hotcold

(29Oct95 )


Think of the four forces of physics as rules for how to make a universe, if there were a universe around to sculpt. We have worked out in great detail how the rules for these four forces work: gravity, electromagnetic interaction, strong and weak nuclear interactions on mass charge color and charm respectively. But we do not know why mass charge color and charm exist. Nor do we know why they are instantiated in particles in the amounts and combinations they are. Still mystery as we look deeper and deeper in.

Behind total vacuum, nothingness, seethes a source of randomness that can create space-time-matter-energy into existence. Particles of matter energy constantly burst on the scene and annihilate each other in vacuum. Perhaps the birth of the universe was that way.

Once a specific amount of space time matter energy miraculously enters the canvas, the four forces sculpt it into patterns. The second law of thermodynamics also comes into play.

These two kinds of rules interact and produce a grand play between them. The four forces play by pulling STME into patterns, discrete particles and govern how they interact, that they in fact do interact, come together and form dynamic patterns. The second law of thermodynamics says: there are more ways to be random than to be organized, correlated. So as the universe bustles around it eventually settles into a disorganized state. You can see they play against each other. This creates the drama of the universe on all scales.


Second law says Big Bang should just evenly spread out into a warm formless haze of heat. But early in the first few seconds of Big Bang some of the four forces kicked in and pulled energy together into particles: photons, electrons, protons.

Still, 2nd law says keep expanding and electrons and protons spread out. But then gravity kicks in and pulls huge masses of protons and electrons together into clumps.

The miracle about these forces and their play with the second law is that the universe never settles down into homogeneity. Heterogeneous structures form at all scales. [actually macro scale of galaxy clusters might have come from quantum scale properties when Universe was small]


So gravity pulls together a nation, a Sun full of protons and electrons and forms a sun. Gravity would pull in all the way and pop the sun out of existence if the there weren't other laws around to interact with it. Especially the second law of thermodynamics. See, once gravity clumps Suns together into existence we have warmth inside the suns and cold outside them. Gravity pulls in more and...

Gravity pulls these protons so close together that energy locked up in their separate form of creation is released as they fuse together with electrons and form helium nuclei. The sun begins to burn with fusion power. Since energy is concentrated in the sun, the 2nd law says pull it out into the cold black space of the universe and disperse it. This flow of energy pouring OUT of the sun BALANCES the pull of gravity INTO the sun, and allows the 2nd law and the four forces an opportunity to balance for the millions of years of the life time of a sun.

If gravity had not clumped the universe into sun and cold space, but instead we had an even expanse of energy production then as much energy would flow into the "sun" as would flow out of it. It's only because between the suns is cold that energy flows out of the sun from hot to cold.

This is the way it is. the four forces constantly set up heterogeneous clumping of higher concentration of energy and lower concentration of energy and the 2nd law then sets in to causing energy to flow between these two potentials. All the drama is possible because of this separating out and flowing back. This Universe is an interesting place after all!


But what HAPPENS to Suns! The miracle that this universe is, is this: I can write down on one page the mathematical formulae for these four laws that make up the set of instructions with which to shape s t m e. Yet that simple set is enough to create unbelievable heterogeneous pattern.

What I am talking about is the creation of the incredible wealth of color, texture, taste, size, smell, sound of what is immediately around me. Brown wooden window sill, transparent glass panes, air to breath, hills clothed in green trees, multicolored butterflies, hills made of 2000 different kinds of minerals, plastic pen, aluminum tip, cotton clothes, cardinal birds that have learned how to sing and fly!

We take this for granted, this over 10 million species of creatures, 10,000s of colors, 10 million smells, 2000 different minerals, 100,000 different man made materials.

Surely if Big Bang proceeded out of a mind combined out of Michaelangelo, DaVinci, Bach, and Shakespeare, then it would be easy to imagine how this wealth of creation occurred. But of course then we are left with the puzzle of where did THAT mind come from? Science has found a different way.

Some examples will show that given a set of simple rules, it is possible to create this spectacle.

(1) Conway life:
http://www.geocities.com/richfragrantchaos/conway2.txt

(2) Zero one laws on random graphs
http://blackskimmer.blogspot.com/2007/03/zero-one-laws-in-random-graphs.html

(3) classification of finite simple groups
http://blackskimmer.blogspot.com/2007/03/classification-of-finite-simple-groups.html

(4) Xnew=mXold(1-Xold) and Mandelbrot set


So these simple laws of physics don't allow THIS dull story: Random cloud of hydrogen atoms. Gravity pulls it inward and gets denser and denser and denser until it pops away as a black hole. The end.

On every level phase transition sets in. [See (2)] First of all, convection happens on the surface of a star. Magnetic fields form. Simple laws of nuclear physics creates for us the heterogeneous pattern of possible nucleii that fusion can form. [See (3)]

Matter doesn't fall out as some kind of infinitely divisible, infinitely blendable clay, but breaks up into a heterogeneous family of discrete nuclei.

