“It’s 10:00 pm, do you know where your photons are?”
As parents, we try to know where our kids are at all times. We teach them that, when they want to play outside or at a friend’s house, they need to let us know where they will be. If we were to ever find out that they were not where we expected them to be, we would go ballistic! Well, could you imagine being the parent of a photon?
A group of scientists at Tel-Aviv University performed an experiment that shows you may not get a sensible answer when you ask a photon where it has been. Soon to appear in Physical Review Letters, “Asking photons where they have been,” demonstrates that the past of a photon cannot be represented by a continuous trajectory, or even by the superposition of continuous trajectories. To quote from their paper:
“The photons tell us that they have been in the parts of the interferometer through which they could not pass!”
Interrogating Discontinuous Trajectories in Quantum Mechanics
I have previously mentioned two puzzling aspects of the quantum universe: non-locality and the intrinsic, probabilistic nature of outcomes. I typically caveat these two properties with “apparent”, i.e. apparent non-locality and apparent probabilistic nature. That is because it is still possible (although not certain) that there could be some underlying causal and realist explanation. In fact, explanations may already be available, we just do not know how to validate them.
Another mystery that our classical brains struggle with is the apparent discontinuous nature of the trajectories of quantum particles. What I love about this new result from the Tel-Aviv group (Danan, Farfurnik, Bar-Ad, and Vaidman) is that, not only does it demonstrate a unique and important property of quantum physics, it does so with a straight-forward and conceptually easy to understand experiment.
The scientists used a nested Mach-Zehnder interferometer (MZI). You may recall that I discussed a MZI in “The Transactional Interpretation of Quantum Mechanics.” However, in this case, they nested two MZI together – one leg of a MZI includes another MZI nested within one of it’s legs (see the figure below).
Photons enter the apparatus from the source in the upper left corner of the figure. The unlabeled squares represent beam splitters. After passing through either the lower leg or the nested interferometer in the upper leg, photons are detected by a quad-cell photo-detector (D). The unique and essential feature of this experiment is that the mirrors (A, B, C, E, and F) vibrate around their horizontal axes at different frequencies fA, fB, fC, fE, and fF, with very small amplitudes. This induces oscillations of the vertical positions of photons after they encounter each particular mirror along their path. Hence, each photon carries a record that describes which mirrors they encountered, and thus which path they took through the apparatus.
Each photon’s signature is extracted by measuring (at D) its position coming out of the interferometer. This data is then Fourier-analyzed to produce a power spectrum of the different frequencies present in the output signal. When the vibration frequency of a certain mirror appears in the power spectrum, the scientists logically conclude that at least some of the photons have been near that particular mirror.
Trajectories That Appear to be Continuous
The first run of the experiment that we will consider is the one depicted above. One third of the beam power was sent into the lower arm and two thirds of the beam power was sent to the nested MZI in the upper arm (the beam splitter used to split the two legs of the outer interferometer was specifically designed for this one-third, two-thirds spilt; other beam splitters produced a 1:1 split).
The interferometers were aligned to ensure that all the photons ended up at the detector. The power spectrum showed peaks at all frequencies, as intuitively expected. The peaks at fE and fF were higher due to the larger fraction of photons in contact with them. The power spectrum at the output of the experiment shows, unsurprisingly, frequencies from all five mirrors.
So Much for Common Sense: Discontinuous Trajectories in Quantum Mechanics
The surprising result was obtained when the interferometer was modified to be a “which-way” experiment. By slightly shifting mirror B, the nested MZI was aligned so that there would be complete destructive interference between the light reaching mirror F from A and the light reaching mirror F from B (see the figure below but ignore the red and green lines for now).
So, in effect, there were no photons at F. Hence, there were no photons that could possibly reach the detector D from the upper leg, right? By that reasonable bit of logic, any photons detected at D should have come from the lower arm of the interferometer. We would therefore expect that any photons reaching the detector would have interacted only with mirror C. The punch-line is that the scientists observed three peaks in the power spectrum: the expected one at frequency fC, and two more peaks at frequencies fA and fB.
Common sense tells us that any photons passing through the inner interferometer (so that they could encounter mirror A or B and pickup oscillations at frequency fA and fB) must by necessity have also encountered mirrors E and F. However, frequencies fE, and fF were not seen in the output power spectrum. How did photons pick up oscillations at frequencies fA or fB, associated with mirrors A or B, and make it to the detector without also encountering mirror E or F?
Interpreting Discontinuous Trajectories in Quantum Mechanics
Although the conventional interpretation of quantum mechanics can predict the correct outcome for this experiment, it offers little insight into what is going on. The authors offer an alternative that provides an improved conceptual understanding. The interpretation they prefer is the two-state vector formalism. This is a time-symmetric interpretation of quantum mechanics; both forwards and backwards evolving quantum states are required to describe a quantum system. This includes a state vector that evolves from the initial conditions towards the future, and a second state vector that evolves backwards in time from the final conditions of the experiment. That is to say, the state vector describing the pre-selected state as well as the state vector for the post-selected state are both required to fully describe the system. This highlights another intrinsic aspect of QM that makes it distinct from classical physics: the past of a quantum particle does not uniquely determine its future. Past and future measurements, taken together, provide complete information about the system.
In the present experiment (see the above figure), a standard forward evolving quantum state is depicted by the red line and a backward evolving quantum state is depicted by the green dashed line. There is no continuous path for the forward evolving state to proceed through the inner MZI and reach the detector. However, there is a non-zero probability for the photon to have existed anywhere that both forward and backward quantum wave functions are present. Hence, this includes the nested MZI in the upper leg, inside mirrors E and F, but in the region of mirrors A and B.
The transactional interpretation (TI) also provides a conceptual explanation of this experiment. Additionally, at least in my opinion, the TI provides a more straight-forward way of calculating the probability for the photon to be in the inner interferometer, and hence simplifies the prediction of the power spectrum at the output.
Will We Ever Understand Particle Trajectories, Much Less Quantum Physics?
Making progress towards the goal of fully understanding what nature is up to in the quantum world requires that you have a full grasp of the variety of experimental evidence and theoretical results. If you have been reading my posts up to now, hopefully I have been filling in some gaps. Don’t get too comfortable, yet. There is a lot more to the story about trajectories, a story that is being told through “weak measurements”.
Considerations of pre- and post-selected systems lead to the theory and practice of weak measurements. In an upcoming article, I plan to discuss what I mean by weak measurements, and how they are being used to survey and reconstruct the properties of quantum particles between pre-selection and post-selection measurements. The results of these measurements are amazing just due to the fact that they are possible, as well as due to the enlightening results that they provide. These experiments give me confidence that, as a result of the amazing work of skilled quantum physicists, we are making steady progress along the road to a proper conceptual understanding of our quantum universe.