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.  (In fact, the effects of that curvature are what you are experiencing as a downward pull toward the Earth's surface right now.)

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 near it, 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 are 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:

1.00000000000000000000000000000000000000000000000000000000000000

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 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 I dealt with in a little more detail last year).  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 next Big Bang -- and maybe even beyond.

****************************************

Everything evaporates

In the episode of Star Trek: The Original Series called "Metamorphosis," the crew of the Enterprise encounters a man who has been kept alive and healthy for centuries by an entity he calls "the Companion."  I don't honestly remember it all that well -- it was kind of the usual Star Trek fare, as I recall -- but one line has stuck in my head all these years since I saw it: "Immortality consists largely of boredom."

I remember thinking as a kid what a bizarre statement that was.  Given the choice, who wouldn't want to live forever?  And, on the bigger scale, who wouldn't want the universe to exist for eternity?

When I was in high school, though, I started to run into some disquieting scientific ideas that made me realize what a pipe dream this was.  The Second Law of Thermodynamics -- that over time, all closed systems devolve toward chaos.  The fact that even the stars have births, lives... and deaths.  The three possibilities of the ultimate fate of the universe -- a collapse back into a singularity, a "flat universe" that slows its expansion but never quite gets to zero, and an accelerating universe that eventually speeds up until spacetime itself gets pulled apart.

None of which would be survivable by any life as we know it.

It all seemed so... bleak.  I remember rooting for the collapse ("Big Crunch") model, because some scientists thought this might result in an oscillating universe, one where death was followed by rebirth, a new Big Bang that would reset everything and start over.  It somehow seemed preferable to the clock simply winding down and eventually stopping.  But even that hope was dashed by the cosmologists; from the data we have, it appears either the universe is flat (the middle scenario) or hyperbolic (the third scenario).  

So it looks like the cosmos has a finite lifespan.  (If you've got a half-hour to have your mind blown, watch the wonderful YouTube video "The Timeline of the Universe" -- which takes us from now to the end, at least as far as current cosmology understands things.)

And a new piece of research has found that even the objects in that expanding, cooling universe aren't immortal.  Working at the Radboud University of Nijmegen, theoretical physicists have found that the phenomenon of Hawking radiation doesn't just apply to black holes -- it applies to everything.

In other words, everything eventually will evaporate.

[Image is in the Public Domain courtesy of NASA]

You probably know that empty space isn't really empty; it's filled with a seething foam of virtual particles that pop into existence in pairs (one matter particle and one antimatter particle) and, almost always, immediately mutually annihilate.  The overall result is nothing that generally impacts us on the macroscopic scale, since the lifetimes of these virtual pairs is measured in nanoseconds.  (It does contribute to the overall mass-energy density of empty space, however, something called the Casimir effect, which has been experimentally measured and agrees with the theoretical prediction perfectly -- so as bizarre as they sound, virtual particles are a real phenomenon.)

But there's more to it than this, and the key is the word "almost" in "almost always immediately mutually annihilate."  When the virtual pair is produced near the event horizon of a black hole, sometimes one of the particles gets trapped inside the event horizon, and the other escapes, radiating away into space.  This mass and energy is lost to the black hole, so it shrinks a bit -- and over large amounts of time, the black hole itself will evaporate away.

That's the Hawking radiation.  But what the current research showed is that this evaporation happens to everything -- not just black holes.

"[This research] means that objects without an event horizon, such as the remnants of dead stars and other large objects in the universe, also have this sort of radiation," said Heino Falcke, who co-authored the paper.  "And, after a very long period, that would lead to everything in the universe eventually evaporating, just like black holes.  This changes not only our understanding of Hawking radiation but also our view of the universe and its future."

So I guess the band Kansas might want to reconsider their lyric, "Nothing lasts forever but the Earth and sky."

The whole thing bothers me less now than it would have when I was younger.  It's not that I'm fond of the idea of death, mind you; I'm not ready to check out any time soon.  It's more that I've accepted its inevitability.  It's why the wonderful television series The Good Place was so incredibly poignant.  The main characters finally come to understand that maybe an eternity in the Good Place (heaven) isn't all it's cracked up to be, and that our appreciation of the beauty of the universe and what life has to offer comes from the fact that it is finite.  

