joigus

A big part of the problem may be rooted in muffled racist attitudes in sectors of society, economic inequality factors, political unwillingness to face certain facts, political convenience and who knows what else political or socioeconomic. Most everyone of you know much more than I do about this problem, and I'm more than willing to take a sit and learn. But, from my humble experience in the inner cities and the like, I can tell there is a regular profile of teenagers who want to make it into the police force in cities where the living is not easy. Quite a considerable number of the boys I've met who just wanted to become a policeman whatever the cost fell into the category of frustrated, misfits, racist, etc. types who would do anything for some adrenaline rush, doesn't matter whether it's one side or the other of law enforcing. I'm not saying that's the driving factor, but I think it's definitely a factor to be considered. As long as these people are not carefully monitored, we will have a problem no matter what side of the world we are. Maybe the US has a bigger problem because of the Second Amendment. But there are factors other than political, that's all I'm saying.

OK. Maybe so, but I see at least three problems with your strategy. 1st) It's not about how I define macrostates based on arbitrary assumptions such that the number of macrostates always overwhelms the number of microstates. Microstates for any reasonable definition of them are vastly more than macrostates. That kind of reasoning in science is called ad hoc, and I'm sure you know why it's not a useful avenue. Besides, what do these macrostates mean? How do they play in the general structure of known physics? 2nd) Macroscopic distinctions in physics always have to be measured. In the case of pressure, temperature or volume, it's through pressure gauges, thermometers and length scales marked up in the container. How do you measure your runes? 3rd) I've been talking about macroscopic distinctions with no further qualifications, but the truth is physics only permits you to apply the laws of statistical mechanics in a reasonable way that allows you to subdivide the system in a so-called canonical/macrocanonical ensemble, and get to something like the Maxwell-Boltzmann distribution, when you consider quantities whose balances between the cells of the canonical system can be reasoned about in terms of local exchange. IOW: quantities that satisfy local conservation laws. That narrows down the list essentially to energy, number of entities (mass, moles, molecules,) angular momentum, linear momentum, or things directly related with energy, charge conservation and rotation, like magnetic moments, etc. I'm sorry but, no matter how interesting runes are in your theoretical mind, and they may be from a POV of pure intelectual exercise, nature doesn't care about them. Runes, and other fantastically complicated to define --and fantastically irrelevant-- quantities are probably created and destroyed every nanosecond without being transferred anywhere near where they are formed. There's no exchange of runes. There's no local conservation of runes. There's no equipartition for runes. There's no near T=0 freezing of the rune DOF. And I even see more severe problems with QM, in which most observables you can write down are really incompatible. That's probably why runes don't appear in the laws of statistical mechanics. As to time-stopping, it was only meant as an intuitive phrasing. From the macroscopic POV, times does disappear from the problem once equilibrium is reached. Period. If you're not convinced, try to sit down in front of a gas at room temperature and see how much you have to wait for a rune to appear, or AAMOF for anything noticeable to happen, and how long it takes for it to disappear after you've waited several Earth life's worth of time for it to appear. That's a simple enough experiment to conduct. And there are some more things, but in due time.

Things to say, but very little time now. My entropy must be acting up. A whole new ballgame, both with the two molecules and with the universe. For completely different reasons. One is very small N (number of DOF,) and the other the possibility of frustrated thermalization due to cosmological parameters. Maybe we should get @Mordred interested in the discussion. Very interesting case for quantum systems near T=0, probably done to death by the experts but interesting to discuss nonetheless, and see if we learn something from discussion. Talk to you later. Very stimulating conversation.

Here I think you're being persuaded by a subtle misconception. When entropy has reached a maximum, the system has undergone total thermalization and nothing statistical depends on time. Things keep changing, but only microscopically. All the physical parameters are fixed at their average value. Any changes will manifest themselves in second order effects or fluctuations. If temperature is high, the system will be very efficient at erasing these deviations from equilibrium very quickly. Some months ago, I developed a picture meant to illustrate these concepts, only for educational purposes, and inspired by some musings due to physicist Tony Zee, that temperature is some kind of inverse relaxation time for the system, or proportional to it. It probably overlaps with formalism that other people have developed, because in physics it's very difficult to come up with anything that's really original and new. So in your initial OP, there is already a problem, and I should have detected it right away had I been cleverer. Namely: Will entropy be low much of the time? There is no time in entropy. Entropy kills time. That's its job description. I have a perception that we're faced with entropy at the surface of a black hole, because something is killing time there too! But those are just speculations. Although I very much like your post. Those are very intelligent questions. +1 I hope that helps.

