February 27, 2006

So what?

Ok, so the explanation of the origin of the quantum was a bit abstract and technical. Here are a couple of interesting thoughts that writing about this stuff brought to the surface of my mind:

Is there a physical reality to the concept "infinity"? In other words, is there such a thing as "infinitely small" in the real universe? Alternately, is the universe infinitly big, has it existed forever, or, will it exist forever? Whenever infinities crop up in mathematics, they cause things to break. A lot of 20th-century theoretical physics was driven by the desire to get rid of infinities in the theories, so that sane results could be derived. Planck's work showed that black-body radiation only makes sense if infinitely small amounts of energy cannot be absorbed by atoms. To my mind, it would be equally amazing if the universe contained something infinite, and if it didn't.

Planck needed statistics to get his results. Most people think of physics as a science of exact predictions: if you have this starting state, apply these rules, and you can predict what will happen next. In practice, it seems, physicists were already dealing with such complicated systems in 1900 that they had to turn to calculations of probability. This is something we'll see more of in later discoveries.

Coming next: Hormones, which will be a lot less abstract.

February 24, 2006

The Quantum

Max Planck On the Theory of the Energy Distribution Law of the Normal Spectrum 1900

The story of this paper begins, as do many great discoveries, with a puzzling observation.

By the end of the 19th century people had figured out how to make colour filters for light, and measure the brightness of light by comparing it against light sources of known strength. With these tools, people could measure the intensity (brightness) of any source of light at any frequency (colour), and, as scientists are wont to do, make graphs of intensity vs. frequency. Such a graph is called the spectrum of a light source.

Any light that strikes an object is either reflected back, passes through the object, or is absorbed by the object. Light that reflects or passes through is unchanged, and therefore relatively uninteresting, but something very interesting happens to the light that is absorbed. Atoms aren't any good at keeping absorbed energy, so they quickly re-emit it, usually at a different frequency. This changes the spectrum in interesting ways.

To study this effect, scientists used to measure black-box radiation; that is, they would cut a small hole in a box and see what light came out. If the box has been left closed up for long enough, you can be quite sure that any light that comes out has been absorbed and radiated from the interior walls of the box many times, so there can be no reflected light from an exterior source left inside. (At reasonable temperatures, of course, all the light inside a box is at frequencies below those we can see. You'll just have to take my word that there is, in fact, light inside a dark box.)

The puzzling observation was this: black-box radiation has a spectrum which can be predicted solely from the temperature of the box. At first glance this seems reasonable... until you start thinking about it. It doesn't matter what shape or size the box is, or even what it's made of. As long as they're the same temperature, boxes of any size or material produce exactly the same spectrum, called the black-body spectrum or the normal spectrum.

Since scientists had already observed that atoms of different materials re-radiate absorbed light in different ways, this was very upsetting. Even more upsetting was that then-current theories produced impossibly wrong answers when used to calculate what should be observed from the interior of a black box.

To understand black-box radiation, Planck needed statistics. In 1900 it was known that if every configuration of a system is equally probable, then one can calculate the number of possible configurations of some known system, and calculate its probability. A very simple example is rolling two dice: every possible roll is equally likely, but there's only 1 way to roll a 12 (6 and 6) and 6 ways to roll a 7, so a 7 is six times more probable than a 12.

Small changes to a system (like re-rolling one of the dice) are more likely to move the system toward a probable state than an improbable one. Once a system reaches the most highly probable state, any small changes are more likely to keep it there than move it towards an unprobable state. In other words, a system being subjected to small changes will reach an equilibrium, a steady state, and that state is exactly the most probable one.

The temperature of a black box is, in effect, a measurement of its total energy. Planck wanted to calculate the most probable distribution of energy among the atoms and colours of light in the interior of a black box. To do this, he was forced to assume that atoms cannot absorb or radiate arbitrary amounts of energy. In other words, there must be a smallest possible amount of energy that atoms can absorb or radiate, or else there would be an infinite number of ways to distribute the energy in the box, which causes the probability calculations to break. This is the fundamental idea, what Planck called "the most essential point of the whole calculation". Later, this smallest possible amount of energy would be named the quantum.

Planck showed that if the size of the quantum is determined by the frequency of the light being absorbed or radiated, then the normal spectrum is the equilibrium state inside a black box. In doing this, he provided the first valid explanation for the universality of the normal spectrum.

