ENTROPY

 

INTRODUCTION

 

In general terms, entropy is a measure of disorder which always seems to be increasing.  Entropy allows us to distinguish between past and present and places implacable constraints on the evolution of the universe.   This elegant but recondite concept is thus one of the most profound aspects of the universe.  It describes no less than where we came from, where are going, and how we will get there.  

 

In the mid to late 19th century the concept of “entropy” was invented by Rudolf Clausius and William Thomson (Lord Kelvin) to quantify the maximum amount of useful work a steam engine could perform as the Second Law of Thermodynamics.  About the same time entropy was associated with more fundamental principles of atomic motion and given mathematical rigor by Ludwig Boltzmann, who had a pivotal equation inscribed on his gravestone.  In modern times entropy is so well verified in so many experiments as to be nearly unassailable.  And today it has applicability to every field of physical science.

 

Nor is entropy a strictly scientific consideration but has profound philosophical implications as well.  Since the universe was more ordered in the past and has not yet entirely degraded, it could not have existed into the infinite past.  Rather the observation is that we are still able to make use of the flow of order to disorder to power our machines and ourselves.  Thus the entire universe must have begun at some finite time in the past in a well-ordered state that has attempted ever since to maximize its entropy.    This means the universe must have had a moment of creation in what science can only label a “supernatural” event [1].

 

And this original event is not describable by science.  Rather the absence of nature and natural law logically requires a “super-natural” agency (i.e. above nature).  The idea is that if there is nothing physical, no space, energy, matter, time, or any of the fundamental forces, no physical cause is available to create anything.  The universe must have been created “ex nihilo” in a way we can never physically describe.  This is a logical requirement of cause and effect, was recognized by the Greeks in learned treatises nearly a millennia before Christ, is a founding principle of modern science, and continues to confound would be atheists even into the 21st century.

 

Atheists as we may recall emphatically deny the supernatural and especially the existence of God the Creator.  The difficulty of course is that if everything is purely physical governed entirely in principle by natural law, then every observable effect must have a predictable cause.   And there must be an infinite regression of this chain of happenings into the unfathomable past.   Unfortunately, the manifest observation of entropy says this is impossible.

 

So as our scientific knowledge advances, atheism is ever more forced into the gaps of what logic and mathematics and science has yet to discover.  And so atheists are forced to believe, with a blind faith bordering on mysticism and superstition, that our well tested principles of physics are somehow mistaken.   The best escape mechanism or rationalization any nihilist has yet offered is that instead the cosmos existed forever.   This does remove the logical necessity of a supernatural creation event but also blindly denies most of the understandings and observations of modern science.

 

And since the ultimate consequence of the anti-scientific atheist delusion is the denial of an absolute moral code that permits one’s libertine and profligate instincts free reign, this is perhaps its greatest attraction.  And in a manner analogous to entropy, this mental disorder is also increasing and likewise shows no signs of abating.

 

QUANTIFYING DISORDER

 

Things that are more mathematically probable are more likely to happen.  And they are more probable by definition if there are more ways for them to happen.   It is for instance easier to lose the lottery than to win it because there are many more ways to lose by a factor of literally hundreds of millions.   And the probability of the total entropy of any closed system reversing is much less than that.  For even small simple systems, for instance a cubic millimeter of air, probabilities are so small they are astronomically insignificant even over the lifetime of the universe raised to an exponential power.   For anything larger, the probabilities decrease and again exponentially.

 

S = kB log W

 

ERGODIC HYPOTHESIS

 

The basic idea is that for a given number of gas molecules in a chamber, they can arrange themselves in any number of ways.  Any particular molecule can be in middle or near the walls or anywhere in between.  Each instantaneous arrangement of all the molecules is called a configuration.   Unfortunately the microscopic details, that is the position and velocity or each of the molecules that constitute a configuration, are impossible to determine.  But what we can measure is some macroscopic property like perhaps the pressure or the temperature.  And we can repeatedly take measurements, each measurement taking a short length of time.

 

What we would like to know is the macroscopic property, e.g. pressure or temperature, averaged over all the configurations.  Unfortunately while we assume all the configurations are equally likely and that the system will eventually experience each and every one, this would take a very long time.   In fact the time is so astronomically huge, it boggles the imagination.  But this would be the theoretically correct average value.

 

So what the Ergodic Hypothesis says, is that the measurements we can make, i.e. the repeated macroscopic ones, are good enough.  That is to say that measuring the temperature with a thermometer which has had time to equilibrate with the gas in the chamber would be exactly the same as if we calculated the average for all possible microscopic configurations.

