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sethoflagos

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Everything posted by sethoflagos

  1. I specifically stated the centre of mass of the gas because this is precisely the quantity that you are trying to move around relative to the CoM of the box to establish your case.
  2. If the centre of mass of the particles remains stationary at the centre of the box, then it's possible that no nett work has been performed on the gas. Now explain to me how that centre of mass can move towards the sides of the box to any reasonable degree without the box performing work on the gas.
  3. Another interesting rabbit hole. By coincidence, I asked a question the other day about the strength of coupling between a CMB photon emitter and its TV aerial absorber. Mordred informed me that contrary to what I'd inferred from what I'd read of GR, they weren't actually touching since the photon wasn't a valid frame of reference. Obviously, I've no grounds whatsoever for disputing this, and too many Minecraft projects planned to try and get to grips with it. I just accept that for now and the foreseeable future, such fields are beyond my understanding. Not my system. You define your system as you wish. If you can. It's not easy, and perhaps will give some idea of why the microcanonical ensemble has given statistical mechanics some headaches in the past. The canonical and grand canonical ensembles find easier application in the real world and have no aberrant conflicts with classical thermodynamics. There is now an exchange of work between particles and box. It has become your very own 'undisclosed piston'. Do you now see and understand the issue?
  4. An interesting rabbit hole! Firstly, consider what is happening to your system centre of mass, and account for its apparent irregular motion. I look forward to your well considered response (which I'll not preempt here)
  5. My point. We're agreed. Agreed. The V/2 state perforce requires some combination of W and Q which must be reflected in a balancing change in U. 2nd Law implies a minimum increase in U (and hence T) under simple compression. They said it. Obviously. Absolute zero microstates are allowed into their ensemble by their reasoning. How do you propose to explain all the particles appearing in one half of the box? My inference is that there must be something equivalent to an undeclared piston compressing the system which, as you say, violates the conditions of the problem. That in itself is a clarification: the hypothesis is probably BS.
  6. Your point that classical thermodynamics largely time independent, I accepted without seeing the need for further comment. Which was the other point? I'm 100% with Mordred on this issue. Would you be happy to simplify the thread and leave it at that? Then we are in agreement. Obviously. Hope all is clear
  7. You do like to nit-pick! Depends a little on context. Formally, in my day job, it usually infers that the system is in a state of minimum Gibbs Free Energy - e.g there are no bulk convective processes going on within it. For a constant V, T system (I rarely encounter these) it would be a state of minimum Helmholtz Free Energy. In the OP scenario, the presenters start with an equilibrium V, T condition and claim that it can evolve spontaneously to occupy only V/2. This requires a bulk convective flow (eg a piston compressing it) and represents a fundamental change of state. The presenters concentrate on the position distribution of their system and fail to mention any impact on the momentum distribution. Do we infer the temperature has remained constant (breaking the 1st Law and the 2nd)? Has it increased as it would if it had been compressed by a piston (2nd Law preserved but not the 1st)? Or indeed has it decreased. We are left to guess. The only clue we have is that the presenters claim to have 'proven' evolution to a low entropy condition. If we believe them, this eliminates the higher temperature case from consideration. What we are left with is a proposed sudden and significant random change of state breaking both 1st and 2nd Laws. It's perhaps a personal flaw, but I've a habit of ridiculing such proposals by highlighting an extreme case that becomes allowable if their assumptions are correct. Such as a spontaneous jump to absolute zero. Of course the presenters do not state this inference explicitly as it would make them appear very foolish. But I'm quite happy to point out a logical extension of their false reasoning.
  8. A hole as little as 1m below the water line of an atmospheric tank will produce a water jet around 4 m/s without being accelerated by anything other than the potential energy of its top surface, whereas suction lines for typical common-or-garden centrifugal pumps are rarely designed to run above 1 m/s, often much less. So the potential energy of the liquid top surface is more than sufficient to flood a pump suction without any assistance from the pump. The fact that some pump suctions are able to run at a partial vacuum is because the pump internals are sealed within an air-tight casing and cannot 'see' atmospheric pressure. The actual operating suction pressure is set by suction side static liquid head less friction losses and is independent of the pump. The pump simply adds its rated differential head to whatever absolute liquid head it's provided with at its suction flange, and that sets its discharge liquid head. As I said, there's no such force as suck.
  9. I did. A box of volume V with all its contained particles sat in the left half is a non-equilibrium state, isn't it? As were each and everyone of the previous10^(big) intermediate microstates necessary to create this scenario. You're Wikipedia link introduced 'N .... a small number of particles'. I thought it might be useful to firm up the order of magnitude where this concept may have some significance. Something a bit smaller than say N = Avogadro's number. Similarly, you're link stated this small number of particles 'may show significant statistical deviations from that predicted by the second law' without quantifying it by example. So I provided an example. I wasn't changing the parameters. I was merely plugging in representative numbers where they had been left unquantified, woolly, and uninformative. Please read the quote this comment refers to: it paraphrased the Youtube presenters. For me, the relative temperatures of the two states were undefined therefore so were the relative entropies.
