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And it is precisely that problem that invalidates your proposal. For your concept to be taken seriously you must propose a practical, sustainable, effective solution. Otherwise you do not have a solution, merely a wish list. Most of us might well wish for what you propose, but without a plausible mechanism to implement you are just daydreaming.

Oh, what sweet delicious irony. Everyone else's imaginary friends are imaginary, but my imaginary friend is real. Lol

Yes. I have been thinking about this some more, and there is something else that has been omitted - the fact that, if a horizon forms during the collapse process, it will initially do so in the interior of the collapsing mass. This divides the overall spacetime into three distinct regions: 1. The interior of the collapsing mass below the horizon - containing only mass-energy 2. The interior of the collapsing mass between horizon and surface of the mass - this contains both the mass distribution and Hawking radiation 3. The exterior spacetime - containing only Hawking radiation Each of these regions has a distinct energy-momentum tensor, and thus its own metric as a solution to the field equations in that region. The overall solution for the entire spacetime is a metric that is has to ensure that spacetime remains smooth and differentiable at the boundaries between these regions, which introduces additional constraints on the overall geometry. None of this has been accounted for by the aforementioned paper.

Here's a list a well over a hundred.

Accepted let's move on. Clearly all those years of experience, plus more which must have been spent in study of the subject, have given you command of Applied Thermodynamics (along with other subjects). As shown below You are not the only one who has had additional thoughts as a result of our discussion. It has also made me realise something I should have realised before. Thank you for that. +1 In another recent thread here at SF, a teacher of thermodynamics asked how to introduce the subject of entropy, without using the traditional second law approach. The discussion in your thread made me realise that of course you cannot use much of the mechanism of the second law if you are going to do this. This must be why the early diefintion did not mention entropy : entropy had yet to be defined. Hindsight allows an applied thermodynamicst to use formulae and techniques out of the logical sequence of the definition. This is in fact what I was doing and led me to my original agreement that you cannot use the classical approach to prove or disprove the kinetic interpretation. You need additional material for this. Perhaps my digression to show why the early pioneers always referred to cyclic processes was excessive, but I hope you have come to realise that since the kinetic approach is non cyclic in basis, you cannot use that part of classical thermodynamics which is defined only for cyclic processes. So another way must be found. But the kinetic question in the OP is not applied thermodynamics it is more fundamental than that. So discussion must follow and hold to a formal logical sequence of definitions and results. I don't know if you have heard of the Massieu and Planck functions ? These two provide the (mathematically derivable) link between the classical and the statistical approach, so that this is often referred to as 'the Massieu Bridge'. All of this is expounded detailed in Guggenheim's Advanced thermodynamics. (I would not recommend the Wikipedia pages on this they are rather unhelpful and not completely comprehensive or correct) However, just are there are several approaches to classical thermodynamics, there are several versions of the statistical approach. Unfortunately the statistical versions do not always completely agree with the classical versions, fluctuations being one such area of divergence. Epstein, in his famous textbook, included a whole chapter on the experimental evidence for and theoretical basis of such divergence. Epstein A textbook of Thermodynamics A free pdf is available here. https://archive.org/details/textbookofthermo031032mbp/mode/2up I am not sure of free pdfs for Guggenheim.

24 hours has passed which I guess is enough. For what it's worth, T2 = T1 + W/2nCv which defines the maximum value of Q2*(T2-T1) for the system, but that's now by the by. Certainly there was no ad hominem intended (and many sincere apologies if it appeared otherwise). I was simply the stating that the heat pump example you asked me to consider seemed to shed no light at all on the OP paradox. I present three main grounds in support of this assertion. Firstly, in the OP case, the Youtube presentations claim that the 2nd Law has been broken by 'statistics'. ie that some quantity of system entropy has somehow vanished. I think I've demonstrated clearly enough that the heat pump at least preserves initial total system entropy. So here, it seems uninformative. Secondly, the presentations claim that the gas has somehow contracted from some initial equilibrium state to occupy half of its original volume purely through its own internal mechanics. ie that the contraction happens without any external nett energy exchange with the environment. Again, for the heat pump case I've demonstated that all volumetric changes have exactly matching Q and W terms, so again, it seems uninformative. Lastly, as stated earlier, it dawned on me on Saturday that there seemed to be a strong conservation of occupied volume arising from the conservation of angular momentum. I don't see how the heat pump example was leading us toward such a conclusion. In hindsight, perhaps a centrifuge would have been a more effective guiding light - the volume restoring forces here are quite explicit and macroscopically large. In conclusion, it's become clear that the Youtube proposal of a broken 2nd Law is nothing but a red herring. Their real stumbling block arises from overlooking fundamental 1st Law constraints. Their loss of control of the 1st Law simply results in entropy being undefined, even in qualitative terms. Lies, damned lies and statistics again. Anyway many thanks to you all for your assistance in clarifying and solving the OP paradox so completely. I'm most grateful for your time and patience.

Yes. Evolution requires time. As does essentially every other thing across the entirety of everything.

Well, I'll be damned. One wave of the hand, and 5+ billion of us, who just happened to be born into non-Christian cultures, sentenced to burn in hell for all eternity. Makes me wonder just which of those two guys to blame, really.

Just to add to that, it's not like in SR where each observer also has a different notion of simultaneity, but each of those is physically meaningful. Eg. in flat spacetime, any two events that can be considered simultaneous by someone will have intersecting future light cones, where different future observers can agree or disagree on whether the events were simultaneous. In GR you must make a choice of how to define the surfaces of a foliation, that's not just based on a physically meaningful connection between its events. You'd choose it to make a useful tool, not a 'real' representation of simultaneity throughout the universe for a given observer.

Finally graduated magna cum laude as an MD. Although I have received the wonderful opportunity to specialise in neurosurgery, being a neurosurgery resident is just a dog's life I could not lead for the lengthy duration it has. Because of lots of reasons, I've decided to carry on as an aspiring future anaesthesiologist.

Good question Paul, answer is that many look at Thoth/Hermes and have done for millennia, He's had many names in different areas - Thoth, Tioti, Tahuti, Tuti etc etc, ages ago I was reading online and saw a mention of an Uto-Aztecan word "Tuti", which the author had said meant "Sandals", I looked into Thoth myself and refer to Him as Tioti, the way I'd translate Ti-O-Ti would be from Sumerian Cuneiform(Which was found at Armana), from this Ti-O-Ti would mean Life-Ring-Life(Ti-Me = Life-Exists), once I'd realised this it reminded I of the brilliant physicist Richard Feynman, in particular His and Wheeler's Time-Symmetric Theory where Time(at the beginning) began to propagate in two opposite directions simultaneously from the same Centre. Ti-Me meaning Life-Exists in regards to Ti-O-Ti, the 'Ti' in Tioti can mean time, because without an Observer ie A Life how can Time exist?