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?
much as it's inspired us, check it out at the Space Time merch store. Now on to the episode.
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–Werner​ or COW
​experiment 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-Bohm​ 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​ ​Pikovski'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 has​ ​the 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 it​ ​in a superposition of its ground state
and its excited state. This triggers the quantum system​ ​to begin evolving in a predictable
fashion, with the phase of the system evolving at precisely​ ​the 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 shift​ ​is 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 mechanics​ ​may
have to give up its single clock ticking in the background and instead treat time
as a​ ​quantum 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.