Modern physics is weird.

In quantum mechanics we have the Schrodinger's cat thought experiment, a cat in a quantum superposition of being simultaneously alive and dead.

And in relativity the twin paradox thought experiment, a space-faring twin ages less than her stay-at-home sibling.

But what if we could combine these and send our quantum twin around the galaxy.

Could we be simultaneously old and young?

What would that tell us about the quantum nature of time?

And would we need schrodinger birthday candles?

Time is both the most intuitive and most mysterious feature of the universe.

It seems fundamental and unavoidable, but physicists and philosophers have argued over its true nature forever.

Even our best modern theories of physics don't agree.

In our strangest modern theory, quantum mechanics, time is surprisingly straightforward.

It appears the Schrodinger equation as a well defined parameter that moves at the same rate for all particles-even if those particles have all the other sorts of quantum weirdness.

That's just as it is in good ol' Newtonian physics, time is a global parameter that ticks the same for everyone and everyone agrees on a singular "now".

But in relativity, time isn't global, it's local.

The rate of its passage depends on the relative location and speed of a clock compared to whoever's watching the clock.

Even the definitions of past, present and future get warped in relativity.

That leads to strange scenarios, like the twin paradox, where one twin goes on a quick space adventure at close to the speed of light and returns to find her stay-at-home sibling has been worried sick for decades.

An essential step in our quest for a unified picture of reality is to bring together quantum mechanics and the full relativity theory-general relativity.

At a bare minimum that means they need to agree on what time is.

In relativity, there's a beautiful symmetry between the nature of time and the nature of space.

But in the quantum, time remains .. special somehow.

For example, a quantum object can occupy two places or travel two paths at once-like in the double slit experiment.

But can an quantum object occupy two times at once, or have two different ages at the same time.

We really don't know how to "make time quantum".

Well, one thing we can try is to explore the strange relativistic effects of time on truly quantum systems.

Maybe something like a quantum twin paradox.

But what does that even mean?

One approach might be to take a two different quantum particles and send them on different routes-with different speeds and/or different positions in a gravitational field-and then see how they age differently.

In fact, this has been done already and with incredible precision.

The quantum particles in question are the cores of atomic clocks.

I'll come back to exactly how atomic clocks work later, because they may be the key to this whole thing.

The first twin paradox experiment-the 1971 Hafele-Keating experiment-involved sending an atomic clock on a plane ride around the world and comparing to one that stayed at home.

Time on the traveling clock slowed due to relative speed-we'll call that motional time dilation-but time sped up due to its increased distance from Earth's center-that's gravitational time dilation.

The resulting difference was exactly as predicted by Einstein's relativity theory.

By the way, relativistic time dilation had already been measured decades earlier using muons and other unstable particles, but the Hafele-Keating showed it directly with atomic clocks.

Modern atomic clocks are so precise that motional time dilation can in principle be observed taking an atomic clock for a walk, and gravitational version is measurable by moving an atomic clock up by centimeters.

As fascinating as these experiments are, they aren't measuring anything quantum about time, even if the mechanism at the heart of the clock is quantum.

Really there are just precision measurements of a purely relativistic version of the twin paradox.

What we really want to do is some sort of quantum twin paradox.

The quintessential weirdness of quantum mechanics is superposition-the fact that quantum systems can occupy multiple states simultaneously.

So what about doing a twin paradox experiment where, instead of sending identical twins on paths that have different time flows, we send the same particle on two separate paths at the same time by using quantum superposition.

Well, that sounds like the double-slit experiment but with time dilation.

In the double slit experiment, the "wavefunction" of a single particle travels through two slits, recombining on the other side to be detected as a single particle again at a screen.

Although each particle is detected at a single point, successive particles build up an interference pattern that reflects a wave-like passage though both slits.

The interpretation is that each particle travels through both slits as a probability wave, and is more likely to be detected where the two components of this wavefunction stack up or are "in phase".

In general, clean, double-slit interference is observed when there are strong phase correlations between the two paths.

A disruption of that phase correlation blurs and ultimately erases the interference pattern.

