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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.
  1. Self-gravitation:

  2. If, as Newton claimed, a gravitational attraction were present betweeen any two bodies with a force proportional to the product of the two masses and inversely proportional to the square of the distance, then what is to keep the universe from collapsing into a single blob? A glib answer is that they are so far away. But Newton's law doesn't say the gravitational force goes to zero, it just gets small. When a small number is multiplied by infinity, infinity always wins. Even if the force were miniscule, say, a fly's sneeze acting over eternity should have profound effects. The only proposed way to avoid this consequence is to assume that the matter in the universe were distributed so evenly as to cancel out the attractive force. Worse than that, one must assume that something actively kept the universe as smooth as butter lest the slightest wrinkle or perturbation should initiate a catastrophic collapse. For a materialist, that answer was worse than the problem.

  3. Olber's paradox:

  4. Any 5-year old can ask, as Heinrich Olbers asked in 1826, another conundrum. If the universe extends forever, and there are an infinite number of stars, infinitely far away, then why is the night sky mostly black? Shouldn't we see a sky packed cheek to jowl with stars? The glib answer was, well, there's dust out there too that absorbs the starlight. But with the success of thermodynamics, we know that every object will eventually come into temperature equilibrium with its surroundings, so if the dust is absorbing starlight, even the dust should eventually rise to the temperature of the stars at some point in eternity, and glow with white hot heat. If the sky is dark, then either the stars are not eternal, or the heavens do not obey thermodynamics, neither a popular materialist position.

  5. Thermodynamics:

  6. For that matter, if the earth is surrounded by hot stars for an eternity or two, why isn't it and us, at white-hot heat? And why would there be any termperature differences at all in the universe? Wouldn't maximum entropy require that the universe all arrive at the same temperature, in the famous "heat-death" end of the materialist universe?

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.

19th Century 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.

20th Century Creation

(This lecture parallels the Augustine lecture, mentioned early in the course.)

The 20th century dawned with physics at its zenith. Not one, but several famous luminaries made predictions that all the basic physics was understood and mathematically described with a few minor puzzles that just needed a little tidying up. This triumphalism meshed perfectly with the spirit of the age. In Germany, Hegel could write about the high spiritual attainment of civilization. In England, hymnwriters were extolling the immanent arrival of the Millenium, the 1000 years of peace and prosperity promised in the final book of the Bible. Mark Twain commented on the turn of the century as "the gilded age", when net world trade had reached a peak not exceeded until the late 1980's. So it is not surprising that physicists should have gotten so cocky, everyone was.

So in 1905, when Albert Einstein published his papers on "special relativity" and "the photoelectric effect", it had the impact of a bombshell on smug scientific complacency. The world was not as advertised, indeed, not even as it appeared. The full consequences of these two papers were not appreciated by the young, 24-year old Einstein, but grew greater with each passing year culminating 40 years later in a fireball that outshone the sun in the high desert of New Mexico. Although the full significance wasn't immediately appreciated, nonetheless, all of the great physicists of those decades: Bohr, Einstein, Fermi, Pauli, Heisenberg, were unsettled by the metaphysics revealed in these discoveries. For both papers deeply undermined scientific materialism.

Let us summarize then, the consensus view of materialism that was so deeply shaken. Remember Newton's trinity of time, space and matter. Two centuries of work had elaborated the third point slightly with the thermodynamic laws for particles, which we expand as below.

  1. Time is eternal
  2. Space is infinite
  3. Matter is indestructable
We have mentioned three eternity paradoxes that have trouble with this materialist trinity. a) Newton's paradox, which asks whether or not all the stars would have coalesced from gravitational attraction given an eternity; b) Olber's paradox which asks whether the night sky should be white, which is to say, if one looks long/far enough in any direction one should find a star; and finally c) Entropy paradox which asks why there should be any temperature difference at all after an eternity in a constantly increasing entropy universe.

Various solutions were proposed, none were very satisfactory. Newton supposed that an infinite universe with no edges and very evenly distributed matter might be in gravitational equilibrium. Olber's paradox was supposed that either dust obscured the stars (which was only a temporary solution, since eventually the dust would be as hot as stars), or the universe was finite. The entropy problem had no good solution, other than to suppose that an infinite supply of matter in an infinite universe might not reach thermodynamic equilibrium for an infinite time, or perhaps that the universe was not eternal. The answers varied, but you get the drift. After a few infinities, the mind would boggle a bit and accept anything. It was into this muddied cosmology (wrested from theology!) that Einstein's theory started giving answers no one particularly wanted.

Einstein's Special Theory

SpaceTime

As is well known, Einstein was a firm believer in symmetry and isotropy. He argued in a famous 1905 paper that if you had two physics labs, one in your garage and one on a train, the physics should look exactly the same no matter how fast your train was going. This answered the famous Michelson-Morley experiment that attempted to find a bias in the speed of light travelling upstream or downstream to the Earth's motion through space. No, said Einstein, light travels the same speed in all reference frames. But this could only be done with a weird tranformation that squished space and stretched time. In fact, Einstein's special theory of relativity suggested that time = space. This immediately caused problems with the finite space solutions that might have solved Olber's paradox, or the finite time solutions to the entropy paradox. It also made the answers to one paradox tangle with all the others. For if space and time were the same, two of the four possibilities are excluded:
  1. time eternal, space infinite
  2. X time limited, space infinite
  3. X time eternal, space finite
  4. time finite, space finite
But the first solution is the one we were having all the problems with earlier. So it seems that Einstein is driving us toward the last position, the one for which Tyndall had previously destroyed in the name of materialism, the finite space & time solution which was the theological position of Augustine.

