Clausius' famous principle "Entropy always increases" (which, according to A. Eddington, holds "the supreme position among the laws of Nature") was deduced in 1865 in the way presented by Jos Uffink on p. 37 in:

Jos Uffink, Bluff your Way in the Second Law of Thermodynamics, p. 37: "Hence we obtain: THE ENTROPY PRINCIPLE (Clausius' version) For every nicht umkehrbar [irreversible] process in an adiabatically isolated system which begins and ends in an equilibrium state, the entropy of the final state is greater than or equal to that of the initial state. For every umkehrbar [reversible] process in an adiabatical system, the entropy of the final state is equal to that of the initial state."

Clausius' deduction was based on three postulates:

Postulate 1: The entropy is a state function.

Postulate 2: Clausius' inequality (formula 10 on p. 33 in Uffink's paper) is correct.

Postulate 3: Any irreversible process can be closed by a reversible process to become a cycle.

All the three postulates remain unproven even nowadays; Postulate 3 is almost obviously false:

Jos Uffink, p.39: "A more important objection, it seems to me, is that Clausius bases his conclusion that the entropy increases in a nicht umkehrbar [irreversible] process on the assumption that such a process can be closed by an umkehrbar [reversible] process to become a cycle. This is essential for the definition of the entropy difference between the initial and final states. But the assumption is far from obvious for a system more complex than an ideal gas, or for states far from equilibrium, or for processes other than the simple exchange of heat and work. Thus, the generalisation to all transformations occurring in Nature is somewhat rash."

Pentcho Valev

As far as I'm concerned, you guys are mired in nonsense.

Firstly, I assert that there is no platonic realm; there is only this physical universe. So, what is the physical reality behind the numbers and complex numbers that seem to be necessary to explain reality? Numbers are symbols that represent something about physical reality; otherwise you must posit that they are entities that exist in their own right. Get the basics right first.

Secondly, you all have an unwarranted BELIEF, nothing but a BELIEF, that reality is necessarily 100% deterministic. It is not quantum theory that is odd; what is REALLY ODD is the mob mentality with its very tame, but unshakable, belief that the underlying reality will be found to be 100% deterministic.

    " ... unshakable, belief that the underlying reality will be found to be 100% deterministic."

    And your belief that reality is probabilistic is objectively based on ... ?

      Quantum entanglement gives psychics and the paranormal something to work with. Grey aliens and UFO's could be some dark matter life form popping in for a visit. Ghosts and spirits could be some kind of quantum entanglement form of life. And with the millions and millions of people who have experienced these things, they make the whole subject matter respectable.

      Now let me give you some examples of woo. Time travel. The MWI interpretation of quantum mechanics. Those things are so in conflict with what we know about physics, conservation of energy, causality, etc., that they are not only impossible, but they are not observed by anyone.

        Lorraine,

        The underlying reality *IS* found to be 100% deterministic. It is only by politically suppressing the evidence presented that the physics community is able to maintain the façade of inevitable indeterminism (cf. Tom's rhetorical question below).

        It was the Higgs field that toppled materialism as a philosophy that describes nature; basically, the idea that particles are just hard spheres is dead. If nature allows invisible fields to exist, like the Higgs field, and nature also allows invisible matter to exist, than it is clear that the laws of physics do not oppose the existence of ghosts. In contrast, time travel is going to create paradoxes which make it impossible.

        If you treat a ghost like a quantum field, than it fits in very nicely with quantum mechanics. It goes a long way in explaining why so many people have had experiences with ghosts, shadow figures and other disembodied entities. Lot of people have seen the glowing red eyes of otherworldly entities. There is physical evidence of attacks by ghosts, which include scratching, biting, shoving. There are tons of poltergeist events.

        Skeptics are free to disbelieve. But in my view, it makes more sense. If the nature of reality is made of particles and fields, then it suggests that life forms should be able to exist as fields as well as particles.

        • [deleted]

        I never said "reality is probabilistic". Seemingly you must consider that there are only 2 possible options for the nature of reality: probabilistic or 100% deterministic.

        I might as well ask you : "And your belief that reality is 100% deterministic is objectively based on" what experimental evidence?

        Do you have anything to say about, or any ideas about, what it is that NUMBERS represent about the nature of physical reality, or are you a platonist?

