Tuesday, July 07, 2009

The Divine Role of Entropy

The Divine Role of Entropy

When the the Universe as a whole is considered, its fate is generally considered to be some variation of heat death. There are a few other variations, such as scenarios where the Universe gravitationally collapses back upon itself. Stars will eventually run out of hydrogen fuel, and other elements that can be fusioned. Galaxies will dim as fewer stars are born from interstellar gas clouds, and gas clouds between galaxies will thin as the Universe continues to expand. Even the microwave background radiation (at a chilly 4 degrees Kelvin above Absolute Zero) will be red-shifted to lower and lower temperatures until the universe freezes and no life, is possible.

The dominant player, if not the driving force, in all of these scenarios is entropy. Entropy is usually thought of as a measure of disorder, and as such, it plays the part of the villain. The second law of thermodynamics is that in any closed system, entropy always increases. It is as though writ upon all our universe is the saying, “In the day thou eatest thereof, thou shalt surely die”.

There is no other option. You can't win and you can't break even. You can't even get out of the game - it really is the only game in town. Even if this is a humorous rephrasing of the laws of thermodynamics, it is no less accurate.

If entropy is exclusively thought of as disorder, you can see that this becomes a very pessimistic scenario. But is entropy really the villain we make it out to be? And should we really despise it so readily?

While the Second Law of Thermodynamics (as well as the others) is quite true, the more precise older brother of Thermodynamics called Statistical Mechanics has more to say. Entropy not a measure of disorder specifically, but only incidentally. Properly, it is defined in terms of numbers of possible states for a system to be in. The system we will be most interested in is the universe itself, and the components of the universe are all the atoms and photons and every other particle in it.

Specifically, entropy is defined asS is the traditional symbol for entropy, k is a constant of proportionality that is of no interest to us here, and omega is the number of possible microstates (the positions and state of each and every electron and atom) that correspond to a single given macrostate ( pressure, volume, temperature, number of particles, etc) counting each microstate with equal probability. Entropy is often thought of as a measure of disorder because there are more disordered microstates for a given system, than there are ordered states. For instance, a china plate has more ways to arrange broken pieces than it does to arrange a whole unbroken plate. Unless we are very careful then, we will find that the china plate in the statistically preferred condition – broken in several pieces! Likewise, there are more ways to arrange particles of dust around a room than there are ways to arrange them in a dustbin.

Statistical mechanics is based on the definition of entropy and the derivatives of energy, which is defined as variables here stand for energy (E), temperature (T), entropy (S), pressure (P), Volume (V), chemical potential (μ), and number of particles (N). I will consider most of these self-explanatory, except for temperature and chemical potential. Pressure and volume will not be of importance for most of our discussion and will be neglected.

Despite its ominous and mysterious name, chemical potential is simply the amount of energy it takes to add one more particle to the system. temperature, despite its familiarity, is a more complicated beast than we usually take for granted. formula means that two systems have the same temperature if they gain entropy at the same rate. In fact, this is part of the conditions for equilibrium. Two things (systems) are in equilibrium if their temperatures are the same, their pressures are the same, and their chemical potentials are the same. If one of those is not the same, their will be a flow of entropy, volume (ie, relative size), or particles from one thing (system) to the other until equilibrium is reached.

Statistical Mechanics may also be formulated to examine other topics such as economics. In such a comparison, energy (E) is capital (in units of money), temperature (T) is standard of living or “market index” and entropy (S) is production. Likewise, μ is wages or salary. Volume (V), which we did not use in our analysis, can be here used for degrees of personal freedom, which may be suggestive of future applications.

Consider the simple case of an ice cube in a glass of water. Normally for the same amount of energy, increases of entropy at low temperature are greater than increases of entropy at higher temperature. The ice cube increase more in entropy than the water loses. In other words, the fact that entropy seeks to be maximized ensures that the ice cube take energy from the water until an equilibrium is reached and everything is the same temperature.

