The RSS subscriptions which populate my Google Reader mainly fall into two categories: scientific and other. Sometimes patterns emerge when superimposing these disparate fields onto the same photo-detection plate (my brain.) Today, it became abundantly clear that it’s been a tough week for hidden variable theories.

Let me explain. Hidden variable theories were proposed by physicists in an attempt to explain the ‘indeterminism’ which seems to arise in quantum mechanics, and especially in the double-slit experiment. This probably means nothing to many of you, so let me explain further: the hidden variables in Tuesday’s election weren’t enough to trump Nate Silver’s incredibly accurate predictions based upon statistics and data (hidden variables in Tuesday’s election include: “momentum,” “the opinions of undecided voters,” and “pundit’s hunches.”) This isn’t to say that there weren’t hidden variables at play — clearly the statistical models used weren’t fully complete and will someday be improved upon — but hidden variables alone weren’t the dominant influence. Indeed, Barack Obama was re-elected for a second term. However, happy as I was to see statistics trump hunches, the point of this post is not to wax political, but rather to describe the recent failure of hidden variable theories in an arena more appropriate for this blog: quantum experiments.

The November 2nd issue of Science had two independent papers describing the results of recent delayed-choice experiments. The goal of these papers was to rule out hidden variable theories as an explanation for aspects of quantum mechanics. More specifically, the experiments showed that the wave-particle duality which results during measurement in the double-slit experiment cannot be explained by combining classical mechanics with local hidden variables. This won’t come as a surprise to people who deal with quantum mechanics on a daily basis (consciously), but it’s nice to have additional material to refer to quantum naysayers, and the experimental set-ups were impressive.

Before describing these two experiments, I want to introduce John Wheeler’s delayed choice thought experiment. As a primer, one should first be familiar with the double-slit experiment, but read along anyways even if you’re unacquainted, because there are interesting ideas accessible at all levels. Also, maybe it will motivate you to ponder the double-slit experiment, which Feynman is often quoted as saying ‘contains the only mystery of quantum mechanics’ (measurement is weird.)

The tragic life of a photon: from creation to annihilation in nanoseconds, and misunderstood along the way. This image shows the experimental setup for the delayed choice double-slit experiment. The set-up differs from that of the usual double-slit experiment because the detection plate is removable. When it is in place, the wave-like nature of photons is probed. When it has been removed, the photons travel to two telescopes and will be measured to arrive in only one of them, thereby probing the particle like nature. If the distance between foil and plate is large enough, then the experimenter can decide whether to keep or remove the plate once the photons have already passed beyond the foil, thereby ruling out hidden variable theories (other than those which can perturb the photon in free space.)

As a brief review, one version of the dual slit experiment proceeds as follows:

  1. A ‘photon gun’ fires a single photon towards a detector.
  2. Before reaching the detector, the photon passes through a sheet of aluminum foil which has two slits cut into it (imagine two medieval arrow-slits, but smaller.)
  3. After passing through the foil with the slits, the photon travels through free space for a while and then arrives at a photo-detection plate (this is similar to photographic paper, which is originally black and records a white dot every time a photon hits a point on the paper.)
  4. The weirdness happens in between steps 2 and 3. If any attempt is made to observe the photon after it has passed beyond the foil with the slits, or if one of the slits itself is observed, then the photon behaves as a particle. If no observations are made until after the photon hits the photo-detection plate, then the photon behaves as a wave. These different behaviors are confirmed by sending many photons through the device, but only one at a time. If you’re unfamiliar with this experiment, you should think through what would happen if you sent a water wave versus shooting infinitesimal pellets through the slits.

That’s probably mind-numbingly boring review for most of you, but you might not be familiar with Wheeler’s delayed-choice twist. There used to be a school of physicists which advocated that the dual slit experiment could be explained in terms of local hidden variables. Imagine there were hidden variables at the double slit, so that as the photon passes through the slits, the hidden variables “tell it” whether its wave-like or particle-like nature will be measured. The act of passing through the slits could then change the state of the photon into the appropriate paradigm: wave or particle. Wheeler proposed the following thought experiment:

  1. Change the experimental setup slightly by moving the photodetector plate far away from the double slit — far enough that the experimenter will be able to manipulate the plate in the time interval between when the photon passes through the slits and arrives at the plate. Also, position two telescopes behind the plate, with one telescope pointed at each of the two slits.
  2. Now for the delayed-choice part. After the photon has passed through the slits, the experimenter flips a coin, and depending on the outcome, either keeps the photodetector in place and probes the wave-like nature of the photon; or removes the photodetector so that the photon travels towards the telescopes and then is measured as only going through one of them — thereby probing the particle-like nature of the photon.

If the act of flipping the coin and then moving the photodetector was “space-like separated” from when the photon passed through the slits, and wave-particle duality was still observed, then local hidden variables alone could not explain the experimental outcome (at least hidden variable theories which could only influence the photon when it interacted with some non-trivial part of the system.) Versions of this experiment had previously been carried out which decisively demonstrated the wave-particle duality that we’ve come to expect from photons. However, the two recent Science papers in question used quantum-information variants of this delayed-choice experiment to hammer additional nails in the coffin of local hidden variable theories.

In the first paper, “A Quantum Delayed-Choice Experiment,” a team from the University of Bristol used tools from quantum information to perform a variant of the delayed-choice experiment. More specifically, they send polarized photons through a Hadamard gate which splits each photon into two polarization modes, they then apply a relative phase shift to one of the modes, followed by a controlled Hadamard gate which recombines these modes. Using some fancy footwork they are able to carry out a delayed-choice experiment where instead of carrying out step 2 above (flipping a coin and then moving the detector, in a space-like separated manner,) they test a Bell inequality and obtain non-local correlations which violate said inequality. This has equivalent ramifications as step 2 above and as what Wheeler originally proposed.

In the second paper, “Entanglement Enabled Delayed-Choice Experiment,” a French team used entanglement as their surrogate for space-like separation. More specifically, they use a pair of polarization entangled photons, where one is the test photon, and the other is the “corroborative” photon. Even after detection of the test photon, depending upon how they measure the “corroborative” photon, they can toggle whether they probe the wave-like or particle-like nature of the test photon. They can do this even after detecting the test photon, as long as no one has looked at the results (they can know that the photon arrived at the photo-detection plate, but they can’t look at the white dot yet.) Quantum mechanics truly is weird. Along these lines, a Caltech professor once made an off-handed comment which stuck with me: “the greatest opportunities are in the extremes.”

In conclusion, not all of the undecided American voters showed up at the polls on Tuesday and suddenly decided to vote for Mitt Romney — as some of the “momentum” espousing pundits expected. These election based hidden variables proved to be inconsequential. Hidden variable theories also had a tough week in physics. My personal take-away is this: I’m going to be an obedient grad student by trusting the data and shutting-up and calculating… at least for the next few days.