## Friday, April 23, 2010

### Red edge: entropy and life

If you take a photograph of plants in the infrared, they appear extremely bright, especially the leaves:

In fact, as Sean Carroll correctly explains in The Red Edge, this behavior of the plants on the photographs can be reduced to their spectrum:

Note that the plants absorb lots of the visible light - the left portion of the picture (except for the chlorophyll bump at 500 nm) - but they instantly begin to reflect the infrared light. The huge jump between the visible and infrared spectrum is known as the red edge. A similarly striking signature has been proposed as a sign of life on other planets. Is that sensible?

First, we should understand why the plants behave in this way. This question can be approached in two basic ways: by looking for a microscopic explanation, and by finding the purpose or the evolutionary survival advantage that the plants gain by this behavior.

Why is there a red edge?

Concerning the first strategy to address the question, well, this is the kind of spectrum you get e.g. for crystalline water, among other things. That's why not only plants but even mundane "dead" objects such as clouds look extremely bright on the infrared photographs. This is the first indication that the edge is not necessarily connected with life.

As far as the second strategy goes, the plants try to maximize the absorption of the visible light simply because a lot of it manages to penetrate through the Earth's atmosphere - because of the spectrum of the atmosphere. There is no sharp drop of the solar spectrum measured near the surface in the vicinity of 700 nanometers but the plants just decide to make it sharp. It's like the cutoff that the members of admission committees know very well.

The abundance of the visible light is also why our eyes are optimized for the visible band. They're not "canonically" or "perfectly" optimized - after all, some other mammals can only see two independent colors, not three, and the precise sensitive bands may be shifted - but it is a qualitative argument why it is more likely for organisms to have eyes that are sensitive to the electromagnetic radiation that is easily available rather than the "rare" forms of light. You simply don't need too sensitive gadgets to "see" if there's enough light.

So the plants' processes are optimized for particular frequencies that sit inside the bands where there's enough light so that they don't have trouble to find the light. Again, different plants use different frequencies for photosynthesis: much like in the case of the mammals' eyes, these technical details are not universal.

However, the plants try to reflect most of the other unnecessary electromagnetic radiation because that wouldn't help the photosynthesis - and the plants want to avoid overheating during photosynthesis. They want to keep their temperature differences.

Jovian plants

Different planets would have a different composition of the atmosphere - and consequently, their hypothetical plants would be adapted to different frequencies. too. I agree with the sentiment that the "sharp drop" in the activity as a function of the frequency suggests that something similar to life is going on - but as demonstrated by the example of the clouds, it's surely no "proof of life". Of course, the "red edge" would probably be located elsewhere on a different planet.

On the other hand, we may understand the selective absorption of the abundant forms of light just as another "generic negative feedback" that is likely to occur in any sufficiently complicated stable system: see my comments about Le Chatelier's principle. If something is abundant, the players try to use it and consume it.

There's simply a lot of visible light on the Earth which is why the complex processes that consume the light that is abundant will be more likely to occur. I don't think that such a negative feedback immediately implies some "life", and surely not "intelligent life": after all, even most plants on our clever planet are not terribly intelligent. However, these statements depend on the definition of "life": if you find out that the clouds are doing a similar job, which is almost certainly the case, at least in some sense (think about the "iris effect"), you could also include clouds into some "generalized life forms".

The Hubble Space Telescope is 20 years old but it just produced the prettiest picture yet today - from the star-forming Carina Nebula. Don't these clouds look like a couple of bisons on top of each other? OK, I added one to the original picture.

So far, they haven't become terribly intelligent, as far as I can say, but who knows: maybe the scientists among the clouds watch the global warming alarmists and they are also immensely shocked that life forms as stupid as the global warming alarmists may exist on the same planet as the intelligent life that is led by those clever clouds. :-)

Does life decrease the entropy?

I am finally getting to the main topic which is the relationship between the "amount of life" and the "entropy increase". Sean claims that the life is connected with some excessive, unusually high, or even maximal production of entropy.

Well, you know that I am convinced that Sean Carroll fails to understand elementary thermodynamics and elementary statistical physics. And this question is no different. He has simply no clue.

In general, there is no "excessive" increase of entropy linked to the existence life. If there's some dependence on the amount of life, it's the relative decrease in entropy. The outgoing radiation following a smoother black body curve - without the "red edge" - would have a *higher* entropy simply because the more generic - more uniform - states of the electromagnetic field would be used. Non-uniformities in the distribution of energy always signal a reduced entropy! You have more states if you can split the energy among photons of arbitrary energies pretty much equally. Recall that the gas that happens to concentrate in the left half of your room has a lower entropy than the uniform gas. A selective reflection concentrated in some bands produces a lower entropy than a more color-blind spectrum.

So while some creationists are completely wrong if they say that the second law is violated in Nature, they surely get the correct sign when they say that life is connected with the "unnatural" ability to lower the entropy locally, and/or with an increase in the total entropy by a smaller amount than the non-living objects would normally manage. Of course, there's nothing purely "biological" about the local reduction of entropy: a fridge can do it, too. But one can still tell the difference between a fridge and an animal when she sees them.

Sean Carroll tries to present his crazy opinions about the entropy and life as a dispute between evolutionists like himself on one side and those who disagree - the creationists - on the other side. That's, of course, a completely preposterous statement. It's even worse news that there's not a single reader of the Cosmic Variance who would both know the right answer and who would be allowed to post comments over there.

