joigus

I don't understand. I quoted directly from your post before your last one. Yes, sorry. "That" is this: I never said that the whole point of thermodynamics is to model what a box of gas is going to do. That's what I thought you were pointing at. But thermodynamics is certainly powerful and sometimes you can predict behaviours in processes, define and measure coefficients, etc. Nevertheless, sometimes when I start reading through the forum I'm a bit tired and there's a danger for me to misinterpret. And I don't see criticism --of ideas-- as a bad thing. And as to the 'salt and pepper' I'm afraid I did it again. Now I understand what you meant, and that would be a good analogy for the runes IMO. You --unwillingly, of course-- had me looking for 'salt-and-pepper' idiom definitions at some point. LOL Here. That's what I said. Any comments, further qualifications or criticism welcome.

I never said that. Thermodynamics is about much more than that, of course. There are reversible processes, irreversible ones, and different interesting coefficients we've talked about before. But a gas is a good example to start talking about to illustrate its power and generality. I must confess, @studiot, that I wasn't following your arguments in this particular post as closely as I follow them in other posts, as I was following the OP's. And that's because the OP was rather lengthy already. I haven't been even able to follow all the details about the runes and the states based on them either --maybe lack of time and tiredness among other things. I thought I understood more or less what the OP was trying to do and tried to warn them as to what I called the "subtle misconceptions" in their approach. I thought it was an honest attempt at understanding the subtle concepts underlying the formalism. Any of your 'salt and pepper' explanations are welcome on my part. And even the ginger and lemon tea ones.

Nothing is pre-nothing here. It's gone full circle a few times already. But please keep going. I'm planning on getting myself a really good GR monograph by copying and pasting Markus' detailed explanations.

Exactly! Have you heard of Boltzmann brains? Well, I haven't shown you that your idea is wrong. I haven't shown you much, AAMOF. I've argued to you, I think, it's not plausible if you take it seriously to make a model of what a gas in a box is going to actually do. I've argued from general concepts derived from what I know. But there are qualifications to be made in cosmology. I would have to think about them deep and hard, or maybe have some expert in cosmology tell us what they think. The universe is not a boring place most of the time we are given to watch it because, in the case of the Earth, it's governed by fluxes of energy, coming in, and going out. Open systems like those are not Poincaré recurrences. They are the kind of systems that can hold something like life. There are very interesting models of systems which undergo self-organization under those conditions. But the universe is not like a closed box which thermalizes after some time. And I don't think the universe as a whole satisfies Poincaré recurrences. That's what I meant when I said, So if you don't like a universe that will thermally die, who knows, maybe that's not gonna happen and you (or some version of you in some far far away future or in some far far away cluster of the multiverse, is having that expectation fulfilled. Does that help? Maybe the universe repeats itself geometrically, by some periodicity condition. There may be many possibilities. They're going on. For example, some of the molecules I'm breathing now will be gasped by the last breathing creature that will live on Earth, and others were inhaled by the 1st breathing creature that lived on Earth. But I'm none the wiser. Yet, if the temperature goes up one degree, I will notice. Nice conversation.

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.

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.

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.

"Occasionally, an obsession does turn out to be something good." Chen Ning Yang The key word here is "occasionally." "It was a crazy idea, I grabbed the back of a napkin and did the necessary calculations." Murray Gell-Mann The key words here are "necessary calculations."

Interesting... Tidal effects come to mind at your suggestion, because those are second-order effects, which requires an order-2 tensor.

Boy, was that a good explanation! +1 And this was intended as a joke. Coordinates mean nothing, it's the metric tensor contracted with the coordinates, as Markus so brilliantly has explained. Just to clarify...

That's only because I'm a remote object, and you're giving me the wrong coordinates. Apology accepted.