Curiously, this elimination of double-slit interference seems to precisely track how much knowledge we can gain about which path the particle took.

If a measurement is strong enough to tell you with certainty which path was traveled, it also scrambles phase information and eliminates the interference pattern.

If the measurement is weaker and leaves uncertainty as to the path, then the interference pattern will be blurred rather than destroyed.

So, what happens if one of the double-slit paths experiences a different amount of time?

For example, we could orient the experiment so the paths have different altitudes so that gravitational time dilation slows the clock of the lower path relative to the upper.

The easiest way to do this is to use a Mach-Zehnder interferometer-an MZI-rather than a classic double slit experiment.

In this version, a source of particles is split into two paths by a beamsplitter and then the two paths are brought back together and scrambled by a second beamsplitter.

The "interference pattern" is observed in the relative probability of the particle being seen in each of the final detectors.

Those probabilities shift with any phase shift of the particles along the paths.

And if we do something along those paths to determine which path was taken, interference fades or vanishes just like with the regular double-slit experiment.

So what if the MZI paths are at different altitudes?

Particles should accrue more age on the upper path compared to the lower path.

Measuring the age of the particle should tell us which path it took.

Or, if a particle travels both paths simulaneously it should be simultaneously older and younger.

At the very least, checking Seems simple, right?

Well, this requires incredible precision, but it's "simple" enough as an experiment that we actually did it half a century ago.

Back in the 70s the Colella-Overhauser-Werne or COW xperiment sent neutrons through a MZI-style interferometer and found that the neutrons taking the elevated path showed a phase shift you'd expect from the tiny speedup of time at their higher altitude.

On the surface this feels like it can only be explained with both quantum mechanics and general relativity, bringing us closer to a union between the two.

And maybe that's right.

But this isn't a slam dunk.

It turns out that this effect can be perfectly well described with quantum mechanics plus good old Newtonian gravity.

If we treat gravity as a simple force rather than some timey-wimey thing, then we find that the force induces exactly the same phase shift in the neutrons.

This effect has been called the "Gravitational Aharonov-Bohm Effect," where the regular Aharonov-Boh effect is the same thing but for an electric field.

So, yeah, relative particle phase shift can track relative time, and the COW experiment is consistent with seeing a superposition of gravitational time dilation this way.

But the interpretation is a bit muddy.

But to really say for sure that we've observed a superposition of different time flows, we need something closer to an internal clock for our particle rather than a simple phase.

And that's exactly what Magdalena Zych and company proposed in a paper 15 years ago.

Actually they proposed something a bit simpler-an internal quantum pendulum rather than the full quantum clock.

More precisely, a superposition of two internal energy states whose relative quantum phase evolves predictably.

They propose that if gravitational time dilation changes timeflow of our two paths at different heights, then the tick-tocking of this quantum pendulum will get out of sync for the superposition components of a particle traveling the two paths.

Each component should build up an internal memory of the path it took, recorded in the flow of time that it measured.

So when those components are brought back together, they would "know" which path they took.

Now if you remember from the double-slit experiment, path information disrupts the appearance of an interference pattern.

Such a disruption in this case could be taken as evidence of a superposition of different particle ages-the two superposed clocks got out of sync, so they have a record of the path taken, so can no longer interfere perfectly.

On the other hand, if no change is seen in the interference pattern, then there's no path information and it must be the clocks remained in sync.

That might indicate that both wavefunction components were kicking to the same global clock.

In practice, this quantum pendulum gives an imperfect measure of the time and so an imperfect determination of the path traveled.

The result is a blurred interference pattern, but it turns out that the amount of this blurring can be precisely determined by the difference in time flow between the paths.

So, time dilation should in principle be measurable this way and would be less ambiguous in its interpretation than the COW experiment which depends on simple phase difference along the paths.

On the other hand, some have argued that even the internal quantum clock of a Zych-type experiment can be interpreted in terms of the phase of those internal degrees of freedom.

So, I dunno, maybe there's no way to disentangle the interpretations of phase decoherance vs.

time dilation as a which-path marker.

So maybe the COW experiment got it right 50 years ago.