But it should definitely focus our minds and hearts on appreciating what we have now.  I'll end with a quote from a different Star Trek episode, which (in my opinion) is the best one in the entire franchise: the Star Trek: The Next Generation episode "The Inner Light."

"Seize the time, Maribol.  Live now.  Make now always the most precious time.  Now will never come again."

****************************************

A black hole's warm glow

Once again I was sent a link by my buddy Andrew Butters, of the wonderful Potato Chip Math, who is not only a great writer but has a keen eye for a cool science article.

The link was to a story in Science Alert, and was titled, "Scientists Created a Black Hole in the Lab, and Then It Started To Glow," by Michelle Starr.  But before I tell you what the gist is, I have to bring up a peevish complaint about the headline (which may not have been Starr's fault; many times the headlines aren't written by the journalist herself, so I'm not jumping to blaming her for it).  The researchers, as you will see, did not "create a black hole;" what they did was create something that models some of the behavior of a black hole.  Which is cool enough, but doesn't have the cachet that black holes have, so Science Alert apparently thought they needed to jazz things up.  The headline is wildly misleading; no massive stars were destroyed in the course of this experiment.

Of course, this is not going to stop people from reading only the headline and then posting hysterical screeds about how those Mad Scientists Are Trying To Destroy Us All and undoubtedly tying in CERN, HAARP, the Illuminati, and Reptilian Aliens From Zeta Reticuli.

You know how it goes.

Anyhow, back to reality.  What the scientists really did was pretty amazing, and may give us some inroads into figuring out one of the biggest puzzles in physics; why theoretical physicists have been unable to reconcile the equations of quantum mechanics and those of relativity.  When they attempt to accommodate gravitational effects on the scale of the very small, the equations "blow up" -- they result in infinities -- usually a sign that something is very wrong about our understanding.

The reason black holes play into this question is that in the extraordinary gravitational field at the event horizon (the "point of no return," where the space is so strongly curved that even light can't escape), there is a quantum effect that becomes important on the macroscopic scale.  It's called Hawking radiation, after Stephen Hawking (who first proposed it), and deserves some closer attention.

 To start with, empty space isn't empty.  There is an inherent energy in space called zero-point energy or vacuum energy, and it is possible for this energy to be "borrowed" to produce particle-antiparticle pairs (such as an electron and a positron).  There's a catch, though; the pairs always recollide (in a minuscule amount of time, the upper limit of which is determined by the uncertainty principle).  So the pairs pop into existence and right out again, creating continuous tiny, extremely short-lived ripples in the fabric of space.  Not enough for anyone even to notice.

Well, unless you're near the event horizon of a black hole.

[Image is in the Public Domain]

The huge gravitational field at the event horizon means that vacuum energy is much higher, and pair production happens at a much greater rate.  And because of that boundary, sometimes one member of a pair falls into the event horizon, while the other one doesn't.  At that point, the survivor radiates out into space -- taking a little of the black hole's mass/energy along with it.

That's the Hawking radiation.  What it implies is that black holes don't last forever -- eventually they evaporate, finally exploding in a burst of gamma rays.

The problem has been that the Hawking radiation is impossible to study experimentally; we're (fortunately) not near any black holes, at least so far as we know, and the faint signature of the radiation would be lost in the general white noise of the universe.  But now -- and this is where we get to the current research -- a team led by Lotte Mertens of the University of Amsterdam has developed a model that simulates this behavior, and found that just like the real thing, it emits radiation exactly the way Hawking predicted (this is the "it started to glow" in the headline).

What they did was to lock together a chain of atoms that provided a path for electrons to move, and by fine-tuning the rate at which this happened, they created a simulated event horizon that caused some of the electrons' wave-like behavior to vanish completely.  The result was an increase in thermal radiation that matched the Hawking model precisely.

Why this is significant is that it could provide a way to study the quantum effects of gravity in the lab, something that has been impossible before now.  It's not like we can hop a spacecraft and fly to a black hole (which would be inadvisable anyhow).  So this fascinating experiment might be the first step toward one of the prime goals of physicists -- finding a way to unify the quantum and gravitational models.

So even if they didn't "create a black hole in the lab," the whole thing is still pretty freakin' cool.

****************************************

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:

1.00000000000000000000000000000000000000000000000000000000000000

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!]