When these nuclei are later shed from a Sun who explodes, they will collect electrons and when you pump in the ascending scale of numbers 1, 2, 3, ... 106 into Schrodinger's equation you get a surprisingly complex and varied set of properties for each of the 106 elements.


I want to point out why it is so surprising and how gracious we ought to be that out of these simple laws can come this cast of characters: Hydrogen, Sodium, Potassium, Magnesium, Calcium, Iron, Aluminum, Silicon, Carbon, Nitrogen, Oxygen, Phosphorus, Sulfur, Chlorine, and just a dash of Copper, Zink, Vanadium, Molybdenum, Nickel, Chromium, Cobalt. Over 99% of everything we see, touch, taste, hear, smell, is made of only that many kinds of building blocks.

When we find the creation of Earth we will see what extravagant play this simple set of characters can create.

* * *


"Fourteen tribes, some similar and some very different."

So is Earth some huge solid clay ball with colorful fuzz of a world painted in its surface by a Michaelangelo, God? Let's look deeper.

Of the 15 common elements, Iron and Nickel being the densest sink to the core when the Earth was molten or at least very hot.

Earth was made of 15 kinds of characters:

H
...............................C N O
Na Mg .................Al Si P S Cl
K Ca .......Fe Ni

Why couldn't Earth just be a random mash of evenly dispersed neutrons, protons and electrons? See, the universe goes through cycles. Matter flows through these cycles of alternate cooling and heating.

See, the universe starts out ultimately compact with only energy at a very high temperature. Then it expands and cools, and as it does so protons and electrons condense out. But now it is too cool for the nuclear forging to take place to stick these protons together and form the wealth of elements we got. But then gravity kicks in and pulls protons together and heats them up again. They jostle around and bang into each other and stick together to form the 96 different distinct nuclei that our Earth is made of. Of course, up to iron, these arrangements are actually at more of a state of equilibrium than were the separate protons, but in order to get over the hump of activation energy to get to that lower energy state closer to ultimate equilibrium, they had to be heated a little. Still, in a massive enough star, if things stay this hot and under such high pressure, eventually ALL the nuclei stick together into one huge ball of neutron star. Again, nothing interesting. So the star blows up and spews all its new made elements into the clouds of space and as they cool, they can no longer fuse, so we get the wonderful mix of DISTINCT atoms that make up earth.

Now they cool even more and no longer make up a plasma and electrons can once again settle back in place around nuclei and make atoms. But too cool, and they will never be able to join and make interesting arrangements. So again they may settle into the local equilibrium well unless we heat them up a little so they get some activation energy and they can form new bonds and finally settle into the molecules with the lowest potential energy. Till they find the lowest potential energy well.


Hydrogen atoms, but then heated and squozen to be forged, fused together to heavier nuclei. But when cooled off and released to relatively cool and small planets they separate out. Different conglomerations of nuclei are stable at different pressures.

How can I say this? Once the high pressure forging is stopped and for a little while discrete atoms form and exist in a cooled state, they can't fuse and rearrange their nuclei anymore. So we are stuck for a while with a discrete set of elements.

Neutron stars and white dwarfs, grey dwarfs... and surely most of the universe will settle down into that state of balance between nucleon repulsion and gravity. In that state the star will be a solid still ball of atoms. Or if the star is more massive and it becomes a neutron star then it becomes one solid ball of neutrons and that is one huge nucleus, no mix of different kinds.

But as I said, we are blessed with happening on a very special and gifted place, a planet between Sun and Void.


So this myriad of only 14 different kinds of atoms are stuck here in their distinctness. Now let's look at our caste of characters.

So no clay of nuclei to sculpt willy nilly ( but who would sculpt it?) So these 14 kinds of atoms sculpt the world from the inside, each obeying relatively simple rules. Look at the personality map that I placed these 15 elements on, the so called periodic chart of elements. From sodium to chlorine we have one progression of personality types; sodium gives away all its electrons and chlorine hoards all the electrons it can get as tightly as it can. From top to bottom, we get larger and larger atoms. That means more room to make connections, but looser ones.

For instance, Carbon and Silicon like to form all kinds of chains and loops and webs but they do it slightly differently. Carbon is what makes wood, clothes, plastic, supple living people possible, and Silicon supports the variety of rocks and minerals in the world. There is no continuum of elements in between carbon and silicon, with intermediate properties! These are the two possibilities, that we are stuck with. This is what quantum rules give us. So we do not live in a psychedelic nightmare haze of formless mush exhibiting the continuum of all possible properties between rocks and fleshy creatures. Only carbon and silicon form out of the nucleons and no others.

