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To observe the quantum nature of gravity and of spaceime itself, we need a particle collider the
size of the solar system. Or we could just physics smarter and build one on a lab bench. Here's how.
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The quantum world is certainly strange. Objects in multiple places and states at once. Random
transitions between states and places. weird instantaneous communication over large distances.
All that good quantum weirdness. But perhaps the strangest thing about quantum mechanics is that
its rules seem so different from the classical large scale world. And yet the latter comes
from the former. But how? And at what size does that happen? A related mystery is the connection
between gravity and the quantum. Gravity seems more in line with the classical world. It is
crisply defined and very non-random. But gravity is the fabric of spacetime which is knit together
on scales far smaller than the quantum. So at what point does spaceime itself become quantum?
The question of the quantum classical transition and the related quantum gravity connection are
notoriously difficult to probe directly due to the challenge of accessing the minuscule quantum world
and the minuscular quantum gravity world. But maybe the answer is not to build tiny experiments
or giant colliders, but to make the quantum world big enough to meet gravity and the classical world
halfway, perhaps inside a regular laboratory. The known laws of physics can be pretty clearly broken
up into these two realms, those describing the large scale classical world and the tiny quantum
world. Classical physics works great above about a micrometer where objects are made of many many
atoms. Everything larger is as we say macroscopic. Quantum mechanics rules below the nanometer scale.
At single molecules and atoms and smaller but the in between scale, the meos scale feels both of
these worlds. It is, as we say, semiclassical, behaving mostly classically in some ways,
but exhibiting quantum effects in certain conditions and when carefully coaxed. Today,
we're going to look at approaches and some example experiments for probing fundamental questions
by looking at this intermediate space where both classical and quantum mechanics are at play. Maybe
we don't have to wait for that solar system size particle accelerator to do this cool stuff. We'll
look at two paths. One is to look for a breakdown in our classical understanding of gravity at the
mesos scale. The second will be to look for true quantum effects in as large a system as possible,
but also in the mesos scale. So, we're going to try to make gravity small and then make quantum
big. If we can get them to meet somewhere in the middle, maybe we can even make gravity quantum.
Let's start with an experiment so elegant and simple that it's been our go-to for measuring
the strength of gravity since we well first tried to measure the strength of gravity. When Newton
first wrote down his law of universal gravitation, he reasoned his way to the proportionalities based
on a falling apple and the orbit of the moon. The force of gravity had to be proportional to
the product of those masses divided by the square of their separation. But he had no idea of the
value of the constant of proportionality, the gravitational constant. For that,
he would have needed to know the Earth's mass. But how do you weigh the Earth? The answer is that you
first measure G with known masses and then work your way back to the planet. But that requires us
to measure the minuscule gravitational attraction between masses that we can make and then weigh.
And it wasn't for another century after Newton's law that this became remotely possible. The guy
who did it should have been John Mitchell, the most underrated of the geniuses of physics.
This is the same guy who first conceived of the Newtonian version of the black hole, the dark
star. Mitchell's idea was to measure the minuscule gravitational pull between a pair of metal spheres
using a remarkable device, the torsion pendulum. This cutting device suspends a rod on a thin wire.
Rotating the rod twists the wire leading to a restoring force that pulls it back. This can
produce pendulum-like oscillations. But it can also be used to measure the strength of the force
doing the initial displacement. The restoring force increases with twist. So more twist means
more force. And the torsion pendulum is almost completely free from friction. With a thin wire,
it can be sensitive to extremely tiny forces. Perfect for the minuscule gravitational force
exerted between non-planet-sized objects. Mitchell actually built his torched pendulum, but he died
before he could complete the experiment. His close friend Henry Cavendish inherited the device,
refined the design, and saw the experiment through. It looked something like this. Two lead
balls of around a kilo uh were fixed to the arms of the pendulum while a pair of 160 kg balls were
fixed near these two with the intention of them gravitationally attracting the smaller balls. The
amount of twist in the pendulum would measure that force and because all the masses and distances
were known, the gravitational constant should fall out as the last unknown in the equation.