The relationship between the size of the quantum and the frequency of light that Planck discovered is simple: multiply the frequency of light in question by a constant. Planck called the constant h, and calculated it (based on observations of black-box light) to be 6.55 x 10-27 erg seconds. An erg is a very small amount of energy, so h, when multiplied by some frequency of light, gives you an astonishingly small amount of energy: the quantum of that frequency.

February 23, 2006

Reading List: The Discoveries

The Discoveries: Great Breakthroughs in Twentieth-Century Science, Including the Original Papers by Alan Lightman, 2005

This is a wonderful book. It contains 25 of the most important papers of this, whoops, the last century in physics, chemistry, and biology, accompanied by essays describing the context in which the discoveries were made, the background of the author(s), and the jargon necessary to understand the papers. You can get a lot out of this book even if you never read the papers themselves.

If you really want to understand how the universe works (e.g. you were disappointed by the lack of detail in A Short History of Nearly Everything), this is the book for you. Here are the discoveries chronicled by the papers:
  1. The Quantum
  2. Hormones
  3. The Particle Nature of Light
  4. Special Relativity
  5. The Nucleus of the Atom
  6. The Size of the Cosmos
  7. The Arrangement of Atoms in Solid Matter
  8. The Quantum Atom
  9. The Means of Communication Between Nerves
  10. The Uncertainty Principle
  11. The Chemical Bond
  12. The Expansion of the Universe
  13. Antibiotics
  14. The Means of Production of Energy in Living Organisms
  15. Nuclear Fission*
  16. The Movability of Genes
  17. The Structure of DNA*
  18. The Structure of Proteins
  19. Radio Waves From the Big Bang*
  20. A Unified Theory of Forces
  21. Quarks: A Tiniest Essence of Matter
  22. The Creation of Altered Forms of Life
* 2 papers

I'm planning to post something about each of these discoveries. That's right ladies and gentlemen, I'm actually going to be posting regularly for the next few weeks. Along the way I'll get to ask questions about the nature of reality, the inner workings of scientific discovery, and the purpose of life as we know it.

Now, time for a plug. A few of you (especially those who studied cognitive psychology) might be interested in the following blog/discussion: True Artificial Intelligence, in which various theories of the nature of conciousness are being discussed by articulate, intelligent people.

February 11, 2006

Reading List: The Algebraist

The Algebraist; Iain M. Banks; 2004

Finally, a new non-Culture science science-fiction novel by Iain Banks.

This novel would have been awesome, except I guessed the Big Secrect somewhere around page 80, which kind of ruined the big revelation at the end. However, I'm sure anyone who doesn't figure it out until the end will be suitably impressed.

The wider setting is a chaotic, war-torn galaxy where the only method of going FTL is to use wormholes, which are both massively expensive, and prone to getting blown up by hostile forces. As a result, there have been an awful lot of dark ages for galactic civilization. Among other nastiness, the current superpower has taken to hunting down AIs as a threat to organic life.

The narrower setting is Ulubis, a star system that was cut off from the wormhole network a few centuries ago (it got blown up by hostile forces), but will be reconnected within a few decades. The protagonist, Fassin Taak, is a Slow Seer, one who studies the Slow, the intelligent species that have been around for billions of years. Fassin, of course, is human, one of the Quick species that come and go in 10s of thousands of years. In particular, he studies the Dwellers, who inhabit Ulubis' largest gas-giant.

Since most of the book is about the Dwellers, their society gets fleshed out a lot. Banks has avoided the cliche of making his gas-giant dwellers into huge, mysterious gasbags that speak in thunderous farts, which is good. Figuring out why the Dwellers behave as they do is half the fun of reading this book (aside from the plot, characters, etc). In short, go read it yourself.

February 08, 2006

Reading List: The Baroque Cycle

The Confusion
The System of the World
- by Neal Stephenson

The Good:
- manages to explain some interesting abstract ideas
- points out some really interesting etymologies*
- makes the era come alive for the reader

The Bad:
- 3000 pages, plus acknowledgements
- Doesn't have enough plot to fill that many pages (Although there is an interesting plot, and action. There just isn't enough, that's all.)

The Ugly:
- I love some of Neal Stephenson's other writings, but the best I can say about these, his largest works to date, is that they weren't bad enough for me to abandon before finishing them.

* For example, the word "mob", as in "a mob of people", was originally a contraction of "The Mobility", a term used to describe the random citizens who appear out of nowhere to watch fires and other urban catastrophes in progress, in deliberate contrast to "The Nobility". Apparently puns were just as annoying in the 1700s as they are today.