Science Seen Physicist and Time One author Colin Gillespie helps you understand your world.

# Could the Universe Have Only Two Dimensions?

It’s strange but true: Physics is now studying the universe as if it is a two-dimensional hologram. How did this come to be? And what does it mean?

The 3D/2D duality is known as the holographic principle. Two decades ago American theoretical physicist Leonard Susskind described it this way: ‘In a certain sense the world is two dimensional and not three dimensional as previously supposed.’

The concept arose from the clash between the two well-established theories of twentieth-century physics. Attempts—known generally as quantum gravity—to reconcile deep contradictions between quantum theory and general relativity spawned string theory, a bold new exploration of physics at the incredibly tiny Planck scale. String theory led to new views about the very early universe and about black holes. Black holes led to speculation about what happens to the information that falls into them. Answer: It must be located on the event horizon, the edge of the zone from which even light cannot escape. And this is a 2D surface.

This looks like an exciting advance. It links Planck-scale physics concepts with ever-more-precise observations of cosmic microwave background radiation from the Big Bang and with recent observations of black holes using gravitational radiation. At last the very smallest stuff is shedding light on the very largest and vice versa.

But so far the holographic principle has mostly opened up new vistas for science fiction writers. Yet it has serious consequences if it describes reality: For example, it imposes a new upper limit on the amount of information in the universe.

Here is a way to think of it. Let’s say the universe is N Planck units across. We need ~N3 bits of information—position, etc.—to specify the 3D view of them. Here, the ~ sign means ‘in the order of’.  But we need only ~N2 bits of information for the 2D view, ~N-fold fewer. As N is very large (~1062 or more) the 2D view is a far simpler specification. But is it real?

The 2D event horizon of a black hole is a real surface. It certainly contains the black hole. But what surface can contain the whole universe? Let’s follow Einstein in a brain-bending thought experiment. Imagine a sphere with you inside. Now expand it like an inflating balloon. When it gets so big it includes half the universe, go to the edge and step outside. You find yourself in what looks like another sphere that holds the other half the universe. This sphere is the same sphere, seen from its flip side. Step back to your side and watch as it keeps on expanding to include more of the universe. You know the flip-side sphere must be getting smaller. So in the end your surface not only fails to enclose the whole universe; it ends up being a small sphere right back where you began, but now you are outside it. Simply put, though finite, the universe has no edge. Or, as Time One puts it, ‘In Einstein’s universe a sphere can’t really have an inside and an outside; it only has two sides.’

So where can the universe’s 2D surface be? The answer’s simple: Like all else it is inside the universe. Time One tells us how.  Just as string theory proposes, it sees space as made of Planck-scale Calabi-Yau manifolds, so there are ~N3 of them. It sees them not as mathematical abstractions but as real and fundamental constituents of everything, quanta of space called flecks. As they replicate to bring space into existence they are connected by a 2D fleck-to-next-fleck ribbon that forms a single ring that runs through every fleck exactly once. Thus this thin ribbon gives every fleck in the universe a number that is like its street address.

But there must be ~N3 addresses. So how can this surface yield the N-fold simpler specification? Bring on Australian topologist Sundance Bilson-Thompson. He shows how all the known particles of matter and energy can be composed of half-twists in fundamental ribbons. Between fleck and next fleck all there is to know is: Is the ribbon twisted; and if it is, is it a left- or right-handed twist? Here’s the key: There are only ~N2 twists in the universe. So the entire universe is specified by ~N2 twist addresses as the intervening addresses have no twists.

Thus our asking what this strange 3D/2D duality means for the whole universe leads to some interesting conclusions. Its surface too may be real. And it may give us another window into the strange world of Planck-scale physics.

String theorist and science writer Brian Greene depicts the duality as a parallel universe and says that ‘it suggests, remarkably, that all we experience is nothing but a holographic projection of processes taking place on some distant surface that surrounds us.’

Seems we don’t need a parallel universe; the universe we have can handle this job nicely. And it can do this with a surface that does not surround us in the manner Greene imagines. It is not just in us; it is us and everything else.

Sources:

Leonard Susskind (1994), “The World as a Hologram”, J.Math.Phys., v. 36, p. 6377; https://arxiv.org/abs/hep-th/9409089

Brian Greene (2011), The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, New York: Alfred A. Knopf, p. 8.

Image credits: AsaLegault; [e.g., http://www.deviantart.com/tag/cloudsa?offset=26]