Previously published in here I’ll repost it in this blog so that its contributors may see what we will be discussing at the end of Griffith’s book:

In recent times two articles that can do the seemingly impossible in Quantum Mechanics have been published and they generated some buzz on the interweb.

This first article Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer is notable because the authors show how they were able to observe the trajectories of photons in a double slit experiment and still managed to observe a clear interference pattern. A thing that is impossible to do according to the Complementarity principle.

In the second article, Direct measurement of the quantum wavefunction, the authors computed the the transverse spatial wavefunction of a single photon by means that they consider to be direct. For me, that haven’t read the article, so far it doesn’t seem to be a so direct method as claimed, but nevertheless the level of experimental expertise even to get an indirect computation of the wave function is certainly worthy of respect.

These spectacular achievements were possible because these two teams used weak measurement techniques, together with statistical ensembles of photons and non simultaneous measurements of the complementary variables they set out to determine.

The two abstracts are here (the bold isn’t in the original):

**Direct measurement of the quantum wavefunction**

The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities by way of the Born rule. At present,

**the wavefunction is determined**through tomographic methods which**estimate the wavefunction most consistent with a diverse collection of measurements**. The indirectness of these methods compounds the problem of defining the wavefunction. Here**we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system**. The crux of our method is that the first measurement is performed in a gentle way through weak measurement so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method.**We show that the concept is universal, being applicable to other degrees of freedom of the photon, such as polarization or frequency, and to other quantum systems**? for example, electron spins, SQUIDs (superconducting quantum interference devices) and trapped ions. Consequently,**this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations**. We expect it to expand the range of quantum systems that can be characterized and to initiate new avenues in fundamental quantum theory.**Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer**

A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or ?trajectory? that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa.

**Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles**. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.

And an excellent explanation of why this was possible can be found in this blog post Watching Photons Interfere: “Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer”