I spend a lot of time thinking about entropy and physical information and the nature of life and regretting never taking a college-level physics course, and one question that’s been nagging me lately is how can it be that a churning ball of fire consisting primarily of the simplest atoms possible, and so heavy that it’s crushing the very matter it’s made out of, is in such a much, much, much higher state of order than the planet earth, a planet covered (albeit in a very thin layer) with incomprehensible numbers of incomprehensibly complex molecules arranged in incomprehensibly complex patterns.
I know life doesn’t violate the 2nd Law of Thermodynamics, and I intuitively understand why that is. But I don’t understand how a mass of incandescent hydrogen represents a state of lower entropy than, say, a hemoglobin protein.
I think you have a fundamental misunderstanding of entropy (or at least of the Second Law of Thermodynamics).
Life doesn’t violate the Second Law because there is a huge fiery ball of entropy that we call the Sun. The Second Law is restricted to closed systems. Life is not a closed system. Life happens because Life receives energy… from the Sun. In terms of the Second Law, you can’t look at Life and not include the Sun.
I have no idea why you state that the Sun is more ordered than the Earth. That sounds flat out wrong to me.
I wonder if you are confusing the Sun itself, here, with the Sun-Earth system. The large temperature difference between the Sun and the Earth system does indeed mean that there is a relatively low state of entropy in that system, and it is this negentropy off which life ‘feeds’, as it were. (At least, that is how I understand it. I am no physicist.)
I haven’t heard about the Sun/Earth either, but if you consider that the Earth is basically made of of “ashes” from nuclear fusion in stars, then an equivalent mass of the Sun will have a lower entropy; e.g. more energy can be produced. That is, a star of mainly hydrogen can produce more energy from fusion, which forms helium, which has less potential energy available. Eventually, you end up with iron, which can no longer release energy from nuclear fusion (you have to add energy, which means you are no longer talking about a closed system, where entropy can only increase). This is however only considering how much energy is available from fusion; the Earth and the lifeforms on it are obviously more ordered than the Sun.
Because, as you said, the Sun feeds energy into the Earth. The Earth, separated from the Sun, would quickly cool within a matter of days and all interesting life would rapidly die; the Sun keeps life on Earth going by pumping energy into it, and that energy is used by life to construct highly ordered patterns of matter.
But the Sun separated from the Earth would continue blithely on as it has for another few billion years. So, Earth’s apparent order is the result of stealing some tiny part of the Sun’s order as it violently sloughs it off at a disgusting rate while appearing hardly affected, and the Sun therefore must have, quite literally, order to burn.
What’s so counter-intuitive to me about this is that a Hydrogen atom appears so small and simple. How does even a large cloud of tiny atoms represent more order than a single large, discrete molecule that represents stored information? I freely accept that I don’t have a good handle on what ‘order’ means in physics, but then that’s why I’m asking this question.
It’s hard to judge entropy based on intuitive notions of order. You should leave aside your common sense definitions when working with this stuff.
Entropy is based on the log of the number of indistinguishable microstates. Sometimes that corresponds to order, but other times not–gravitational systems in particular look almost to be reversed, since a collection of isolated black holes (the end state for a collection of matter) seems to be more ordered than a diffuse gas, and yet the former has a far higher entropy.
Also, remember that entropy is a relative thing. It doesn’t matter if some particular spot on the Sun has a higher entropy than some protein or whatever on Earth. What matters is that the Sun *can *increase its entropy, because it’s not yet in thermal equilibrium with its surroundings, and in the process can radiate energy to Earth and cause a local decrease in entropy. There’s no limit to how much more “ordered” the Earth can be compared to the Sun as long as the total entropy of the system always increases.
Stored information in the way we normally think of it does contribute to entropy, but it is such a microscopic speck of the total that it is basically irrelevant in any calculation. The bulk of the entropy (or lack thereof) comes from the way the fundamental components are structured. Even the energy that the Sun extracts by converting hydrogen to helium, etc. is a small fraction of the possible increase; to go further you rip apart the structure at finer levels of detail, like with neutron stars and black holes.
So don’t think of it in terms of the relative orderedness of hydrogen vs. biological molecules. Think of it as the amount of headroom a clump of matter has to increase entropy further. All ordinary matter is so far away from the ultimate limit (a black hole) that it is all essentially the same.
I’m not using a “common sense” definition, I don’t think, but it is somewhat intuitive. I think of order as “containing physical information”. I’ve read “A Brief History Of Time”, and it makes sense to me that black holes have maximised entropy- they reduce all things to one thing. Throw in a copy of The Catcher In The Rye, an adult rhinoceros, an amethyst geode, a kilogram of plankton, and a cubic meter of Earth’s atmosphere, and they will all be crushed down to the exact same sub-atomic matter, only escaping as randomly radiated X-Rays, devoid of all information they contained. So, my understanding jells fine with black holes being disordered. On the other hand, it doesn’t make much sense of the diffuse gas, even though I understand factually why they must contain more order than black holes, so I’m clearly missing something there.
I don’t know if the sun is more ordered than the Earth or not, but if it is I suspect it’s just because it’s much bigger than the Earth. How long could an Earth-sized chunk of the sun keep us going?