The experimental design and the care taken were extraordinary. So much so that in 1798,
Cavendish measured the gravitational constant to within 1% of the best modern value. Fun side fact,
Caendish described his experiment as weighing the Earth because with G in hand, we could now
calculate the Earth's actual mass just from the gravitational acceleration at the surface. In the
225 plus years since Cavendish's measurement, this experiment has been greatly refined,
but we've improved on that first measurement only by about one more decimal place because Cavendish
and Mitchell did such a good job. However, we're also now able to do this experiment with much
smaller masses, perhaps even small enough to see if the rules change as we approach
the quantum realm. And there are some reasons to think they might. In a previous episode,
we talked about how gravity might deviate from the Newtonian inverse square law at very short
distances if there are extra coiled up dimensions on those scales. Essentially, gravity leaks
into those dimensions very close to the source, causing it to weaken faster. But at longer ranges,
it settles into the regular inverse square fading. But there are other reasons to think that gravity
might behave this way. In string theory, there are ways for gravity to behave like the quantum forces
whose coupling strength changes with distance due to self-shielding. There's also the hypothetical
chameleon field, which is a dark energy candidate that has a distance dependent variable mass that
could do something similar. And give a theorist enough chalk and a sbatical, I'm sure that they'll
come up with several more options. But how to test? The problem is performing a Cavendish
type experiment with quantum or even meoscopic masses brings with it a new slew of noise and
possible interfering effects that not even Cavendish's dedication to precision could
overcome. For starters, we know the gravitational force is absurdly weak between two small masses
when compared to the other forces of nature. For example, the gravitational attraction between two
electrons is about 42 orders of magnitude weaker than the repulsive electromagnetic force pushing
them apart, making it essentially impossible to measure gravity. In that case, we can use neutral
masses, but even those tend to have internal electric charge distributions that can lead to
dipole interactions when objects are close by. And when surfaces get very close, the Casmir force and
the Vanderwal's force come into play, typically with much greater strength than gravity. Even
if we could compensate or outright avoid these effects, there are many other potential sources
of noise. natural vibrations in the experimental setup, seismic noise, and even gravitational noise
from nearby massive objects. A recent example of a successful teensy tiny Cavendish experiment came
from a group of physicists in Vienna. They built a Cavendish setup with tiny gold spheres a thousand
times lighter than the original lead source mass at under 100 mg. These 2 mm gold beads kept a
pendulum rod suspended on a wispy silica thread. This experiment was all about minimizing external
noise and interference. As with typical modern Cavendish experiments, this one was conducted in
a high vacuum and the masses were carefully discharged here using ionized nitrogen. A
conductive Faraday shield between test and source ensured no electromagnetic interactions between
the balls. The tiny gravitational field they were trying to measure between the balls which were
separated by about 2 and 12 mm was no stronger than that of a grad student standing 2 and 1/2
m away or a vianese tram rumbling by on the street outside. To help quieten the gravitational noise,
the experiments were done mostly between midnight and 5:00 a.m. during the quiet Christmas season.
And I guess grad students were positioned strategically and asked to remain motionless
on top of asking them to stay up all night and to miss the holiday. Even with these precautions,
more cleverness was needed to make the measurement. Now Henry Cavendish directly
measured his displacement of the torsion pendulum arms by seeing how far they moved. But in this and
other modern Cavendish experiments, researchers have a way to massively amplify that signal.
They oscillate the position of the source mass. So the test mass experiences a varying gravitational
field. The pendulum also oscillates and the varying gravitational field will very slightly
perturb that oscillation. This allows a direct measurement of the gravitational acceleration
caused by the source mass. The benefit of this method is that the researchers can watch for long
periods of time as the tiny pertabbations build up. By integrating the signal for say half a day,
they can detect a gravitational acceleration of 10 the power of minus 10 meters per second squared.
That's a 100 billion times smaller than what we feel at Earth's surface. The gravitational
constant measured in this experiment turned out to be consistent with the known gravitational
constant as measured by Cavendish and later experiments. There was a difference of around
9% but that's within the experimental uncertainty of this setup. So, the laws of gravity may not be
too different for these sub hundred milligram masses, but since the gold balls used here are
more comparable to a baseball in size than to an atom, that may not be too surprising.
It's impossible to know exactly how small we need to go to see if the strength of gravity changes,
if it even does. But this team feels that it should at least be possible to get down to the
plank mass nearly 10,000 times smaller than the current experiment with several significant but
plausible refinements of the methods. If we wanted to get these experiments down to truly quantum
scales, then we need to go down another 9 to 12 orders of magnitude. That may not be possible
with the Casemir setup, but other approaches like levitating nano particles or cryogenic
suspension may make it possible. So, we've been talking about measuring gravity down to the near
quantum scale. The other way we can go is try to observe quantum effects on as large a scale
as possible. One of the most defining of quantum phenomena is quantum entanglement in which a pair
of quantum objects can become correlated with each other in a way that defies classical explanation.