The Zych et al paper was 15 years ago.

And no one has managed to actually pull it off yet.

To be fair it's a very hard experiment to do, and although there are many clever ideas of how, we haven't managed to main quantum coherence on paths separated by enough height and with enough length for a measurable relative time difference to build up.

Hopefully that experiment will come along.

But actually we may not need it.

There's a much "easier" way to measure a quantum superposition of time in an actual quantum clock.

In September last year, a new paper came out by Gabriel Sorci and colleagues in Igor ikovski's group, together with the experimental teams at the national institute for standards and technology--NIST-- and Colorado State.

This idea brings us back full circle to the atomic clock that we started with.

The experiment proposed by the Zych team used only the heart of an atomic clock-a quantum pendulum, more technically a quantum oscillator.

But every clock in history hathe same basic anatomy: an oscillator and something to count the oscillations.

Like the pendulum of a grandfather clock and the gear system to tick over on each swing.

Now nature gives us a very precise pendulum: the electron transition inside an atom, which in some cases can oscillate between two states with near perfect regularity.

To turn such a quantum pendulum into an atomic clock, you take an ion and hit it with a laser pulse that places itn a superposition of its ground state and its excited state.

This triggers the quantum systeto begin evolving in a predictable fashion, with the phase of the system evolving at preciselthe transition frequency.

By locking the frequency of a laser to that oscillator, and then "gearing down" to lower frequency laser, the oscillations can be counted.

The resulting clock can be so precise that it loses less than a second in precision over the entire age of the universe.

The reason that no one has sent a full atomic clock through a full double-slit or MZI-like experiment is that we haven't figured out how to create a quantum superposition of different spatial paths for such complex systems.

But there's another way to create a superposition of different rates of time flow without the spatial separation.

Now we've been talking about gravitational time dilation-time ticks slower when you're deeper in gravitational fields.

But remember there's also the motional time dilation due to relative speed.

Now that doesn't sound immediately useful.

If you try to put an object in a superposition of two different speeds moving in a straight line then one will outpace the other and end up on different spatial trajectories ... which we just figured out was hard to do for an atomic clock.

But the idea of Sorci et al.

is to put the quantum oscillator in a superposition of different internal motional states.

Take an atom with an electron that can move between energy levels in a way that makes it a good atomic clock.

The atom can have a net charge-it's an ion-and that means it can be trapped in an electric or magnetic field.

Then it can be made to vibrate back and forth in that EM trap.

Its motional states are also quantized-it can be moving back and forth with specific frequencies.

The higher the frequency, the faster the motion, and so, in principle, the more relativistic time dilation.

The critical thing here is that if these motional states are really quantum, then the ion can be in a quantum superposition of moving slower and faster at the same time.

Without any time dilation, this superposition state would be stable and lead to a regular oscillation in the interference between the states, which is measured by the laser.

But with motional time dilation, the superposition of speeds means also a superposition of rates of time flow.

The "faster" motional state accrues time slower than the slower motional state, and so they become increasingly distinguished from each other.

The regular interference pattern is disrupted, and this is picked up by the coupled laser.

In this proposal, the superposition of speeds of the trapped ion takes the place of the superposition of paths in the various interferometer experiments.

But the powerful thing here is that no large spatial separations are needed.

A downside is that this is a purely special-relativistic effect, and gravity is irrelevant.

So it's not the quantum-general relativity link everyone is desperate for.

There's also debate about how to interpret the math of this proposal-is the flow of time changing due to motion, or is the motion changing the internal mass of the system, which in turn affects the evolution of that motion.

Whatever the interpretational limitations, being able to actually do an experiment counts for a lot.

And according to the Sorci paper we do have the measurement precision to do this experiment now.For example, for an Aluminum-ion clock, the time shifts of order few parts in ten billion billion.

But the best NIST ion clocks do now have the precision to measure that discrepancy.

This means soon quantum mechanicsay have to give up its single clock ticking in the background and instead treat time as auantum property of each branch of the wavefunction, just as the double-slit experiment does with space.

One step closer to a unified quantum description of spacetime.