desj@brahms.BERKELEY.EDU (David desJardins) (03/26/86)
Here is an interesting topic that came up in a private discussion. I wrote: >>Two definitions are equivalent iff they define the same set of things. And Matt Wiener replied: >Only in mathematics! > >Just because things turned out to be the same, didn't mean they HAD to be >the same. Is 'heat' the same as the thermodynamic definition of 'heat', >(which I shall call td-heat) ? If so, what *was* heat >200 years ago? >Is td-heat the best definition of heat or merely the most useful definition >of heat? In other words, does td-heat capture the *meaning* of heat or >merely a physical law aspect of heat? > >My very ability to ask these questions, and to sense an underlying intent >behind the question convinces me that td-heat is only an operational aspect >of something wider. But what that something is is beyond my ability to >define. > >In other words, td-heat describes a particular relationship between a >microscopic configuration and macroscopic state, whereas, heat is merely >the macroscopic state, without the underpinnings. To me, heat and td-heat >describe the same things, not because they *mean* the same thing, but >because physical law is what it is and not something else. Unfortunately (?) you have stumbled onto another of my favorite topics: entropy and time-reversal. The answer, which I feel very confident about (as opposed to my philosophical ramblings) is that heat (like entropy) is a *statistical* property. And, in fact, heat is the statistical abstraction of td-heat. To explain what that means, I am going to give you one of my standard examples. I am going to use very classical models of matter, although I am pretty sure that more modern physics can be incorporated later if need be. Suppose we take a block of wood and let it slide down an inclined plane. When it reaches the bottom its gravitational potential energy has been converted to heat. But at a microscopic level all that has happened is a series of collisions/interactions between particles. And in classical physics all of these interactions are time-reversible. So now take that block and reverse the direction of motion of all of its component particles! We still have an equally random distribution of energy (td-heat). And also reverse the direction of motion of all of the components in the inclined plane. Again nothing deep, the same amount of td-heat. But now what happens? The td-heat gets converted back into gravitational potential energy as the block slides back up the plane! All of the time- reversible interactions that just took place are reversed! It looks like our td-heat wasn't really random enough! It was just right to make the object slide back up the plane! But of course *every* possible distribution of heat energy is going to behave this way in *some* (very unlikely, of course) situation. Does this contradict the laws of thermodynamics? Of course not, because they are *statistical* laws. When you talk about an object with a certain heat, you are really talking about a "typical" object with that td-heat. And, in general, you can also do the converse, in that an object with a specific td-heat can *generally* be expected to behave as a typical object with that heat. But nevertheless each object individually *can* have its own behavior; thermodynamics just talks about the statistical behavior of them all as a class! All that thermodynamics is is *statistical physics*. Take the laws of physics, apply them to large collections of particles, and you find (!) that these large collections behave in ways that can be understood without any analysis of the motions of individual particles. You only need to measure a few statistical properties (like heat!) to predict the statistical behavior of these systems. Entropy lets you predict the probability of exceptional event like the block sliding up the plane; the probability is exactly the exponential of the difference in entropies! Now the fact is, that our universe *does* consist of large collections of particles. So we *do* in fact *see* this sort of statistical behavior. We can see that there is a fundamental property that we call heat, *even if* we don't understand the fundamental nature of this property! As an interesting aside, if our universe were less complicated it would be harder to understand! If there were only 10^4 atoms/human the statistical statements would not be nearly as strong! And so the behavior of a chunk of matter would be much *harder* to analyze, because you *would* have to deal with the motions of the individual particles. -- David desJardins
torek@umich.UUCP (Paul V. Torek ) (03/26/86)
Heat is too the same thing as its microphysical realization, and it was even 200 years ago. What are different are our *ideas* of temperature and mean kinetic energy. Pardon my naive realism, but the idea of a thing and the thing itself are different. --Paul Torek torek@umich
weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/28/86)
In article <541@umich.UUCP> torek@zippy.UUCP (Paul V. Torek ) writes: >Heat is too the same thing as its microphysical realization, and it was >even 200 years ago. What are different are our *ideas* of temperature and >mean kinetic energy. Pardon my naive realism, but the idea of a thing >and the thing itself are different. No one denied that heat and td-heat (the microphysical realization of heat) are the same thing. Indeed I said as much in my article. What is unclear is whether 'heat' and 'td-heat' *mean* the same thing. ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
torek@umich.UUCP (Paul V. Torek ) (03/29/86)
In article <12736@ucbvax.BERKELEY.EDU> Matthew P. Wiener writes: >No one denied that heat and td-heat (the microphysical realization of heat) >are the same thing. Indeed I said as much in my article. What is unclear >is whether 'heat' and 'td-heat' *mean* the same thing. Well, what sort of "meaning" are you after? Apparently not reference. Maybe something more along the lines of Fregean "sense" (a way of thinking about a referent)? Well, that's up to English speakers to stipulate, and now that we know that heat == td-heat, why not make them mean the same? --Paul Torek torek@umich
desj@brahms.BERKELEY.EDU (David desJardins) (03/29/86)
In article <541@umich.UUCP> torek@zippy.UUCP (Paul V. Torek ) writes: >Heat is too the same thing as its microphysical realization, and it was >even 200 years ago. What are different are our *ideas* of temperature and >mean kinetic energy. Pardon my naive realism, but the idea of a thing >and the thing itself are different. We make models of the universe. These models have properties which we give names. One very effective model is called thermodynamics and it contains concepts called "heat" and "entropy" (among others). The "laws" of thermodynamics make statements about the behavior of large- scale systems based on these macroscopic variables (e.g. heat flows in a certain direction). This model has three main weaknesses. It describes only macroscopic and not microscopic behavior (e.g. energy distribution among individual atoms/molecules). Its correspondence with the real world is not precise (it is impossible to come up with a consistent definition of heat that applies in all cases; for example is vibration in a normal mode of a crystal lattice "heat"?). And its predictions are only *statistical*; that is, even given an appropriate correspondence with the real world its predictions can (with small probability) be incorrect. What we are doing here (Platonists and conceptualists agree) is defining an *abstract* concept called "heat" which satisfies certain ideal properties (always well-defined and always obeys the laws of thermodynamics). It is this *concept* that is useful in actual scientific practice (e.g. we pretend that a thermometer actually measures this ideal quantity). "Td-heat" (which Matt and I are using to describe the actual heat computed from the actual velocities etc. of the constituent particles) does not satisfy any of these properties (even if you could define it in general, which you can't). In particular the "laws" of thermodynamics are *not* laws when applied to this actual quantity, but only statistical approximations. I guess I am saying that I agree with you that "heat" and "the concept of heat" are not the same thing--the actual heat in a physical body is what I am calling "td-heat," and our idea of what that heat represents is what I am calling "heat." Maybe I should give the latter its own special name ("id-heat," for ideal) to avoid confusion. -- David desJardins