We typically think of entanglement as existing between truly quantum scale entities. For example,
a pair of electrons may have entangled spins. Each spin direction undefined when taken separately,
but those entangled spins are defined relative to each other. For example, as having opposite
directions, entanglement should exist between large systems. But the larger the system,
the harder it is to observe. The correlations between individual particles can be smeared
out and lost to the surrounding environment in a process called decoherence. Decoherence plays
a huge role, perhaps the entire role in making the quantum classical. And we could understand
that process a lot better if we could somehow observe entanglement in a macroscopic property
of a macroscopic system. One of the most promising approaches is in the field of optochanics. Imagine
a laser light bouncing between two mirrors. We call this an optochanical cavity. The mirrors
in this case are suspended so they can oscillate forward and back. A photon from the laser hitting
the mirrors will transfer momentum that depends on the photon frequency. That sets up an oscillation
in the mirrors which in turn changes the size of the cavity which in turn changes the frequency
of the modes of light in the cavity. This leads to a feedback cycle in which the oscillation of
the mirrors is correlated with the frequency of the photons. And done carefully enough,
this correlation can be a true quantum entanglement. This has been achieved with
very very tiny mirrors. The first was in 2010 with an entanglement demonstrated between a
light field and just a single membrane of silica nitride as the mirror. But in 2011, a pair of
mirrors was put into entanglement, not just with the bouncing photons, but also with each other.
That means two macroscopic systems in a state of entanglement with each other. So here we are
really blurring the line between the quantum and the classical. But these mirrors were still tiny,
really messcopic. It would be nice if we could achieve the same result for something truly
macroscopic. Of course, it would be incredibly expensive to build a much larger optochanical
cavity with all the precision engineering, the noise mitigation tech, etc. to even attempt a
macroscopic optochanical entanglement measurement. Good thing we already built one. The laser
interroter gravitational wave observatory, LIGO, was designed to detect space-time ripples, but in
principle could be used to detect correlations in the oscillations of the mirrors that point
to true entanglement between these genuinely macroscopic objects. Many of the challenges for
doing this with LIGO have already been solved. In order to detect actual gravitational waves,
incredible work was done to minimize random noise, to flag and remove seismic vibrations, and even
remove spirious gravitational signals. The major outstanding challenge is dealing with a special
type of noise that can confuse the entanglement signal. This is non-marovian noise which unlike
regular noise develops correlations over time sort of like a memory that can be confused for
the entanglement source correlations. Motivated by the goal of teasing out any signs of entanglement
in LIGO, in 2024, a group of researchers went back through the LIGO's data, now equipped with new and
improved models to account for the non-makovia noise, and they haven't found anything yet.
But with better noise modeling and more integration time, we may spot the quantum whisper
of entanglement between LIGO's 40 kg mirrors which span its 4 km arms. Detecting entanglement between
classical or semic-class objects can help us understand the boundary between the quantum
and the classical. The Cavendish experiment we started with was about exploring the quantum
nature of gravity. Now the holy grail would be to bring these goals together to detect entanglement
between systems in which the entanglement is actually mediated by gravity. If gravity can
do this, it means that gravity itself must have quantum properties. Now we did look at
one approach a while back with a stern-gerlach type experiment in which nano diamonds in a
super position of positions nudge at each other gravitationally and so become quantum entangled.
But there are other proposals that don't require the super position of positions. For example,
putting test masses in a superp position of spin states whose energy difference then leads to a
difference in the gravitational fields that they generate. or even a real Cavendish-like experiment
in which a pair of oscillating pendula develop non-class correlations over long periods of time
that can only have arisen from a gravitationally mediated quantum connection. All of these ideas
are still in early phases from thought experiment to active planning. The technological hurdles are
major but the crazy thing is that the hurdles are just technological and there are clear paths to
solving them. This is what's so cool. We will soon have a lab bench experiment that can start to map
the quantum classical divide and even observe the quantum behavior of gravity. Physics is cool. Just
a couple hundred years from lead balls suspended from wires to the quantum nature of spacetime.
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