The Edge of an Infinite Universe

SPEAKER_1 (0:01)

This episode is brought to you by State Farm. Listening to this podcast instead of doom scrolling? Smart move. Another smart move? Getting help from one of State Farm's 19,000 local agents when you choose to bundle home and auto. Bundling, just another way to save with the personal price plan. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state.

SPEAKER_2 (0:27)

This episode is brought to you by Accenture. When you're advertising operations fall out of sync, everything else follows. Spotify and Accenture are working together to reinvent the rhythm of ad sales. Using automation, analytics, and smarter workflows to simplify campaign delivery and access better data across the business. The result, less time spent on operations, more time connecting brands with the moments and fandoms that matter most. Learn more at accenture.com/spotify.

Matt O'Dowd (0:56)

Have you ever asked, what is beyond the edge of the universe? And have you ever been told that an infinite universe has no edge? Well, you were told wrong. In a sense, we can define a boundary to an infinite universe. At least mathematically. Although it turns out that that boundary may be as real or even more real than the universe it contains.

Our universe may be infinite. In order to wrap our puny human minds around such a notion, we like to come up with boundaries. For example, we have the observable universe. That patch that we can see and beyond which light has not yet had time to reach us. Its boundary is called the particle horizon. Beyond it, there exists at a minimum thousands and possibly infinitely more regions just as large.

Our observable universe is like a tiny patch of land in a vast plain. We define its horizon like we might build a little picket fence around our little patch. Meaningless from the point of view of the plain, but it makes our patch feel more homey and us less crushingly insignificant.

We visited these cosmic horizons in one of the early Space Time episodes. To review, the particle horizon defines the limit of the visible past. And there's also the cosmic event horizon defining the limit of the visible future.

But these correspond to actual spherical boundaries in space whose distances can be calculated. How mundane. There's another way to define the boundary of the universe that isn't so shy in the face of an infinite cosmos. In fact, if we twist our human intuition and our mathematics to its limit, we can build our picket fence around an infinite universe. A mathematical boundary at infinity turns out not to just be useful for doing calculations in physics, but may be as real as the physical universe it contains. It may encode that universe as a hologram on its surface. In today's episode, we're going to talk about two ways to define this infinite boundary, and this will set us up finally for laying open the holographic principle. I promise. Let's start with a quick review of types of universe, at least the three basic types described by Einstein's general theory of relativity.

The only type of non-infinite universe or closed universe is the one that curves back on itself, like the 3D analog of the 2D surface of a sphere. We call that positive curvature. Travel far enough around, and you get back to where you started. Geometry is a bit broken in such a universe. For example, two parallel lines will eventually converge and cross each other.

SPEAKER_1 (3:58)

This episode is brought to you by State Farm. Listening to this podcast instead of doomscrolling, smart move. Another smart move, getting help from one of State Farm's 19,000 local agents when you choose to bundle home and auto. Bundling, just another way to save with the personal price plan. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings and eligibility vary by state.

SPEAKER_2 (4:23)

This episode is brought to you by Accenture. When your advertising operations fall out of sync, everything else follows. Spotify and Accenture are working together to reinvent the rhythm of ad sales. Using automation, analytics and smarter workflows to simplify campaign delivery and access better data across the business. The result, less time spent on operations, more time connecting brands with the moments and fandoms that matter most. Learn more at accenture.com/spotify.

Matt O'Dowd (4:53)

In general relativity, we call the universe with this geometry, De Sitter Space, after Dutch astronomer Willem De Sitter. Then there's the Flat Universe, classic straightforward geometry, parallel lines, stay parallel, and it goes on forever.

In GR, this is Minkowski Space, after Herman Minkowski, teacher and colleague of Albert Einstein. Finally, there's the universe with negative curvature, and the 2D analog of that is the hyperbolic surface, like an infinite saddle or pringle.