Opposites: Open and closed

Are they really so opposite?

As Niels Bohr used to say, the opposite of an ordinary truth is a falsehood, but the opposite of a profound truth is another profound truth. I offer this opposite pair:

1) All systems are open.
2) All systems are closed.

A closed system is a set of physical things which can be regarded as isolated from the rest of the universe. An open system, in contrast, is affected by things outside itself, even if those things are not directly observed. So these statements are certainly opposite. How are they both true?

What defines 'the system'?

Experiments try to isolate variables, but we can never achieve perfect isolation. Vacuum chambers are made of steel walls, and over time a few stray gas atoms always percolate in and out of tiny cracks or pores in the steel surface. No laboratory building is perfectly insulated from vibrations. High energy cosmic rays can pierce any barrier; and so on. It may be possible to achieve isolation that is excellent for all practical purposes, but all physical systems are open, strictly speaking. 

If we really want to speak strictly, however, then the very concept of a ‘system’ is inherently an approximation. There is really only one system: the universe. The universe as a whole is closed by definition, so all systems are closed. Of course, it is no less impossible in practice to describe the whole universe than it is to seal off a portion of the universe in perfect isolation from the rest. It is often possible, however, to describe a very large closed system.

And indeed this is precisely what we normally do, to identify the distinctive physical features of an open system: we analyze a large closed system, and then discard all the information that does not refer directly to the small sub-system that represents our ‘open system’.

So any system is open, if we want it to be: it is only a matter of how low we set our threshold for ignoring slight influences from external factors. Conversely, however, any system is closed, if we want it to be: it is only a matter of how large we are willing to make our system, to bring relevant external factors within its frame. The distinction between open and closed systems is an important one, but it is not a distinction between two different ways things can really be. It is a distinction between two different ways of thinking about things. Both ways can be good ways of thinking. Both truths are profound.

An engine would still run inside a large box.

It seems to me that too many physicists today have lost sight of the second truth, however. The most profound mystery that physics still faces is the origin of irreversibility. We don't understand why we can't remember tomorrow. And whatever is going on in quantum measurement, it seems to be an empirical fact that all quantum measurement devices rely crucially on thermodynamically irreversible processes to achieve their extreme amplification. No-one can find a clear explanation of irreversibility within closed-system Hamiltonian mechanics, but few people want to accept that our mighty science is still stumped by such a basic question after a century of breakneck progress, so most people like to think that the open system generalization must be the simple solution.

Open systems can't be the basic explanation of irreversibility, because all systems are also closed. Whether or not a system is open is not a physical fact, but an arbitrary choice of perspective in deciding what to include within the system. So the openness of physical systems cannot make a fundamental difference to anything; anything that can be explained as an open system must also be explicable as a larger closed system. A steam engine would still run, at least for a good long time, inside a big impermeable box.

A Cup of Heat, Monsieur?

Pierre-Simon de Laplace and Antoine-Laurent de Lavoisier
thought that heat was an invisible liquid.

18th century physicists thought of heat as something much like electricity: an invisible fluid that could flow through other materials or soak into them. They named this hypothetical fluid ‘caloric,’ and it was thought to be a distinct form of material, like air or water, only different. If an object had absorbed a lot of caloric, like a sponge soaking up water, then it was hot. If the caloric drained out, the object cooled.

This was a sensible theory. We all know that objects can become electrically charged and that this changes their properties. A charged balloon can stick to the ceiling, or make your hair stand on end; a charged metal sphere can give you a zap. Electric current really is an invisible fluid, composed (most usually) of material particles called electrons. Most of the time they are bound up in atoms, but when they come loose they can flow into things, or out of them or through them. Things can become charged by soaking up extra electrons.

Soaking up electric charge. 
(Image by Wikimedia user Dtjrh2, 
used under Creative Commons license.)

In a similar way, it would seem, objects can also soak up heat. Hot objects may expand or cause burns, just as charged objects stick to ceilings or shock people. Heat flows from high to low temperatures, just as electricity flows from high voltage to low. Appealing as it is at this basic level, the analogy turns out to work well even in finer detail. Antoine Lavoisier and Pierre Laplace developed an extensive body of caloric theory that was able to explain heating and cooling and many other thermal phenomena with quantitative accuracy. 

So in the eighteenth century it only made sense to think of heat as something similar to electrical charge. In the following century, heat engines and electric motors would be developed in parallel, and engineers would still think of them in similar terms. Today again people are deciding whether to have a car powered by an electric motor instead of a combustion engine, and the differences seem to be ones of practical detail. 

