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Lecture 24: Eternity Paradoxes

There was just one hitch in this wonderful synergy of atomism and thermodynamics; if thermodynamics were true, then the universe could not have existed forever. It would have run down long before eternity. The whole problem, of course, is that eternity is a very long time, which materialists insisted upon in order to avoid the question of creation. But if eternity really were that long, there were a number of glaring inconsistencies, especially in astronomy, but more specifically, with general physics that could not be explained away. Since Maxwell, like Gassendi before him, had not wed atomism to anti-creationism, it is significant that these puzzles were of metaphysical origin, not physical. That is, the whole problem was that Epicurean metaphysics was getting a free ride with atomic physics, and intentionally so, for there was a great desire to use atomism as a vehicle for crushing Augustinian metaphysics. Could Gassendi or Maxwell be vindicated, could atomism be a valid physical theory without the anti-creationist metaphysics? I will take the scientifically unpopular view and say no, that metaphysics is essential to the formulation of physics. As Thomas Kuhn described a century later, Maxwell's attempt to fit atomism with Christianity is symptomatic of a "paradigm shift", when conflicting evidence is gerry-rigged into the creaking system. It convinces no one so well as oneself, and in the end, dies an unlamented death. Thus it was entirely appropriate that Deism languish in the grip of materialism. But materialism too, had a few problems left to address.

Since cosmology, as Tyndall claimed, was the battlefield for materialism, it is appropriate that Astronomy should be the scientific answer to Augustine. That is, if there were a scientific answer to Genesis, it would lie in cosmology, a subfield of Astronomy. Unfortunately Astronomy was not a sure bet either, for it had a number of "eternity" puzzles, that did not fit easily into a materialist metaphysics. As the blackbody radiation problem or the photoelectric effect were to physics, these niggling details became in the 20th century, the undoing of astronomy. Let us list a few of these "eternity" puzzles.

Self-gravitation:

Olber's paradox:

Thermodynamics:

Thermodynamics, a brief introduction

Perhaps this paradox requires a little more elaboration. Remember that one of the victories of 19th century scientific materialism was the proof that all matter is made up of atoms. We know this about water and air and rocks because we can do experiments with them, as Maxwell demonstrated in his lecture. But how can we be so sure that stars, as Aristotle conceived them, are not made of more heavenly stuff? What evidence do we have that the whole universe is composed of atoms? That is where the subdiscipline of Thermodynamics comes to play.

The field of thermodynamics, as most fields in science, arose from the need to build better heat engines. If you recall, the industrial revolution began with the harnessing of water power, with vast mills built beside fast-flowing rivers, such as Burlington VT. A water wheel (or whole fleets of water wheels) would drive a huge leather belt that ran the length of the mill, and every machine had its little belt driven off of the main shaft. This was transformed by coal fired steam engines, that enabled, for the first time, for a mobile energy source. No longer were the industrial machines of the 1800's bound to a location near a river, but wherever coal could be shipped. (The leather belts remained, however, until electricity provided a means of liberating machinery from its tether.)

The first steam engines of James Watts design were hardly efficient, gobbling enormous buckets of coal to operate, such that they were initially only used at coal mines to run the pumps. Many bright young engineers improved on the steam engine, until it became the marvel seen today in vintage steam locomotives. A very modest amount of coal could now be used to propel an enormous piece of machinery. Just how efficient could engineers make this system? Could it ever be run on so little coal that, say, the boiler could be heated at the roundhouse and return without restoking? One needed to know how much energy it took to run the engine and how much energy was in the coal. Benjamin Thompson, an American scientist before the Revolution (where he spied for the British, and thus abandonned his hometown of Woburn, MA) had shown that one can harness horses to a cannon boring machine and generate heat from work. Studying these equivalences seemed to show that energy can be converted from one form to another, say, from heat to motion, but never destroyed. This became known as the first law of Thermodynamics.