Similarly, carbon forms partnerships with up to four other partners at a time. Fairly low energy bonds and so moderately stable. But Nitrogen bonds with only up to three partners, and nitrogen bonds with itself so strongly that many nitrogen compounds gladly explode so that the nitrogen atoms can come back together and hug each other. but only two at a time. So no webs and loops. Since N2 molecules don't stick together in larger groups they form a gas, most of our atmosphere, in fact. But carbon is more sticky and does not form a gas. Anyway, they have quite distinct properties and again, there are no intermediate elements between them.

So only fourteen distinct personalities. Still, our immediate response to this Earth with its 14 different kinds of elements would be, that if you cobbled 14 different colored clays together in a big gob and mixed it, you would get a boring grey gob of clay. but we aren't dealing with dumb clay. This universe is not created by a distinction making god-artist out of dumb clay.

Two sources of creativity exist that works here. One occurring at equilibrium, and the other far from equilibrium. We have described the cycling through temperatures that is required to bring things into equilibrium structures. But there is a whole other form of interestingness, dynamic self organizing beings that can form in a system far from equilibrium.


Equilibrium. Recall that the second law and the four forces hold forth with their battle. Recall that the 2nd law attempts to bring all pattern into randomness.

The elaborate webworks of electron dances around nuclei can be arranged in order of their energy level or likelihood. i.e. the pattern of O=O and N#N is of higher energy, is more complicated than O=N etc.. Of course there are potential humps to be leaped by activation energy...

Is it possible to calculate the equilibrium structure for a set of, say, nine carbons, 2 nitrogens, three oxygens, one sulfur, and 14 hydrogens, if we begin at 5000 degrees Fahrenheit and slowly bring it down to 70 degrees? Does a unique one exist? Nevertheless, there are sets of arrangements of atoms which have different enthalpies.

We must mention that as long as we are above absolute zero degrees of temperature, the mix of molecules at a given temperature has a Boltzman distribution of energies. Kinetic energy, which means that molecules in a gas are whizzing around bouncing into each other, molecules in a liquid are swirling around each other, sticking together, coming apart, molecules in a solid can even creep a little. In all states the molecules are always vibrating, spinning, and their constituent atoms are vibrating against each other like balls connected by springs. So the molecules are always jostling each other. There will always be some with an energy high enough to leap activation energy and if they can find a form which can be found at a lower energy... then they will come together and form it. After all the four forces have arranged this mix on Earth at a height state of potential energy and 2nd law will always pull energy out of it to cold dark space until all potential is leveled.

The final structure which HNaKMgCaFeNiAlSiCNOPSCl will attain will merely be an elaborate solution to the Schrodinger equation for that mix of nuclei.

Nevertheless, this structure can be formidable for the same reasons the structure of properties across the periodic chart is. Only one level of complexity more.


Earth would not have begun at equilibrium because atoms in space spewn from life giving suns explosions are open to bombardment with high energy photons and particles. Getting hit by one of these, an atom might get to an activated state, and in that state collide with another atom and form a bond. Thus molecules with high potential energy are formed. The second law can work with these and make stuff happen and things will once settle down to the lowest energy level of equilibrium.

* * *


So what's the cast of characters?

First aspect to their personalities is their discrete quantum character. One valence electron for H out of a possible two it can attain. One for Na out of a possible eight it can attain, that's too high so it opts for loosing its only electron. Two out of eight for Ca, four out of eight for C, that puts it in the middle of the personality chart. Ditto for the next row, but these atoms are a little bigger so there is a little more room for extended valence.

H, Na, K give up one electron, and become positive +1 ions. Mg, Ca give up two electrons and become positive +2 ions. Fe can become +2 or +3 that's interesting. Al becomes +3, C, Si +4 or -4, N, P, become -3, O, S become -2, Cl becomes -1. First part of the story. The natural thing happens.

Na can get an electro-magnetic charge of +1, Cl can get -1, so of course they stick together. They make crystals, which are moderately hard, melt at a high temperature and dissolve in water. Interesting palette of properties just from two atoms. So obviously all these ions can stick together in all kinds of combinations.

Now the miracle again is why don’t they don't just all stick together in one huge grey gob all averaging out to zero charge? Why if we evaporate water containing Na+, K+, Mg++, Ca++, Al+++, Fe++, Fe+++, Cl-, CO3--, B4O6----, PO4----, SO4---, NO3--, doesn't it all evaporate into one huge gob of a crystal with all the ions evenly mixed? Instead, what happens is that different combinations crystallize out at different times depending on the increasing concentration of the salts in the water as the water evaporates. Each distinct combination makes a distinct crystal of its own forming boundaries with the other crystals.

