Vanity thought #963. Below zero

This year started with a quiet announcement that scientists have achieved a seemingly impossible feat – created a negative temperature. Actually, it wasn’t even for the first time but no one talks about it because the explanation is too technical for average people. Still, how could it be possible? Read on.

We all have been taught about absolute zero, 0k, the starting temperature point on Kelvin and Fahrenheit scales. By definition there cannot be a negative temperature then. Even 0k itself is unachievable, it’s just a theoretical limit. Thermodynamics, as we’ve been taught, do not allow for it for one simple reason – you can’t cool a system to the temperature of the coolant, you can approach it but the coolant will always be just a smidge cooler and your system will always be just a smidge warmer. We can’t cool a system to temperatures below the coolant either, so if we don’t have cold stuff at 0k temperature we can’t cool anything to it. How did they get negative temperatures then?

There’s a lot of weird, counterintuitive stuff going on at the edges of modern day science. Quantum mechanics is full of such illogical, irrational magic. There are things like uncertainty principle and quantum entanglement that go against everything we observe in real life, what to speak of matter being made of vibrating strings in twenty six different dimensions. This negative temperature, however, is not about quantum mechanics, it’s our familiar, general stuff science gone unhinged.

If we have a bowl of soup we take a spoon, put some soup into our mouth, and we will know whether it’s warm, cold, or burning hot. Indians are smarter than using spoons, they eat with their hands and so nothing dangerously hot can burn their tongues, they test the stuff with their fingers first. Not to be left behind, civilized westerners invented thermometers. You stick a thermometer in and you know the accurate temperature. It’s not only about soup, of course, we can measure temperatures of lots of things and then have weather shows to tell us about the results.

We can’t measure everything, though, and that would be unscientific, because in science we have theories and formulas and we can accurately calculate things like temperature or energy without actually touching the stuff.

So scientists pondered this for a while and came up with a mathematical definition of temperature. Turns out it’s a ratio between changes in energy and changes in entropy. Energy is easy – you heat soup up, you add energy, so the change is positive. What is entropy, however? It’s one of those things that thermodynamics can’t live without, it’s everywhere in their formulas, it’s one of their fundamental features, but it’s hard to define in layman’s terms and even if you do you’d be left wondering why you needed to invent such a complex thing in the first place.

For the purpose of this post, entropy is a degree of variety in a system. By system I mean a quantity of water, gas, etc, that we assume to be isolated from the rest of the world so we can control and measure all energy added or extracted from it, a pot of water on a stove, for example. So entropy is a degree of variety within such system, a degree of disorder.

When the pot of water is just sitting on the stove it’s temperature is uniform throughout, water is at a room temperature then. If we turn on gas and start heating it water at the bottom would become hotter, it will start rising up, and we will have a much bigger variety of temperatures in the pot – cold regions lowering down, hot steams rising up, it becomes a one big mess with bubbles everywhere – entropy increases, variety increases, disorder increases. At absolute zero there’s no energy in the system whatsoever, it’s absolutely uniform, so entropy is zero, too.

Now, usually in the observable world, if you add energy to the system you increase its entropy, so both changes are positive and so temperature, which is mathematically defined as a ratio of these two changes, is positive, too. To achieve negative temperature you need to add energy and see entropy decrease. Then one change will be negative, another positive, and the result of the division will become negative, too. Very simple.

Theoretically, it’s just straight math from fourth or six grade, I don’t remember. Is it possible in real life, though? Theoretically, yes, scientists have figured out such a system a long time ago. Practically, they manage to create it just in these past couple of years. How? Read on.

Entropy, variation, is actually variation in energy levels of all the molecules in the water or gas. Some have higher energy, some have lower. Usually higher energy means that molecules fly around faster, it means they have higher kinetic energy. That’s what they have taught us at school, too. There’s no limit on kinetic energy, even if molecules start flying at the speed of light there’s still no theoretical limit on how much kinetic energy they can have.

This means that if you heat up a system some molecules in it start moving faster. Say you warm the pot for one second, one molecule starts moving faster. Which one? You don’t know, there’s no way to know, any one out of millions in a pot could have move anywhere it wants. After two seconds there will be two of these rogue molecules moving somewhere at unknown speed, after three seconds three molecules will rise up. Where are they? It’s impossible to know, the variety in the system, entropy, increases exponentially.

That’s what we observe in everyday life and that’s why our temperature is always positive (not counting Celsius scale, of course).

