Testing the nature of spacetime via "the squeeze"
An update on the experimental effort to test whether spacetime is quantum via the "decoherence vs diffusion trade-off".
The postquantum theory of gravity is an alternative to quantum gravity. Instead of trying to quantise spacetime it posits that spacetime should be treated as fundamentally classical, and derives the consequences of this. The result appears to be a unique theory which is mathematically consistent with the quantum world.
But it is not only a candidate for a theory which reconciles quantum mechanics with general relativity, it also serves as the alternative hypothesis to the quantum nature of spacetime. If we’re performing experiments to test the quantum nature of spacetime, we can only do so if we can compare what a quantum theory of gravity would predict with the alternative hypothesis. We have very strong reasons to believe that the postquantum theory is the only possible alternative to quantizing spacetime. This puts us in a win-win situation, because we can both test this new theory, while at the same time, testing the more general proposition of whether spacetime has a quantum nature.
A personal note: physics amid turbulent times
One way to test whether spacetime is quantum, is via something called Gravitationally Mediated Entanglement proposed by Sougato Bose among others. Here I’ll discuss an alternative proposal, we like to call “the squeeze”. I was recently in Vienna discussing these experiments with researchers at IQOQI and I’ve been meaning to post an update ever since my return to the UK. I have to admit that posting about physics feels disconnected from the current state of the world – so the draft of this post has been sitting untouched on my hard drive since the U.S. election. I’m sharing it now as a way of re-engaging scientifically with the outside world. I plan some political content as well, because as much as I’d like to focus on physics, we cannot ignore the wider context in which science takes place.
But for today at least, let’s return to science: Physicists often test their ideas about the universe by looking for constants of nature—fixed quantities like Newton’s constant (G), the speed of light (c), or Planck’s constant (ℏ), which underpins quantum mechanics. If spacetime remains classical instead of being quantum in nature, it introduces a new constant, "D". This constant is dimensionless like those which govern all the other quantum fields of nature (like electromagnetism) so that’s intriguing. It determines how random, or wobbly, spacetime must be to keep being spacetime, even in a quantum world. Imagine "D" being like a dial that nature uses to set the level of randomness in spacetime. If the value of "D" is large, then spacetime is very wobbly.
The squeeze
This gives rise to "the squeeze"—a series of experiments designed to put pressure on classical spacetime theories from both sides. We anticipate being able to determine whether the theory is correct or not, in the near term via tabletop experiments.
On one side, we have precision gravity measurements that act as extremely sensitive detectors, listening for any hint of wobble in the gravitational field. If spacetime is classical, it should be wobbly enough that current precision measurements might already detect it. In 2016, a satellite called LISA Pathfinder measured the gravitational field in space, and found that it experienced random fluctuations. Was this just noise due to its instruments or was this randomness due to wobbly spacetime? We don't yet know, but luckily we don’t need to know, because either way, this sets a ceiling, or upper limit on the value of D.
On the other side, we have interference experiments with massive particles. Here, we try to place heavier and heavier particles, into quantum superpositions of different positions. When the particle is in superposition, we often say that the particle behaves like it is in two places at once, and I think that gives a reasonable shorthand picture of what a superposition is, but it’s a bit more complicated than that. At any rate, putting massive particles into superpositions of many places, has been achieved with various molecules, such as those composed of many carbon atoms, but eventually we want to use even denser molecules such as gold or osmium. We have proven mathematically that if spacetime is not very wobbly, then massive particles will have trouble being put in a superposition of two places. We call this “the decoherence vs diffusion trade-off”. The reason for the trade-off is that a massive quantum particle will bend spacetime around where it is, so that spacetime learns where the particle is and causes the particle’s quantum state to collapse into being in only one place. But the more unpredictable spacetime is, the less spacetime “knows” where the particle is, and so the longer the particle can remain in superposition. In other words, the classical nature of spacetime infects the quantum superposition, forcing the particle to become classical in the sense that it forces the particle to localise into a definite location. But the more wobbly spacetime is, the longer this process takes.
Conversely, if superpositions last a long time, then spacetime must be very wobbly to allow this to happen, and we can prove this must hold for any theory in which spacetime is classical. The ability to maintain these superpositions thus places a floor, or lower limit on the value of D.
Now comes the squeeze. The squeeze comes from pushing both the floor and the ceiling closer and closer together. If we manage to make gravity measurements precise enough, and superposition experiments last long enough, until the ceiling is lower than the floor, we can indirectly rule out classical spacetime. This is an indirect test of the quantum nature of spacetime, because it relies on some assumptions about the theory – albeit very mild ones -- namely that the theory is local and generally covariant.
This is different from attempts to verify the Diosi-Penrose conjecture, which is that gravity causes wavefunctions to collapse, because we don’t need to know why a particle stops being in superposition. The particle could stop being in a superposition because of its interaction with classical spacetime, or it could localise because it interacts with air molecules. We merely use the time we can maintain a superposition to put a lower bound on D. Likewise we don’t need to know whether the randomness we witness in the gravitational field is due to spacetime being fundamentally wobbly or due to noise in the experiment, we just use the precision gravity measurement to put an upper bound on D. So the experiment is extremely robust.
Verifying the postquantum theory
On the other hand, if we try to squeeze D from both sides, and find that we can't, that the floor hits the ceiling and can get no higher, it would be a confirmation of the postquantum theory. This would represent a revolutionary shift in how we perceive gravity and quantum mechanics. Note that we have analysed previous experiments which already set a floor and a ceiling to D. That is how we know that it’s possible that LISA Pathfinder could have detected the noise in the gravitational field, and how we know that we can test the theory in the near term.
Part of our optimism also comes from the fact that the goal of experimentalists thus far has been on demonstrating their technical prowess by putting more and more massive objects into a superposition of being at two places. But we’ve discovered that the particle’s probability density is equally important. More precisely, we’ve found that the figure of merit to aim for is τM2/V, where M is the particle’s mass, τ is the coherence time over which the particle remains in superposition and V is the volume of the particle’s probability density in each branch of the superposition1. This volume factor is usually not considered, and suggests that experimental bounds could be significantly improved.
Betting against quantum gravity
I’ve recently received some inquiries about a related experimental proposal that has gotten a bit of attention this week due to this video by physicist and science communicator Sabine Hossenfelder. She has been famously critical of virtually all new theories in physics, but has highlighted the postquantum theory in her top five breakthroughs of 2024. The honeymoon may be over — based on this new experimental proposal, she now seems to be betting it will disprove the postquantum theory of gravity. She doesn’t explain why, but she wouldn’t be the first person to place a bet for quantum gravity. When I get a moment, I may post some thoughts about the new experimental proposal in the comments (I think it’s interesting!), but it is surprising to me that such a proposed experiment would change anyone’s prior as to the outcome.
I am here considering the case where the particle is in a superposition of being in two locations (call them Left and Right). If the particle is on the right, then there is a volume V in which we are highly likely to find the particle, likewise if the particle is on the left, there is another volume in which I’m likely to find the particle, and I here assume this volume is roughly the same. Note that this stems from a non-relativistic calculation, but the relativistic case may add important factors.
I’m not a physicist, but I have questions.
1) As I understand it, you have mathematically proven that 'classical gravity --> stochastic gravity.' You also propose experiments to demonstrate that gravity is stochastic. Suppose we experimentally prove that gravity is stochastic, but purely by the rules of logic, this does not imply that gravity is classical. It could instead be some form of quantum stochastic gravity.
2) Are there any cosmological consequences of the fact that gravity is stochastic? Intuitively, over very large distances, light might deviate from a straight trajectory or scatter in some way.