I don't know exactly. But it has to do with complicated solution sets to shrodinger equation just like the startlingly discrete array of solutions to the classification of all finite groups problem. It also has to do with phase transitions. It seems to be even more basic than physics. It is a mathematical property of systems of many jostling parts that as you change a parameter continuously, like the concentration of the salts in the water decreasing at a steady continuous rate as the water evaporates, the system goes through discrete jumps in behavior, one type of behavior for each region of the parameter.


So anyway, different properties: hardness, melting point, solubility in water, solubility in each other, solubility in the molten mantle of Earth.

Fe, Cu, Co, Ni, etc.. are metals so they may form extended huddles by themselves, sharing electrons. Soft malleable, reflecting, fairly insoluble.

It's the CHNOPSCl part of the smorgasbord of elements that gets interesting. Each can share a distinct number of electrons with the other and thus many different combinations are possible. furthermore, they only share a few electrons at time, unlike the metals, who share all their electrons and the electrons flow from one atom to another and so they can come together in huge huddles. The CHNOPSCL guys only share with a few at a time and so make distinct molecules.

This means that carbon and oxygen and hydrogen and nitrogen can form small chargeless molecules that don't stick together so just bounce around and form gasses: O2, N2, CO2, CH4, NH3...

Or we luck out and find that H2O is such a bizarre molecule that it sticks together just a little with more molecules like itself and we get something in between gas and solid, a liquid, which is rare at the temperatures on the surface of Earth. This liquid is of course water, amazing stuff, which makes oceans, rain, blood. Looking at the physics for the four forces and quantum mechanics and the 2nd law, you would never dream such a substance is possible.

Listen to some of its amazing properties. In the narrow range of temperatures we experience on the surface of Earth water can exist as a solid, liquid or vapor. Three phases for one substance. What heterogeneity! Water forms liquid and not a gas at room temperature because it is much more sticky than almost any other small discrete covalent molecule. This stickiness gives it another incredible property: it can dissolve all those ions in itself. That means it can dissolve all the rocks on this Earth. Slowly. This sticky property of water, we say it's a strongly polar molecule, plays major roles in all the games played here on Earth. And last, its stickiness means that when it freezes it expands ( most substances contract as they freeze). So when water freezes in a lake or pond or ocean it expands and thus becomes less dense and floats to the top. But then this top layer insulates the bottom water from the cold and the bottom of most ponds and lakes and oceans don't freeze in the winter. What amazing luck for all the life that lives in water!

Or, we get networks of carbon and oxygen and nitrogen to form solids like wood, hair and plastic. Its possible that you can even call life itself as a phase of matter somewhere between solid and liquid. Either that or just call it a balancing at the phase transition between solid and liquid that can happen at far from equilibrium, but more about that later.

More surprising details!


We also get small charged ensembles: CO3--, CNH-, CH3-, SiO4----, PO4----, SO3--... So more ions to combine to form ionic crystals. CaCO3, CaPO4, CaSO4... We get seashells and bones.

Now one more surprise before we get on to the dynamics. Carbon, Nitrogen, Oxygen, and Phosphorus can form larger covalent ensembles:

O=C=O, C=N-O-H,

...C=C
../...... \
C ........C
\\..... //
...C--C,

And of course in three dimensions. The possibilities are endless. Graphite is infinite expanse of the first form and you just cut some bonds, make some double, replace some C's with O, N, stick some =O, or -H at the ends to seal it all up, make any molecule you want. Different arrangement of atoms and bonds makes different taste, smell, color, stiffness, reactivity etc...

These molecules range form gaseous, to liquid, to fats, oils, solids of various properties from wax to fat to grease to alcohol, to oil to wood to plastic and on up to the complexity of the 1000 or so radically different kinds of building and functional materials that makes life possible.


Silicon and Aluminum and Oxygen can also play these games to a lesser extent. But you can't seal off the ends with -H or =O, so you only end up with huge expanses of molecules which make the 2000 different mineral crystals that make up all the rocks on Earth. It is the special property of CHNOPS arrangements with the sealed off ends that make possible thousands of small covalent molecules interacting with each other dynamically that makes life as we know it possible.

Again, a wonder that the laws of physics come up with a wonderful character as carbon!


CHAPTER 2


We must now move to dynamics. To describe each of the properties these elements and ensembles have. Two main themes:

(1) Paths of reactions, transformations take place and you notice that many elements, especially C, N, O, S, H, can travel form the atmospheric realm to Oceanic to Earth and round and round. Even the other elements can travel back and forth between Earth and Ocean in the form of their ions.

(2) As the paths ( some even circular) of transformations occur, levels of potential energy will also travel from one ensemble to another. Ultimately from high energy photons of sunlight into pathways around a few times and finally out into cold black space.


The energy potential flows through and is ultimately washed out to cold dark space. But the fixed number of atoms on Earth recycle. [end hotcold]

to be continued...