My dad took a peculiar pleasure in fitting the maximum amount of stuff into the smallest possible space. Whenever we went on a family trip, he packed our suitcases like a 3-D jigsaw puzzle, ensuring there wasn’t a single wasted inch—a laudable skill as far as I was concerned, since I could take all the toys I wanted and he’d find room for them. (The bags weighed a ton, but those were the days of free baggage check.) Later, when I drove off to my first apartment, he managed to get a household’s worth of stuff into a two-door car. He always denied there’s any limit on how much stuff you can pack into a certain volume. It was just a question of ingenuity.
Alas, the theoretical physicists speaking at A Thin Sheet of Reality: The Universe as a Hologram at this year’s World Science Festival have bad news: there is a limit. If you exceed it, the gravitational force exerted by the contents of your suitcase will become so intense that the suitcase collapses into a black hole, and you’ll never see your stuff again. Admittedly, this ultimate limit is pretty forgiving. An airplane roll-on could hold a Jupiter’s worth of highly compressed material before you ran into trouble with black holes. (The TSA is another matter.)
A limit, per se, might not seem terribly surprising. No amount of paternal ingenuity can overcome the fact that material objects unavoidably take up space; however hard you squeeze, you can’t compress them to nothing. But what’s strange about the ultimate packing limit is that it depends on the size of the container. Bigger containers can hold proportionately less stuff than smaller ones. A two-door car, as wide as two suitcases, has room for eight suitcases in all. If I pack each suitcase to its ultimate limit and then jam them all into the car, I will exceed the car’s overall limit and lose the lot. The most I can put in is two. The car promises so much extra room, but as soon as I try to avail myself of it, nature stops me. It is as if the space is a mirage.
This limit on packing is one aspect of what physicists call the Holographic Principle by analogy to a hologram, which, like my old car, gives the illusion of depth. What happens when you pack things together is one of the most important thought experiments for physicists today. When I dropped by Stanford University in February to chat with one of the participants in this festival event, Lenny Susskind, he told me, “I think it’s the most radical lesson that we’ve learned about physics since the Uncertainty Principle.”
What makes it so radical is that the density of matter was supposed to depend only on how compressed each individual scrap of matter can become. It shouldn’t make any difference how many scraps you pile up. That is true not just of density but of other key properties such as how much information each scrap of material can encode. The whole is just the sum of its parts. This intuition is formalized in the modern theory of matter, known as quantum field theory. But the propensity to form black holes means that what one scrap of matter is capable of doing depends on what all the other scraps are doing. The whole is less than the sum of its parts.
Physicists have suspected for over half a century that quantum field theory needs to give way on extremely small scales, eventually becoming unified with the other great pillar of modern physics, Einstein’s general theory of relativity. That is why they have built giant particle accelerators, which act as powerful microscopes to zoom in on the sub-subatomic world. But the Holographic Principle means that quantum field theory also breaks down on large scales. Whereas no suitcase on Earth is at risk of collapsing to a black hole, the limit become pressing as size increases. Objects with the dimensions of the solar system max out at the density of liquid water. The cosmos is filled with black holes that formed when natural processes attempted to pack too much material too tightly. It’s one thing to expect a breakdown of quantum field theory on small scales, quite another to make sense of it on a large scale.
The Holographic Principle also shows that space isn’t what it appears to be. I don’t mean outer space, the realm of astronauts and asteroids, but the space all around us, the space in our suitcases and cars, the space that separates lovers when they part. Space is pulling a bait-and-switch on us: it seems to have plenty of room to hold stuff, yet it doesn’t. The Holographic Principle is one of several clues suggesting that the concept of “space” is an elaborate illusion—or, to be more precise, that it emerges from a deeper spaceless reality, much as living organisms emerge from inanimate matter.
What breathes life into a lifeless jumble of chemicals is the way those pieces fit together and work together. Likewise, the world may develop a spatial structure from the way its most fundamental ingredients fit together and work together. The best-developed theory for how this can happen goes by the somewhat technical name of “gravity/gauge duality,” which uses the concepts of quantum field theory to do the fitting and working. The force of gravity turns out to be a byproduct of the process. One implication is that spatial notions such as distance are derivative. Objects that appear to be far apart may actually be lying right on top of each other, when considered in some deeper sense—which perhaps offers some consolation to the separated lovers of the world.
This panel brings together Susskind and the other father of the Holographic Principle, Nobel laureate Gerard ’t Hooft, along with two physicists who generalized and elaborated on their work, Raphael Bousso and Herman Verlinde.
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