Musings on quantum gravity
Recently I came across this article about an experiment to reconcile quantum physics with gravity, the one fundamental force that hasn’t yet been explained in quantum terms:
The problem with reconciling gravity (which is explained by Einstein’s General Theory of Relativity) and quantum physics is that they seem to follow incompatible laws. Quantum particles can exist in superpositions of more than one state at a time, while gravitational phenomena remain resolutely “classical,” displaying only one state. Our modern interpretation suggests that what we observe as classical physics is actually the result of the quantum states of interacting particles correlating with each other. A particle may be in multiple states at once, but everything it interacts with — including a measuring device or the human observer reading its output — becomes correlated with only one of those states, and thus the whole ensemble behaves classically. This “decoherence” effect makes it hard to detect quantum superpositions in any macroscopic ensemble, like, say, a mass large enough to have a measurable gravitational effect. Thus it’s hard to see quantum effects in gravitational interactions. As the article puts it:
At the quantum scale, rather than being “here” or “there” as balls tend to be, elementary particles have a certain probability of existing in each of the locations. These probabilities are like the peaks of a wave that often extends through space. When a photon encounters two adjacent slits on a screen, for example, it has a 50-50 chance of passing through either of them. The probability peaks associated with its two paths meet on the far side of the screen, creating interference fringes of light and dark. These fringes prove that the photon existed in a superposition of both trajectories.
But quantum superpositions are delicate. The moment a particle in a superposition interacts with the environment, it appears to collapse into a definite state of “here” or “there.” Modern theory and experiments suggest that this effect, called environmental decoherence, occurs because the superposition leaks out and envelops whatever the particle encountered. Once leaked, the superposition quickly expands to include the physicist trying to study it, or the engineer attempting to harness it to build a quantum computer. From the inside, only one of the many superimposed versions of reality is perceptible.
A single photon is easy to keep in a superposition. Massive objects like a ball on a spring, however, “become exponentially sensitive to environmental disturbances,” explained Gerard Milburn, director of the Center for Engineered Quantum Systems at the University of Queensland in Australia. “The chances of any one of their particles getting disturbed by a random kick from the environment is extremely high.”
The article is about devising an experiment to get around this and observe a superposition (potentially) in a “ball on a spring” type of apparatus. What interests me, though, is a more abstract discussion toward the end of the article.
Inspired by the possibility of experimental tests, Milburn and other theorists are expanding on Diósi and Penrose’s basic idea. In a July paper in Physical Review Letters, Blencowe derived an equation for the rate of gravitational decoherence by modeling gravity as a kind of ambient radiation. His equation contains a quantity called the Planck energy, which equals the mass of the smallest possible black hole. “When we see the Planck energy we think quantum gravity,” he said. “So it may be that this calculation is touching on elements of this undiscovered theory of quantum gravity, and if we had one, it would show us that gravity is fundamentally different than other forms of decoherence.”
Stamp is developing what he calls a “correlated path theory” of quantum gravity that pinpoints a possible mathematical mechanism for gravitational decoherence. In traditional quantum mechanics, probabilities of future outcomes are calculated by independently summing the various paths a particle can take, such as its simultaneous trajectories through both slits on a screen. Stamp found that when gravity is included in the calculations, the paths connect. “Gravity basically is the interaction that allows communication between the different paths,” he said. The correlation between paths results once more in decoherence. “No adjustable parameters,” he said. “No wiggle room. These predictions are absolutely definite.”
Now, this got me thinking. Every particle with mass interacts gravitationally with every other particle with mass, so there would be no way to completely isolate them from interacting. For that matter, gravity affects light too. So if gravity is an irreducible “background noise” that prevents stable superpositions, that would explain why quantum effects don’t seem to manifest with gravitational phenomena.
And that does sort of reconcile the two. The decoherence model, that classical states are what we get when quantum states interact and correlate with each other, basically means that classical physics is simply a subset of quantum physics, the behavior of quantum particles that are in a correlated state. So the “classical” behavior of gravity would also be a subset of quantum physics — meaning that relativistic gravity is quantum gravity already, in a manner of speaking. We just didn’t realize they were two aspects of the same overarching whole.
Now, this reminds me of another thing I heard about once, a theory that gravity didn’t really exist. It might have been the entropic gravity theory of Erik Verlinde, which states that gravity is, more or less, just a statistical artifact of particles tending toward maximum entropy. Now, what I recall reading somewhere, though I’m not finding a source for it today, is that this — or whatever similar theory I’m recalling — means that particles tend toward the most probable quantum state. And statistically speaking, for any particle in an ensemble, its most probable position is toward the center of that ensemble, i.e. the center of mass. So I had the thought that maybe what we perceive as gravity is more just some sort of probability pressure as particles tend toward their most likely states.
