Ken Wilson, Nobel Laureate and deep thinker about quantum field theory, died last week. He was a true giant of theoretical physics, although not someone with a lot of public name recognition. John Preskill wrote a great post about Wilson’s achievements, to which there’s not much I can add. But it might be fun to just do a general discussion of the idea of “effective field theory,” which is crucial to modern physics and owes a lot of its present form to Wilson’s work. (If you want something more technical, you could do worse than Joe Polchinski’s lectures.)

So: quantum field theory comes from starting with a theory of fields, and applying the rules of quantum mechanics. A field is simply a mathematical object that is defined by its value at every point in space and time. (As opposed to a particle, which has one position and no reality anywhere else.) For simplicity let’s think about a “scalar” field, which is one that simply has a value, rather than also having a direction (like the electric field) or any other structure. The Higgs boson is a particle associated with a scalar field. Following the example of every quantum field theory textbook ever written, let’s denote our scalar field φ(x, t).

What happens when you do quantum mechanics to such a field? Remarkably, it turns into a collection of particles. That is, we can express the quantum state of the field as a superposition of different possibilities: no particles, one particle (with certain momentum), two particles, etc. (The collection of all these possibilities is known as “Fock space.”) It’s much like an electron orbiting an atomic nucleus, which classically could be anywhere, but in quantum mechanics takes on certain discrete energy levels. Classically the field has a value everywhere, but quantum-mechanically the field can be thought of as a way of keeping track an arbitrary collection of particles, including their appearance and disappearance and interaction.

So one way of describing what the field does is to talk about these particle interactions. That’s where Feynman diagrams come in. The quantum field describes the amplitude (which we would square to get the probability) that there is one particle, two particles, whatever. And one such state can evolve into another state; e.g., a particle can decay, as when a neutron decays to a proton, electron, and an anti-neutrino. The particles associated with our scalar field φ will be spinless bosons, like the Higgs. So we might be interested, for example, in a process by which one boson decays into two bosons. That’s represented by this Feynman diagram:

Think of the picture, with time running left to right, as representing one particle converting into two. Crucially, it’s not simply a reminder that this process can happen; the rules of quantum field theory give explicit instructions for associating every such diagram with a number, which we can use to calculate the probability that this process actually occurs. (Admittedly, it will never happen that one boson decays into two bosons of exactly the same type; that would violate energy conservation. But one heavy particle can decay into different, lighter particles. We are just keeping things simple by only working with one kind of particle in our examples.) Note also that we can rotate the legs of the diagram in different ways to get other allowed processes, like two particles combining into one.

This diagram, sadly, doesn’t give us the complete answer to our question of how often one particle converts into two; it can be thought of as the first (and hopefully largest) term in an infinite series expansion. …

How Quantum Field Theory Becomes “Effective”Read More »

The firewall puzzle is the claim that, if information is ultimately conserved as black holes evaporate via Hawking radiation, then an infalling observer sees a ferocious wall of high-energy radiation as they fall through the event horizon. This is contrary to everything we’ve ever believed about black holes based on classical and semi-classical reasoning, so if it’s true it’s kind of a big deal.

The argument in favor of firewalls is based on everyone’s favorite spooky physical phenomenon, quantum entanglement. Think of a Hawking photon near the event horizon of a very old (mostly-evaporated) black hole, about to sneak out to the outside world. If there is no firewall, the quantum state near the horizon is (pretty close to) the vacuum, which is unique. Therefore, the outgoing photon will be completely entangled with a partner ingoing photon — the negative-energy guy who is ultimately responsible for the black hole losing mass. However, if information is conserved, that outgoing photon must also be entangled with the radiation that left the hole much earlier. This is a problem because quantum entanglement is “monogamous” — one photon can’t be maximally entangled with two other photons at the same time. (Awww.) The simplest way out, so the story goes, is to break the entanglement between the ingoing and outgoing photons, which means the state is not close to the vacuum. Poof: firewall.

You folks read about this some time ago in a guest post by Joe Polchinski, one of the authors (with Ahmed Almheiri, Don Marolf, and James Sully, thus “AMPS”) of the original paper. I’m just updating now to let you know: almost a year later, the controversy has not gone away.

You can read about some of the current state of play in An Apologia for Firewalls, by the above authors plus Douglas Stanford. (Those of us with good Catholic educations understand that “apologia” means “defense,” not “apology.”) We also had a physics colloquium by Joe at Caltech last week, where he masterfully explained the basics of the black hole information paradox as well as the recent firewall brouhaha. Caltech is not very good at technology (don’t let the name fool you), so we don’t record our talks, but Joe did agree to put his slides up on the web, which you can now all enjoy. Aimed at physics students, so there might be an equation or two in there.