        Joy,

        where is the experimental evidence for your belief that all individual physical outcomes are 100% deterministic i.e. the time and space "parameters" for every individual particle outcome is predictable/calculable beforehand?

        Do you have anything to say about, or any ideas about, what it is that NUMBERS represent about the nature of physical reality, or are you a platonist?

        Lorraine,

        I have to admit that as yet I cannot support my claim with unambiguous experimental evidence. All I have so far is extensive theoretical evidence (in 15 papers, a book, and numerous computer simulations) to support my deterministic framework. But I have also proposed an experiment to test this framework, which may someday prove me either right or at least partially wrong. If I am experimentally proven wrong about my framework, even partially, then I may reconsider my position about determinism (more precisely about Bell's no-go theorem).

        Concerning your question about numbers, to me they are simply excellent tools for us to do mathematics and physics. I rather not speculate anything deeper about numbers than that.

        "I never said "reality is probabilistic". Seemingly you must consider that there are only 2 possible options for the nature of reality: probabilistic or 100% deterministic."

        At its foundation, nature is one or the other, or your belief is logically inconsistent. The problem is one of cosmology; the initial condition either had 100% potential for every observed physical outcome, or a probabilistic structure of which the slightest interference predicts 'no determinism.' Classical probability (binary outcomes) only answers the question of existence/nonexistence, and existence implies the continuous function of binary probabilities from the initial condition.

        "I might as well ask you : 'And your belief that reality is 100% deterministic is objectively based on' what experimental evidence?"

        An expanding universe. Self limiting chaotic phenomena. Strong quantum correlations (and if Joy Christian is right, strong quantum correlations at every scale). Want more?

        "Do you have anything to say about, or any ideas about, what it is that NUMBERS represent about the nature of physical reality, or are you a platonist?"

        I think you don't understand what a Platonist is. The best two modern examples are Kurt Godel and Roger Penrose. A Platonist avers that mathematical structures live objectively in a world of their own, even if they have no relation to the physical world.

        My personal view is closer to Max Tegmark's -- that coherent mathematical structures always describe some physical phenomenon, even if we do not recognize the utility; there are numerous examples, the most dramatic of which is Einstein's adoption of Riemannian geometry for general relativity.

        In the science of physics, mathematics is the language that compactly symbolizes the phenomenon it corresponds to. We may get the description wrong, just as we do in natural language, in a statement whose syntax is correct while its meaning is wrong. For example, we can say "The moon shines black" is syntactically correct though the phenomenon is not witnessed in physical reality. That doesn't imply that the alphabet and the rules for making sense of its combinations are not objective. Same with our mathematical tools -- meaning precedes construction, if the construction describes something physical. Meaning is the product of a coherent mathematical theory.

        You say "In the science of physics, mathematics is the language that compactly symbolizes the [physical] phenomenon it corresponds to.". But seemingly you have no idea what physical phenomenon might be compactly symbolized by a number in a physics mathematical equation. Numbers are a common everyday thing. If a view of reality is not able to explain numbers, then perhaps it is too superficial, or just plain wrong.

        Re your belief that reality is 100% deterministic: even Joy Christian wouldn't claim he had evidence that the time and space parameters for every individual particle outcome are predictable beforehand.

        If there were grey aliens made of dark matter abducting humans for their research, or alternatively if there were lifeforms made of quantum fields that were occasionally terrifying humans, the scientific community would be totally unaware of it. Atheists-skeptics are the snobby unimaginative branch of science who play around with trivial things, but then express disdain for very real phenomena. None of you are in search of truth. You are all guilty of protecting your reputation by calling grey aliens, spirits, ghosts, and all these things woo, when it is really scientific theorism that is woo, devoid of imagination, and does not fit with either established physics or the observations of millions of intelligent and reliable human beings. There are more reliable witnesses to ghosts and grey aliens than there are to super-strings, time travel and many-world interpretations combined.

        Come into the light of enlightenment.

        Who knows, you might have some fun if you try to reconcile UFO technology and ghosts with what we know about quantum mechanics and quantum field theory. Maybe there is a way to apply top down engineering to a quantum system, quantum field theory and quantum entanglement. Quantum entanglement is a correlations between two or more particles. Maybe there is a way to reinforce the entanglement, and then remove the particles. If it worked, you would be left with an invisible mesh that could be used as a template to organize new particles that it comes into contact with.