Now, if Stamp’s theory is right, then Verlinde’s is wrong; there must be an actual force of gravity, or rather, an interaction that correlates the paths of different particles. But it occurs to me that there may be some basis to the probabilistic view of gravity if we look at it more as a quantum correlation than an attraction. To explain my thinking, we have to bring in another idea I’ve talked about before on this blog, quantum Darwinism. The idea there is that the way decoherence works is that the various states of a quantum particle “compete” as they spread out through interaction with other particles, and it’s the more robust, stable states that prevail. Now, what I’m thinking is that as a rule, the most stable states would be the most probable ones. And again, those would tend to be the positions closest to the center of mass, or as close as feasible when competing with other particles.
So if we look at gravitation not as an attractive force per se, but as a sort of “correlational field” that promotes interaction/entanglement among quantum particles, then we can still get its attractive effect arising as a side effect of the decoherence of the correlated particles into their most probable states. Thus, gravity does exist, but its attractive effect is fundamentally a quantum phenomenon. So you have quantum gravity after all.
But how to reconcile this with the geometric view of General Relativity, that gravity is actually a manifestation of the effect that mass and energy have on the topology of spacetime? Well, that apparent topology, that spatial relationship between objects and their motions, could be seen as a manifestation of the probabilistic relationships among their position and movement states. I.e. a particle follows a certain path within a gravitational field because that’s the most probable path for it to take in the context of its correlation with other particles. Even extreme spacetime geometries like wormholes or warp fields could be explained in this way; an object could pass through a wormhole and show up in a distant part of space because the distribution of mass and energy that creates the wormhole produces a probability distribution that means the object is most likely to be somewhere else in space. Which is analogous to the quantum tunneling that results because the peak of a particle’s probability distribution shifts to the other side of a potential barrier. And for that matter, it has often been conjectured that quantum entanglement between correlated particles could be caused by microscopic wormholes linking them. Maybe it’s the other way around: wormholes are just quantum tunneling effects.
One other thought I’ve had that has a science-fictional impact: if gravitation is a “correlational quantum field” that helps the most probable state propagate out through the universe, that might argue against the Many-Worlds Interpretation of quantum decoherence. After all, gravity is kind of universal in its effect, and the correlation it creates produces what we see as classical physics, a singular state. It could be that coherent superpositions would only happen on very small, microscopic scales, and quantum Darwinism and gravitational correlation would cause a single consensus state to dominate on a larger scale. So instead of the whole macroscopic realm splitting into multiple reality-states (timelines), it could be that such splitting is only possible on the very small scale, and maybe the simmering of microscale alternate realities is what we observe as the quantum foam. It could be that the MWI is a consequence of an incomplete quantum theory that doesn’t include gravity, and once you fold in gravity as a correlating effect, it imposes a single quantum reality on the macroscopic universe.
Which would be kind of a bummer from an SF perspective, since alternate realities are useful story concepts. I’d just about come around to believing that at least some alternate realities might be stable enough to spread macroscopically, as I explained in my quantum Darwinism essay linked above. Now, I’m not so sure. The “background noise” effect of gravity might swamp any stable superpositions before they could spread macroscopically and create divergent timelines.
However, these thoughts might be applicable to future writings in my Hub universe (and as I’ve discussed before, I’ve already given up on the idea of trying to reconcile that with my other universes as alternate timelines). The Hub is a point at the center of mass of the greater galaxy — i.e. the system that includes the Milky Way proper, its satellite galaxies, and its dark-matter halo — that allows instantaneous travel to any point within that halo. I hadn’t really worked out how it did so, but maybe this quantum-gravity idea provides an answer. If gravity is quantum correlation, and all particles’ probability distributions tend toward the center of mass, then maybe the center of mass is the one point that allows quantum tunneling to the position of every other particle. Or something like that. It also provides some insight into the key McGuffin of the series, the fact that nobody can predict the relationship between Hub vectors (the angle and velocity at which the Hub is entered) and arrival destinations, meaning that finding new destinations must be a matter of trial and error. If the Hub works through quantum gravity and correlation with all the masses within the halo, then predicting vectors would require a complete, exact measurement of the quantum state of every particle within the halo, and that would be prohibitively difficult. It’s analogous to how quantum theory says that every event in the universe is already part of its wave equation, but we can’t perfectly predict the future because we’d need to know the entire equation, the behavior of every single particle, and that would take an eternity to measure. So it’s something that’s theoretically deterministic but functionally impossible to determine. The same could be true of Hub vectors.
Although… we’re only talking about one galaxy’s worth of particles, which is a tiny fraction of the whole universe. So maybe it’s not completely impossible…
Anyway, those are the musings I’ve had while lying awake in bed over the past couple of early mornings, so maybe they don’t make much sense. But I think they’re interesting.