Several weeks ago it was brought to my attention that some of our readers via Facebook wanted to hear my take on the EPR paradox, so I figured I ought to get around to saying something. It turns out, further, that this is an appropriate thing to discuss since it has some applications to particle physics in how we are able to decipher what goes on inside our particle colliders.

So let’s start with the basic idea. The Einstein-Podolsky-Rosen paradox is a thought experiment that was originally proposed to highlight the inadequacies of quantum mechanics. What ended up happening was that the phenomenon of quantum entanglement became the foundation for real-life applications of quantum mechanics, e.g. quantum cryptography.

A fair warning: I’m not going to give a proper, formal treatment of the paradox nor will I further discuss the original motivation. Instead, I’ll give a heuristic description and jump into an application to B mesons.

First, let’s start off by reminding ourselves that we assume that information cannot travel faster than the speed of light. This related to the fundamental principle of causality: if things could travel faster than the speed of light, then in some reference frame, it’s moving backwards in time.

Alright, now onto the EPR paradox. The idea is this:

• You have a particle (the blue guy in the picture above) that decays into two other particles, A and B.
• There is a conservation law that constraints some property of A and B relative to one another. For example, conservation of electric charge says that if the original particle has no charge and A has charge +1 (e.g. positron), then B must have charge -1 (e.g. electron).
• Quantum uncertainty tells us that until we make an observation, the state of the particle is unknown. For example, we don’t know if A is an electron or a positron until we actually check. Further, quantum mechanics tells us that the particles must actually be in some “superposition” of states.
• If, after A and B travel a long distance in this “superposition,” someone checks particle A, then the conservation law determines the state of particle B. In our example, if someone in Fermilab observes that A is an electron, then we can instantly deduce that someone at CERN (which is where B happens to be zooming past at the moment) will observe B to be a positron.
• But the Fermilab scientist could just as likely have observed A to be the positron and thus B would be an electron; until the person at Fermilab actually measured A, it was in some intermediate state. Thus the moment A is measured, it instantly fixes what B must be.
• To be clear: before A is measured, B really is a mixture of states and can be observed to be anything. After A is measured, B can only be observed to be the correct state to satisfy the conservation law.
• So here’s the paradox: how the heck did B know how to behave if it’s so far away from A? (Instead of CERN, B could have been at a distant galaxy when A was measured.) It appears that information travels from A at the point of measurement at a speed faster than light to B. (In fact, at an infinite velocity.)  Einstein called this “spooky action at a distance.”

First, let me say that the effect is real. Indeed, the particles A and B are said to be entangled. (This entangled state is actually rather fragile, since you can’t let the particles interact with any other matter that would allow them to disentangle.) Second, this is not really a paradox. The point is that there is no actual “information” being transmitted since there’s no way to impose a state on A, the initial observation is always random. You can try to think up clever ways around this, but they always fail. There is no paradox. Particles can be entangled and can have weird correlations across long distances, but that’s just a prediction of quantum mechanics that is fully consistent with causality.

Before anyone complains that I’ve oversimplified the problem, let me note that we’ve been very informal about a lot of details. First of all, we haven’t provided a rigorous definition of “information.” For our purposes it’s fine to take an intuitive definition, e.g. can I encode a simple binary message. We also haven’t talked about the specifics of what conservation law we’re using. The EPR paradox usually is described in terms of particle spins so that the conserved quantity is angular momentum. This allows one to think about subtleties regarding spins relative to different axes (x-direction vs. y-direction) that are important for a full discussion, but that we’ll gloss over here. Finally, we won’t say anything about why the related question of why A and B should exist in a superposition when they’re flying away undetected (i.e. what “eigenstate” is produced and detected).

What we’re described is the ‘essence’ of quantum entanglement; we’ve skipped the details, but as usual, the physics is more in the intuition rather than the details. A neat real-life application for this is quantum cryptography, which is a way for two parties to share a secure “key” while being able to check if a third party is eavesdropping. The idea is that information is sent via entangled particles, with one particle of each pair saved by the sender. If a third party tries to view the packets of information, then this would lead to an observable non-correlation of the would-be entangled particles. [Again, we omit the details.]

Someone trying to eavesdrop on a quantum cryptographic communication. No, just kidding. This is actually a photo of the BaBar detector at SLAC. Image via Interactions.org.