But what if the opposite happened? What if, for equal amount of energy transferred, the water gained more entropy than the ice lost? Then the ice would lose energy to the water until some kind of an equilibrium was reached. The state of maximal entropy is always the one nature seeks.

But does an unstable situation like this ever actually occur? It does, though normally because of its unstable nature, it is normally short-lived. I have the dubious honor of having a hand-on experience with this. One evening I thought I would boil myself a cup of water in the microwave. After a bit of time, it had just started to boil, so I put the cup back in the microwave oven and gave it a good minute to warm up. What confused me initially, was the fact the cup of water did not start boiling again, even as I extended the time. Finally, I decided to have a closer look at the cup of water to see what the problem was. I learned the water in the cup was in a condition we called, 'super-heated', which means it has a temperature higher than it boiling point, but is still in the liquid stage – until something perturbs it enough to start forming bubbles of steam. The water in question underwent a rapid phase change, almost instantly changing from tranquil and transparent to explosive bubbles of steam that left the confines of the cup (and into my face) with a bang. I stumbled melodramatically across the kitchen where I fell on a bag of trash. Thankfully I was wearing my glasses at the time.

The phase change involved water moving from the liquid phase to the gaseous phase. Phases changes are a general phenomena associated with a wide variety scenarios and is present in numerous different forms in all of nature. All that is needed, is a large number of interesting things and a changing amount of internal energy.

In terms of economics, this would be like owning two businesses – one that made $1.50 for every dollar invested and one that made $3.00 for every dollar invested. Considering that you make a lot more money with the second business, per dollar, it makes the most sense and profit to allocate the maximum possible capital available for the more profitable business. In other words, in the absence of other constraints, money flows from the first business to the second business because of entropy.

Likewise, in terms of the water, it makes a lot more entropy when it is steam, than when it is super-heated water. The superheated state is not a stable condition because of this.

What does this mean for us - spiritually? There are a lot more ways to sin (spiritual disordered states) than there are to keep the commandments (spiritual ordered states). There are more degrees of freedom and paths that lead to sin, than paths that do not. The number of possible sinful states is much larger than the number of possible righteous states. In this life increasing entropy means that not only is sin and disorder is more likely, statistically speaking, but that because energy flows to where there are the greatest increases in entropy, resources flow towards corruption as well.

Now that we have shown that the universe is condemned to a gradual death and that sin is favored by the very laws that God himself as ordained, should we conclude that the Gospel is at odds with these laws?

Not at all.

Realize that entropy is a measure of the number of states available and that there are two ways of accomplishing this. First, we have entropy related to disorder, and second, we have entropy related to creation of new possible states. These new states could be entire universes, or organization of spiritual matter into spirit children.

I posit, without proof, that only God is capable of creating new universes and new spirit children or in other words, that there are aspects of the creation that only God is capable of accomplishing.

Of course, the intelligences that composes these spirit children are eternal, but without the Father, there is no way they could reach new and higher spiritual “states” by themselves. Because spirits are matter, of some kind, their new condition relates previously unrealizable quantum microstates. They have far more possible states as spirit children then they do as unorganized matter.

Note, this is true regardless of whatever type of advancement is involved from intelligence to spirit body, because we are interested purely in the quantum spiritual aspects. Of course, we have no present way of quantifying this entropy.

But not only is this source of entropy a source of spirit children, but also all spirits- all life, vegetable, animal and otherwise. Notice how God creates life (or creates life capable of learning to live) in all types of environments. Scientists are even becoming suspicious of (but by no means proven yet) bacterial life on Mars. Virtually every crevice of the earth has life; the deepest ocean trenches, soil and rock deep under the earth, hot springs are a few of the inhospitable environments that life lives in. Even caves with water that never sees light may have fish.

Even more than this, God creates universes. Our present universe, at least the part we see, had a birth some 13.7 billion years ago. We have no scientific understanding of how universes are created, but even from a purely physics perspective, the change in entropy from the early Big Bang universe to now is highly remarkable.

God is not incidentally a Father or a Creator, but it is an integral part of both who He is, and How he does it. In this view, God is not merely a Creator occasionally, as a side-job, but continual Creation is a necessary aspect of His very being.

