We’ve gone through Chapters 1, 2, 3 and 4 of Reality Is Not What It Seems. The abstract groundwork has been laid, the rhetorical lumber all trucked in, and now it’s time to start building a brand-spanking-new theory of reality on quantum gravity!
Groovy. This particular post is my attempt to distill what I learned in Chapters 5, 6 and 7 of Rovelli’s treatise on quantum gravity.
Teeny Weenie Itsy Bitsy (and then Some)
As physicists started trying to make general relativity and quantum mechanics compatible with one another, they came up with a variety of ideas. One of them–the one Ravelli favors–is the idea of quantum gravity, an idea that hypothesizes that space itself can be be broken down into teeny, tiny basic components.
How tiny? Rovelli says they would be Planck length, which he describes as follows:
To give an idea of the smallness of the scale we are discussing: if we enlarged a walnut shell until it had become as big as the whole observable universe, we would still not see the Planck length.
So, “tiny” doesn’t even begin to cover it. This is almost the definition of infinitesimal, assuming it actually exists outside the confines of the minds of the quantum gravity theorists.
Space Is a Reticulum
Sometimes quantum gravity is called “loop quantum gravity” because some solutions to what’s known as the Wheeler-DeWitt equation–which is seminal to this school of thought–depends on closed lines in space, aka loops.
Remember Faraday lines from “May the Forces Be With You”? Well, the loops are Faraday lines of the gravitational field (as opposed the electronic fields that Faraday was discovering). These lines are not just in space, according to the theory, they are the stuff from which space itself is woven. How cool is that? I makes me think of the Great Norns of Norse mythology, spinning time and space and the fate of humankind.
In a sense, then, space is an enormous reticulum (or “graph”) in which the lines intersect. The intersections are “nodes” and the lines themselves are “links.” Those nodes are the quanta of space. This means, according to the loop theory, that space is not a continuum, as has long been assumed. It’s made up of those fantastically small atoms of space (though space itself is the gravitational field, according to this theory).
More Networks, This Time Spinning
So, if the gravitational field is woven of these quantum particles of space, then how do we talk about specific networks of them? Well, the lines between the nodes are viewed as half-integers, and those integers are called “spin” in the lingo of quantum physics. And so….Rovelli calls these little networks “spin networks.” The networks “represent a quantum state of the gravitational field.”
I don’t know how to properly conceive of spin networks, so for now I’m thinking of them as molecules. That is, atoms make up molecules and nodes make up spin networks. But this isn’t how Rovelli describes them so I’m probably way off.
One of the ways in which my molecule metaphor fails is that molecules actually exist as a thing (I think) whereas spin networks aren’t really entities at all. Rather, they are, like quantum particles, clouds of probabilities “over the whole range of all possible spin networks.”
But they look pretty simple when depicted on the page:
The image above is identified as a spin network but, unlike the version in Rovelli’s book, the lines are not represented by half integers, which I thought represented the quantum spin. Still, you get the idea.
Let’s allow Rovelli sum it up for us:
At extremely small scale, space is a fluctuating swarm of quanta of gravity that act upon one another, and together act upon things, manifesting themselves in these interactions as spin networks interrelated with one another.
This leaves me visualizing thick clouds of mosquitos down in the Everglades, which may not be quite what he intended. But, ready or not, it’s time to deal with time.
Got No Time
According to Rovelli’s ideas, time doesn’t exist apart from the gravitational field. (Side note: Do we really need to keep calling it the gravitational field? Seems kind of lame for something this essential. How about The Lattice of Existence? Maybe The Network of God, or even The One True Reticulum? As I said before, physicists are usually shit as namers and even shittier as marketers, though I’d admit that stealing “quarks” from James Joyce was kind of genius.)
Anyhow, time pops out of this Lattice of Existence (trademark!).
This may seem a bit nuts, but Einstein has already taught us that time is elastic, relative and linked to velocity and gravity. So Rovelli is just doing Weird Al one better. In a sense, time ceases to exist altogether or at least it does at the Planck scale. Time is only the measure of how the loops and nodes interact. It is emergent.
Spinfoaming at the Mouth
We already discussed spin networks. Now let’s graduate to spinfoam, which sounds a lot like the suds one sees in one’s washing machine as it gyrates noisily away. Here’s how Wikipedia defines it: a topological structure that “consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman’s path integral description of quantum gravity.”
Does that help you? No, me either.
Let’s start again. The “foam” metaphor comes from the foam that you and I are familiar with. I think the image below is a very cool portrayal of literal foam, maybe helping us better visualize the network-like quality of spinfoam.
And the “spin” part, of course, comes from the quantum mechanical notion of spin, to which we alluded earlier.
Rovelli writes that spinfoam “is made of surfaces that meet on lines, which in turn meet on vertices, resembling foam soap bubbles.” My impression is that spinfoam is a tool that merges two calculation techniques used by quantum physicists: a Feynman diagram and a lattice approximation. Rovelli provides more information about these but I’d clearly need a lot more education to understand them to my satisfaction.
You can see a representation of spinfoam here. Spinfoam is apparently what happens when a spin network moves through time. The lines become planes and the nodes become lines. You know how you can draw a series of stick figures on a small pad of paper and then flip the pages real fast to produce the illusion of moving animation? Well, that’s kind of what spinfoam is: the animation of the spin network moving forwards (or backwards!) in time.
The Universe Dresses Up in Spacetime but Is Secretly …
Rovelli argues that if you sand the universe down to the very bottom layer, you don’t find a beautiful hardwood floor (or spacetime or even oodles of particles). You find — dun dun dun! —covariant quantum fields.
Hah, I bet you’re so surprised, thinking I was going to say “gravitational field”! But, no, now we have a new and equally wonky term that stumbles trippingly off the tongue: covariant quantum fields.
Sigh. More Star Trek jargon to be rattled off by Geordi La Forge on the bridge of the Enterprise.
As I said, physicists are shit at naming stuff.
On the other hand, they sure can weave a tale.
Nice job, Professor.
Featured Image: John Tenniel's illustration from The Nursery "Alice" (1889). See https://commons. wikimedia.org /wiki/File: Alice_drink_me.jpg