Today we no longer believe that heat is a material fluid, however. Why not? It's not really as clear-cut an issue as textbooks often make it seem, because today our concept of matter is not as simple as it once was. We know that not even electrons are really these indestructible little specks of hard stuff: they can be created and destroyed in high-energy collisions. And in a lot of ways we still treat heat as if it were a material fluid.

The bottom line, though, is that even though electrons can be born and die, electric charge can't. If electrons appear or disappear they do so together with positrons, so that the net change in charge remains zero. The only way for an object to become charged is for charge to flow into it from elsewhere—or for opposite charge to flow out of the object. There is no way to simply create charge from stuff that is not charge. Heat, in contrast, can flow into or out of things—but that's not the only way to get heat. One can also create heat, without importing it or already having it. It's called friction.

Rub your hands together. Feel it? That's heat. 

You didn't just create any new material substance from nothing. Big Bangs and particle colliders aren't as easy as that. So heat is not a material fluid. What is it, then?

Whatever heat is, you've just made some. It's right there in your hands.

Fire Glows

It's not just bright.

Humans discovered fire a long time ago, but for most of that time we only used it for warmth and light and cooking, rather as Bilbo Baggins used his magic ring for years just to avoid unwanted callers. Only in the 18th century did James Watt show up to play Gandalf, and reveal that our curious little trinket was the One Ring to rule them all. Fire has enormous power.

Even after centuries of technological progress since Watt, we still find it very hard to beat combustion as a source of power. Burning a tank of fuel releases enough energy to lift cargo all the way to the Moon, even with the horrible inefficiency of a rocket engine. Combustion provides energy, as one says, to burn. Why is fire such a tremendously greater power source than, say, clockwork springs or a windmill? I’ve never seen a clear answer to this question in any physics text, but I think I have found a succinct one of my own. 

Fire glows.

Light oscillates really fast.

The fact that fire glows demonstrates that fire is releasing energy from motions (of electrons in chemical bonds) with frequencies in the range of visible light. Those are very high frequencies, around 10¹⁴ cycles per second. As Planck taught us, energy is proportional to frequency. So if human energy needs are for motion at up to a few thousand RPMS, mere hundreds of cycles per second, combustion lets us tap energy resources on a scale greater by a factor of a million million. Combustion delivers so much energy, because molecular frequencies are so high.

This is what an engine somehow does.

It isn’t easy to gear all that power down by a factor of 10¹² so we can use it, though. Electrons whir around in molecules far too fast for our eyes to follow. We can’t just throw a harness over them. Even if we could, they are very light in weight. They bounce off things, rather than dragging them along. To tap them for power, we need some clever way of gently bleeding off their enormous but very rapidly whirring energy, a tiny bit at a time.  There's more to it than just installing an awful lot of tiny gears. 

Getting fire to do work means transferring power across a huge frequency range. That's what thermodynamics is all about. The reason that thermodynamics doesn’t seem very much like the rest of physics is that energy transfer across a huge frequency range is an extreme case, in which certain otherwise obscure aspects of physics become very important. That makes them important in general, though, because high frequencies can deliver so much power. It's well worth learning how thermodynamics really works.

Raising Water by Fire

James Watt dramatically improved the steam engine, but he didn’t invent it. In his time, steam engines were already a practical and economical success. The machines of Thomas Newcomen and Thomas Savery had already begun the new era in human technology. 

Savery had a head for marketing as well as for steam. In 1702 he produced a pamphlet advertising his device as “An Engine to Raise Water By Fire”. His description may have been poetic, but it was literally exact. His engine pumped water by burning coal. Its killer application was draining coal mines. 

Humans may have discovered fire in distant prehistoric times, but the really useful thing about fire was only discovered in the 18th century. Never mind cooking or smelting metal or scaring wolves: fire can raise an awful lot of water. And if you can raise water, you can do pretty much anything, because raising water means you can exert force.

Savery’s and Newcomen’s engines were crude and simple, and by that I don’t mean that they were primitively made, rattling too much or leaking steam. They were just stupid designs, compared to Watt’s machines. They didn’t even use steam pressure to actually do their work, but just let the steam balance atmospheric pressure. Then they condensed the steam, by shooting in cold water, and let the suddenly unbalanced atmospheric pressure do the work. Savery’s engine didn’t even turn any moving parts, but just sucked water through pipes. It wasn’t so much more than a proof of concept, like the aeolipile.