Don't put words in my keyboard. The only one who believes in remote dilation as a frame-independent phenomenon here is you! That remote dilation is only in your mind. You don't even understand that, which says all about you as a "thinker." The fact of whether something suffers frame-dependent dilation or not does involve having things other than photons in it. In fact, in order to write down the geodesic equation for photons you must do an affine transformation, because their proper time is identically zero, so no common-sense clocking will help you describe their histories. But what am I telling you; you know next to nothing about relativity, that not being the worst. The worst being that you don't bother to examine your own assumptions, or anybody's criticism. Can you imagine Einstein telling Hilbert "please consider my silly mistake as a valid assumption"? Einstein quickly re-wrote his paper. Learnt much from Hilbert, and went on to publish one of the most important papers in the history of physics. I will pop up every now and then to see what experts and other serious thinkers have to say. Your post is only valuable in that sense. The only trouble is I will have to check for you twisting everything I or anybody else has said, just because you don't understand the first thing about relativity, you don't read what you write, let alone others, and you stubbornly stick to a bunch of silly pseudo-scientific propositions to no end.

You're most welcome. It's such a pleasure to break the spell. Good luck to everybody else.

And I've I told you: MigL also told you: And, along the same lines, I said: IOW, it's not t2-t1 for the arrival times of the signals that mark up the ticking of the clock --the perceived time, which is the thing you seem to be thinking about, although nobody can be sure-- what determines the clock's ticking, it's the mean average of tout and tin. tout and tin being the delays in the forward and backward trip of your signals. The process repeated for 2 fiducial ticks of the remote clock, and then the calculation. The source of all your inconsistencies about "remote clocks" starts, I'm sure, from the very simple fact that you don't understand what it means to measure time in SR, let alone in GR, which is affected by second order derivatives. There are as many as 20 independent ones, that's known since the 19th Century. We could talk Einstein, we could talk Weyl if you want, but let's drop the tensors for a while, if you please. Please, tell me that you recognize something like what follows in terms of outgoing and ingoing signals in order to define coordinate time: \[t=\frac{1}{2}\left(t_{\textrm{out}}+t_{\textrm{in}}\right)\] where tout is the coordinate time of signal sending in your system, and tin is the coordinate time of signal receiving in your system. The coordinate time of distant events must be defined in terms of the times signals delay. k-calculus was developed by H. Bondi and is a very simple tool to understand this, and if you take my advise and read carefully chapter 1 of D'Inverno, which I recommended you, you will understand. IOW, you can keep your own close observations as your clock, so to speak, but for remote objects, you must send signals and, upon receiving them back, guess the coordinate time for the distant object. It's always like that in any relativity, S or G. Please, oh please, try to understand that and maybe we can talk about something meaningful and go on to tensors. Otherwise nothing we discuss is going to be meaningful. I think that's a preliminary requisite. I don't have much time, sorry if I mistyped or made another similar mistake.

Because I was the one to mention radiation pressure, and just to clarify, I never intended to argue that radiation pressure is a plausible point of departure to build the components of either the energy-momentum tensor, or the Einstein tensor, or anything else in GR. It was intended as a simple illustration that the slowing down of clocks (a frame-dependent effect, as I've repeated here to the OP till I got blue in the face) has nothing to do with the slowing down of photons. And it was in response to this rather bizarre statement by the OP: (my emphasis) And as photons do not slow down in any sense that I know of in a gravitational field, and please correct me if I'm wrong, I surmised that if a clock made of photons (and necessarily other things non-photonic) does slow down in a gravitational field, what other reason could it be attributed to but the fact that it's not made just out of photons, but also massive / charged matter interacting with them? IOW, the photons that are going back and forth inside the clock cannot be accountable for the slowing down of the clock, but the presence of the cavity, with which they interact. What the detailed analysis of this interaction would be is another matter, which I won't even try to analyze here or elsewhere. But there, that's how else you could explain it: because it's not 'just' photons falling! On the other hand, I totally agree with what the experts have said as far as I've been able to read and understand. And specifically concur totally with the point that considering space-time as a "medium" is completely the wrong way to try to approach it. My last point, and sorry for the lengthy argument. I'm not saying that GR is necessarily to stay with us forever, or that I'm 100 % sure of its total infallibility. But for anybody who claims to have come up with something new and/or better to supersede it or rival it, as Strange has been the most insistent to say on on this forum (from which the only thing of interest is the opinion of the learned people who have responded to the tsunami of nonsense) the minimum required is to reproduce its many impressive results. And sorry for the diacritics. They're just to emphasize what I consider the important points I want to make.