+1

Very interesting topic. Patterns are important. I'd like to contribute two: 1) "My theory could still be valid if..." 2) Ignoring the points (often selectively so) you and others have made over and over, and focusing on sarcasm, minute details of an example, etc. Loved this one.

I think about here could be the origin of the "fallacy." Please be aware I'm not trying to prove you wrong. Maybe you're on to something maybe you aren't. Either way it's interesting!!! You're making sense and I want to oblige. The cardinality (number of possibilities) of microstates is what's humongously big. Macroscopic ways of organizing the data are not growing like factorials, or products of factorials, or products of factorials corrected by smaller factorials in the denominators. They're kept constant (maybe humongously so in some sense, but constant) fixed by the number of descriptions you wish to give yourself. Now make the number of microstates grow. That's what's going to dominate everything. The effect of taking the microstates to infinity is going to be the overriding effect.

Yes. Positioning your company is prostituting the internet. I remember a time when I was able to find exactly the page I was looking for by exactly reproducing the mistyping from the author. No longer the case. I'm confident in the fact the combinatorics grows factorially fast though. So probabilities to fall into an undesired ad are suppressed inversely to that.

Exactly. Combinatorics of words much more powerful than choices of single words. +1 I found a source on Google books where it called them "oricycles." Then I tried what @Sensei suggests with "oricycles"+"geometry." Seems to be the case that's old terminology that at some point shifted to "horocycles." The diagrams and definitions/theorems on the book seemed very much to fit the ones on the Wikipedia article. What year is the article? I'm just curious.

Totally agree with Markus Hanke: GR is (highly) non-linear. You cannot understand properties of solutions mixing different aspects in terms of (exact) individual solutions. You must solve Einstein's eqs. from scratch. I just thought @Strange and @MigL (+1,+1) went more in the direction of what's troubling OP AFAI can tell. (Plus shortage of points.) Dark energy is small potatoes when it comes to BH dynamics. BHs are generally very very small in comparison to comparable cosmic masses. DE is only sizable at very long distances.

Entropy is log of the M_a only if P(M_a)=1 and P(neg M_a)=0. Otherwise it's the sum of negative pxlog(p) (the average value of log p.) Now, as a function of the p's, -Sum p log(p) always complies with observable-independent property of concavity: https://link.springer.com/article/10.1007/BF00665928 There are interesting points in what you say. I cannot be 100 % sure I've understood everything. Something that reminds me a lot of what you're saying is Bertrand's circle paradox: https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) IOW: Maximal entropy states p_i depend on observable to be measured. But general properties of entropy don't. Thermo's 2nd law is unaffected, I think. It's quite solid. I'm not completely sure my arguments (if any here) are watertight. But I'm trying to offer you some food for thought that I think goes in the direction you're reasoning.

You're a very bad person!!! Fluid dynamics is an all-scale-coupling spherical harmonics mixing mess of a system of equations. Don't bring trouble here, you dark spirit!!! I was talking micro-causality and micro-retrocausality. Although now that I think of it, my Earth example wasn't very micro. Ooops.

https://en.wikipedia.org/wiki/Horocycle Terminology is a b*tch.

Communication with the past in your causal light cone is no problem, nor is it a paradox, even for classical mechanics, if I'm not mistaken. Notice: All systems are affected by their past. And because physics microscopically is reversible to a great extent (CP violation excluded,) I surmise you could argue that something that you see as the present affecting the past, what really is is you learning about aspects of the state that weren't obvious to you before (see below in relation to @MigL's argument.) The same question turned upside down is: Does the future affect the present? That would sound more paradoxical, but it's not. If you are within the future causal cone, there is no reason why you couldn't say in some sense that the future "affects" the past. It would be a contorted way of saying it, but it would be OK, I think, e.g.: What the Earth is today "determines" what the Earth was more than 4 billion years ago when it collided with planet Theia to form the Earth-Moon system. The real problem would be communication with your "unreachable present." That is, outside your causal light cone. I don't think that's possible and I don't think that's what QM is saying. But if you feel confused, you're not alone. Some 5 years ago I saw a paper, accepted for publication on PRL, and it was about the possibility of sending signals based on the observable to be measured. All the problems people are having for decades (and still are) are to do with (1st): QM not allowing you to think of certain properties A and B at the same time (incompatibility,) even if you devise extremely clever ways to measure A in subsystem (1) and property B in subsystem (2) and then use conservation laws to infer the incompatible property in the other subsystem to circumvent Heisenberg's uncertainty principle. And (2nd): States being in general non-separable. But I wouldn't want to go off topic. And quantum erasing really has to do with removing the effects of a measurement AFAIK, not with affecting the past. I would have to review down to the basics to say more. I agree with @Strange that retrocausality is a human-level perception of the results of the experiment. Something similar happens with so-called "non-locality." It goes more in the direction of not knowing the state precisely, as @MigL suggests, if I understand him correctly. And I don't understand @Kuyukov Vitaly's point. But he may well have a valid one. I do intuit he's thinking really farther afield.