Just to point out a couple of intriguing ideas that have come along in response to the AMPS proposal, one paper that has deservedly received a lot of attention is An Infalling Observer in AdS/CFT by Kyriakos Papadodimas and Suvrat Raju. They consider the AdS/CFT correspondence, which relates a theory of gravity in anti-de Sitter space to a non-gravitational field theory on its boundary. One can model black holes in such a theory, and see what the boundary field theory has to say about them. Papadodimas and Raju argue that they don’t see any evidence of firewalls. It’s suggestive, but like many AdS/CFT constructions, comes across as a bit of a black box; even if there aren’t any firewalls, it’s hard to pinpoint exactly what part of the original AMPS argument is at fault.

More radically, there was just a new paper by Juan Maldacena and Lenny Susskind, Cool Horizons for Entangled Black Holes. These guys have tenure, so they aren’t afraid of putting forward some crazy-sounding ideas, which is what they’ve done here. (Note the enormous difference between “crazy-sounding” and “actually crazy.”) They are proposing that, when two particles are entangled, there is actually a tiny wormhole connecting them through spacetime. This seems bizarre from a classical general-relativity standpoint, since such wormholes would instantly collapse upon themselves; but they point out that their wormholes are “highly quantum objects.” They claim there is evidence that such a conjecture makes sense, although they can’t confidently argue that it gets rid of the firewalls.

I suspect further work is required. Good times.

Entanglement is one of the “spookier” aspects of quantum mechanics. In classical physics, the states of two distinct objects (their positions, velocities, spins, etc.) are specified completely separately from each other. Knowing what this tomato is doing gives you no information, in principle, about what that carrot is doing. But quantum mechanics says there is only one “state of the whole world,” which refers to absolutely everything in it. And, of course, the quantum state is specified as a superposition of possible measurement outcomes, rather than one definite possibility. So the quantum state of two vegetables might take the form “the tomato is in the refrigerator and the carrot is on the kitchen counter, or the carrot is in the refrigerator and the tomato is on the counter.” Although usually we talk about spins and polarizations of particles rather than locations of foodstuffs.

Entanglement is by no means a mystery, in the same way that the measurement problem is a mystery. It’s just a straightforward prediction of quantum mechanics, repeatedly verified by experiments. But it bugs us, because it seems “nonlocal.” In the state described above, I can look at the tomato and instantly infer what the carrot is doing, without ever looking at it. This bothers people, although it doesn’t lead to anything dangerous or immoral, like communication faster than light. That’s because physical information still travels slower than light. Someone wondering about the carrot doesn’t gain any information just because you measured the location of the tomato; you still have to tell them what answer you got.

Still, entanglement is pretty cool. And now Anton Zeilinger’s group in Vienna, one of the leading labs working on quantum experiments, has queried the Zeitgeist and responded in a way appropriate to our internet age: they made a YouTube video. (Since they are also old-fashioned scientists, they also wrote a paper.)

Let me try to explain this as I understand it, but I’ll confess up front this is a bit outside my comfort zone so real experts should chime in. Here we have two entangled photons, which can be polarized either H (horizontal) or V (vertical). The quantum state is of the form HV + VH, which means that we don’t know what either polarization is, but we know that the two polarizations must be opposite of each other. (If the state had been HH + VV, we still wouldn’t know either one, but we would know they were the same.) We send each photon through a merry path, observe one of them (that’s on the left), and see what happens to the other one (on the right). We’re looking at an image of where the individual photons land on a screen. You can see how the state of photon #2 is affected by what’s happening to photon #1.

Doesn’t it seem like you could use this to send information faster than light, if photon #2 is instantly affected by what we do to photon #1? I believe the trick here is that we’re not taking an image of all of the #2 photons. We’re only taking images of #2 if photon #1 was registered in a certain state. That is, we send photon #1 through a filter that only lets horizontal polarizations through. If photon #1 gets through, we turn on the camera and image photon #2. If it doesn’t, the camera never triggers, and photon #2 hits the screen harmlessly. So no superluminal chitchat, you science-fiction fans out there.

Nevertheless, pretty awesome. Quantum mechanics is sufficiently non-intuitive that we would only ever come up with it by having it forced on us by data. Even though experiments like this are completely explained by quantum mechanics as we currently know it, every little demonstration helps us appreciate it a bit more viscerally. As we strive toward a deeper understanding, that’s a crucially important part of the process.