PBS Space Time

Wouldn't it be nice to be everywhere at once? According to quantum mechanics you are, at least a little bit.

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Quantum mechanics is a spectacularly weird theory. One of its basic tenets is that certain properties of an object are fundamentally uncertain. They don't hold well-defined values, but instead must be described as a distribution of possible states of being. Each specific state has a certain probability of being true when the object is observed. Or more accurately, until a quantum object interacts with something, all possible states are just as real as each other, although not necessarily equally likely. There is a distribution of probabilities for each of an object's quantum properties. That distribution, and the way it changes over time, is coded in the object's wave function. The reduction of a fuzzy possibility space into a specific measurable property is sometimes referred to as the collapse of the wave function. We'll talk a lot more about this awesome weirdness in the future. For now, let's just look at the strange consequences of quantum uncertainty in an object's location. This is one of the early realizations in the development of quantum theory. French mathematician and physicist Louis de Broglie figured out that any material object is really a matter wave. It can be described as a wave packet of positioned probability. And that wave packet has a wavelength. This de Broglie Wavelength defines how well determined an object's position is. A large wavelength means a highly uncertain position. A small wavelength means a well-defined position. That's true of subatomic particles, and it's sort of true of anything. Right now I'm mostly right here. But there's also a small chance that I'm here, here, or here. There's an infinitesimal chance that I'm on the moon. Observe me and you'll collapse my wave function and probably find me pretty much exactly where you expect to. See an object's de Broglie wavelength depends on its momentum, so mass times velocity. Higher momentum means a smaller wavelength. In fact, it's the minuscule Planck constant divided by momentum. Humans are made up of several tens of kilograms of thermal moving particles and have de Broglie wavelengths a couple of orders of magnitude smaller than the Planck length. You're everywhere in the universe, but not very much. You're as right there as it's possible to be. But what about something much smaller, say a tightly bound bundle of two protons and two neutrons that we call an alpha particle? On its own, this would be a helium nucleus. But these bundles also exist as parts of heavier atomic nuclei. There an alpha particle is snugly bound into the nucleus by the strong nuclear force. We can imagine an alpha particle as being like a ball trapped in a steep valley of potential energy. It can roll around inside, but unless it has a very large kinetic energy, it will never roll over the edges. But quantum objects aren't at all like balls. Their positions are not well defined. As an alpha particle approaches the force barrier of the nucleus, its wave packet is reflected backwards, usually. See, that wave packet describes a range of possible locations for the approaching particle. But that possibility space does not end suddenly at the force barrier. Instead, it drops off quickly, exponentially, through the steep walls. However, it never quite reaches zero. There remains a tiny tail of probability outside the nucleus, beyond the reach of the strong nuclear force. That means there is a very tiny chance that instead of bouncing off the wall, the particle will, at the last minute, resolve its position in that unlikely outside bit of its possibility space that looks like the particle teleporting out of the nucleus. This process is called quantum tunneling. When it's an alpha particle escaping a nucleus, this is one of the most important mechanisms for radioactive decay. Quantum tunneling also goes in the other direction. Protons, neutrons, electrons, and alpha particles can quantum tunnel into nuclei in various types of fusion and particle capture phenomena. In fact, without quantum tunneling, stars could not fuse hydrogen into heavy nuclei. A variety of modern electronics also rely on the tunneling phenomenon, including the transistor. But how quickly does the alpha particle move through this barrier? Well, as far as we know, it's instantaneous. That suggests a velocity faster than light, which sounds problematic. It's actually extremely hard to test this because we can't make clocks accurate enough to time such a ridiculously quick event. Here's one way you might test this. Remember the LEGO interferometer that discovered gravitational waves? Laser beams are sent down paths at right angles and then brought back together. The photon wave packets interact with each other and produce an interference pattern that is incredibly sensitive to differences in path lengths. Well that's a Michelson interferometer. But let's change the arrangement a bit. We want to send individual photons instead of lasers. And we want to block one of the paths with a very thin reflective barrier, like this. In the absence of quantum tunneling, that barrier should reflect its photon 100% of the time. But just like with the alpha particle, as the photon approaches the barrier the wave packet defining its possible location extends weakly beyond the barrier. About 99% of the time the photon is reflected. But 1% of the time it will resolve itself beyond the barrier and it will continue on its path. If those rare tunneling photons really do travel instantaneously through the width of the barrier, then they should arrive at the detector slightly ahead of the photon that travels the unimpeded path. That will be apparent when their wave packets don't line up perfectly at the other end. But for this to work, the original path lengths of the interferometer need to be very precisely equal. To make that work you need to use a second, and perhaps even weirder feature of quantum mechanics, quantum entanglement. That is a huge topic for another video. It offers another tantalizing hint at faster than light influences. For now, let me just say that in order to produce these entangled states the path length of the interferometer needs to be identical to very high precision. Tune the path lengths until the weird effects of entanglement emerge, and you know that they are equal. At that point, you can get an incredibly precise measurement of any differences in photon travel time. A team of very clever physicists have successfully performed this experiment. Reference link below. What did they find? The tunneling photon does arrive a tiny bit earlier than its partner. It appears to teleport through the barrier and so travel faster than light. Sweet. So scale up from photons to people and we have transporter beams, right? Well, this apparent violation of relativity only occurs deep within the quantum realm. A particle resolves its location anywhere within the vicinity of its de Broglie wavelength. That uncertainty in location allows tunneling. But even without a barrier, this location fuzziness leads to uncertainty in the arrival time of the photon. An unimpeded photon could arrive at the earlier time of the tunneling photon, because its wave packet includes that in its range of possible positions. When you add the barrier, all you're really doing is reshaping the wave packet, selecting only the possibility space of early arrival. This can look like an increase in the speed of light, but only within the uncertainty range defined by the de Broglie wavelength. More accurately, it's within the uncertainty range defined by the Heisenberg uncertainty principle, which is perhaps the deeper principle from which the de Broglie wavelength comes. This is something we'll also get back to in detail. Any macroscopic object is subject to a very well-defined speed limit. But in the quantum realm, Heisenberg uncertainty does seem to allow instantaneous motion, and even perhaps causality violation within quantum limits. Stay tuned for the implications of this on both quantum and cosmic scales of space time.