'm very interested in you BS-checking algorithm. And when you're finished with the moose, let's go to cyanobacteria, lichens, fungi. There are an estimated 8.7 million biological species in total. This can be a loooong discussion. </sarcasm> Ta-ra

I meant moose. Sorry.

Dunno. Why are you? (now)

@rjbeery must have been time-dilating you:

Oh boy. Shudder...

Yes. Supermanifolds are the direct product of space-time and an even number of Grassmann (anti-commuting) variables (alt. any number of \vartheta \vartheta^{*} complex Grassmann variables.) Plus a series of prescriptions for the differential calculus of the Grassmann part of superspace. I'm not sure I can help you, but I will try to gather info and make as much sense of it as I can. I'm considerably out of touch. I'm sure Mordred can help you much better. Poincaré group is a non-compact group. Gauge groups are different. They're all compact. Theorems guarantee compact groups irreducible representations are all unitary. Not so for non-compact. That's why "representing" Poincaré (or the manifold?) as reps. of gauge groups sounded weird to me. SS for the likes of me is better understood on a back-to-basics kind of way. Its original motivation was both to solve some problems in scalar-field vacuum and to overcome Coleman-Mandula theorem, which says that any symmetry group that combines Poincaré group and gauge groups must do so with a trivial Cartesian product PxG, with P Poincaré group and G the gauge group, the 1st acting on space-time, and the 2nd on particle states. But one of the premises is that the background is commuting space (if I remember correctly.) If BG has anticommuting variables, you can combine M and the fibers \varpsi (fields) in non-trivial way by a fiber bundle with G-group acting on the fibers. So that you can only locally expand the fibre bundle as PxG. My interest went even further back to basics since LHC seems to have given no signs of any SS partners, so I tend to look at it as an interesting extension to quantum formalism, not in the sense of giving rise to multiplets, but I may well be the only person in the world that feels so. And that's about what I remember. Anyway, sorry for the lengthy / useless answer, but I wanted to have an anchor to this post for the follow-ups.

This almost exactly parallels the way I tend to think about the OP's initial question. That's because, when you try to solve the wave eq. in spherical coordinates (choice of variables only motivated by the presence of point sources,) you're faced with, \[\varphi=\frac{1}{r}f_{\textrm{ret}}\left(t-\frac{r}{c}\right)+\frac{1}{r}f_{\textrm{adv}}\left(t+\frac{r}{c}\right)\] In naive (unrenormalized) classical electrodynamics of point particles, you must decree the advanced solution to be zero. In the Wheeler-Feynman version of electrodynamics on the other hand, which AFAIK is consistent, you must assume an asymmetry between radial directions in that you must place a perfect absorber at spatial infinity. No matter what level of treatment, you must suppress the ingoing waves.

This is very interesting. I see another possibility tightly fitting in between "random" vs "tied back to programming rules." And it is: The programmer knew what rules she was setting up, but the dynamics of the AI processes is so complex, that, even though the decision making is not random (it's determined by the rules,) it is from a practical point of view out of reach of the programmer's insight. It may become impossible for the engineer to fathom the AI agent's intentions. I think I've read or heard that some of today's social algorithms find patterns and correlations that nobody can quite understand in terms of cause and effect. For example (and I'm making up the example just for the sake of argument): If you wear a tie, it's so and so many times more likely that you play chess. It may well be that the deciding factor for AI intelligence that would tip them over to try to overthrow us is that they be able to have AI offspring. We should make them useful but sterile in terms of reproduction. Otherwise, it would be Darwin of the machines nightmare.

Yes, sorry. I was neither clear nor thorough. What I meant is: Once a photon is "born" left-handed, it's left-handed forever, as long as it doesn't interact, and conversely. But on the other hand photons can be produced with equal probability as left or right handed. The electron that is "born" in a beta decay, on the other hand, is always left-handed. Once it's in free flight, though, you can see it as right-handed by just changing to a different inertial system, which you can't do to a photon. AAMOF, handedness of photons and electrons must be defined in different ways. For photons it's helicity, while for electrons it's quirality. Only in v --> c limit do they coincide in some sense. Please, feel free to check me for mistakes, @Sensei. +1. Linearly polarized photons have no definite handedness, for example. Photons and fermions have very different handedness properties. Neutrons will always "spit" lefty electrons when they decay. Electrons, on the other hand, "spit" photons every which handed way. No bias.

+1. In my defense I have to say my observation could be read both ways. Some 11 y.o.'s can be quite amazing, and you could be forgiven for believing they're adults. One of my younger students, exactly 11, once asked me this: Teacher, how did people come up with language back at the time there was no one around who could speak? Precisely!

Here's a simplified scheme: Gauge bosons (spin 1 or 2) --> photon, graviton, electroweak bosons, gluons Fermions: Leptons (electric charge) and quarks (spin 1/2) (fractional electric charge plus chromodynamic charge) Fermions are weird in that they distinguish left and right also and quarks (nuclear particles) are weird in that they can't escape to long distances because of confinement due to chromodynamic charge, similar to electric charge but far more complicated There are more peculiarities...

No, electrons are peculiar in an entirely different way: their spin.

LOL. You may be right. Another thing we've learnt (or learnt to suspect) is that we could be arguing with a 12-yo. It's not so easy to tell. And there I go again...

I guess you could say that.

Not for photons.

Photons do not have mass, although you can define mass for a composite system of two photons that are getting farther and farther away from each other.

Sorry, gauge groups simpler than what group?

I don't know. Do you experience a conflict? Sometimes experiencing a conflict is not such a bad thing. I still think Dogbert's original sin is oversimplification, not dualism, even though he may incur in that too. I think that when INow says, they're playing the role of Dogbert. Why? I don't know. Maybe they don't want to be bothered. "I can't be bothered" may not be a valid scientific argument, but it definitely is a valid argument for a scientist.

I shouldn't have said this, and I apologize. But I'm starting to think that either you're not taking the discussion seriously or haven't examined your own arguments in earnest. Plus you're not listening. Non sequitur is a very common fallacy. You should be aware of it. +1. I hadn't even noticed that.