which was uploaded to the preprint server arXiv.org on September 5 and has not yet been peer-reviewed.

Emphasis mine. I think I'll hold off on the breathless theorizing til this has been rigorously peer-reviewed.

Man, I wish I wasn’t dumb

So photons, the particle of light, can interact with matter (atoms) in different ways. It could be absorbed by an electron, and then the energy transfered could knock the electron off the atom. That's the photoelectric effect. It could also excite an electron into a higher orbital but not dislodge it, and often the electron will emit a new photon when it drops back down to ground state. That's phosphorescence. The photon could also hit nothing and travel straight through.

If you shot a photon (using a laser) through a cloud of atoms, you could watch for these interactions. Normally, light seems to slow down when passing through a medium (air or water) because the photons get absorbed and re-emitted. In bulk, this causes light scattering and slows travel.

In this experiment, the cloud is made of ultracold rubidium. Rubidium is quite reactive and a pretty big atom, but i dont know specifically why it is used. What surprised the experimenters is that they could measure both the excited states of the atom and the emission of the photon. Sometimes, the atoms would seem to stay excited even though the photon had already been emitted, and also sometimes atoms would get excited even though no photon had been absorbed.

This is interesting but kind of makes sense to me. The quantum properties of reality don't disappear when we move up to bigger scales and aggregates. Rather the quantum properties seem to just "average out." But this has weird effects. Electrons, for example, aren't little balls in orbit around the nucleus. They're waves of energy that get probabilistically smeared out over an "orbital", an area around the nucleus where that electron is likely to be located. When atoms combine into molecules, the orbitals also combine into complex orbitals over the entire molecule. And when lots of atoms get arranged into a crystal (like in metals) those orbitals smear out over the entire aggregate. That's kind of what it is to be entangled with other matter, to be bound up in the same quantum probability function.

So to my mind, looking at how one atom reacts with a small number of atoms in a supercooled cloud doesn't make sense, and gives weird results like negative time. The wave function of the photon must account for the wave function of the entire cloud. The single photon has infinitely many possible interactions through the cloud, which in aggregate always amount to taking longer to pass through while exciting some electrons along the way.

This is a fascinating phenomenon – but fully within current theory. And there's no "inversion of the arrow of time", despite what the sensationalistic, misleading title seems to imply. From the recent paper (my emphasis):

Our results, over a range of pulse durations and optical depths, are consistent with the recent theoretical prediction that the mean atomic excitation time caused by a transmitted photon (as measured via the time integral of the observed phase shift) equals the group delay experienced by the light.

The theoretical explanation is given in this paper:

We examine this problem using the weak-value formalism and show that the time a transmitted photon spends as an atomic excitation is equal to the group delay, which can take on positive or negative values.

It is essentially related to the difference between phase and group velocity of waves.

One more example of how nature – as we currently understand it – offers amazing, fascinating, unexpected phenomena. It doesn't need misleading sensationalism.

What does this mean for Entropy? Is the Arrow of Time still always forward?