When I teach or give talks about relativity, one of my regular angles on it is to discuss how faster-than-light travel (or even communication) creates problems with causality. That is, as I wrote in my book and an old blog post, if matter or information can pass from one point to another at speeds greater than the speed of light, there will be some observer who sees effects happening before the event that caused them. And when you let cause and effect start getting switched around, it's hard to have a coherent model of the universe.

So, I was very interested to see a new paper with the title Experimental verification of an indefinite causal order, and the accompanying press release. The initial description of this makes it sound like they've used quantum physics to make a scenario in which cause and effect may or may not be reversed, which would certainly be a weird thing.

Unfortunately, while the paper is open-access (hooray!), it's also a really difficult read, with a lot of mathematical formalism. I can't spend enough time on it to get every single detail nailed down, but from what I can tell it's a clever experiment, but not quite as radical as it seemed at first glance.

The idea here is that they take a single photon, and subject it to two operations in sequence (A and B) before measuring its state in an interference experiment. The order of the operations is determined by a "control" bit: if the control bit is "0," then operation A happens first, followed by B, but if the control bit is "1," then operation be happens first, followed by A. This is a little tricky to arrange, but if you're clever with optics, you can do it. Then, you put your control bit in a superposition of "0" and "1" and see what happens...

Their scheme (shown in Fig. 3 of the paper) is particularly clever because it uses a single photon for both the target and control: the polarization of the photon is the state that's manipulated by A and B, while the path on which it enters is the control. The incoming photon is put through a beamsplitter, where it has a 50% chance of passing through to the "A" section of the experiment. The A operation starts by measuring the polarization of the photon; if it's horizontal, the polarization is rotated in a particular way, then it's sent off to the B section of the experiment, where another polarization rotation takes place. If the A section finds a vertical polarization, it skips the initial rotation step, and just sends the photon off to B.

If the incoming photon gets reflected at the first beamsplitter, though, it gets sent straight to B, then brought back around and sent into A on a path parallel to but a little bit to one side of the initial entry path. This still hits the polarizing beamsplitter, and a horizontally polarized photon still gets its polarization rotated. After the rotator, though, it misses the mirror that would've sent it off to B, and instead goes off to another beamsplitter, where it's combined with the part of the light that went through A and then B. Likewise, the vertically polarized bit misses the mirror that would've sent it to B, and gets sent to yet another beamsplitter where it's recombined with the vertically polarized bit of light that went through A first and then B.

So, at the end of this, there are two output beamsplitters, each combining the light from two paths (horizontal-at-A is indicated by the yellow lines in Fig. 3, vertical-at-A by the purple line). One path for each involves operation A followed by operation B, the other operation B followed by operation A. And, as always in quantum interference experiments, these paths need to be thought of as involving parts of the *same* photon-- in fact, when they run the experiment, they do it one photon at a time, recording a single photon at one of the four output ports of the two beamsplitters.

Is that confusing? I expect so-- I'm an optics guy, and it took me ten minutes of staring at their figure to convince myself that I knew what the paths were and how the light got on each of the paths. And as an optics guy, just looking at this set-up with light passing through B on three different parallel paths, and two paths through A, makes me twitch. My metaphorical hat is off to the grad students who had to align all this, because, damn...

The end result of all this is a single photon detected at one of four possible outputs. This process is repeated a huge number of times, giving a probability of finding the particle at each of those four states. That probability depends on the details of the exact polarization rotations done in A and B, and the effect those have on the A-then-B path versus the B-then-A path. Verifying that the end result is a superposition of orders is then a matter of finding this probability for a wide range of different settings, and confirming that it agrees with the theoretical prediction for a superposition of orders. The bulk of the paper, in fact, is taken up with explaining how to calculate the necessary probabilities--their "causal witness." The actual optics stuff is pretty standard, if complicated, and only a small piece.

The end result is that their measured probabilities exactly match what they expect for a photon that ends up in a superposition of A-then-B and B-then-A. (The key result is a set of bar graphs in Fig. 4, showing 44 of the 259 different combinations of settings that they measured.) Which means that, from the standpoint of their detection system, the order of those operations is indefinite.

So, have they made a superposition of cause and effect? Not really, since both paths in their experiment experience both operations. A and B have an indefinite "causal order" in that it's not clear which happened first, but they're not causally *related*. The operation done by B doesn't depend on the outcome of the measurement made in A, or vice versa-- A and B do exactly the same thing, all the time, so neither is the cause of the other. So it's not quite as disturbing as it might initially seem, though it's still plenty weird. In the end, though, I don't think this really causes any problems for causality. At least not yet-- there's probably some theorist out there eagerly scribbling equations to find a way to make the measurement done at B depend on the result from A, in which case things will get *really* strange...