Yes. I'm topological at heart. I'm totally enamoured of SU(2)*xSU(2) Ashtekar-Plebanski formulation of gravity with constraints. Gauge groups I tend to see as coverings of ST groups. Probably wrong as groups go deep. But you must simplify at some point. Totally concur with you that scalar field is something to be understood as the final touch after the rest of the variables have been understood. To me it's no coincidence that scalars seem to be key to both cosmology and mass spectrum. Easy to say, but... And probably not for me, but I want to have a first row seat when someone comes up with the answer. I'm not making much sense. It's too late here.

I just thought symmetric contracted with antisymmetric gives naught. After you intervened, I thought "maybe it's something like double-index spinor gravity." But I think now it must go deeper. He's not very talkative. I'll wait and see. I still want to know if the theory is topological. Topological theories are kind of my obsession. I'm scavenging for information in field theories.

Very good point. How would you be able to tell? Something we should never lose sight of is the fact that it's perfectly possible to pose questions that don't make any sense. Some of these questions may be even hardwired in our brains for reasons rooted in survival, so that it's very difficult to shake them off. A kind of question that must have been very natural to ask in terms of the needs and concerns of our ancestors, but is no longer to be considered a proper question would be, e.g., What does the river want from me? It's very easy to understand why a fisherman was naturally driven to ask this kind of question. Questions don't have to make sense.

I've just seen one dP hanging there that you must clear out when dividing by dP. At, \[\left(\frac{\partial H}{\partial P}\right)_{T}=T\left(\frac{\partial S}{\partial P}\right)_{T}+V\]

I'm not sure, but I think he means the Earth is not an inertial system due to rotation --> Coriolis and centrifugal fictitious forces? Is that what you mean, @Nedcim?

Thank you, Studiot. +1. This motivates me a lot to review my thermodynamics. I studied this ages ago, and it all has been ringing a bell while reading. The JT process was announced to us back then as something definitely important. Then I started studying statistical mechanics, which is great, because you get to see how it all works from the atoms to the thermodynamic variables, but you lose sight of many things because of the oversimplification.

Ok. Thank you. It must be an index convention I don't know about. I just wanted to know if the theory was topological. But to no avail. Actually, my question, was pretty stupid. Now I realize, as he implicitly gave the algebra. I'll take a back sit and try to learn something from it.

Do you know the difference between Lorentz invariant and reparametrization (diffeomorphism) invariance? (Rhetorical question.) One final question. Why do you ask, If you're not answering any? Actually, you have answered one very significant question. Only, you don't know you have.

Your energy looks dangerously close to being identically zero. Are there any comm. or a-comm. rules for the A's? Your action (sorry, Schwarzt's) looks dangerously close to being non-diffeomorphism invariant. Care to tell me the p-form character of the A's? Care to answer any of the questions I'm asking? Don't sweat it with your LateX phone, please. Simple worded answers will do. You also have too many contracted indices "i" in your energy expression.

Sorry. I forgot. There's a third category of honest and valid answers, which is "I don't know" or "I'm not sure," or even "I don't know why that's relevant to the discussion."

Thank you. I know what a Wilson loop is. Gauge theories have a lot of redundant junk that you must dispose of. Topological theories are very constrained. They have no propagation, because of the high number of constraints. Solutions are pretty much static. Any other evolution can be removed by local gauge transformations/Lorentz transformations. You must be careful to stick only to gauge invariant properties that are observable. Is your theory a topological theory? That doesn't require to be thoroughly explained. For the time being, it's enough to say "yes" or "no."