What scientists proposed is a system where adding energy would not translate into movement of the molecules. There are other ways molecules and atoms can absorb energy while staying in one place. We still don’t know which ones out of millions absorbed it and in what way exactly, so entropy, variety, disorder, and uncertainty still rises, but not so fast anymore.

Then we imagine situation where we have very high degree of control over how exactly molecules absorb energy, let’s say they start spinning in a certain way. Molecules and atom spins are not random, though, there is only a certain number of possible speeds and directions, so our knowledge of the system becomes more and more complete. The disorder still rises as we add heat but not so fast anymore.

Then we reach a tipping point where we know that nearly ALL molecules are spinning in a certain way with a certain speed, nearly all of them reached their high state of energy. Now we have maybe 5% that are in the low state, then 4%, then 3% – this is where entropy, variety and disorder, decreases. We still add energy but entropy does not grow anymore, its change becomes negative, and so when we divide positive change in energy by negative change in entropy we get a negative result – negative temperature. Voila.

As I said, theoretically it’s a straight up math, practically it’s hard to achieve but not impossible. In this latest case they fixed atoms in space by using magnets and lasers so that they don’t move around anymore, then they kept adding energy to the point where nearly all the atoms were certain to be in their high spin state, and that gave them negative temperature.

Does it mean that it suddenly becomes colder than the absolute zero? No, it still becomes hotter than before. The weird part about this math is that with this formula of first rising and then falling entropy temperature starts at zero, reaches positive infinity, changes to negative infinity, and reaches “negative zero” after that. What could be more counterintuitive?

Our usual number scale start from negative infinity, reaches zero, and then goes to positive infinity. With their definition of temperature they cut this scale in half, took the right part, from “positive” zero to positive infinity, and glued it before the left part, so it became zero, positive infinity, negative infinity, and then zero again.

To avoid this mess some propose to redefine temperature in the formulas so that it grows in a traditional way. However, it would completely mess up how we perceive temperature in everyday life, and we can’t have that.

And this is I became so interested in this subject – science is not as straightforward and logical as people like Neil DeGrasse Tyson make it sound on shows like Cosmos. We still have nine episodes to go so there’s a possibility that he mentions some weird stuff later on but so far his narrative has been safe. Stick to grade school, generic science, avoid controversies, and if any counterintuitive subjects come up, like black holes from episode 4, drown people with CGI graphics and speeches of awesomeness and wonder without showing even a slightest sign of confusion.

If they presented people with science as it is, with all its complexities and obvious irrationality, lots of them would stick to reading the Bible where they are at least straightforward about God working in mysterious ways. NDT presents science as mysterious only in a sense that we still don’t know something, not in a sense that it doesn’t make sense in what we already know without some mind twisting explanations that leave everyone confused.

That entropy thing, the fundamental principle of all modern science, they still don’t agree on it. They agree on definitions but once you try to explain it in simple language there are all kinds of objections. Physics will explain it in a way that chemists would find incorrect, chemists will propose an explanation that statisticians might not be comfortable in return. Statisticians get involved because entropy is about disorder, which is a statistical distribution of all possible states, so it’s not only about temperature and physics, it’s about information systems, too.

What it ultimately leads to is that our illusion of knowing things about this world is just that – an illusion. The world appears logical and reasonable only within relatively narrow limits of our everyday experience and everyone, and I mean everyone, can be pushed to the limits where his brain would just explode with confusion. Science pushes these limits everyday but it hides its realizations from us to lull us into a false sense of security. If one dude figured it out then the rest of us don’t need to worry, they assume.

In the meantime we are being fed some fairy tales and given assurances about science to spare us the trauma of knowing the real thing, and we choose the safety of this illusion ourselves.

As devotees we shouldn’t fall for that, one way or another, we should know that this world is not safe nor sound. Today I talked about temperatures below absolute zero, earlier I talked about infinite addition making up a negative sum, or we could always mention things like birth, death, old age, and disease as everyone can easily understand that without racking their brains.

We should not trust this world at all.

PS. In case you wonder, that magic gas at negative temperatures is hot but not too hot. Without letting atoms fly around and increase their kinetic energy there’s a limit on how hot it could get. It’s not like you could stick your finger into it but it’s not as hot as boiling water. I think they mentioned that its total energy was less that that of one milliliter of hot water, so it’s nothing. Just weird math.

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