  10. This. Rule 1) There is no such force as suck. All the energy for accelerating water out of the container comes from the container and its contents, so you can forget about everything downstream of the hole - it's irrelevant. In the vicinity of the hole the water converts some of its (undirected) internal energy into directed momentum heading left let's say. This results in a localised drop in internal pressure on the left hand side of the container while the right hand side of the container continues to see the higher local fluid pressure, and is hence kicked to the right by a nett reaction force equal and opposite to the momentum of the exiting water stream. In a small system, it's a small effect. Industrially, say when a large pressure relief valve opens - these reaction forces can be many tonnesf and require serious structural support.
  11. Perhaps you didn't read my OP carefully - I dispute that these 'so-called second law violations' exist at all precisely because they ignore the concept of formal states. In particular these examples depict what I presume is a microcanonical ensemble (no heat bath is indicated) which in statistical mechanics (as I understand it at least) has a clearly defined equilibrium NVE state. ie the ensemble consists of all those possible accessible permutations of that number of particles (N) occupying a constant volume (V) within a vanishingly thin band of total energy (E). I trust that you agree that this corresponds to a formal state. The next slide presents (presumably) the same N particles occupying only half the volume, claiming that this an inescapable result of statistical mechanics. Would you agree that this corresponds to an entirely different formal state (with undefined total energy to boot)? Personally, I dispute that such a state could evolve for even the briefest of flickers because in that instant, it 'forgets' its earlier state - the information necessary for restoring it has been irretrievably lost due to the proposed macroscopic drop in entropy. The change would be permanent. This is significant. If we accept the smallest possibility of such an event, we accept higher frequency occurrence of less extreme random deviations and so on until we no longer have meaningful conservation laws - isolated systems would be continuously changing their properties in a continuous random walk with expected deviation propotional to the square root of time elapsed. I am amazed that so many seem to buy into this concept, without apparently the slightest shred of empirical evidence.
  12. Many thanks, swansont. My reading of this passage draws two key inferences: 1) 'Each microstate that the system maybe in' refers specifically and only to the ensemble of microstates whose properties are consistent with those of the initial microstate and for which there is a credible mechanism through which each can be accessed (see ergodic hypothesis). It most definitely does not include any wacky extreme non-equilibrium microstate dreamt up by a Youtube presenter in search of more Patreon support. 2) A snapshot of a small number (like 42) particles doesn't have a precisely defined temperature etc due to the uncertainty principle and the relatively large error bars of a small dataset. However, this measurement problem is just that, isn't it? Hiding away inside the quantum fuzziness is there a possible state of 42 regularly spaced particles all with zero relative motion? I think not. There's no route in and out of such a state. I don't really follow quantum theory but I was under the impression that many of its leading lights were currently touting 'information cannot be destroyed' which pretty much underpins the 2nd Law, doesn't it? Actually there's a third now I think of it. The Wikipedia paragraph you referenced carries no inline references. I was rather hoping to find something on this subject that's been through a proper peer review.
  13. In what way is the 2nd Law 'statistical'? Many notable researchers have used a statistical approach to probe the complexities of thermodynamic systems, but isn't that only because of the computational complexity? Are you claiming that the systems themselves are stochastic in a real sense? If so, then where does the random element creep in?
  14. If fire can only be initiated by an earlier fire, how did the first fire start?
  15. This has been a common trope running round most of the pop-science channels on Youtube over the last year or so. I won't name names but I guess some of you know some of the channels in question. It starts with a box with N particles randomly dotted around inside it. The presenter then changes the cartoon to one where all the dots are shown on the left hand side of the box and states 'Statistical Mechanics says that all random configurations of particles are possible, therefore sometime eventually this low entropy configuration will occur, therefore the 2nd Law only applies sometimes'. Leaving aside the macroscopic shift in centre of mass that shows dereliction of the 1st Law (an easy fix if they cared about it), they present this extraordinary claim without stating what quantities are preserved in the analysis, what if anything has happened to the momentum distribution in the half box scenario, or whether 'statistical mechanics says' the system will ever find its way back to its original thermal equilibrium. Have I missed something somewhere, or is it all just clickbait BS?
  16. Yes and no. It's easy enough to set up a theoretical process for an ideal gas that runs up and down the P, V relation PV^(Cp/Cv) = constant using just the 1st Law and the concept of reversible heating (ie no departure from thermal equilibrium). This relationship is the classic textbook case for obtaining the maximum shaft work output from gas expansion, (or minimum shaftwork for gas compression in the reverse sense). Explaining why this conserved quantity represents a brick wall for power generation cannot be explained by the First Law alone - for that you need a concept that looks a little deeper into this reversible heating idea and recognises that 1 Joule at 1000 K is a hell of a lot more useful than 1 Joule at 100 K. Hence we end up with the idea of entropy S, defined by its derivative dq = TdS and find that PV^(Cp/Cv) = constant is synonymous with S = constant. This conserved quantity is quite distinct and independent of the 1st Law conserved quantity PV/T = constant. For the general case of course dS>0 due to dissipative factors like friction, ergo the 2nd Law. The directional signing of Q and W is purely conventional reflecting industrial processes where heat is typically input to a gas and shaft work is output - Q and W are both defined as positive in this scenario.
