Skeptophilia (skep-to-fil-i-a) (n.) - the love of logical thought, skepticism, and thinking critically. Being an exploration of the applications of skeptical thinking to the world at large, with periodic excursions into linguistics, music, politics, cryptozoology, and why people keep seeing the face of Jesus on grilled cheese sandwiches.

Thursday, May 16, 2024

Non-trivial donuts

In the New Research That Sounds Crazy But Isn't department, we have: an inquiry into whether the universe is actually shaped like a donut.

[Image credit: J. Law, ESO]

The overall shape of spacetime is something that is nowhere near as obvious as it might seem to a layperson.  From the look of it, we seem to live in a completely Euclidean universe; perpendicular lines meet at a perfect ninety degree angle, parallel ones never intersect, and all of the other happy stuff you learned in high school geometry class.  But as mathematicians Leonhard Euler and Nikolai Lobachevsky showed, this isn't the only possibility.  The fabric of space could have an overall spherical shape, where there are no parallel lines (a 2-D example of a spherical geometry is the surface of the Earth).  On the other hand, in a hyperbolic space, given a line and a point not on that line, there is an infinite number of parallel lines passing through that point.  (It's harder to picture, for me at least, but a 2-D analog to a hyperbolic space is the surface of a saddle -- or a Pringle's potato chip.)

To our best measurements thus far, however, it looks like the simple solution -- that spacetime is flat and Euclidean -- is correct.  (That's on the largest scales; on small scales, anything with mass warps the geometry of spacetime.  However, it appears that those local divots and dimples are in a spacetime which is, overall, flat.)  

But according to a paper in the journal Physical Review Letters, there might be other possibilities we haven't considered -- ones even more mindblowing than a spherical or hyperbolic universe.

Theoretical physicist Glenn Starkman, of Case Western Reserve University, has proposed that the universe's geometry might have a nontrivial topology.  Euclidean spaces -- and also spheres and saddles -- have what topologists call a trivial topology; the simplest way to think about this is to consider what happens if you draw a closed loop anywhere on one of those surfaces, and then make it shrink.  On a surface with a trivial topology, no matter where you draw it, you can continue to shrink the loop all the way down to a single point.  On one with nontrivial topology, there are at least some loops that you can't do that to without deforming the shape of the surface.

Consider, for example, a donut.  A loop that goes around the donut longitudinally (i.e. through the hole and back around again) can't be shrunk indefinitely; neither can one that runs all the way around the hole.  Shapes with a single hole all the way through are called genus one tori.  A donut is a genus one torus, as is a mug with a single handle.  (Giving rise to the old joke that topologists are so smart that at breakfast, they can't tell their coffee cups from their donuts.)

This may seem like nothing more than intellectual noodling about, but if the universe has a weird non-trivial topology, it could explain ongoing mysteries like the asymmetries (and unexpected symmetries) in the cosmic microwave background radiation.  One possibility is that the geometry of the universe is some kind of multiply-connected hypertorus -- a bit like a three-dimensional version of the old game PacMan, where if you exit the screen on one side, you reappear on the opposite side.  This would mean when you look out into space in one direction, your sight line comes back at you from the other direction.  This could potentially explain another long-standing and vexing problem in physics, the horizon problem -- which is the question of why space is so homogeneous, despite the fact that there are regions of space that, if space has a trivial topology, have been causally disconnected since the time of the Big Bang.  If when you peer one direction into the night sky, your visual line travels in a gigantic loop, the horizon problem kind of goes away; you're seeing the same stuff out at the edges of the universe no matter which way you look.

Of course, even that is not as complicated as it can get.  Starkman and his colleagues have proposed a total of seventeen different possible geometries that aren't ruled out by the observational evidence.  In some, the universe twists as it loops around, so that (using our PacMan analogy) when you exit the screen and reappear on the other side, you're now upside-down.  They are currently proposing looking for similar patterns in regions of space on opposite sides of the universe, but also have to consider that the pattern on one side may be inverted with respect to the other.

As you might imagine, doing this kind of comparison work is way beyond the scope of human analysts; it's going to require some heavy-duty computational firepower.  They're planning on turning over new survey data from the JWST and ESO to rapid machine-learning software for analysis, and we might actually have some preliminary answers by the end of the year.

If they get positive results, it'll be an incredible coup -- not only proposing a whole bunch of new physics, but simultaneously making inroads into solving the long-standing flatness and horizon problems.  I'm not holding my breath -- it's all too often these odd ideas fail the test of empirical evidence -- but wouldn't it be wonderful if it holds up?

I know I'd celebrate by eating a donut.


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