        " ... seemingly you have no idea what physical phenomenon might be compactly symbolized by a number in a physics mathematical equation."

        E = mc^2

        "Numbers are a common everyday thing. If a view of reality is not able to explain numbers, then perhaps it is too superficial, or just plain wrong."

        You have a quite innocent view of mathematics, of which 'number' is but a semantic element. What do you mean by number? Counting numbers? Rational numbers? Transcendental numbers? Complex numbers? R, C, O, H?

        "Re your belief that reality is 100% deterministic: even Joy Christian wouldn't claim he had evidence that the time and space parameters for every individual particle outcome are predictable beforehand."

        He does, however, have the measurement framework for a theory with potential to explain all quantum correlations. Do you understand what that means?

        Thomas,

        There is clearly no evidence that reality is 100% deterministic/classical: there are only theories and proposals for experiments that might result in such evidence, and unquestionably these experiments must be performed. However I think that there will be no such evidence: "spooky action at a distance" and other seemingly strange quantum mechanical outcomes are the true nature of reality. I think that these outcomes will never be tamed, but they will eventually have a better explanation. In any case, I will be interested to see the results of Jon Barrett and Matt Leifer's work (and hopefully Joy Christian will someday test his theory via experiment).

        Re numbers:

        The numbers found when nature is measured are some sort of ratio relating to the "measuring sticks" used. There are seemingly no questions about that aspect of these numbers.

        If reality is 100% deterministic, the above numbers are seemingly ultimately derived from laws-of-nature and initial conditions. Law-of-nature relationships are represented by equations which may contain numbers e.g. a form of the Einstein field equations contains the numbers 2 and 8, and also the non-algebraic number pi. Initial conditions are represented by a number assigned to each parameter/category in the equations.

        If reality is not 100% deterministic, then one implementation of this might consist of windows of opportunity where new information is injected into the system (by subjects), representable as numbers assigned to parameters/categories of information. These numbers are not derived from any laws-of-nature, and they are like a resetting of an initial condition for that parameter.

        So what is the physical reality behind these two types of "initial condition" numbers, and what is the physical reality behind numbers like pi?

        Lorraine

        Hey, Lorraine, I'm all for you believing whatever you wish. I'm just trying to give you some facts to help inform your opinion.

        You really need to know the difference between determinism and probabilism:

        Determinism doesn't mean that every event can be predicted, and probabilism doesn't mean that no events can be predicted. This, however, has absolutely nothing to do with your idea of the role that numbers play, or don't play, in science.

        You ask, "So what is the physical reality behind these two types of 'initial condition' numbers, and what is the physical reality behind numbers like pi?"

        None. Numbers don't have physical reality. No pi in the sky.

        Peter,

        I agree. "the theory which they established aimed only to describe systematically the response of the apparatus".

        Physicists could learn a lot about the nature of information and entropy, if they would study modern communication systems, starting with techniques such as Decision Feedback Equalization. Such techniques are the means by which modern communications systems remove "the response of the apparatus" as well as "interfering information, coming from sources of no interest", leaving behind only the information from the source of interest. This, and this alone, is what has made it possible to, for the first time in history, reliably recover information, at rates very near the Shannon Limit. One cannot get any better than that.

        Rob McEachern

        Even if the laws of physics are 100% deterministic, that does not mean that reality is. Deterministic laws are a necessary, but not sufficient condition, for reality to be deterministic.

        In order for reality to be deterministic, all the initial conditions (positions, momentums etc.) must also be deterministic (pseudo random, rather than random). There is no evidence that that is the case. Indeed, the existence of free-will provides a good piece of evidence that it is not the case.

        Rob McEachern

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        Rob,

        DFE means: "the distortion on a current pulse that was caused by previous pulses is subtracted". I see a main problem of theorists like Tom and many physicists already in their lacking readiness to accept that the distinction between earlier and later is more fundamental than their trust in a mathematically constructed world. We EEs don't operate with undirected arrows between boxes that symbolize transfer functions while theorists like Wheeler admit the wheel of history rotating back.

        That's why I question Minkowski's spacetime and the necessity to integrate over future time too when analyzing past data.

        Eckard Blumschein