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.

Wednesday, December 23, 2020

Flat space, Hawking radiation, and warm spots

Ever wonder if the universe is flat?

No, I haven't taken Wingnut Pills and decided that the Flat Earthers make sense.  This is an honest-to-Einstein problem in physics, one that not only raises eyebrows about the supposed "fine-tuning" of the universe but has a huge effect on its ultimate fate.

By this time most people who are reasonably scientifically literate (or at least watch Star Trek) know about curved space -- that the presence of mass warps space-time, a little like the way a heavy weight on a trampoline stretches and deforms the flexible sheet it's sitting on.  The trampoline analogy isn't a bad one; if you have a bowling ball in the middle of a trampoline, and you roll a marble on the surface, the marble's path will be deflected in such a way that it appears the bowling ball is attracting the marble.  In reality, however, there's no attraction involved; the bowling ball has warped the space around it, and the marble is only following the contours of the space it's traveling through.

Bump up the number of dimensions by one, and you've got an idea of how curved space-time works.  The trampoline is a 2-D surface warped into a third dimension; where you're sitting right now is a 3-D space warped into a fourth dimension.

The "flatness problem" asks a seemingly simple question; okay, matter deforms space locally, but what's the shape of space as a whole?  In our trampoline analogy, you can visualize that although the bowling ball deflects the surface nearby, as a whole the trampoline is flat.  Harder to picture, perhaps, is that the trampoline could be a different shape; the surface of the entire trampoline could be spherical, for example, and still have indentations on the surface corresponding to places where massive objects were located.

That, in a nutshell, is the flatness problem.  The key is the matter/energy density of the entire universe.  If the universe is flat as a whole, the matter/energy density is exactly right for the outward expansion from the Big Bang to slow down, asymptotically approaching zero, but never quite getting there (and never reversing direction).  A universe with a higher matter/energy density than the critical value would eventually halt, then fall inward again, resulting in a "Big Crunch" as all the stuff in the universe collapses back to a singularity.  (This is sometimes called a "spherical universe" because space-time would be warped into a four-dimensional hypersphere.  If you can't picture this, don't worry, neither can anyone else.)  If the matter/energy density is lower than the critical value, the universe would continue to expand forever, getting thinner and more spread out, eventually reaching the point where any particular cubic light year of space would have very little chance of having even a single atom in it somewhere.  (This is known as a "hyperbolic universe," for analogous reasons to the "spherical universe" mentioned above, but even harder to visualize.)

[Image is in the Public Domain courtesy of NASA]

So, which is it?

There doesn't seem to be a good reason, argued from first principles, that the universe has to be any particular one of the three.  When I first ran into this concept, in high school physics class, I was rooting for the spherical universe solution; ending the universe with an enormous collapse seemed (and still seems) preferable to the gradual attenuation of matter and energy that would occur with the other two.  Plus, it also raised the possibility of a rebounding second Big Bang and a new start, which was kind of hopeful-sounding even if nothing much would survive intact through the cusp.

Because there seemed to be no reason to expect the value of the matter-energy density -- known to physicists as Ω -- to be constrained, figuring out what it actually is occupied a great deal of time and effort by the astrophysicists.  It was a matter of some shock when by their best measurements, the value of Ω was:


To save you the trouble, that's exactly one, out to the 62nd decimal place.

So in other words, the universe is flat, or so close to it that we can't tell the difference.

This engenders more than a few other problems.  For one thing, why is Ω exactly 1?  Like I said earlier, nothing from the basic laws of physics seems to require it.  This brings up the issue of cosmological fine-tuning, which understandably makes us science-types a little twitchy.  Then there's the problem that the outer reaches of the universe that we can see -- so places farther away in space, and further back in time -- are moving away from us a lot faster than they should if the universe was flat.  This has given rise to a hypothesized repulsive "dark energy" to account for this, but what exactly dark energy is turns out to be even more problematic than the "dark matter" that appears to comprise over a quarter of the overall mass/energy of the universe even though we haven't been able to detect it other than by its gravitational bending of space-time.

