At What Point Does Spacetime Become Quantum? (SCRIPT)

To observe the quantum nature of gravity and of spacetime 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 or 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 the quantum world 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’s crisply defined and very non-random. But gravity IS the fabric of spacetime, which is knit together at scales far smaller than the quantum. So at what point does spacetime 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 miniscule quantum world, and the minisculer— quantum gravity world.

Well, maybe the answer is not to build tiny experiments, but to make the quantum world big enough to meet gravity and the classical world halfway. 

The known laws of physics can be pretty cleanly broken up into two realms—those de scribing the large-scale, classical world and those describing 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 inbetween scale, the mesoscale, feels both of these worlds—it is “semi-classical”, behaving mostly classically in some ways, but exhibiting quantum effects in certain conditions or when carefully coaxed.

Today we’re going to look at approaches, and some example experiments, for probing these 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 a solar system-sized particle accelerator to do some of this stuff.

We’ll look at two paths: one is to look for a breakdown in our classical understanding of gravity at the mesoscales. The second will be to look for true quantum effects in as large a system as possible—also the mesoscale. So, we’re going to try to make gravity small, then make the quantum big. If we can get them to meet 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 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 the 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 miniscule 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 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 miniscule gravitational pull between a pair of metal spheres using a remarkable device—the torsion pendulum. This cunning 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 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, and with a thin wire can be sensitive to extremely tiny forces. Perfect for the miniscule gravitational force exerted between non-planet-sized objects.

Mitchell actually built his torsion pendulum, but 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 one kilo were fixed to the arms of the pendulum while a pair of 160kg balls were fixed near these two, hopefully, gravitationally attracting the smaller balls. The amount of twist in the pendulum would measure that force, and because all masses and distances were known, the gravitational constant would 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—Cavendish described his experiment as “weighing the Earth” because, with G in hand, we could now calculate earth’s mass just from the gravitational acceleration at the surface.

In the 225+ years since Cavendish’s measurement, this experiment has been massively refined. 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 over 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 regular inverse-square fading.

 But there are other reasons gravity might do this. In string theory there are ways for gravity to behave like the other forces, whose coupling strength changes with distance due to self-shielding. There’s 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 sabbatical and I’m sure they’ll come up with several more options.

But how to test? The problem is, performing a Cavendish type experiment with quantum or even mesoscopic 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. 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.

We can use neutral masses, but even those tend to have an internal electric charge distribution that can lead to dipole interactions when objects are close by. And when surfaces get very close, the Casimir force and van der Waals 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 teensie tiny Cavendish experiment came from a group of physicists in Vienna. They built a Casimir setup with tiny gold spheres 1000 times lighter than the original lead source mass, at under 100 milligrams. These 2mm gold beads capped a with pendulum rod suspended on a wispy silica thread. This experiment was all about minimizing external noise and influence. As with typical modern Cavendish experiments, this one was conducted in high vacuum and the masses were carefully discharged, here using ionized nitrogen. A conductive Faraday shield between test and source ensured no electromagnetic interaction between the balls. The gravitational field they were trying to measure between the balls separated by 2.5mm was no stronger than that of a grad student standing two and half meters away or a Viennese tram rumbling by on the street outside. To help quieten the gravitational noise, experiments were done between midnight and 5am 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 miss the holiday.

Even with these precautions, more cleverness was needed to make the measurement. Cavendish directly measured the displacement of the torsion pendulum arms. In this and other modern Cavendish experiments, researchers have a way to massively amplify the 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 measure 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 perturbations build up. By integrating the signal for half a day, they detected a gravitational acceleration of 10^-10 m/s^2; 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 about 9%, but that’s within the experimental uncertainty of this setup.

So, the laws of gravity may not be too different for these sub-100 mg masses, but since the gold balls used are more comparable to a baseball than an atom, that may not be 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 be possible to get down to the Planck 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 a Casimir setup, but other approaches like levitating nanoparticles or cryogenic suspension may make it possible. 

So, we’ve been talking about measuring gravity down at the near-quantum scale. The other way we can go is to 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 may be undefined when taken separately, but those two entangled spins are defined relative to each other, for example, as having opposite directions.

Entanglement should also 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 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 optomechanics. Imagine a laser light bouncing between two mirrors. We call this an “optomechanical cavity”. The mirrors 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 frequencies 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 silicon 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. 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 optomechanical cavity with all the precision engineering, the noise mitigation tech, etc. to even attempt a macroscopic optomechanical entanglement measurement. Good thing we already built one. The Laser Interferometer Gravitational Wave Observatory—LIGO—was designed to detect spacetime ripples, but in principle could also 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 spurious gravitational signals. The major outstanding challenge is dealing with a special type of noise that can confuse the entanglement signal. This is non-Markovian noise, which, unlike regular noise, develops correlations over time 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 LIGO’s data, now equipped with a new and improved sophisticated model to account for non-Markovian noise. And they found … well, nothing yet. But with better noise modeling and more integration time, we may spot the quantum whisper of entanglement between LIGO’s 40kg mirrors spanning its 4km arms.

Detecting entanglement between classical or semi-classical 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. 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. 

We looked at one approach to doing this with a Stern-Gerlach type experiment, in which nanodiamonds in a superposition of positions nudge at each other gravitationally and so become quantum-connected. But there are other proposals that don’t require a superposition of positions, for example putting test masses in a superposition of spin states whose energy difference leads to a difference in the gravitational fields they generate. OR even a Cavendish-like experiment in which a pair of oscillating pendula develop non-classical 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 experiments 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—that we’ll soon have lab-bench experiments 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.