MassEnergy

A second consequence of Einstein's special theory of relativity showed up a few months after the first bombshell, 1905, in a very short 2 page paper entitled, "Does the inertia of a body depend on its energy content?" in which he argues for the rest mass of a photon, and argues that m = E/c2. (Nope, he never said E=mc2). Einstein's paper uses a somewhat arcane thought experiment, which I always believed was better illustrated by a simple TV monitor. We can time the electrons on their journey from the gun at the back of the monitor to their destination as a spot on the screen. When we up the voltage, we are increasing the energy, and simple physics suggests that the velocity of the electron should be related to Energy as E=1/2 mv2. That isn't what we find. Instead, the electron approaches but never exceeds the speed of light, no matter how much voltage we give the electron. So why won't it go any faster? Where does all the extra energy go? Well, it seems to have gone into the mass and gotten heavier, sort of like a retired prizefighter. A calculation of the extra weight the electron gained reveals the famous relation, E=mc2. But if energy can be converted into mass, can mass be converted into energy? Absolutely, as nuclear physics began to reveal electron-positron pair production from light, and their subsequent annihilation into light, the first discovery and Nobel prize going to an experiment using cosmic ray showers recorded on film high in the Alps, which showed muons and a whole zoo of nuclear particles produced in the energetic collisions of mundane matter.

That claim strikes at the heart of Newton's third trinitarian belief, the indestructibility of matter, and no doubt contributed to the cult status of this equation. For if Matter can be destroyed into or created out of energy, then we cannot really talk about laws of entropy and energy conservation! For if number or energy is not conserved, we can no longer argue that the entropy must always increase. But wait, surely a little theory can't reverse centuries of experience? Can't we just do some fine-tweaking of the theory. Could we construct something that looked like "mass-energy" conservation to replace it? This is certainly what is suggested in most physics books.

But the bookkeeping starts to unravel when we ask the question, "what is the gravitational potential energy doing?" The problem is that gravitational energy is negative. Depending on assumptions of where to "normalize" the gravitational potential, the total mass-energy content of mass, kinetic, and gravitational energy can be made anything one desires. Even more fundamentally, as QM later argues, the energy of a system is known only in inverse proportion to the time: ΔE Δt = h. Thus for short periods of time, the energy can be anything. All these arguments leave the concept of mass-energy conservation in a bit of a shambles. It works fine under most laboratory conditions, but fails to work at those critical moments when you most need it, like at Creation.

SpaceTime and MassEnergy

Einstein didn't leave well enough alone either. He kept working on the problem of acceleration, which wasn't in his original 1905 "special theory". Finally after 11 years of working on it, he published his "general theory of relativity" in 1916. In it he argues that just as physics looks the same on all trains, so physics should look the same in all elevators. That is, just as light travels the same speed in every reference frame, so light looks the same in all accelerated (whether by motion or by gravity) non-inertial reference frames.

A thought experiment is appropriate here. Suppose you are in an elevator far away from the earth, say, in intergalactic space. (Okay, Einstein should have said rocket ship, but perhaps elevators were high tech in 1916). You would like to know how fast you are accelerated, and invent the laser-pointer accelerometer. A small laser pointer is affixed to the side of the elevator and shines on the opposite wall where its position is marked. If the elevator accelerates, which you immediately notice by the extra weight you feel on your feet, then the light will fall behind the marked spot, simply due to the motion of the elevator during the time it takes the light to cross the elevator. That's reasonable enough.

But then, Einstein claims, this must also be true of the elevator sitting at rest in the basement of your office building. The laser pointer should make a spot lower down, because gravity is pulling down the light. "Gravity, affecting light?", you could almost hear the derision. But that is exactly what Sir Arthur Eddington found when he took an expedition in 1919 to measure star positions around the sun during an eclipse (when we can see the stars in the daytime!) The stars appeared to move closer to the sun, showing that the sun bent the starlight inward like a dent in a shiny fender. Suddenly Einstein was propelled to fame and glory, beyond that even of Isaac Newton. And suddenly physicists were struck with a dilemma greater than Newton's static universe.

Newton had feared that gravitational attraction would cause the stars to all clump together, but Einstein now demonstrated that not only the stars but space itself would clump together, producing what we now call a giant black hole. Einstein didn't know about black holes, and he certainly wasn't going to predict them, so he did what you and I would do in his shoes, he fudged the equations. That is, he added what he called "the cosmological constant" which just balanced the inward bending of gravity to keep space-time flat, sort of like a paintless dent repair tool. It should be clear that Einstein When Edwin Hubble, after painstaking nights of measuring the faint light from galaxies and passing it through a prism was
Last modified, Feb 24, 2003, RbS