Application to B Physics. Now we get back to particle physics! Above is a picture of the BaBar detector at the Stanford Linear Accelerator Center (”SLAC National Laboratory”). It’s an experiment that finished data taking last year whose purpose was to examine the decays of B mesons and their antiparticles. The antiparticles are written with a line over the B so that people usually call them “B-bar,” hence the name of the experiment: “B, B-bar” became “BaBar.” They even got official permission to use BaBar the elephant as a mascot.

There are a few types of B meson. Like all mesons, they are made up of a quark and an antiquark. B-mesons are those which contain an (anti)-bottom quark. A neat thing about neutral mesons is that they have well defined, distinct anti-particles (e.g. a down/anti-bottom meson would have a bottom/anti-down anti-meson) even though these particles have the same charge. The charges of the constituent quarks change, but the total B meson system doesn’t change charge. This means, for reasons that I won’t go into, neutral mesons and their antiparticles can mix quantum mechanically. The B-meson, in particular, have the nice property of ‘oscillating’ on roughly the same time scale as they decay. This means that we can produce a B meson and it’ll wiggle between wanting to be a B and an anti-B about once before eventually annihilating into other stuff.

A B-meson... and a bee.

Now here’s the point: we’ve discussed in a previous post that matter and antimatter are related by CP symmetry. We know that this symmetry must be broken because our universe is made up of a whole lot of matter and practically no antimatter. So there’s something different about matter and antimatter, and it would be very interesting to see how these differences appear. Naively, if CP symmetry were exact (e.g. if matter and antimatter were truly mirror images) then whenever a neutral B meson decays into something (say, a muon, anti-muon pair) then we would expect the anti-meson to also decay into that something with the same probability. (See why this only works with neutral mesons? If the mesons were charged then the anti-meson could not decay into the same final state without violating conservation of charge.) It would be really great, then, if we could just look and see how often B mesons decayed into these states versus B-bar mesons.

Unfortunately life isn’t that simple. Because the B decays very quickly (i.e. before it reaches the detector instrumentation), all we actually see are the remnants of its decays. That means that we can observe a large sample of events that decayed into muon, anti-muon (and, realistically, some pions) that point to the center of the beam pipe where we expect the B’s to come from. There appears to be no way to figure out which of these events came form B’s and which came from B-bars!

Now this is where entanglement comes in. I should apologize in advanced to my experimental colleagues for my simplified explanation. What the clever physicists at BaBar (and its Japanese counterpart, Belle) do is to collide electrons and positrons at just the right energy to produce lots of a particle called the Upsilon-4S. This funny-named particle then decays to an entangled B and B-bar pair. Each of these particles will “oscillate” quantum mechanically between actually being a B and a B-bar, but once one of them is identified as a B (or B-bar), the other is uniquely identified as well. Most of the time both of the particles decay into things like the muon signal that we want to compare. As stated above, this is unhelpful because we can’t figure out how to count each event as coming from a B or a B-bar decay.

However, some of the time one of the particles will decay into something that only a B can decay into. We don’t care about the rate for those decays, but observing it means—via entanglement—that the other particle must be a B-bar (or vice versa). In the case where one particle undergoes such a “signature” decay and the other particle decays into the muon/anti-muon decay of interest, we can definitively count that muon/anti-muon as coming from the appropriate B or B-bar meson.

An example of a "golden event" at BaBar where the red lines represent the unique decay products of a B meson, which "tags" the yellow tracks as the remnants of a B-bar meson. Image from Interactions.org

In this way, the so-called B-factories (because they produce lots of B-mesons) were able to measure differences in the decay rates of B and B-bar mesons to these muon/anti-muon final states. In other words, they directly observed CP violation: a difference between the behavior of matter and antimatter. The information gleaned from these experiments help us constrain the source of matter/antimatter asymmetry that eventually allowed the universe to form things like galaxies and planets instead of annihilating into a big mess of photons. And we were able to do this using a strange property of quantum mechanics that Einstein originally dismissed as “spooky action at a distance.”

Before I sign-off, this whole question of information traveling at superluminal velocities reminds me of my favorite string theory joke:

These days there are so many string theory papers being written that one might be concerned that they are being written at a rate that is faster than the speed of light. One needn’t worry, however, since no information is actually being transmitted.

Zing! (I hope my string theory friends don’t read this blog.)

Cheers!
Flip

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