text: The Quantum Physics Of Fenced-In Dogs
  | May 5, 2015, 10:31am EDT
  (To the extent that I can claim to be famous, it's because I talk to my dog about physics. This is one of those conversations; there's some more details at the end...)
  It's a beautiful spring day, and I find myself with an hour to kill before I need to go pick up SteelyKid and The Pip from day care. Napping in the sun seems like a great idea, so I stretch out on the lounge chair, with Emmy lying on the deck by my side.
  Not for long, though. I hear the jingle of her collar tags as she stands up, then her nails clicking across the deck. she goes down the steps, then sniffs her way all along the fence between our yard and the neighbors' (the new family that moved in has a dog, and Emmy does not approve...). She comes back, and pokes my arm with her nose.
  "The perimeter is secure."
  "Yes, I know that. Their dog has been inside for hours. Lie down." She lies down, but not for long. Jingle, jingle, click, click click, then a mad dash across the yard toward a squirrel. Once it's up a tree, she sniffs around the base, then comes back.
  Poke. "Squirrel incursion defeated."
  "Great. Good job. Now lie down." A few moments of peace, then click click click, jingle jingle.
  "HEY! YOU POODLES! STAY OFFA MY LAWN!"
  "Emmy! Stop barking!" I sit up. She's at the gap between the fences, where she can see into the front yard.
  "But, those poodles.."
  "We've had this conversation. It's a public street, other dogs are allowed to walk on it. No barking." She comes over, sheepishly. "Why can't you just lie down and enjoy the nice day, hmm?"
  "Well, I would. But, you know... Quantum."
  "I would love to just lie in the sun, but I can't. You should understand-- it's quantum physics."
  I'm going to regret this. "Oh, fine. How does quantum physics explain your inability to quietly bask in the sun without getting up every two minutes?"
  "I'm glad you asked. See, it's all about confinement. Since you have me fenced in here, I can't help but be moving around all the time. It's all about... Ungenauigkeit." She's very proud of her German Shepherd ancestry.
  "You fidget and fuss all the time because of quantum indeterminacy? You're going to invoke the Heisenberg Uncertainty Principle, here?"
  "Well, yeah. I mean, by putting up that fence, you've limited my position uncertainty, which means I must have a bigger momentum. So I've gotta move around a bunch, because quantum."
  "Technically, it means you have to have a big uncertainty in momentum, but that's not the real problem here. Quantum uncertainty just doesn't apply in this situation."
  "Dude, you're not going to try to deny the existence of zero-point energy, are you? Because you can get that from the Uncertainty Principle." She wags her tail smugly, like she's proved a point.
  "No, I'm not denying the zero-point energy, and yes, you can get a decent estimate of it from the Uncertainty Principle. For the record, though, that's not the really fundamental way to think about it."
  "No? What is the right way?"
  "Well, like basically everything in quantum physics, it comes back to the dual particle and wave nature of matter. the Uncertainty Principle itself is really a consequence of the wave nature of matter."
  "Ooh! I enjoyed that cartoon!"
  "Right. The zero-point energy is also a consequence of the wave nature of matter. When you confine a quantum particle to some region of space, you limit the possible wavelengths it can have. In particular, you prevent it from having any wavelength longer than about twice the size of the region you're confining it it."
  "And this leads to higher energy because... oh! I know! Wavelength is momentum."
  "More precisely, wavelength is Planck's constant divided by momentum. So when you exclude the really long wavelengths for a particle, you rule out its having a really low momentum. And energy is related to momentum, so forcing a particle to have some minimum momentum also forces it to have some minimum energy."
  "Which is the zero-point energy!"
  "Exactly. Any quantum-mechanical object that's restricted to some region of space will always have some minimum energy. This is a big difference between quantum and classical physics-- a quantum object is always in motion."
  "And this is a real thing, because people have measured it."
  "Sure. In fact, one of the ways Eric Cornell and Carl Wieman showed that they had made Bose-Einstein Condensation for the first time back in 1995 was related to this. Their BEC was a big bunch of atoms all together the lowest energy state available in their trap, which was tighter in one direction than the other. The shape of the BEC, and the way it expanded, matched the quantum prediction for their trap. It helped get them a Nobel Prize in 2001."
  "So, then you agree."
  "Agree... with what?"
  "That quantum is responsible for me moving around, silly!" She wags more smugly than ever. "I'm a confined object, and quantum physics says that confined objects must move around, so therefore..."
  I sigh heavily. "No, I don't agree with that. You're right about the quantum part, but that only applies to very small things. You are not a small thing, therefore, you can't blame quantum confinement for your fidgeting."
  "Yes I can. I just did."
  "OK, you can try, but the math doesn't work. The back yard is about 20 meters wide, and your mass is around 20kg, so the speed that would correspond to the maximum allowed wavelength for you in our yard is... 10-38m/s. That's 37 zeroes between the decimal point and the one; it'd take you a quadrillion years to move the width of a proton."
  "Oh." She looks dejected.
  "You wouldn't catch many squirrels that way."
  "So, can we let go of this idea of confinement as the source of your constant fidgeting?"
  I sigh. "OK, now what."
  "It's not quantum this time, but I still think that confinement to this yard is the problem."
