Quantum mechanics is more successful than the founders’ wildest dreams. The lives and times of atoms, governed by quantum mechanics, play out before us on the great 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 – react to this shifting stage, but they have no influence on how it distorts and flows around them.
This is a mystery to us. Why is it so one-sided: General relativity affects quantum mechanics, but quantum mechanics does not affect general relativity? It is a puzzle that arises from human expectation rather than evidence. We expect that since quantum mechanics is characterized by sharp jumps, somehow space and time should do the same.
It is also expected that if space and time worked more quantum-like, the equations of general relativity would behave better. In general relativity, it is possible to bend space and time sharply infinitely. This is something we simply cannot understand: what would an infinitely curved space look like? To most physicists, it seems like something that can’t be real, indicating a problem with the theory. Could this be where the actors influence the stage?
Quantum mechanics and relativity on the clock
Trying to catch the actors adjusting the stage requires the most precise experiments ever devised. Nothing we have so far brings us close, so a new idea from a few German physicists is very welcome. They focus on what is perhaps the most promising way to detect quantum influences on space-time: time dilation experiments. Modern clocks rely on the quantum nature of atoms to measure time. And the passage of time depends on relative speed and gravitational acceleration. Therefore, 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 so 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 a later date, it has a seventy-five percent chance of being in state A; also later it will certainly be in state A. Keep going, though, and the chances of being in state A begin to dwindle, and continue to do so until the atom is definitely in state B. Provided the atom is undisturbed, these oscillations will continue.
Superposition is nothing more than addition for waves. Let’s say we have two sets of waves that overlap in space and time. At any given point, a valley can align with a peak, their peaks can align, or anything in between. Superposition tells us how to add these waves up so that the result recreates the patterns we observe in nature.
These periodic oscillations make for the perfectly ticking clock. We simply define the period of an oscillation as our basic unit of time. To link this to general relativity measurements is in principle quite easy. Build two clocks and place them side by side. At some point we will start counting ticks from both clocks. For example, when one clock reaches one thousand, we compare the number of ticks of the two clocks. If we’ve done our job right, both clocks should be at a thousand ticks.
However, if we blast one into space and run the same experiment, and relativity requires the clock to register in orbit more then ticks the clock on earth. The way we record the passage of time is through a phenomenon that is purely quantum in nature, as the passage of time is modified by gravity. These experiments work very well. But at the moment they are not sensitive enough to detect any deviation from quantum mechanics or general relativity.
That’s where the new ideas come in. The researchers essentially propose to create something similar to an atomic clock, but instead of tracking the oscillation of atomic states, they want to track nuclear states. When I talk about atoms, I usually ignore the nucleus completely. Yes, it’s there, but I’m only concerned with the influence the nucleus has on the energetic states of the electrons around it. In one important way, however, the nucleus is like the electron cloud that surrounds it: It has its own set of energetic states. It is possible to induce nuclear states (using X-rays) and then return to the ground state by emitting an X-ray.
So let’s imagine that we have a crystal of silver 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 greatness 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 they all absorbed a small part of the photon. This shared absorption now means that all silver atoms enter a superposition state where they have absorbed and not absorbed a photon. This superposition state changes with time, just like an atomic clock.
In the absence of an outside environment, all silver atoms will change in one fell swoop. 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 were emitting a partial photon. These photons are added together and a single photon flies off in the same direction the absorbed photon had traveled. Essentially because all atoms are in lockstep, the charge oscillations emitting the photon only add up in phase in the direction the absorbed photon flew.
However, gravity causes the atoms to get out of alignment. So when it comes time to transmit, 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 slightly ahead of those at the bottom of the crystal. This is the direction in which the individual contributions add up in phases not in the same direction as the flight path of the absorbed photon, but at a very small angle.
How big is this angle? That depends on the size of the crystal and how long it takes for the environment to randomize the emission process. For a crystal of silver atoms less than 1 mm thick, the angle could be as high as 100 microdegrees, which is small but probably measurable.
However, that’s just the beginning of a series of clever ones. If the crystal is placed on the outside of a cylinder and rotated during the experiment, the top atoms of the crystal move faster than the bottom, meaning that the time dilation experienced at the top of the crystal is greater than at the bottom. top of the crystal. bottom. This has exactly the same effect as placing the crystal in a gravitational field, but now the strength of that field is determined by the speed of rotation.
In any case, spinning a 10 mm diameter cylinder very quickly (70,000 revolutions per second) greatly increases the angular displacement. For example, for silver, it reaches 90 degrees. With such a large signal, even smaller deviations from the predictions of general relativity should be detectable in the lab. Importantly, these anomalies occur at very small length scales, where we would normally begin to think about quantum effects in matter. Experiments like this may even be sensitive enough to see the influence of quantum mechanics on space and time.
A physical implementation of this experiment will be challenging, but not impossible. The main problem is probably the X-ray source and performing some photon experiments in the X-ray regime. After that, the crystals must be extremely pure and something called a coherent state must be created in them. This is certainly not trivial. Given that it has taken atomic physicists a long time to achieve this for electronic transitions, I think it will take a lot more work to get this to happen at x-ray frequencies.
On the positive side, free electron lasers have come a very long way and they have much better control over beam intensities and stability. This is hopefully the kind of challenge that beamline scientists live for.
Nature photonics2015, DOI: 10.1038/NPHOTON.2015.7