  17. Actually, having a point particle filling the observable universe was what I was trying to get around - by taking the point of view of the photon whose spacetime universe is of atomic dimensions - at least looking down the wormhole of its momentum vector. 4D geometries fry neurons
  18. I know when I'm flogging a dead horse. Sleep well, Mordred. Good night.
  19. I appreciate that dt perforce =0 but if ds also =0 surely we can consider the measured ratio at v=0.9c, v=0.99c etc and infer that at v=c, 0/0 still =c, can't we?
  20. Yet from the photon's point of view, all of future spacetime is condensed into a singularity since it can in principle access any of it instantaneously? ie the totality of its future light cone is local.
  21. Okay, well the restriction on valid reference frames to v<c is a new one on me, however ... You agree that the spacetime seperation is zero in the direction of photon travel, which is my starting point. Does this mean that the emitter and absorber are physically adjacent (despite the huge separation in our own spatial and time reference frame), with a consequently strong electromagnetic coupling, and hence that the exchange of a photon between them reduces to a local event. I'm not looking for transfer of information from absorber to emitter as such, but whether the existence of an available absorber (removed in time) can be sensed by the emitter. Or does the emitter simply chuck out a photon irrespective of its ultimate destiny. No handshake in either direction.
  22. I was musing on the life experience of a CMB photon travelling from its source emitter - perhaps some excited hydrogen atom at recombination - to it's absorber which for sake of argument might be a TV aerial. Am I right in thinking that the spacetime interval between these events is zero? And in particular that the photon 'travels' zero spatial distance in zero time (due to Lorentz contraction)? Is there a sense that the photon is sitting for an instant inside some weird tiny spherical(?) surface, in intimate contact with all its possible futures (one of which is said TV aerial), a myriad of even tinier exits to all available absorbers peppered within a matrix of paths forbidden by destructive interference, and/or routes to some eternal void? Because if source and destination are touching perhaps there's no need for any significant energy investment in filling up its light cone with .... stuff (insert correct jargon). Just pick a destination that matches up and hey presto it happens instantaneously (give or take 13-odd billion years).
  23. I set up an excel spreadsheet to integrate the following system by first order forward difference equations: 2/(k-1)*dc/dt + du/dt = 0 in direction dr/dt = u + c 2/(k-1)*dc/dt - du/dt = 0 in direction dr/dt = u - c With r=0 boundary conditions u=Asin(wt), c = c0, I got a solution that was a very good fit to u=Asin(wt)cos(wr/c0) which is the expected result for a standing wave in a cylinder. How good a fit? Well the integration yielded maximum variance values of 0.5 in both r and t trends over one wavelength, and subtracting the above expression reduced this by 99.9954% in the r trends, 99.99902% in the t trends. A pretty good fit. However, looking at the residual and experimenting a little, I found that adding a further term wr(A/c0)^2/pi*sin(2wt)cos(2wr/c0) removed 99.75% of the r, and 98.97% of the t remaining residual max variances. This term may have a very small value over one wavelength, but the proportionality to r means that eventually the second harmonic will dominate the waveform, and the proportionality with A^2 means that it's proportional significance increases with input amplitude. Any suggestions as to how I might go about determining whether this term is no more than an artifact of non-linearities in the forward difference method, or if it really is a true component of the system? In passing, the small residual that remains is almost equal to a simple product of sin(2wt)sin(2wr/c0), leaving something closely proportional to r^2sin(3wt)cos(3wr/c0). And still, little sign of randomicity. Many thanks in advance for your time, Seth
  24. We're getting too hung up on t=0 here. Question 1) is really a general question about whether the quantum fields for a finite system at any particular instant extend throughout spacetime (even if the precise future geometry of spacetime were somewhat indeterminate).
  25. The Big Bang says nothing about T=0. It only describes what happens once expansion begins. I don't know what your first statement means, maybe you could re-frame it ? Difficult to rephrase it without presupposing part of the answer. As I picture it, it's a Schrödinger equation describing the time evolution of the universe (or all possible universes courtesy of the superposition principle of quantum mechanics) in some kind of primordial Hilbert space. Don't know where 'preferable' came from, Your invention not mine. The 2nd Law of Thermodynamics favours such outcomes. I guess I'm looking for some parallel between the 2nd Law and the time evolution of superimposed quantum states. They are both essentially statistical in behaviour after all,
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