As easy as putting one foot
In front of the other
Although now that I think of it
That took me about a year to learn
As well
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Methodical simplity: As easy as putting one foot In front of the other Although now that I think of it That took me about a year to learn As well |
| date | 2000-11-09:16:13 |
| Physics |
Here's another way of looking at STATE, lifted from Michael Jackson's book Software Requirements and Specification (no, not that Michael Jackson, the other one): A STATE is everything that is true of a system at one time. Different states are distinguished from each other by different things being true. This definition is interesting because it already carries with it the idea of the subject--truth and falsity are in my view properties of meaning, and meaning is a verb. Any definition of state must include the idea of time: STATE is the way a system is (or everything that is true about a system) at one time. Are these two definitions of STATE equivalent? When might they not be? ================================= HEAT is the energy stored in the random motion of atoms in a material. Any block of matter is in exactly one state at any given time. Different states will in general have different amounts of heat energy associated with them. But it's also the case that for any given amount of heat energy, there will be a large number of states that have exactly that energy. These states are distinguished by the micro-states of the atoms--consider two atoms, A and B. In one state A moves at 100 m/s and B at 101 m/s. In a different but energetically-identical state A moves at 101 m/s and B at 100 m/s, and all other atoms are the same as they were in the previous state. As time passes, the system bounces randomly from one energetically-identical micro-state to another, as atoms bounce off each other. ==================================== TEMPERATURE is a measure of how thinly spread the heat energy is across the energetically-identical states. In particular, T = dQ/dS, where Q is the heat energy, S = log(N) and N is the number of energetically-identical states available to the system. S is known as the entropy, and is a measure of the number of ways the system can be rearranged microscopically and still have the same energy. ==================================== The HEAT CAPACITY or SPECIFIC HEAT of a material is the rate at which its temperature changes as the amount of heat energy changes. That is, c = dQ/dT, and combining this with T = dQ/dS we get c/T = dS/dT. But S=log(N), so we now have a way of relating an emperically measureable physical property of a material (the heat capacity) to the number of possible states is has! This means that by looking at the heat capacity we can determine if the particles that make up the material are distinguishable or not, which is what the whole point of this argument is. ==================================== In ordinary materials, particles are distinguishable. All the particles in an ordinary crystal are distinguishable by their positions. But for some materials this is not the case, notably liquid helium. When 4He is cooled below 2.8 K, it's heat capacity becomes huge, because the number of energetically identical states it has becomes very small, because the particles that constitute it become indistinguishable, so all the trivial re-arrangements of this particle for that no longer introduce new states. The behavior of superfluid helium is described exactly by quantum theory, on the basis of the statistics of individual particles. There are many other cases where comparable results are observed. Ergo: it is empirically the case that indistinguishable particles are not just indistinguishable by us, but are indistinguishable absolutely, despite the fact that the particles are not the same particle. ================================== Corrollary: God does not exist. Proof: Definition: GOD--an omniscient, omnipotent being. Being omniscient, God would know the difference between indistinguishable particles. But this would mean that superfluid helium could not exist. But it manifestly does. Ergo, God does not. |
| Poem | Dear patient Caro has been trying to get me to think (or at least to argue!) more linearly for about a year. She recently pointed out that my argument in "Physics" was getting all diffuse again. So today I disciplined myself to break the entry up into the equivalent of index cards, as per her advice, and the bits of the argument that I've been struggling with fell seamlessly into place. |
| Reading |
Homer really pisses me off. It's been a good fifteen years since I read the Iliad and I'm now 100% with Plato on the subject: this stuff is bad. The poetry is beautiful--I think Fagles has done a much better job here than with the Odyssey--but the whole things is an apology for collectivism, obedience, violence and the glorification of the ethic of, "Rape, kill, pillage and burn." |