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.


At February 28, 2006, Blogger JeremyHussell said...

There are other possible infinities too. For example infinitely fast (which seems to have been ruled out), or infinitely massive, or indeed infinitely <insert property of particle here>.

At March 08, 2006, Blogger Pharaohmagnetic said...

Great Posts.

Infinity is indeed a fascinating concept, and there's a great treatment of it here.

In this book, David Foster Wallace shows how pretty much the entire history of science and philosophy hinges on the fundamental issue of infinity.

There are many popular books about Cantor and his theories on the denumaribility of sets, but this one is refreshingly terse, casual, and technical all at the same time.

The first conceptual question on infinity is not "how fast" or "how massive," but "how many?" At which point the answer may indeed represent something "real," especially if subject of the question is "parts." It's a question that bothered everyone from Plato to Dedekind.

At March 11, 2006, Blogger JeremyHussell said...

Yes, "infinitely many" is a good one. If it really exists, it automatically implies either "infinitely small" (for the objects in question) or "infinitly large" (for the universe which must contain them).

Zeno's paradoxes are a simple explanation of why infinities cause problems. Although we've invented some math that deals with infinities without too much trouble (the rigorous formulations of calculus, for example), it would be interesting if these problems were resolved in the real world by there simply not being anything that is infinite in any way.

Of course, there may not be any way to determine this. (See The Particle Nature of Light.)


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