Following the motion picture projector analogy, the film spool that collects frames that have already passed the projection port are “expired QUANTUM EVENTS” (history?). The film spool that contains frames remaining to pass through the projection port are QUANTUM POSSIBILITIES. The sytem is reversible.

Basically, he posits that there is no time–only NOW.

My analogy is that of film in a motion picture projector. As per Barbour (my interpretation), only the frame actually in the projector window is “reality”.

And yes, a cylic Universe would imply that eventually in some distant cycle I will be typing these exact words under my own free will again. Cheers!

In a small particle system ( < 1000 newtonians simulated on a computer) it seems obvious that “chaos” is the “norm” without recourse to quantum mechanics.

At what number of particles does it become necessarry to “invoke” the existence of quantum microstates?

Sean’s article is just one of many which fails to even address this simple question.

However, it doesn’t really matter. In terms of what we now call “broken” and “unbroken” eggs, there are certainly many more ways to re-arrange the molecules within the set of broken eggs than within the set of unbroken eggs. That’s an objective fact about the world, so you can’t just choose to insist that broken eggs have a lower entropy. You could choose some very specific form of broken eggs to define a particular kind of macrostate, and if you do it carefully there will be very few microstates that correspond to that choice; but in that case, unbroken eggs will almost never evolve into that specific form, so it will still be true that entropy almost always increases.

Now interestingly, those forward looking beings may also record data that registers them to be in existence, prior to the big-bang.. if the current signal being Dark Energy?

Is our percieved times-arrow, just like the archers arrow that has rebounded off its aimed target, and gone through a permiable target on the rebound, of area (vacuum)of less density?..the low density of a cold crunch?

Please excuse the delay in my answer, I couldn’t find an earlier time.

That entropy is indeed statistical is well known since 1877 and, by now, universally accepted. This is due to Boltzmann’s profound discovery expressed in his celebrated equation:

S = k log(W), where S = entropy, k = Boltzmann’s constant, and W = the number of different molecular microstates, assumed equiprobable, available to the gas in the macrostate corresponding to S.

We are not speaking here of the level of statistics that other thermodynamic state variables — temperature, pressure, etc. — are subject to. Unlike these, entropy is not a particle-average of a conserved quantity, such as energy or momentum, that survives the averaging to become a global system variable; it is related to an average of a quantity which is itself statistical in nature. Actually, no physical property of a system’s micro constituents exists the average of which can be interpreted as the system’s entropy.

The bulk-thermodynamics facet of entropy — being a proper thermodynamic state variable and appearing in the 2nd Law and theorems derived from it — is, of course, fully consistent with the statistical view.

Since about 1948, due to C.E. Shannon, the concept of entropy has broken through the boundaries of strict thermodynamics to become a major player in information theory, as a measure of the amount of information. At first one might think that information entropy and thermodynamic entropy are just similar or analogous, or that the term has been borrowed by one from the other and is used concurrently with different meanings. But no, they are one and the same. Entropy is the amount of information not only in a phonebook, in a movie DVD, on a communications satellite beam or in the whole of Cyberspace; it is also the amount of information in a volume of hot gas pushing on a car engine piston.

Algorithmic randomness and its mean are indeed quantifiable. This is now a huge field and I cannot possibly do any justice to it — or to you — in a blog comment. But if I did succeed in arousing your curiosity enough to follow the lead I can assure you plenty of exciting reading and revelations.

Yours truly
Dov Elyada, Ph.D.
Haifa, Israel

I take it that’s a no comment. For if you might find it interesting, this paper by John Moffat shares some features with your model (and to a lesser extent, my one too).

Best wishes

Peter

If you are so inclined would you elaborate on your statement, “Entropy of a system is…the MEAN algorithmic randomness over all system states”.

Is “mean algorithmic randomness” quantifiable, perhaps as a measure of randomness? But isn’t entropy an energy term in a thermodynamic equation, and how does that square with “mean randomness”, which is more a statistical value?

Thanks again for your insights.
Rich Wilson

Since my sophomore year some 4 decades ago, when I first met ENTROPY, I’ve been pondering the darned thing (not continuously, of course,) desperately trying to make sense of it. My efforts certainly included Boltzmann and Gibbs, but not before I came across Shannon and informational entropy did I make any significant progress. I think I can now identify the culprit impeding my understanding: it was the culturally entrenched qualitative description of entropy as a measure of “disorder.”

The disorder explanation is widely used, especially when addressing scientists outside of physics, and the general public. In his SciAm article, Sean uses it several times, and with great stress. I claim that THE EXPLANATION OF ENTROPY AS A MEASURE OF DISORDER IS MISLEADING. But because it has become a culturally ingrained MEME that gets passed on uncriticized, even some accomplished physicists who were raised on it turn out to actually not understand entropy at all, let alone undergrads, engineers, non-physics scientists, science writers, the educated public and self-confident philosophers.
 