 

And this works pretty well.   The pressure, for instance, is caused by molecules bouncing off the walls and varies a lot micro-second to micro-second.  If we measure the position of a piston with a weight it seems to be an unchanging constant from a macroscopic point of view for as long as anyone has had the patience to study it.  But from a nitpicking theoretical viewpoint this equivalence has not absolutely been proven and remains a thorn in the side of physicists.

 

STEAM ENGINES

 

It is temperature differences that permit useful work to be done.   If everything is very hot but uniform, no work can be extracted from the system.  Energy which is uniformly distributed permits no net flows that can drive a steam engine.  This disordered energy is called entropy and is proportional to the number of accessible states. 

 

If hot steam is separated from the colder outside air, it has low disorder or a small number of possible configurations by virtue of being confined.  When the steam is allowed to expand driving a piston and equilibrate in temperature with outside air useful work is done, the number of accessible configurations increase, and so does the entropy.

 

ENTROPY OF THE UNIVERSE

 

If the volume of the universe is increasing, then all the stuff in it like people, planets, stars, galaxies, and whatnot have a lot more places they can be.  So the accessible configurations and entropy increases.   Stephen Hawking thought this might reverse if the universe were to begin shrinking perhaps caused by a gravitational collapse.  That is entropy might retrace it steps as the volume of the universe got smaller.  Later he admitted his mathematics were faulty and that entropy would in fact not decrease.   That this means the universe had supernatural moment of creation he admitted but then spent the rest of his life in a fruitless attempt to find a loophole.

 

The interesting point is that a collapsing universe would not return to the original state, even for a superhot plasma shrunk to some very small space, perhaps 10-33 cm, even though that tiny volume once enclosed the universe when it first began.

 

INFORMATION THEORY

 

Claude Shannon was an electrical engineer concerned with quantifying the amount of useful information could be transmitted over noisy channels.   In the process he invented “information theory.”  His famous quote on this new field of study was

 

My greatest concern was what to call it. I thought of calling it ‘information’, but the word was overly used, so I decided to call it ‘uncertainty’. When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, ‘You should call it ‘entropy’, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name. In the second place, and more importantly, no one knows what entropy really is, so in a debate you will always have the advantage [2].”

 

Stephen Hawking struggled with this but finally had to admit the current formulation of entropy when he published that his prior reservations were unfounded and disproven.

 

BLACK HOLES

 

CONCLUSIONS

 

Questions related to the origin of natural law bear on considerations of a clockwork universe by raising the possibility of a hidden and higher order of things than can be described by physics alone.

 

That is not to say that much fundamental work in theoretical physics has not been done in attempting to describe the evolution of the very early universe, once the initial seeds came into existence by other erstwhile means, and from a variety of perspectives.

 

Recent work in string theory suggests the universe exists in 10 or perhaps 26 dimensions most of which are so tightly curled up that one circles back to the starting point after traversing only a microscopic distance along any one of these. But they do provide an elegant, but unfortunately unverifiable, framework for the possible collision of multidimensional surfaces enclosing higher dimensional spaces, or branes, which might give rise to a succession of big bang events creating a string of multiverses. Working out the mathematical details, however, verifies that from an entropic, as well as a quantum mechanical, perspective that such a progression could not have continued indefinitely; and thus still does not remove the necessity of a beginning of everything at some point in the past.

 

REFERENCES

 

1.      “Why Physicists Can’t Avoid a Creation Event”, by Lisa Grossman, New Scientist, January 11, 2012; http://www.newscientist.com/article/mg21328474.400-why-physicists-cant-avoid-a-creation-event.html?

2.      “Information Theory and Thermodynamics”, by Tribus Helvetica Physica Acta (1963).

3.      “The Beginning of Time” lecture by S. Hawking, online at http://www.hawking.org.uk/the-beginning-of-time.html

4.      “Relativity, Thermodynamics, and Cosmology” by Tolman, Oxford University Press, Oxford, UK, (1934), [Early work on cyclic universes with Einstein somewhat out of date].

5.      “A Larger Estimate of the Entropy of the Universe,” Egan and Lineweaver, Astrophysical Journal Volume 710 (2010), page 1825.

6.      “Inflationary Spacetimes Are Incomplete in Past Directions”, Borde, Guth, and Vilenkin, Phys. Rev. Lett. 90, 151301 (2003).

[Basically, a stricter accounting of entropy already present in an accelerating universe seems to eliminate the possibility of some of the more fanciful cyclic models.]