Many other relations followed from this. One could hook up a heat engine to a refrigerator. If the refrigerator were perfect, it could return the heat that the heat engine needed to operate. If it were perfect, this would produce a perpetual motion machine, but since the Garden of Eden mankind has been cursed with perpetual work, making such machines impossible. By this sort of reasoning, it was possible to show that one cannot efficiently turn heat into work, and then use that work to generate more heat to run itself forever. The name given to this "rule" was the 2nd Law of Thermodynamics, "Entropy must always increase." A bright French engineer by the name of Sadi Carnot, worked out the properties of steam (or of any heated gas), and concluded that to take water to steam, expand it, collect the work of pushing a piston, cool it and start over again, could be plotted on a pressure-volume graph. The states of this closed cycle engine did not retrace precisely its steps on this graph paper, but made a triangle or rectangle whose area was equal to the work produced, and in which the heat is added in a known way (boiling the water). In such a way, Carnot was able to calculate the maximum amount of work that could be extracted from a given amount of heat input. It turns out to depend on the temperature; the higher the temperature of a given amount of heat, the more work could be done. I like to think of this as better quality heat, (sort of like a better water heater for your shower), or equivalently, the lower the entropy. This "efficiency" calculation, relating entropy and temperature, was given the title, "The third law of Thermodynamics".

All of these Laws of Thermodynamics were worked out with gases and steam engines and chemistry sets. In other words, it was an empirically derived science based on macroscopic (large scale) properties of matter. Powerful in itself, it was not yet fundamental physics until its theorems could be based on the mathematics of statistics. This was the work Maxwell began, and Boltzmann developed. One of the first things that Boltzmann did when he got hold of Maxwell's equations, was to take the experimental discovery of his advisor, Stefan's law of temperatures that the energy radiated by a hot object rises as the fourth power of the temperature, and prove this result mathematically by assuming the existence of atoms. This was a powerful argument for the existence of atoms, since just about everything hot will glow according to Stefan's law. It allowed physics to replace empirical laws with mathematical theorems.

The power of this accomplishment cannot be understated. A rule that was empirically derived from observations, an inductive generalization from a limited set of data, could always be disproven by new observations. "Mr Kent, this kryptonite doesn't obey Stefan's Law of temperatures!" But when an empirical result can be proved to be the result of a mathematical theorem concerning large collections of atoms, it takes on the nature of deductive truth. "Well then, kryptonite cannot be made of any atomic material science knows about." That is to say, thermodynamics was based on measurements of laboratory matter, and could not easily be extrapolated to astronomical objects like the Sun. But when Boltzmann found a relation between atoms and light, he enabled future astronomers to analyze the light from stars and infer many of the properties of the stars. In such a manner, stars were found to be made of all the same ingredients as earth-based materials. Thus Boltzmann's pioneering work enabled Thermodynamics to explain not just Earth, but the entire matter of the Universe.

To summarize these results, a hot atom will transfer its excess heat to a cold atom, useful motion always decays into less useful random motion, entropy always increases. The power of thermodynamics, then, was that atoms everywhere and at all times and places must obey the same laws. Either thermodynamics is true everywhere, or it is not true at all. So we come at last back to the eternity paradox. If the Earth violates thermodynamics by remaining temperate, despite being heated by all the stars in the universe for a very very long time, there is a serious problem that physics alone cannot solve. The irony is that the very tool used to vindicate materialism is now also sharpened against materialism. (Thermodynamics continues to cut both ways, and is a topic often subject to scientific agnosticism, disguised with the nearly incomprehensible word, "entropy".) Let me state this one more time. The power of statistical mechanics is that it generalizes thermodynamics to all atoms everywhere, so if the universe does not obey statistical mechanics then there is a serious problem either with our cosmology or our thermodynamics.

Conclusions

All these puzzles arrive because of the assumption of the eternity of the universe, which despite our attempts to minimize, is a really long time. And all these puzzles vanish when one adopts Augustine's view of creation. Despite this easy solution to the problem, prior commitment to materialist metaphysics kept nearly all scientists muzzled. Thus these self-contradictions within scientific materialism were labelled "paradoxes" and left for future (materialist) science to explain. It is an embarassment, but scientific agnosticism is far too often employed to maintain or even evangelize for a self-inconsistent metaphysic. To a certain extant, the abandonment of logic evident in late 20th century post-modern critique has its precursors in late 19th century metaphysics. One could reinterpret Thomas Kuhn's "Structures of Scientific Belief" to be not about theories, but about metatheories, or metaphysics. His paradigm shift is a truly a metaphysical war, in which the victors rewrite the history to claim the utter rationality and invincibility of their arguments, while the battlefield is littered with the corpses of true observations and factual conclusions.

Yes, at the end of the 19th century, scientific materialism had won the battle on the power of atomism and thermodynamics, but it was to prove a short-lived and Pyhrric victory that the 20th century reversed.

Last modified, April 30, 2002, RbS