Everyone who has thought about these basic issues knows that Carroll is wrong. The "establishment" in the topic of "life and entropy" is not quite defined by the creationists but rather by people like Erwin Schrödinger, John Bernal, Eugene Wigner, John Avery, and even James Lovelock. But all of them would agree that the characteristic property of life is that it can (locally) reduce its own entropy, not that it increases the entropy more than non-living objects!

In his famous 1944 book about this subject, "What Is Life?", the father of wave mechanics Erwin Schrödinger theorized that life, contrary to the general tendency dictated by the second law of thermodynamics, decreases or maintains its entropy by feeding on negative entropy.

I think that the term "negative entropy" or "negentropy" was unfortunate but the basic statements he wanted to convey are surely correct. The life on Earth doesn't depend on the energy from the Sun itself - there's a lot of heat elsewhere in the Universe, too - but on the temperature difference between the Sun and the Earth that allows objects on the Earth to lower their entropy (as long as this reduction is accompanied by pumping of a bigger entropy than their own entropy decrease to the environment).

Because the photons from the Sun are re-emitted as the Earth's thermal radiation whose frequency (and therefore energy) is smaller by a factor of 20 or so, see my text about black bodies, and because the entropy carried by one photon is pretty much constant, and the number of Earth's thermal photons has to be 20 times higher than those from the Sun (energy conservation), the photons emitted by the Earth carry roughly 20 times higher entropy than the photons from the Sun that brought us the required energy.

This fact about the non-living Earth guarantees that the second law of thermodynamics is safely satisfied, so the organisms are allowed to lower their own entropy by comparable amounts as the entropy of the incoming solar radiation (or as much as 19 times bigger) without any risk of violating the second law. And indeed, because life is very efficient in creating the "organization" and reducing the "disorder", the organisms on the Earth partially use this "free lunch" and they indeed do reduce their entropy. Don't get me wrong, the total entropy always increases. But the existence of life makes this increase smaller than what it would be without life.

The existence of the "red edge" is just another example of this fact about the life's ability to reduce the entropy (relatively to the situation without life); the inhomogeneous, structured content of an egg (or anything else that is alive) is a more well-known example.

So Sean Carroll has obtained wrong signs to all these basic questions. Carroll must know that what he's saying is ludicrous. The systems that maximize the rate of increase for the entropy are black holes. If a Schwarzschild black hole is formed, the mass is pretty quickly transformed to a form of matter with the highest entropy that an equally heavy bound system can have. And there's not much life inside or near the black hole: after all, black holes are extreme "life killers" and what is left after the black hole gets stabilized is as dead as you can get. Carroll's rule would present black holes as the most intelligent and most lively life forms which is absurd.

In 1964, James Lovelock of the Gaia fame was one of the folks asked by NASA to define the methods to look for life on Mars. What are the general features linked to life? Lovelock gave an obvious answer:
I'd look for an entropy reduction, since this must be a general characteristic of life.
This answer is, of course, a very qualitative one. But the sign is right. Life adds negative terms to the total entropy change, not positive ones, while the "hospitable environment" adds the (larger) positive terms that make the entropy-reducing life possible and compatible with the second law. I am amazed that Sean Carroll hasn't been able to realize that he has a sign error in this very fundamental question as well - even though millions of readers of popular books (such as Schrödinger's book) must know what the right answer is. In this battle between Carrollian darrwinism and the coalition of creationism and others, creationism and others won. ;-)

Discovering extraterrestrial life

Finally, as I explained in the text Extraterrestrial life: I am a skeptic, I would be stunned if people found non-Earth-imported microbes on other celestial bodies. I actually believe this won't happen in the next millennium (or longer). Intelligent life elsewhere that is still detectable sounds unlikely to me. But even if it exists, it's likely that we would first encounter some non-intelligent life because it's probably much more likely than the intelligent life.

Even on our own unusually intelligent Earth, the life has only been "really" intelligent - included sophisticated "greetings" or languages - for a few thousand years which is one part per million of the time of the Earth (apologies to some clever dinosaurs whom I have missed and who may feel offended). And today, we already have calls to return to a non-intelligent Earth without a carbon footprint, without the conventional GDP growth, and without the independent thinking of the people.

If we saw another planet where the environmentalists would be in charge for a few centuries, it would look non-intelligent to us, too. It remains to be seen whether the intelligent civilization on our Earth will last for thousands or millions of extra years (or less). It's something we may influence, too. Unfortunately, it's not just the sensible people who want to influence it.

Meanwhile, I think that the observational numbers indicate that the concentration of life - and intelligent life - in the visible Universe is low.

1. Excellent, and very interesting read.
Have you perchance seen the simple paper: "Life on Earth - flow of Energy and Entropy" by Roland-Mieszkowski?
http://www.digital-recordings.com/publ/pdfs/life_on_earth.pdf

2. Dear Dr. Motl,

Regarding the bison, it seems that you have great paranoiac-critical skills. :)

I think that the darker material on the surface of the Moon also looks like a bison. I see the bison's giant head on the left and its back legs on the right by tilting my head 40 degrees to the left when viewing:

http://en.wikipedia.org/wiki/File:Full_Moon_Luc_Viatour.jpg

** This picture "Full Moon view from earth In Belgium (Hamois)" is by Luc Viatour (http://www.lucnix.be).

3. Funny, but I don't drink alcohol. I was just born this way. :)

4. Actually, come to think of it... that's not entirely true. I did have a couple of very delicious Pilsner Urquell beers two New Years Eves ago, but you see my point. :)