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One Way Streets: Black Holes and Irreversible Processes, Part I

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July 8, 2013 Tags: Earth, Universe & Time

Today's entry was written by Aron Wall. Please note the views expressed here are those of the author, not necessarily of The BioLogos Foundation. You can read more about what we believe here.

One Way Streets: Black Holes and Irreversible Processes, Part I

Note: Today and tomorrow on the BioLogos blog, join physicist Aron Wall for a look into the thermodynamics of black holes. Aron begins this two-part blog with a brief tutorial on entropy, which is helpful for understanding black holes in more detail. (If you’d like to read more from Aron Wall, visit his blog.)

A lot of things in life are irreversible: they only ever happen in one direction.

If you drop an egg on the floor, it breaks open and the yolk comes out.  But eggs never reassemble themselves and leap into your hand.  If you mix hot water with ice water, you get lukewarm water.  But if you have a glass of water just sitting on the table, you’ll never see half of it freeze and the other half boil!  Why is this?

It turns out that the answer has to do with counting possibilities.  Take the example of the glass of water—let’s imagine there’s a specific glass of water in front of you.  It contains a great many water molecules: in a normal sized glass there are about 1025 of them.  There are a huge number of different ways to arrange these water molecules inside the glass (something roughly like 101025).  But it turns out there are only a finite number of possibilities that look similar to your glass of water.

That’s because you know the temperature of your glass of water.  If the molecules are moving around too quickly, they have a lot of kinetic energy and the water will be hotter than yours is.  So there’s a limit as to how quickly the molecules can be moving around.

You might think that there are an infinite number of possible positions of the water molecules in the glass, since space is continuous.  But if you try to measure the position of all the water molecules too precisely, you’ll run into trouble with quantum mechanics.  Heisenberg’s famous uncertainty principle says that the more accurately you can determine the momentum of an object, the less accurately the position can be determined, and vice versa.  Since we have a limit on how fast the water molecules can be moving, we also have a limit on how accurately their positions can be measured.*

When you work this out, you get a finite (but huge) number of different ways for the glass of water to be.  Physicists describe this using a number called the entropy.  Systems with a big entropy have many different possible ways they can be, while systems with smaller entropy have fewer possible ways they can be.**

The Second Law of Thermodynamics states that the entropy of the universe increases with time. Once you know that the entropy is just counting the number of ways things can be, it makes sense that it should always increase:

Imagine you have a jigsaw puzzle solved inside its box.  If you vigorously shake it, the pieces will break up and it will become unsolved.  However, if you shake an unsolved puzzle, it won’t solve itself.   There’s no law of physics which prevents the pieces from happening to fall in just the right way to solve the puzzle.  The reason is that there’s so many more different ways the puzzle can be unsolved than solved.  So you wouldn’t expect it to happen. 

The same thing is true for things like mixing hot and cold water.  There are enormously more ways to arrange the molecules in a lukewarm glass than a glass which is half-hot and half-cold.  Suppose there are X different ways to arrange the hot/cold separated water, and a much bigger number Y different ways to arrange the lukewarm water.  If we start with the hot/cold water and let it sit for a few minutes, we nearly always get lukewarm water—this is possible because the X states of the hot/cold water turn into X out of the Y possible configurations of the lukewarm water.  However, practically speaking we can’t tell any more which of the Y configurations the lukewarm water is in—they all look the same to us since we’re too big to see the molecules—so we say that the entropy increases.

But if we start with the lukewarm water and wait a few minutes, we are starting with Y different possibilites, and at most X of these can turn into hot/cold water.  (The laws of physics require that possibilies which start out being different have to keep on being different.)  The rest of the Y configurations would have to do something else, like remain lukewarm.  So the probability of the water separating into hot/cold is at most X/Y.  Since Y is enormously bigger than X, this probability is very, very close to zero.

So things only ever go in one direction.  The odds of it going in the reverse direction are so tiny, that for all practical purposes you can bet on it as certain.

