The hunter's horn is ringing in my mind
Echoes across the landscape of my soul
Truths all elusive I set out to find
Knowing that I will hunt them to thier hole
Or fox's earth where they lie curled so warm
'Til unexpected hands reach in and haul
Them into air so cold; they yelp, forlorn
Not knowing that they're safe, wrap into ball
Of self-protection that needs teasing out
Until a little nose lifts up to sniff the day
Then happy voice is raised in joyful shout
Upon their feet I send them on their way
For truths long hid in hibernating earth
Need strong warm hands to prove to them their worth
I'm trying to show that we can know the number of possible states a system has, and from that we can know if the particles that constitute the system are distinguishable: that is, if it is possible to know by any means whatsoever which particle is which. This is uncontroversial, but it seems something that many people outside of the physics community seem unaware of, and within the physics communtity I think there's a lack of appreciation of its significance.
Before going on, there's an important distinction between the quantum world and the classical world. "Quantum" means "bit" or "piece" or "unit". When things are quantized, they come in discreet rather than continuous increments. This is very important when considering the number of states a system can have. Classically, systems can infinite numbers of states, because everything varies continuously. In the example of the bead on the wire, the most miniscule change of the bead's position or momentum would constitute a new state.
But in the quantum world--that is, the world we live in--there is a smallest possible change in a particle's position or momentum that is distinguishable. Any change smaller than that is invisible behind the veil of the uncertainty principle, and therefore, as we shall see, does not exist. This means that for quantum systems, we can just count the number of distinguishable states that the system may be in, and as the arguement I'm developing here will show, "distinguishable" does not mean "distinguishable by us" but rather "distinguishable as such."
The question now is: how do we tell how many states are available to a system? The short answer is: we measure its heat capacity.
In the systems we've considered so far the particles or beads have been free to move without bound along at least one line. Most interesting physical systems aren't like this--they involve particles that are bound somehow, limited in thier range of motion. Solids and liquids, for instance, consist of atoms that are bound in place (in the case of solids) or bound by the surface (in the case of liquids). In a solid, each atom is free to move just a little way back and forth. It still has as many degrees of freedom as a free atom does, and it still requires six numbers (x,y,z,px,py,pz) to specify the state of an atom, but the atoms can no longer move freely. Instead, they vibrate in place.
There's a name for the energy stored in these vibrations: heat.
The extended argument under "Physics" must seem a bit diffuse, and it probably is. The problem is that I'm trying to write things that people with no background in physics can understand, which means bringing them up to conceptual speed. Doing this kind of thing makes me really aware of the power of abstraction--I was able to explain the entire argument I'm developing here to Barry Hill-Tout in about five minutes, because he already knew all the basic abstract ideas, and it was just a matter of me showing him a slightly different way of putting them together.
The point of all this is three-fold: to clarify the argument in my own mind, to put it in terms that Carolyn can deal with, and to popularize some of these ideas. The third purpose is mostly incidental--the first two are about equally important to me, and are pretty close to each other, because if I can't make it clear to Caro, then it probably isn't clear in my own mind, and the whole point of making it clear to her is so she can help me make it even clearer, less ambiguous, and most importantly free of error. She's much better at logical thought than I am, having been formally trained in it to a degree that I am not.
|Poem||Sonnets are generally too metrically strong for my current taste, although I still play around with them. I showed this one to Caro and she said she was in suspense while reading it, thinking I was going to kill the little critters off! Would I do a thing like that?|
|Movies||In following up on King Arthur, rented Excalibur, which is a pretty good film. It works the elements of the story fairly well, putting together a much more sensible narrative than Tennyson or (presumeably) Mallory gives us. The best bit is that the ending is completely changed, so that the forces of good (such as they are) really do triumph, rather than going down to a pretty sordid defeat as they do in Mallory.|
Deciding that lighter fare was in order, I'm finally getting around to finishing Hitch Hiker's Guide to the Galaxy, which is as entertaining as I remember.
The manic inventiveness and spoofing of the conventions of science fiction is as fresh now as it was twenty years ago.