The reason this warped topic comes up is research by the groundbreaking and often controversial Nobel laureate Roger Penrose, who published a paper in Monthly Notices of the Royal Astronomical Society this summer that identified six "warm spots" that had been detected in the background radiation of the universe, and which Penrose believes are "Hawking points" -- places where a black hole evaporated due to its "Hawking radiation" eventually bleeding off mass (a topic that deserves a whole other post).  The problem is, the evaporation of a black hole by Hawking radiation generates theoretical lifetimes for your average black hole of many times the current age of the universe, so the presence of six of them indicates something funny must be going on.

What that funny business is, Penrose claims, is that we're seeing the ghosts of black holes that evaporated before the Big Bang that formed our universe.

In other words, in a previous universe.

"The Big Bang was not the beginning," Penrose said in an interview with Sarah Knapton in The Telegraph.  "There was something before the Big Bang and that something is what we will have in our future.  We have a universe that expands and expands, and all mass decays away, and in this crazy theory of mine, that remote future becomes the Big Bang of another aeon.  So our Big Bang began with something which was the remote future of a previous aeon."

So he's not talking about a spherical universe, collapsing in on itself; Penrose thinks that even if the universe is flat or hyperbolic, eventually random quantum fluctuations will generate an expansion that will start it all over again.  This may seem a little like the example my thermodynamics teacher used about random motion -- yes, it's possible that all the molecules in your cup of coffee will by chance jitter in the same direction at the same time, and your coffee will fountain up out of the cup.  He had us calculate the odds, though, and it turns out it's so remote that it's virtually certain it has never happened anywhere in the universe, during its entire thirteen-odd billion year existence.

But if you consider that a flat universe would have an essentially infinitely long time span, all it takes is the coffee to jitter in the right direction once, and you generate a new Big Bang.

Metaphorically speaking.

Whether Penrose is right about this remains to be seen, but it must be pointed out that he's had ideas before that have seemed "out there" and have turned out to be correct.  Martin Rees, Astronomer Royal and Fellow of Trinity College at the University of Cambridge and no faint light himself, said, "There would, I think, be a consensus that Penrose and Hawking are the two individuals who have done more than anyone else since Einstein to deepen our knowledge of gravity."

So I'm disinclined to shrug my shoulders at anything Penrose says, however odd it may sound.  And it brings me back to the hopes for an oscillating universe I first held when I was seventeen years old.  If Penrose is right, there was something that existed before our current universe, and likely something will exist afterward.  Even if those are in the impossibly remote past and future, it still seems preferable to the miserable demise of a standard flat or hyperbolic universe.

So the issue is far from settled.  Which is the way of science, after all.  Every problem you solve brings up two more new ones.  Meaning we should have enough to keep us occupied until the nest Big Bang -- and maybe even beyond.


Not long ago I was discussing with a friend of mine the unfortunate tendency of North Americans and Western Europeans to judge everything based upon their own culture -- and to assume everyone else in the world sees things the same way.  (An attitude that, in my opinion, is far worse here in the United States than anywhere else, but since the majority of us here are the descendants of white Europeans, that attitude didn't come out of nowhere.)  

What that means is that people like me, who live somewhere WEIRD -- white, educated, industrialized, rich, and democratic -- automatically have blinders on.  And these blinders affect everything, up to and including things like supposedly variable-controlled psychological studies, which are usually conducted by WEIRDs on WEIRDs, and so interpret results as universal when they might well be culturally-dependent.

This is the topic of a wonderful new book by anthropologist Joseph Henrich called The WEIRDest People in the World: How the West Became Psychologically Peculiar and Particularly Prosperous.  It's a fascinating lens into a culture that has become so dominant on the world stage that many people within it staunchly believe it's quantifiably the best one -- and some act as if it's the only one.  It's an eye-opener, and will make you reconsider a lot of your baseline assumptions about what humans are and the ways we see the world -- of which science historian James Burke rightly said, "there are as many different versions of that as there are people."

[Note:  If you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

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