Only case in which I thought that could make any sense is about static solutions. But not even there. Thank you very much. +1 Eqs. rendered badly, prob. because insertion of HTLM tags. Dunno. Anyway, I meant, To be more precise. Einstein demanded, \[ \sqrt{-g}=1\] with, \[g=\textrm{det}g_{\mu\nu}\] which, as Hilbert pointed out, can't be in a diffeomorphism invariant theory. His first version of field eqs. was, \[R_{\mu\nu}=\frac{8\pi G}{c^{4}} T_{\mu\nu}\] which doesn't covariantly conserve matter energy, his goal. As, \[D_{\mu}R^{\mu\nu}\neq0\] The moral of all this: Einstein was carefully scanning for mistakes in his proposal. You don't come across like you are, rjbeery.

To be more precise. Einstein demanded, \[\sqrt{-g}=1\] with, \[g=\textrm{det}g_{\mu\nu}\] which, as Hilbert pointed out, can't be in a diffeomorphism invariant theory. His first version of field eqs. was, \[R_{\mu\nu}=8\pi GT_{\mu\nu}\] which doesn't covariantly conserve matter energy, his goal. As, \[D_{\mu}R^{\mu\nu}\neq0\]

That's very interesting. Thank you. The concept of photons was Einstein's pride and joy, but it took decades for people to buy into it. It's not an easy concept and it remains so to this day. At the time when he published GR's founding papers, the concept hadn't still made it through the barrier of incredulity. Another thing is the concept of "invariance under general coordinate transformations," which to this day finds physicists discussing as to what it means exactly. In my opinion, it was a simplifying assumption that Einstein took, because he was in direct competition with David Hilbert to be the one to get first at the final form of the field equations. AAMOF, Einstein made a mistake on the first paper, including a condition that the determinant of minus the metric be 1, which is not an invariant constraint. Hilbert immediately noticed, and so told him. Einstein corrected it, and went on to learn about the Ricci tensor, which gave him the final form of the field equations. So did Hilbert too. Science historians admit today that Einstein got there first.

Right you are. It's absorbing photons. I hadn't noticed. Thank you. But as far as I've been able to read the photon clock made in Caltech does use radiation pressure. The point I was trying to make is that if you build a periodic system (clock) by having photons bounce back and forth, such photons aren't free-falling anymore; they are interacting by means of non-gravitational forces. What the OP was arguing, at the point that the question surfaced, was that free-falling photons must slow down. The reason being (as I understood the OP) that bouncing photons in a photon clock must slow down too to account for time dilation and length contraction. My argument, IOW: any such clock is not just made of photons bouncing in mid air, so to speak. It involves matter and interactions.

This is only valid for static solutions!

And it does. Welcome to our world (the real one.) Radiation pressure is proportional to the number of photons per unit time that hit the mirror and the average energy of the photons, which is, \[\hbar\omega\] which is affected by frame-dependence. Inverse time transforms exactly like frequency. In GR is a bit more complicated, but it can be locally understood in terms of inertial frames. So it's not an invariant (or your cryptic "absolute" word.) Radiation pressure is a frame-dependent object as well. I rest my case. This is about the first time that you've asked a question. I think you can learn some relativity in a reasonable time (compared to Eddington's years) today thanks to the fact that you've got lots of material, in the form of online courses. Many people here can help you. There are wonderful free e-books out there. You're not dumb, you're just sticking to your guns to the point of nonsense. You can teach yourself relativity by reading good books and following excellent courses, but you've wandered alone for too long. Neither Einstein nor Eddington were lone wanderers. Every (static) exact solution in GR carries with it what you call an acceleration field. What the meaning of it is is far less clear to me. What's sure is that changing coordinates to locally flat (inertial) takes you to what the free-falling observer sees. But the starting point from the exact solution is far less clear in my opinion. I'm looking forward to what the experts in this community have to say. Mercury's precession is already a solved problem to 43'' of arc per century. Bettering that is a pretty tall order. I would start with vector calculus and a relatively simple model of field theory, like Maxwell's equations. When Einstein postulated his equations, he took Maxwell's as a model.

Missed this. This really says it all. A viewing angel is telling me from nth layer that you're mistaken. Cheers