The Second Law only says that the entropy of the whole universe has to increase as time passes.  If two systems interact, it’s possible to transfer entropy from one system to the other.  For example, life on Earth is possible because the sunshine falling on the Earth has low entropy, while the heat radiation emitted to outer space has high entropy.***

Now let’s think about the past and the future.  For the most part, the basic laws of physics don’t distinguish between the past and the future, yet the Second Law makes them quite different.  Why is that?  There are some mysteries here which scientists still argue about.  But the best explanation seems to be that God must have started out the universe in some very special state with low entropy.  From that time onward, the entropy began to increase.  (If He had instead decreed that the universe would end in a low entropy state, then entropy would decrease and everything would run backwards!  But we wouldn’t be able to tell, since we would go backwards too, remembering the “future” and anticipating the “past.”)

After the Big Bang, the matter in the universe was very hot, uniform, and dense.  The universe expanded (increasing the range of possible positions for the particles), while the matter cooled off and slowed down (decreasing the range of possible velocities).  Eventually gravity caused the matter to become clumpy, producing galaxies, stars, and planets (decreasing the entropy stored in positions), but at the same time reheating the objects (increasing the entropy stored in velocities).  In all of these complicated changes, each decrease in entropy was more than compensated for by increases in the entropy of something else.If God were to continue guiding the physical universe along its current course, without any intervening changes to the regular pattern of events, it would eventually reach the maximum entropy state, which seems to be something like a universe with really tiny temperature in which all particles are separated by astronomical distances.  It would then remain that way forever (except for occasional random fluctuations into more special states).  Before that time, life would have to go extinct and all interesting processes come to an end.  As St. Paul says, “the creation was subjected to futility” by the will of God.   Although the Second Law is needed to support the beauty and life in the universe, it reminds us that this is only on the condition of inevitable decay and death.

However, Paul goes on to add that this was done in hope; hope that the creation will be “set free from  slavery to decay, into the glorious freedom of God’s children.”  As Christians, we expect important supernatural events (such as the Second Coming of Jesus and the Resurrection of the Dead) to take place before life goes extinct. It’s interesting to speculate on what the laws of physics might be like in the New Heaven and New Earth, but obviously we simply don’t have enough information to say.

However, in the currently existing Heavens, there are already peculiar objects which challenge our ideas about how to count possibilities.  These objects are black holes, and the challenge which they present will be described in Part 2.

Notes

*A complete analysis would also have to include the orientation and rotation of the molecules, as well as the motions of the individual H and O atoms within the water molecules, but I’m not trying to be too precise here about the details…

**To be more precise, the entropy is the logarithm\ (http://en.wikipedia.org/wiki/Logarithm) of the number of possible configurations.  But don’t worry if you don’t know what a logarithm is, it won’t be important to the discussion.

***For more on this, see our question on The Second Law of Themondynamics and this ASA article on thermodynamics.

 


Aron Wall is a postdoctoral researcher studying quantum gravity and black hole thermodynamics at UC Santa Barbara. Before that, he studied the Great Books program at St. John's College, Santa Fe, and earned his doctorate in physics from U Maryland. You can learn more at his blog Undivided Looking.

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Roger A. Sawtelle - #81776

July 8th 2013

Comparing entrophy with history as this essay seems to do is misleading and false.

History, both natural and human, does not seek to return to a natural state of wholeness.  Salvation history goes from a state of naivette to a state of perfection in God.  We cannot say from our vantage point how this will happen, but God is in charge. 

On earth nature conserves and recycles so that it is renewed.  This oviates the power of entrophy which requires a static system.   


mikitta - #81849

July 14th 2013

I think the argument being made above is that we do observe entropy in nature - and in the Universe.  Without the direct intervention of God, we will expect to see all systems slow to a stop at full entropy.  Dr. Wall isn’t trying to say history is entropic, rather that creation is because that is how it has been created.