He must create faster than disorder increases – creation both of universes, worlds, animals, plants and also of children.

Now, let us back up a bit and recall the conditions for equilibrium in statistical mechanics, namely that temperature and chemical potential are equal and homogeneous. Temperature, by definition, is
, or the rate at which entropy increases, per cost of energy. For instance, if we had two regions that gave us two units and one unit of entropy respectively, for every single unit of energy, then energy will flow to the first from the second until for some higher total energy of the first, the rates of entropy per energy become equal.

Remember the mug of superheated water I mentioned earlier. It separated itself into two portions (steam and hot liquid water) according to a difference in entropy for a given limited quantity of energy, until both both steam and water had the same temperature. Let us now compare the temperatures of the different degrees of glory.

Either, the different kingdoms will be in equilibrium, or they will not be. Keep in mind, that while we mentally associate hell with hot and heaven with cool, in this context a high temperature, or high rate of creation entropy is good. Total entropy will be written as

If we first assume equilibrium, then we can say that Tcelestial = Tterrestial = Ttelestial . This can be rewritten as
, but there is no a priori reason to assume this, and it would seem to be more of a constraint than a desirable situation, because of the strong limitations it would entail.

What if, on the other hand, these temperatures (rates of entropy) were not equal? If their temperatures are not equal AND the kingdoms are in contact, energy will flow from one to the other. It would flow from the lower entropy producing kingdoms to the higher kingdoms. Presuming these rates are constant in time (these are eternal kingdoms) then energy would flow from lower to the higher until they froze at absolute zero, ie had no energy at all.

But neither of those sound like ideal situations. Considering that the different kingdoms can not have equal chemical potentials
– ie. they do not have the same capability, per unit of energy, to create new states (spirit children, for instance), we should probably consider them as out of equilibrium. Likewise, the celestial is promised dominion (energy) “without compulsory means it shall flow unto thee forever and ever” D&C 121: 46

The alternative to all of this is, for the different kingdoms to have different temperatures, but to be separated, or at least have limited contact. Contact in this context refers to the ability to exchange energy, particles, or volume. I propose that the lower kingdoms have lower rates of entropy than the Celestial kingdom (at least once we begin to create Creation Entropy as God the Father does), but in order for them to remain with some energy, they are separated. This is not unlike how the US has higher entropy, even though places like Ethiopia are more disordered. The alternative would be for the Celestial kingdom to bleed the other kingdoms dry of energy. They are separated from the Celestial to protect them.
A material is called 'frozen' when it can not change its temperature. A physical example of this would be energetic atoms in the solar wind escaping at high speed, but incapable of cooling down, because there is nothing for them to interact with, in the vacuum of space – ions can be easily as much as a meter apart. Because the electrons in the atom are in an elevated energy state, the atoms have a very high temperature, but without nearby influences to help perturb the electrons, they will not drop back down to their ground state (cool temperature).

In this context, the lower kingdoms are 'frozen' – they can not have eternal progression, but they are saved both from being bleed dry of energy ( from Entropy of creation), as well as from the disorder of lower kingdoms (Entropy of disorder).

Jacob's warning about spiritual entropy was no idle threat: “For behold, if the flesh should rise no more our spirits must become subject to that angel who fell from before the presence of the Eternal God, and became the devil, to rise no more. And our spirits must have become like unto him, and we become devils, angels to a devil, to be shut out from the presence of our God...” 2Ne. 9: 8

This suggests that either the Resurrection or entry into the Celestial Kingdom precipitates a kind of phase change – not only a incremental change in glory, but a qualitative change in type or kind of life we can live. We might do better to associate the different kingdoms to phases of water, than a smoothly graduated continuum.

Hence, Satan's boast, “Now is the day of my power” shows that he realized that the entropy that favors
disorder would only benefit him temporarily. In the long run, the entropy of disorder is overwhelmed by the entropy of creation which is tied most closely with the nature of God himself.