[PBS Digital Studios chime] This episode is brought to you by Curiosity Stream. Winter may be coming, but be comforted; true, absolute zero is impossible. We'll always have quantum fluctuations to warm our chilly bones. [Space Time theme music] The mystical-seeming quality of heat is nothing more than the motion of a substance's component particles. Temperature is just a measure of internal kinetic energy. So then, the feeling of cold is the relative absence of internal kinetic energy. But what if we reduced temperature so much that all particle motion ceases? This state of absolute cold is the zero point in the Kelvin temperature scale, corresponding to −273.15 Celsius. Many experimental physicists have spent their careers trying to cool things to absolute zero. Using lasers and magnetic fields we've now managed to cool certain substances to less than a billionth of a Kelvin. Doing so has revealed some bizarre quantum states of matter. But quantum mechanics may also prevent us from ever reaching absolute zero. Understanding the limit to cold will lead us to an understanding of the nature of the quantum vacuum itself. We're all familiar with the states of matter;
solid, liquid, gas. Heat up any solid and eventually it'll melt into a liquid, pump in more energy and all liquids will vaporize into gas. Now that's not the end of it. Yet more heat causes electrons in any gas to escape the bonds of their atoms resulting in the less-known plasma state. In these states of matter, particles have an enormous range of individual energies; some moving or vibrating fast, some slow. Temperature just represents the average kinetic energy of the countless particles. And while a substance can theoretically have any temperature above absolute zero its component particles cannot. Those particles are quantum creatures; they can only occupy certain energy levels of vibration or motion. Much like the discrete electron orbitals in an atom. This quantum nature is revealed when we look at the spectrum of light produced as those particles hop between energy levels. This is the black-body radiation described by Planck's law. Its mathematical form was our first hint at the quantum nature of the subatomic world. The influence of the quantum world becomes far more apparent in the strange states of matter that exist at the cold end of the heat spectrum. An example is the Bose–Einstein condensate. As we sap energy out of certain substances its particles drop into the lowest possible energy state. Once nearly all particles occupy that one quantum state they share a single, coherent wave function. This causes them to behave in a strange, collective way: they become immune to individual excitation. Individual particles can no longer be bumped or jostled out of that lower state. This means that they flow with no resistance whatsoever. In certain solids, bonded pairs of electrons — Cooper pairs — condense into this state. They flow unrestricted through the material, making it a superconductor. However, if the entire substance can somehow remain a fluid when it reaches the critical temperature for Bose–Einstein condensation it becomes what we call a superfluid. It has zero viscosity; it can pass through the smallest openings, sustain whirlpools that last forever, and even climb over the walls of its container. Only one substance is known to produce a superfluid for conditions possible in a lab. And that's Helium. In particular, Helium-4. Helium-4 has a total spin of zero, which makes it a boson. So: a particle with integer spin. Bosons are able to occupy the same quantum state as each other unlike the half-integer spin fermions which cannot. The other unique property of Helium is that it can't be frozen — it remains a liquid down to the smallest possible temperature. Every other substance freezes into a solid before it can become a superfluid. The unfreezability of Helium reveals an even deeper quantum mystery. See, there's an absolute limit to how cold a substance can become. In theory, absolute zero temperature means no thermal energy so no internal motion of particles whatsoever. But what does it mean for a particle to be completely still? Well, its position relative to its neighbors would be fixed and its momentum would be zero. However, the most fundamental law of quantum mechanics forbids this. The Heisenberg Uncertainty Principle tells us that there's an absolute limit in the knowability of particular combinations of properties. For example, the more precisely a quantum particle's position is defined, the less defined is its momentum. And this isn't about measurement; a particle with a perfectly-defined position has a perfectly-undefined momentum. So try to fix a particle's position perfectly — try to hold it still — and its momentum enters a state of quantum haziness. That momentum can then fluctuate, potentially to very high values. At the lowest temperatures particle motion acquires a sort of quantum buzz. This translates to a very real minimum in average energy and to a minimum temperature. That temperature is just a teensy bit higher than absolute zero. We call the lowest-possible energy of a quantum system its zero-point energy. For a group of particles that make up any form of matter that zero-point energy isn't actually zero. There's always a little bit of kinetic energy remaining and so it's impossible to reach absolute zero in temperature. Other quantum systems also have non-zero zero-points and that leads to even stranger phenomena. For example: The quantum fields that fill our universe also fluctuate due to the uncertainty principle resulting in what we know as vacuum energy. And some quantum fields have an intrinsic non-zero zero-point before even bringing Heisenberg into it. This leads to the famous Higgs mechanism and possibly also the phenomena of inflation and dark energy. To understand the universe we need to understand how it behaves absent heat, absent light, and absent matter. But we're getting ahead of ourselves. We'll need another episode to explore the quantum nature of nothing as we peer deeper into the coldest, darkest, and emptiest patches of spacetime. This episode is brought to you by Curiosity Stream: a subscription streaming service that offers documentaries and non-fiction titles from some of the world's best filmmakers including exclusive originals. It's also a great place to study up on some of the concepts we cover in Space Time. For example, Brian Greene’s “Exploring Quantum History” delves much more deeply into the Heisenberg Uncertainty Principle. Check it out if you're curious. Get unlimited access today and for our audience the first two months are free if you sign up at curiositystream.com/spacetime and use the promo code "spacetime" during the sign-up process. This week we hit the crazy milestone of one million subscribers. Wow! We never would've guessed we'd reach this point when we started making Space Time early in 2015. We had no idea there'd be such an amazing community of smart, curious folk out there. We are so incredibly grateful to have found you, and that you found us. Of course we have to give a Space Time T-shirt to our one-millionth subscriber, SeventyFive, that means you. Shoot us an email at pbsspacetime@gmail.com and we'll make that happen. And for everyone else, how about we keep making Space Time for as long as humanly possible? Last week in Space Time Journal Club we talked about the new observation of a potential pair of binary supermassive black holes orbiting only one light-year apart. You guys had the best questions. RCOATES89 asks whether we're going to have to wait billions of years for this black hole binary to spiral together from losing angular momentum to gravitational waves. Well the— the answer is no, we'll probably only have to wait many thousands to millions of years. We know for sure that supermassive black holes do merge — otherwise they could never have got so big. Also, we'd see more binaries if they didn't merge. So they probably lose angular momentum by dragging against gas in the centers of galaxies, but we don't know how long that takes. Hopefully this and other systems like it will help us figure that out. Dillan Burris asks, "What, besides a supermassive black hole, lives in the centers of galaxies?" Well the answer is stars. Lots and lots of stars. The density of stars in the Milky Way core is around a hundred times that of the Milky Way disk. We also expect there to be a good number of stellar remnants like neutron stars and black holes that have fallen towards the center from the surrounding galaxy. And, when galaxies get stirred up by an interaction or collision with another galaxy we expect that gas will be driven into the core also. There it might trigger some quasar activity until it all gets gobbled up by the black hole. Joseph Gamble points out that if this binary pair is a whole light-year apart then for us to see them orbiting each other they'd need to be traveling insanely fast. Well, good observation. That's absolutely right, but actually we haven't seen them orbiting each other. We just know they must be in orbit because their probable masses are large enough that they must be gravitationally bound. They would actually take a few thousand years to complete one orbit, so that's still a long wait. Rubbergnome, I'm sorry I didn't have more faith in your QFT fu. Your criticism of my Lagrangian from the previous week's episode was just about my bad LaTeX fu — not about the equation being wrong. I stand corrected.
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