However, there are certain historic events that show God changes things a bit - such as the virgin birth, or the resurrection (the ultimate high entropic state being reversed fully to low entropy).

If I follow where he is going with this, I believe Dr. Wall’s direction with the black holes will be as universal recyclers, mini big bangs if you will - that is they suck up matter and upon reaching a critical mass, eject it back into the system, containing high entropy - which would allow the entire system to run in perpetuity without slowing down and dying.


mikitta - #81850

July 14th 2013

ere black holes ejecting matter containing low entropy back into the system ... sorry.


mikitta - #81852

July 14th 2013

found part 2 and no, he didn’t go in that direction - but that isn’t automatically discounted ... it will be interesting to see what comes of his research.


Aron Wall - #81887

July 16th 2013

mikitta,

Thanks for your comment.  Your summary in the first paragraph seems fairly accurate.

I agree that God changes things when he likes—-but I have no idea whether or not the Resurrection decreased the amount of entropy in the universe!  That’s because to me as a physicist, entropy is a technical term for counting possibilities (as I explained above), not a synonym for “decay” and “death”.  The entropy increases when people are born, just as much as when people die.

Since the Resurrection inaugurates God’s plan to create a New Creation out of the old one, and since there will be no death in the New Creation, one could guess that this is because entropy can decrease in the New Creation.  But this is just a guess, since we don’t really know enough about what God is planning to say for sure!

What the Resurrection (and Ascension) do show, is that the observable physical universe is not a closed system.  There are other realities besides this one, and information can come in and out.


Jon Garvey - #81777

July 9th 2013

There seems to be a lot of heat generated about entropy in relation to evolution, some of which runs contrary to common sense.

The sentence about sunlight light having low entropy, and earth’s IR radiation high entropy, is thermodynamically true, but hardly complete or in any way explanatory of life. It only explains one of many reasons why life is not a physical impossibility. It gives no more actual insight than saying the existence of matter shows why life is not impossible, since matter makes up life.

As a comparison, it’s that same entropy “gradient” on earth that makes it possible for the heat from burning coal to be able to do the work of, say, solving complex problems on an electronic computer. But that’s only so if in between the heat and the work is a complex generator, a national grid, a series of electronic component and computer factories, a mass of software and programming languages etc, all of which require human input to design the machines which (by year one mechanics definition) are required to turn mere energy into work and temporarily buck the entropy trend.

You could put your problems on a coal fire for a quadrillion years, and there still wouldn’t be any organisation of a solution to them - just ash and infra-red. That should be uncontroversial.

In information terms, entropy is only decreased by the immaterial information in the system. To reflect Roger’s thoughts, it is only decreased by the activity of the Logos that brings order to what is “without form and void”, ie to a cosmos with high entropy.


Peter Hickman - #81779

July 9th 2013

For a more detailed treatment of the physics of this and related topics, Brian Greene’s ‘The Fabric of the Cosmos’ makes an interesting read. No theology in it, of course!

http://www.amazon.co.uk/Fabric-Cosmos-Texture-Reality-Penguin/dp/0141011114

 


Roger A. Sawtelle - #81816

July 10th 2013

Entropy has a entity start from a position of high organization and then move to a situation of low organization.

What humans experience is birth with low organization, then move to growth to adulthood with a high organizational peak and then decline as seniors to less organzation ending in death.  Humanity is renewed continually by the birth of babies.

Organizations and nations also seem to follow the pattern of rise and fall.  Hopefully nations do not have to fall with the chaos and disruption that accompanies this, but can change and adapt in order to keep on growing. 

Nature seems to be able to go from one form of organization to another, instead of an inevitable decline.  This is what ecology is all about, waste is not waste, but the raw material for a new organization.  Death is not the end, but leads to new life. 

Monism would seem to lead to inevitable death, because sameness does not produce creativity and growth.  Dualism produces only conflict.  Triunity produces creativity and growth.  