  "Well, if you get up and take me for a nice long walk, I'll be much calmer!" She wags her tail so hard she almost loses her balance.
  "Oh, fine. I'll get the leash."
  "Yippee!" She jumps off the porch and runs in a big circle, as I head inside, giving up on my nap.
  One of the most famous predictions of quantum physics is that material particles behave like waves. Getting to this idea was a long and surprising process (I go through an abbreviated history in this video, or you can watch a cartoon version at TED-Ed), but once you have the idea of quantum particles behaving like waves, all the other weird stuff follows as a natural consequence of that.
  The notion of zero-point energy-- that any confined quantum particle can't be holding perfectly still-- is one of these consequences, and it runs hard against our everyday notion of how things behave. We naturally expect that confined objects shouldn't be moving very much-- after all, they're confined-- and many people find it strange to learn that quantum physics tells us that confined objects necessarily have more energy. And, in fact, the tighter you confine something, the higher its energy must be. This gap between everyday expectation and quantum reality is, unfortunately, often exploited by scam artists who claim to have found a way to extract this zero-point energy, extracting venture capital funding and even some government interest for what are essentially perpetual motion machines.
  None of these schemes can possibly work, though, because the zero-point energy is a fundamental and inescapable consequence of the wave nature of quantum particles. The only way to "extract" that energy would be to fundamentally change the nature of the universe to make particles stop behaving like waves, and that's not something within the reach of human technology.
  As described in the conversation above, the fundamental issue is that a moving particle has a wavelength, and that wavelength must fit within whatever space the particle is confined to. This is a well-known phenomenon in classical physics, and the basis for some amazing art:
  That's a video of Richard Thompson playing "1952 Vincent Black Lightning," one of the most impressive guitar displays you'll ever see. And it works because of the same physics that underlies the idea of zero-point energy. The strings of Thompson's guitar are fixed at the ends-- on one end by their attachment to the guitar, at the other by his finger holding the string down-- and that limits the frequencies the string can vibrate at to one of a set of "standing waves" that fit a complete wave into the space between the fixed points.
  Each of these standing wave modes has a particular wavelength, and that wavelength corresponds to the frequency of the sound waves it produces as it vibrates. The longer the wavelength, the lower the frequency, and the lower the pitch of the sound. The general pattern looks like this:
  Most of the vibration in a guitar string will be at the longest wavelength, which is twice the length of the string between the fixed points, but there will be small contributions at the shorter wavelengths, providing the overtones that give a real musical instrument a rich sound. A virtuoso guitar player like Thompson uses this to produce music by rapidly changing the position of his fingers to play notes at different pitches-- a string that vibrates at a fairly low frequency for one note can be forced to vibrate at a much higher frequency an instant later, by moving his finger to shorten the length of the vibrating string.
  The same basic idea carries over to quantum physics, but there, the wavelength is not related to the pitch of a sound, but the momentum of a particle, which in turn is related to the velocity. The shorter the wavelength, the higher the momentum, and the faster the particle is moving. And, of course, faster motion means higher energy. The mathematical relationship between these is just what Einstein and Planck introduced back in the early 1900's.
  If you take a random region of empty space, seen in the top part of the figure below, you can have particles passing through with pretty much any wavelength you like, from the very long (at the bottom, with the lowest energy) to the very short (at the top, with higher energy).
  If you ban the particles from appearing in some region of space, though-- indicated by the grey boxes in the bottom part of the figure-- you exclude everything but a limited set of waves. In particular, the only allowed wavelengths are those that fit cleanly within the region that isn't excluded, which rules out very long wavelengths. This means that a particle confined to some region has a maximum wavelength (roughly speaking, twice the length of the non-excluded region), and thus a minimum energy.
  For a confined particle-- a quantum particle trapped in a box, or an electron bound to the nucleus of an atom-- this minimum energy corresponds to a constant random motion. In a very lose sense, you can think of the particle as bouncing back and forth between the walls of the box, always moving at some minimum speed, or the electron as zipping around the nucleus in a random orbit. You can increase the speed of the motion by putting energy into the system-- sending in a photon, say, that excites the particle to a shorter-wavelength standing wave-- but you can never decrease it below the minimum energy, because that's inconsistent with the wave nature of matter.
  Now, as I explained to Emmy in the conversation above, this is completely insignificant for everyday sorts of objects, because the zero-point energy is absurdly small for anything confined to a region whose length is multiple meters. When you start looking at the world of the really small, though-- rubidium atoms in a Bose-Einstein Condensate, or electrons in one of the tiny structures used for nanotechnology research-- it becomes incredibly important. And what counts as "really small" keeps getting bigger-- people working on the field of "cavity optomechanics" are getting silicon wafers down to the minimum energy imposed by quantum mechanics, and the next few years should produce exciting results in the field. There are even some experiments that hope to reach the quantum limit for mirrors with a mass of several grams, a project that would've seemed insanely ambitious 20 years ago.
  It'll be a long, long time, though, before anybody observes the zero-point energy of anything as big as a dog. Which is probably a good thing, because they're a lot more fun when they're moving around at everyday speeds. Even if they do make it kind of hard to get any peace and quiet...