While entropy properly applies to a SYSTEM — the totality of all system states of non-zero probability, represented by an ENSEMBLE — I think most people intuit order and disorder, as I once did, as attributes of a state. Consider, for example, a rigid cubical vessel full of an ideal, monoatomic gas in thermodynamic equilibrium. For simplicity of discussion look at the gas particle locations only. In one PARTICULAR state, call it DG1, the particles are evenly distributed throughout the volume, but randomly, unlike in a crystal. To specify DG1 completely one must list all its particle coordinates — no data compression possible. This is what one would call disorder. In another PARTICULAR state, OG1, the particles are also evenly distributed, but periodically, as in a crystal, and conforming to the vessel walls. Few parameters are needed to specify OG1 and natural language would call it an ordered state. Yet both DG1 and OG1 are states of the same system and, being fully specified, are equally probable. But to neither of them does the concept of entropy apply. It does apply to the ensemble of all such states, is related to their number in the ensemble, and is divorced from their degree of order or disorder. (If most system states happen to possess a high degree of order, then, one may argue, their number must be relatively small and so must be the system entropy. While being true, this roundabout argument has hardly any didactical value.)

Consider now the example of the broken vs. whole egg that stars in Sean’s SciAm article. Again, for the sake of simplicity, consider a PARTICULAR whole egg named Humpty Dumpty (HD) and ignore its macroscopic mechanical motions (e.g., sitting on the wall,) and its microscopic thermal motions. Under these restrictions there exists just one distinguishable object that qualifies as a member of the set {HD}. Consequently, {HD}’s entropy is zero and we are justified in praising HD as a neat and orderly dude. Next, let HD have a great fall. The mess thus created surely deserves to be called “disgustingly disordered.” To determine the entropy of the new situation we would usually define an ensemble, a new set called “Broken Humpty Dumpty,” {BHD}, and enlist in it all distinguishable objects that qualify bona-fide as broken Humpty Dumpty. Since there is a vast number of such objects — the vast number of different ways HD might splinter and splatter and create Jackson Pollocks — the entropy of {BHD} is great and beyond the powers of all KH and KM.

But notice that the above definition of the set {BHD} is quite arbitrary. In deterministic physics one can mean by {BHD} the actual configuration HD assumed after his historical fall on that fateful afternoon of 15 July 1648, the fall that was documented by notable eyewitness historians in the famous nursery rhyme. In that case, {BHD}, too, contains only a single member and, despite its remarkable messiness, its entropy still equals zero.

A system may have many possible states, most may be “disordered” and some may pass as “ordered.” But regardless of whether the system accidentally or fleetingly occupies an ordered state or a disordered one, ITS ENTROPY IS THE SAME! That’s because THE ENTROPY IS RELATED TO WHAT THE SYSTEM MAY BE, NOT TO WHAT IT IS.

(A plausible measure of state disorder may be the “algorithmic randomness”, a.k.a. Kolmogorov complexity, of the state — the size of the shortest algorithm that generates a specification of the state on a Turing machine. A theorem due to C. H. Bennett (I think; Int. J. Th. Phys. V21, N12, 1982, p.938) demonstrates that the entropy of a system is all but indistinguishable from the MEAN algorithmic randomness over all system states. This is instructive, because the mean of state-disorder taken over all system states does qualify as a system disorder measure. Nevertheless, as said above, this explanation is not at all transparent and hardly serves for clearing the entropy=disorder confusion.)

I think it’s high time to exorcise the demon of disorder from academia and pop science alike. The wrong mental construct of entropy=state_disorder is very readily formed, in students as well as in the educated public, because people feel they understand, from everyday experience, what disorder is. But what they envision are disordered states, not disordered absract ensembles. Once the wrong construct takes root, however, uprooting it is next to impossible, especially as it has become a meme. It had played havoc with my own understanding of entropy and is surely detrimental to the understanding of all who has been exposed to it. [See Carson & Watson, Roy. Soc. Chem., 2002.] I was glad to find in Wikipedia’s ”Entropy”, in the paragraph entitled Energy Dispersal, a full support of my position and some research-based references. For the sake of saving that trouble from future generations I hope that the new approach will become a trend and that Sean’s next SciAm article will contribute towards it.

Brian Greene says the only thing expanding as fast as the cosmos is consciousness. Albert Einstein said our perception of ourselves as individuals is something of an “optical illusion” of consciousness.

These points of view have practical everyday implications that are difficult to bring up most of the time.

Cordially wondering,

Garrett

Sean, I would be curious to hear how you would respond to my comments. Think of it as a friendly/collegial cosmological call out.

Best wishes

Peter