Even the universe did not start with high organization but has continued to grow.  Certainly the earth did not start as a highly organized system but has continued to grow.  How long this can last remains to be seen since there may be a limit.

The question I am raising is how significant really is entrophy in our understanding ourselves and our world if it goes against way things change, which is more like a bell curve, rather than a downward slope.     


Nick Gotts - #81859

July 15th 2013

There are some mysteries here which scientists still argue about.  But the best explanation seems to be that God must have started out the universe in some very special state with low entropy.

Hang on a minute! Where is the evidence that “God” had anything to do with it?

 


Nick Gotts - #81862

July 15th 2013

Only the first paragraph should be quoted. The commenting system here leaves a lot to be desired!


Aron Wall - #81888

July 16th 2013

Nick,

if God exists and created the whole universe, then he has to do with everything.  So perhaps you are asking me why I think God exists?

In my post, I was presupposing Christian doctrine, and attempting to explain scientific theories given that background knowledge.  That’s why I wrote that sentence the way I did.  But I agree that statements about God should also be based on evidence. 

The fact that the universe came into being, and supports life, is in my opinion some evidence for theism, but I think the strongest evidence comes from the historical testimony for specific miracles.  Going into that would be off-topic for this post, but you can find more information about that on my website or blog.


Dan Iezzi - #82327

August 4th 2013

I have had more time to research my original proposal. The logic is as follows: There is a huge rectangular solid object comprised of cold and dense neutrons with a pit in it that opens up into outer space that was initially sealed with neutrons. These neutrons got pulled by gravity through the pit in order to fall to the other side. This pit fills up with layers of quark-gluon plasma that is hotter and denser in a smooth transition through the depths. So closer to where the pit opens into outer space it is cool for the phase transition from a quark-gluon plasma state so that the nucleus of a proton can form and also an electron. So, this pit becomes like a three dimensional Dirac Sea filled with particles in a continual state of particle annihilation. Instead of one could describe these as the waters. In this three dimensional visualization there is the phase change to a quark-gluon plasma, at a deeper depth there is the planck unit where every is set to one, and at a greater depth there is the Planck Particle which is around 1.77 times more massive and is where gravity and the electromagnetic force is joined together as a drop of gravity filled to the event horizon. Time has nothing to do with this. The Planck Particle temperature, pressure, density, entropy, and volume as filled to the event horizon gives this a finite description. Since this particle is filled to the event horizon it could transfer heat if in contanct with a cooler quark-gluon plasma so it could not be eliminated on that basis. Would it be possible that this could become a Standard Model definition for a drop of gravity? The pit configuration above could be maintained indefinitely. In this case would light be forced to exit into the vacuum of outer space? Once the contents of nucleus of a proton are cooled to the where these can gathered under the gluons then it is time for the proton to appear, and the electron. These move along on winds that are like the jet of a quasar jet. Along the way thermonuclear fusion would occur. There is evidence for concurrent brightening and gamma ray bursts now so I am not quite ready to rule this out yet. These jets will then fill up a great portion of the visible Universe with a plasma that would explode much like a star-like supernova explosion. There may be a gravitational collapse mechanism involved that could form blackholes, and a blowout mechanism that could begin plowing matter outwards towards the intersections where the filaments meet. If enough matter got concentrated enough to form blackholes either through the sweeping of and plowing of matter into each other then that would explain that, and the dark matter becomes parts of the nuclei that never reformed into a nucleus. I still don’t quite understand the baryon acoustic oscillation as well as I can yet. So, in essence the cosmic microwave background radiation would be the result of looking at a supernova explosion from the inside out after recombination occurs. I finally understand that now. If you have any feedback it would be greatly appreciated. I sure would like to make a contribution for a scientific inquiry that would finally explain something to me. I guess the most important would be a theory of quantum gravity, and whether or not gravity can be quantised to fit within the Standard Model, and also GR and SR. I sure would like to rest.

 


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