Hindsight is 20/20, of course, and it’s not really fair to call Savery and Newcomen stupid. Watt’s proper steam-pressure engines also needed stronger boilers. The point is that even the crudest engines were such a quantum leap in power technology, compared to wind, water, or animal power, that they rapidly changed the world. In effect they turned lumps of coal into unprecedentedly huge amounts of practical work. Up until 1775, the Russian navy had been using two enormous windmills to drain its dry docks at Kronstadt; each time they drained the docks in order to work on a ship, the draining job took a year. When they installed a single Newcomen engine, it did the job in two weeks.

With coal-fired steam engines, the human capacity to exert physical force suddenly soared. Even today, the biggest problem with changing to power sources other than combustion is that fire can provide so much more power than, say, sunlight or wind. We humans keep thinking wistfully about switching away from combustion, to some form of clean energy, but we really want to maintain our current energetic lifestyle. We're like a big city lawyer who wants to quit the firm and become a social worker, but also wants to keep up the mortgage payments.

Why is fire so very good for raising water? I have some thoughts on this, based on the fact that fire glows.

Vitruvian Machine

Sometime in the late first century BCE, the Roman architect Marcus Vitruvius Pollio described the oldest known steam engine: the aeolipile. Devices of this type were described again in the following century by Hero (or Heron) of Alexandria, who gave more detail about their construction. Aeolipiles were hollow metal tanks with angled vents, filled with water and mounted on a pivot over a fire. When the water inside the tank boiled, the jets of steam hissing out through the vents would make the whole tank spin.

While the later Hero is remembered more often than the earlier Vitruvius in connection with these ancient gadgets, Hero himself refers to even earlier work on them by another Alexandrian, Ctesibius. No writings by Ctesibius have survived, and although later writers attributed several inventions to him, they do not mention the aeolipile as one of them, so the actual inventor may have been even more ancient.

Hero’s explanations imply that aeolipiles were temple showpieces whose rotation astounded but did nothing useful. There are no records or remains to suggest that any form of steam power was ever applied practically in ancient times. But Vitruvius had a different notion of what aeolipiles were good for. He referred to the aeolipile almost as an ancestor of the particle accelerator: “a scientific invention” which could be used to “discover a divine truth lurking in the laws of the heavens.”

Vitruvius was still a classical writer. The book in which he mentions the aeolipile also expounds the theory of architectural proportion, based on the human form, whose illustration by Leonardo da Vinci would become the Renaissance icon of classical humanism: Vitruvian Man. Vitruvius had no idea of the enormous practical potential of steam engines. He mentions the aeolipile in a chapter on weather. The truths he learned from the spinning tank of steam were about wind, not heat and power.

The aeolipile was a toy. It could barely turn itself, much less produce the labor power of a single slave. A far greater advance in power technology than the aeolipile was the medieval invention of the collar harness, which let horses replace oxen as draft animals. The uselessness of the aeolipile is an excellent example of the vastly under-appreciated role of materials in technological development. Whoever invented the aeolipile was a brilliant scientist, who must at least partially have understood deep principles of force and reaction, and then made them work in a real device; but it would be two thousand years before vessels could be forged that would hold enough pressure to let steam power change the world.

Nevertheless the aeolipile did indeed demonstrate a divine truth lurking in natural law. It may not have shown just how much power a machine could deliver, but it showed that a machine could have power to move. It hinted at the future power of artificial heat engines to do work beyond the limits of the human body.

What is heat?

Heat is amazing. The energy you could in principle extract, by lowering the temperature of any amount of water by a barely perceptible one degree Celsius, would be enough to lift that same amount of water to a height of over four hundred meters. And the energy you could extract by condensing any amount of steam into liquid water would be enough to lift that same amount of water into space. This is why the Industrial Revolution was such a big deal. Harnessing heat, in fuel-burning engines that drive pistons or spin turbines with hot gases, is what has let us hair-challenged primates conquer the planet. Heat is magic. What is it?

Until the mid 19th century, people thought that heat was a special kind of fluid, like air or water but different, and invisible. They called it "phlogiston", or "caloric". Some considered that cold was a distinct fluid, "frigoric", while others argued that cold was simply absence of heat. These were by no means stupid or crazy theories. Electrical charge is a phenomenon which is about as basic and important as heat, and it really is carried by two different kinds of stuff, namely electrons and protons (as well as other much less common particles), which each carry opposite charge. Objects can become positively or negatively charged if they pick up excess protons or electrons. It was not silly to imagine that objects might become hot or cold by picking up excess caloric or frigoric.

