Shining an X-Ray torch on quantum gravity

Quantum mechanics has been successful beyond the wildest dreams of its founders. The lives and times of atoms, governed by quantum mechanics, play out before us on the grand stage of space and time. And the stage is an integral part of the show, bending and warping around the actors according to the rules of general relativity. The actors—atoms and molecules—respond to this shifting stage, but they have no influence on how it warps and flows around them.

This is puzzling to us. Why is it such a one directional thing: general relativity influences quantum mechanics, but quantum mechanics has no influence on general relativity? It's a puzzle that is born of human expectation rather than evidence. We expect that, since quantum mechanics is punctuated by sharp jumps, somehow space and time should do the same.

There's also the expectation that, if space and time acted a bit more quantum-ish, then the equations of general relativity would be better behaved. In general relativity, it is possible to bend space and time infinitely sharply. This is something we simply cannot understand: what would infinitely bent space look like? To most physicists, it looks like something that cannot actually be real, indicating a problem with the theory. Might this be where the actors influence the stage?

Quantum mechanics and relativity on the clock

To try and catch the actors modifying the stage requires the most precise experiments ever devised. Nothing we have so far will get us close, so a new idea from a pair of German physicists is very welcome. They focus on what's perhaps the most promising avenue for detecting quantum influences on space-time: time-dilation experiments. Modern clocks rely on the quantum nature of atoms to measure time. And the flow of time depends on relative speed and gravitational acceleration. Hence, we can test general relativity, special relativity, and quantum mechanics all in the same experiment.

To get an idea of how this works, let's take a look at the traditional atomic clock. In an atomic clock, we carefully prepare some atoms in a predefined superposition state: that is the atom is prepared such that it has a fifty percent chance of being in state A, and a fifty percent chance of being in state B. As time passes, the environment around the atom forces the superposition state to change. At some later point, it will have a seventy five percent chance of being in state A; even later, it will certainly be in state A. Keep on going, however, and the chance of being in state A starts to shrink, and it continues to do so until the atom is certainly in state B. Provided that the atom is undisturbed, these oscillations will continue.

These periodic oscillations provide the perfect ticking clock. We simply define the period of an oscillation to be our base unit of time. To couple this to general relativity measurements is, in principle, rather simple. Build two clocks and place them beside each other. At a certain moment, we start counting ticks from both clocks. When one clock reaches a thousand (for instance), we compare the number of ticks from the two clocks. If we have done our job right, both clocks should have reached a thousand ticks.

If we shoot one into space, however, and perform the same experiment, and relativity demands that the clock in orbit record more ticks than the clock on Earth. The way we record the passing of time is by a phenomena that is purely quantum in nature, while the passing of time is modified by gravity. These experiments work really well. But at present, they are not sensitive enough to detect any deviation from either quantum mechanics or general relativity.

Going nuclear

That's where the new ideas come in. The researchers propose, essentially, to create something similar to an atomic clock, but instead of tracking the oscillation atomic states, they want to track nuclear states. Usually, when I discuss atoms, I ignore the nucleus entirely. Yes, it is there, but I only really care about the influence the nucleus has on the energetic states of the electrons that surround it. However, in one key way the nucleus is just like the electron cloud that surrounds it: it has its own set of energetic states. It is possible to excite nuclear states (using X-Ray radiation) and, afterwards, they will return the ground state by emitting an X-Ray.

So let's imagine that we have a crystal of silver sitting on the surface of the Earth. The silver atoms all experience a slightly different flow of time because the atoms at the top of the crystal are further away from the center of the Earth compared to the atoms at the bottom of the crystal.

To kick things off, we send in a single X-Ray photon, which is absorbed by the crystal. This is where the awesomeness of quantum mechanics puts on sunglasses and starts dancing. We don't know which silver atom absorbed the photon, so we have to consider that all of them absorbed a tiny fraction of the photon. This shared absorption now means that all of the silver atoms enter a superposition state of having absorbed and not absorbed a photon. This superposition state changes with time, just like in an atomic clock.

In the absence of an outside environment, all the silver atoms will change in lockstep. And when the photon is re-emitted from the crystal, all the atoms will contribute to that emission. So each atom behaves as if it is emitting a partial photon. These photons add together, and a single photon flies off in the same direction as the absorbed photon had been traveling. Essentially because all the atoms are in lockstep, the charge oscillations that emit the photon add up in phase only in the direction that the absorbed photon was flying.

Gravity, though, causes the atoms to fall out of lockstep. So when the time comes to emit, the charge oscillations are all slightly out of phase with each other. But they are not random: those at the top of the crystal are just slightly ahead of those at the bottom of the crystal. As a result, the direction for which the individual contributions add up in phase is not in the same direction as the flight path of the absorbed photon, but at a very slight angle.