Is Reality a Hologram?
An excerpt from Spooky Action at a Distance
by George Musser
String theory outgrew its name long ago. It postulates not just one-dimensional strings, but also two-dimensional membranes and higher-dimensional analogues—as theorists call them, 1-branes, 2-branes, 3-branes, 4-branes, and so on. Some branes, designated by D, can act as the endpoints of strings. At the bottom of this pecking order is the humble D0-brane, a type of particle. Being a true geometric point lacking size or any other spatial attribute, the D0-brane is the perfect building block for space. Confirming this intuition, theorists calculate that the D0-brane has the right properties to serve as the graviton, the particle that has been hypothesized for decades to convey the force of gravity.
Matrix models take this particle as fundamental and construct the universe entirely from lots of them. Every particle can interact with every particle, and their interactions are not simply on or off, but can vary in strength and in quality. The more energy you inject into a pair of particles, the tighter their bond will become. The namesake matrix of numbers quantifies this web of interactions. For example, if you read down to the eighth row and then across to the twelfth column, the number there will tell you how strongly particle number eight interacts with particle number twelve. To express not just the raw strength but also the quality of the connection, you need several such matrices.
Each matrix is a square, and running diagonally from the top left corner to the bottom right is a special set of numbers—where the eighth row meets the eighth column, the twelfth row meets the twelfth column, and so on. These tell you how much each particle interacts with itself. Self-interactions are a core feature of matrix models. The particles are subatomic narcissists, the physics equivalent of Facebook users who always “Like” their own posts. Their self-interactions have a carefree, unrestrained quality; you can dial their strength up or down without having to pump in energy…
… Matrix models do have some peculiarities, but they establish a remarkable principle: a bunch of particles obeying quantum physics can organize themselves so that you’d swear they live and move within space, even if space wasn’t in the original specification of the system. And it turns out that this principle is very general. Not just a swarm of D0-branes but almost any quantum system contains spatial dimensions folded inside it like a figure in a pop-up book. Most such systems don’t bootstrap space from utter spacelessness, as matrix models do, but prime the pump with a low-dimensional space in order to generate a higher-dimensional one.
The AdS/CFT duality that I mentioned in the previous chapter is such a system. It starts with a three-dimensional space and generates a nine-dimensional one. One reason string theorists like this scenario so much is that the universe can sustain much less complexity than the principle of locality would lead you to expect. The complexity is reduced by just the amount you’d expect if one of the dimensions of space were illusory. In the AdS/CFT scenario, that’s because the dimension in question is illusory. It can be collapsed down like an accordion because it was never really there. (“Illusory” is perhaps the wrong word. “Derived” or “constructed” would be better, if less poetic. The dimension may not exist at the lowest level, but it is still very real to anything larger than a brane.)
The disposable dimension reflects a particular aspect of order in the underlying quantum system. In fact, the requisite order is familiar to us from everyday life—specifically, the fact that big things and small things live as if in worlds apart. Our planet trundles around its orbit oblivious to human affairs, just as we spare little thought for the bacteria that lodge in our skin. Conversely, we have only a vague awareness of riding on a giant ball of rock, and bacteria know nothing of our daily struggles. Nature is stratified by scale.
Sound waves are an especially simple example of this stratification. Sounds of long and short wavelengths are oblivious to each other; if you sound a deep bass note and a high treble pitch simultaneously, each ripples through the room as though it were the only sound in the world. Their mutual independence is analogous to the autonomy of spatially separated objects. Suppose you play two piano keys, middle C and the adjoining D key. The C key creates a sound wave with a wavelength of 1 meter 32 centimeters, and D produces one with a wavelength 14 centimeters shorter. These waves overlap in the three dimensions of space through which they propagate, yet they’re independent of each other, as if they were located in different places. In a sense, you can think of the sound waves as residing 14 centimeters apart within a fourth spatial dimension.
The farther apart the keys are on a piano keyboard, the farther apart they are within this imaginary dimension; a given distance along the keyboard translates into a given distance within the dimension. You don’t see this dimension as such; to you it’s an abstraction that captures the acoustical independence of sound waves. But it’s a remarkably fitting abstraction. Musicians call the difference between pitches a musical “interval,” which has connotations of distance, as if our brains really do think of the differences between pitches as spatial separation. AdS/CFT duality takes this abstraction literally and suggests that one of the dimensions of the space we occupy represents the energy or, equivalently, the size of the waves within the underlying system.
Raman Sundrum, a string theorist at the University of Maryland, has a dramatic way of putting it. Suppose you’re an artist painting the National Mall, with an ice-cream stand in the foreground and the Washington Monument in the background. To evoke a sense of distance on the flat canvas, you draw these two objects at different scales. Something like that is happening for real in the AdS/CFT scenario. The universe looks three-dimensional, but could really be a two-dimensional canvas, and what we perceive as distance along the third dimension is ultimately a difference in scale. “The depth dimension could be recreated in the way that artists have to do it: by just drawing the Washington Monument really small and drawing something in the foreground really big,” Sundrum says. A faraway object is actually sitting right next to you; it looks small because it really is small. You can’t touch it not because it’s distant but because it’s so tiny that your fingers lack the finesse to manipulate it. When things grow or shrink, we perceive that as movement. It sounds fanciful but is backed up by rigorous mathematics.
Things of different sizes aren’t strictly independent; they interact with things of comparable size, and the effects can cascade from one scale to the next. Consider the proverb of the nail: for want of a nail, the shoe was lost; for want of a shoe the horse was lost; then the knight, the battle, and the kingdom. A nail shortage in a single blacksmith shop didn’t immediately cause the monarch’s downfall; it exerted its influence indirectly, via systems of intermediate scales. Sound waves of different pitches can also behave like this. A Chinese gong begins rumbling at a low pitch and gradually vibrates at successively higher pitches. The necessity of propagating through scale explains why spatial locality holds in the emergent dimension. What happens in one place doesn’t jump to another without passing through the points in between.
It’s not automatic that the underlying quantum system would possess this kind of hierarchical order. Just as a painting must be composed in just the right way to produce the sense of depth, so must the system have a certain degree of internal coherence to give rise to space. What ensures this cohesion is entanglement among the system’s particles or fields. To produce space as we know it, those particles or fields must be entangled by scale: each particle with its neighbor, each pair of particles with another pair, each group with another group. Other patterns lead to different geometries or systems that can’t be thought of as spatial at all. If the system is less than fully entangled, then the emergent space is disjointed, and an inhabitant of the universe would be trapped inside one region, unable to venture elsewhere. “Quantum entanglement is the thing that is responsible for connecting up the spacetime into one piece,” says Mark Van Raamsdonk, a theorist at the University of British Columbia. When we first encountered entanglement, it seemed to transcend space. Today, physicists think it might be what creates space.
George Musser is a contributing editor at Scientific American and Nautilus magazines and the author of two books, Spooky Action at a Distance and The Complete Idiot’s Guide to String Theory.
*All of the excerpts on my website are from books that have stayed with me for some reason—because the concept was awe inspiring, changed how I view the world, was beautifully expressed, or all three. I personally curate all of the book excerpts and always obtain the author’s approval before posting their work.
Photo Credit: Drew de F Fawkes on Flickr