But early physicists figured out that this was wrong, mainly from carefully observing how grinding metal keeps on making it hotter, even when the grinder and the metal are kept well apart from any other objects that might conceivably be able to inject a steady supply of caloric into them. They concluded that heat is actually some form of energy, and that the more familiar kinds of energy carried by moving objects can be converted into heat, through friction; while heat may in turn be converted into motion and useful work, in engines.

But then just what is the difference between heat and work, as forms of energy? It's not easy to get a straight answer even from a fully trained physicist, because the truth is that we're still not completely sure what heat is. If I have many bazillions of atoms all zipping around in a big box, bouncing rapidly off each other and the walls, making up a gas, then I can use statistical mechanics to say an awful lot about heat and pressure and temperature for this gas. But if I have one single atom, perhaps ionized and trapped in a strong electric field, I know that the concept of heat is not even relevant. With one atom, I can compute the motions of its nucleus and of its electrons, rather as I worked out the motion of solid objects in freshman physics. It does not even make sense to ask whether the atom is hot or cold. Usually no single atom has heat, but a billion atoms do. So heat is somehow an emergent property of large numbers of atoms together.

"Emergent property" is a fine bit of fashionable philosophical mumbo-jumbo, which spends rather too much time in the blogs of wild-eyed crackpots and tenured philosophers, to be comfortably welcome among respectable scientists. But in the case of heat, you can slurp an emergent property from a cup of coffee. Heat rules the world. It's quite concretely real. So what is it?

Well, we're working on it. There is ample precedent in perfectly well understood physics for new behavior to emerge in larger systems; it's just that in this particularly fundamental case of heat there are still some major obscurities in exactly how it works. But in just the past few years, atomic and optical physicists have gained the capability to make extremely precise and direct measurements on small samples of gas, with only hundreds to thousands of atoms. If heat emerges, we're soon going to be able to catch it in the act. Watch this space.

Statistical Mechanics

Most people these days have heard of quantum mechanics, and how it somehow brings chance and probability into physics on a basic level. This is a misleading truth, because actually quantum mechanics is perfectly deterministic, and not probabilistic at all, until we come to measure anything. Then the probabilities come in, and only then. The problem is that quantum measurement is a very subtle thing that is far from fully understood. And one thing we do know is that inferring how things really are, from how things look, is uniquely tricky in quantum mechanics.

To appreciate the subtlety of quantum mechanics, it helps to know about the older and less tricky place that probability has in physics: statistical mechanics. I doubt that most non-physicists have ever heard of statistical mechanics. In many places one can even earn a Bachelor's degree in physics without ever taking a course in it. This is unfortunate, because statistical mechanics is so important, that a physicist who doesn't know about it is like a Scout who doesn't know that fire needs air. Statistical mechanics is a sort of post-processing stage that has to be performed on virtually all the rest of physics — even including quantum mechanics — in order to make sense of anything but the very simplest and most controlled experiments.

Mechanics without statistics is the physics we learn in school. A rock flies through the air, falling under gravity. Ignore air friction, and model the rock as a point with a given mass — a particle. Apply Newton's Laws to particles: that's mechanics.

'In principle,' we may be told, 'the universe is a large number of particles, governed by Newton's Laws.' In practice, of course, most of these particles are beyond our control, beyond our observation, or at least beneath our notice. We do not see the vast swarms of air molecules that surround us and fill our lungs. And even if we could mark their paths, solving Newton's equations for so many interacting particles is far beyond our computational power. Thus do we see the vast gap between the pristine principles of physics, and the practical real world.

Bah. Physics doesn't care about pristine. Sure, part of physics is about trying to reduce everything, 'in principle', to some elegant little Theory of Everything. We're writing one big long footnote to Plato, who wanted everything to boil down to the five regular polyhedra. But that whole grand unified simplicity thing is really the hood ornament of physics, not the engine. The thing that drives physics is putting principles into practice, and codifying practice into principle. So no, the fact that we can't follow every atom does not make a huge gap between physics and reality. There is a whole huge branch of physics which is all about the principles and the practice of dealing with huge numbers of particles that cannot be individually observed, predicted, or controlled.

And that is the branch of physics called statistical mechanics. It uses probability theory to get the best results we can from what we do know, in spite of what we don't. Whether or not God plays dice with the universe, physicists do, to make up for the fact that we're not God.