The Sun is much hotter than the space around it. The huge difference in temperatures is a kind of “order.” When the sun cools down, and is at a temperature closer to (or the same as) the space around it, that “order” will have disappeared.
Sure, the sun doesn’t seem to have much internal order. But when you’ve got a huge amount of energy here, and almost none at all there, that difference is called order.
A charged battery has a lot more “order” than a discharged one. A hearty slice of pizza has more order than the same volume of (ew!) poop once it has passed through my innards.
Wikipedia says the Sun’s mass is 332,946 times the Earth’s mass:
5,000,000,000 divided by 332,946 equals about 15017.45, so one Earth’s mass of the Sun’s fuel ought to be enough to keep the entire solar system toasty and maintain our current contribution to total galactic light output for over fifteen thousand years, three times the length of recorded human history, assuming all the many, many assumptions this calculation involves doesn’t make it completely meaningless.
Earth is the middle part of a three-stage flow of energy: The sun, Earth, the 3K blackness of space. It’s this flow of energy that powers life, allows it to decrease in entropy locally while the system as a whole increases in entropy. If you removed the energy source, the sun, life would cease. If you removed the energy sink (that is, somehow prevented Earth from dumping energy into space), life would again cease.
Life is like a waterwheel stuck into a fast-flowing stream; the wheel doesn’t prevent the water from flowing but taps into it do to work. The passage of energy from the sun to deep space is just delayed slightly by its detour through the biosphere.
Not only is this notion mistaken, it’s actually completely backward. A high-entropy system contains more information than a low-entropy one, not less. Consider, for instance, a system consisting of a whole bunch of pieces of printer’s type. The lowest-entropy state (or at least, one of a number of states tied for lowest entropy) would be to have all of the pieces sorted neatly in alphabetical order: A whole bunch of As, then a whole bunch of Bs, then the Cs, and so on. But this contains almost no information at all. On the other hand, if you re-arrange those letters into a higher entropy state, you can have Shakespeare, or Cervantes, or the directions for assembling your Ikea bookshelf: There’s plenty of information there now.
To go along with what Chronos said–that this makes sense to you is a sign you don’t understand it :). It should in fact be deeply unsettling because there is an unimaginable amount of information packed into a point. Some physicists certainly don’t like the idea, and so they try to come up with alternatives to black holes such as fuzzballs, gravastars, dark-energy stars, etc. These models also “fix” other problems but what they have in common is that they spread out the matter to a larger volume than just the singularity.
True, I should have mentioned that. The entropy of everything in the Universe except black holes is defined in terms of their information content. Black holes are weird, because they show every sign of having an extremely high entropy directly proportional to the area of their event horizon, but they also appear to contain almost no information. This is in fact one of the biggest puzzles of modern physics.
I can’t remember the particular players, but the debate about life and order is not a new one. I’ll look through my library tonight, I think there was a great essay by Schrodinger on the topic.
To summarize the conclusion: life creates “order”, but the amount of energy required to do so leaves a net loss in “order.”
Yep! Harold Morowitz, in his (excellent!) book, “Mayonnaise and the Origin of Life,” coined a phrase that ought to be engraved over the lintels of every Biology Department building: “The flow of energy through a system tends to organize that system.” Energy flow is anti-entropic. Just as one non-living example, look at how wind can organize sand into highly regular series of rippling dunes. The information doesn’t magically come out of nowhere; it is caused by the flow of energy (moving air) over the sand.
The rich chemical mixtures at the earth’s surface have loads of energy flowing through them. Sunlight, volcanic heat, the gravitationally-powered churning of the tides…even a few ergs from starlight.
Dang it, you guys are hurting my head. So what you’re saying is, years ago when I read A Brief History Of Time, I accurately picked up the high entropy/low information nature of black holes, but mistakenly thought this represented a metaphor that could be used to understand entropy in all environments, when in fact this state is highly anomalous.
But, if order isn’t synonymous with information, and entropy isn’t synonymous with the loss of information, then why is the term ‘entropy’ used to describe the decay of mundane earthly objects? Isn’t the death of a living thing or the destruction of a manufactured object an example of information being lost?
That’s right. Since ABHoT was written, there has been a lot of development in this area, but as usual it’s opened more questions that it has answered. For instance, it was then a completely open question whether or not information could be destroyed when it passed into a black hole. The consensus now is that it’s not destroyed, but it raises at least two more questions: where does the information go, and how can it get back out again?
I recommend The Black Hole War by Leonard Susskind for an excellent primer on this material as well as some interesting backstory.
Decay of mundane earthly objects, as you say, really isn’t a great analogy for entropy. It’s used because it fits our common-sense notions of irreversibility, which is fundamental to thermodynamics. The analogy is usually something like “you can’t unscramble an egg”, which is true enough but maybe not for the obvious reasons.
As far as we know, information is never lost in the universe (even in black holes). This is essentially a result of the underlying laws being reversible. So you can unscramble an egg, in principle. The problem is that the information gets distributed and itself scrambled, to the point where there’s no practical way to go back.
So if the physical laws are reversible, then why is thermodynamics irreversible? This is a very difficult question but the short answer is that it always takes more energy to make use of this information than anything you get out of it. In the process there is always a net increase in entropy.
Who says it is? It’s news to me.