Paradoxes within paradoxes

Sometimes the simplest, most innocuous-seeming questions can lead toward mind-blowingly profound answers.

I remember distinctly running into one of these when I was in -- I think -- eighth grade science class.  It was certainly pre-high-school; whether it was from Mrs. Guerin at Paul Breaux Junior High School, or another of my teachers, is a memory that has been lost in the sands of time and middle-aged forgetfulness.

What I have never forgotten is the sudden, pulled-up-short response I had to what has been nicknamed Olbers's Paradox, named after 18th century German astronomer Heinrich Wilhelm Matthias Olbers, who first thought to ask the question -- if the universe is infinite, as it certainly seems to be, why isn't the night sky uniformly and dazzlingly bright?

I mean, think about it.  If the universe really is infinite, then no matter what direction you look, your line of sight is bound to intersect with a star eventually.  So there should be light coming from every direction at once, and the night sky shouldn't be dark.  Why isn't it?

The first thought was that there was something absorptive in the way -- cosmic dust, microscopic or submicroscopic debris left behind by stars and blown outward by stellar wind.  The problem is, there doesn't seem to be enough of it.  The average density of cosmic dust in interstellar space is less than a millionth of a gram per cubic meter.

When the answer was discovered, it was nothing short of mind-boggling.  It turns out Olbers's paradox isn't a paradox at all, because there is light coming at us from all directions, and the night sky is uniformly bright -- it's just that it's shining in a region of the spectrum our eyes can't detect.  It's called the three-degree cosmic microwave background radiation, and it appears to be pretty well isotropic (at equal intensities no matter where you look). It's one of the most persuasive arguments for the Big Bang model, and in fact what scientists have theorized about the conditions in the early universe added to what we know about the phenomenon of red-shifting (the stretching of wavelengths of light if the space in between the source and the detector is expanding) gives a number that is precisely what we see -- light peaking at a wavelength of around one millimeter (putting it in the microwave region of the spectrum) coming from all directions.

[Image licensed under the Creative Commons Original: Drbogdan Vector: Yinweichen, History of the Universe, CC BY-SA 3.0]

So, okay.  Olbers's paradox isn't a paradox, and its explanation led to powerful support for the Big Bang model.  But in science, one thing leads to another, and the resolution of Olbers's paradox led to another paradox -- the horizon problem.

The horizon problem hinges on Einstein's discovery that nothing, including information, can travel faster than the speed of light.  So if two objects are separated by a distance so great that there hasn't been time for light to travel from one to the other, then they are causally disconnected -- they can't have had any contact with each other, ever.

The problem is, we know lots of such pairs of objects.  There are quasars that are ten billion light years away -- and other quasars ten billion light years away in the opposite direction.  Therefore, those quasars are twenty billion light years from each other, so light hasn't had time to travel from one to the other in the 13.8 billion years since they were created.

Okay, so what?  They can't talk to each other.  But it runs deeper than that.  When the aforementioned cosmic microwave background radiation formed, on the order of 300,000 years after the Big Bang, those objects were already causally disconnected.  And the process that produced the radiation is thought to have been essentially random (it's called decoupling, and it occurred when the average temperature of the universe decreased enough to free photons from the plasma and send them streaming across space).

The key here is the word average.  Just as a microwaved cup of coffee could have an average temperature of 80 C but have spots that are cooler and spots that are hotter, the fact that the average temperature of the universe had cooled sufficiently to release photons doesn't mean it happened everywhere simultaneously, leaving everything at exactly the same temperature.  In fact, the great likelihood is that it wouldn't.  And since at that point there were already causally disconnected regions of space, there is no possible way they could interact in such a way as to smooth out the temperature distribution -- sort of like what happens when you stir a cup of coffee.

And yet one of the most striking things about the cosmic microwave background radiation is that it is very nearly isotropic.  The horizon problem points out how astronomically unlikely that is (pun intended) if our current understanding is correct.

One possible explanation is called cosmic inflation -- that a spectacularly huge expansion, in the first fraction of a second after the Big Bang, smoothed out any irregularities so much that everywhere did pretty much decouple at the same time.  The problem is, we still don't know if inflation happened, although work by Alan Guth (M.I.T.), Andrei Linde (Stanford), and Paul Steinhardt (Princeton) has certainly added a great deal to its credibility.

So as is so often the case with science, solving one question just led to several other, bigger questions.  But that's what's cool about it.  If you're interested in the way the universe works, you'll never run out of things to learn -- and ways to blow your mind.

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Seeing through the fog

There's something a little unsettling about the idea that when you're looking outward in space, you're looking backward in time.

If it seems like we're seeing things as they actually are, right now, it's only because (1) the speed of light is so fast, and (2) most of the objects we look at and interact with are relatively close by.  Even the Sun, though, which in astronomical terms is right on top of us, is eight light-minutes away, meaning that the light leaving its surface takes eight minutes to cross the 150 million kilometers between it and us.  If the Sun were suddenly to go dark -- not, mind you, a very likely occurrence -- we would have no way of knowing it for eight minutes.

The farther out you go, the worse it gets.  The nearest star to the Solar System, Proxima Centauri, is about 4.2 light years away.  So the awe-inspiring panorama of stars in a clear night sky is a snapshot of the past.  Some of the stars you're looking at (especially the red supergiants like Antares and Betelgeuse) might actually already have gone supernova, and that information simply hasn't gotten here yet.  None of the stars we see are in exactly the same positions relative to us as they appear to be to us right now.  

Worst of all is when you look way out, as the James Webb Space Telescope is currently doing, because then, you have to account not only for distance, but for the fact that the universe is expanding.  And it hasn't expanded at a uniform rate.  Current models support the inflationary model, which says that between 10^-36 and 10^-32 seconds after the Big Bang the universe expanded by a factor of around 10^26.  This seems like a crazy conjecture, but it immediately solves two perplexing problems in observational astronomy.

The Carina Nebula, as photographed by the James Webb Space Telescope [Image is in the Public Domain courtesy of NASA/JPL]

The first one, the horizon problem, has to do with the homogeneity of space.  Look as far out into space as you can in one direction, then do the same thing in the opposite direction, and what you'll see is essentially the same -- the same distribution of matter and energy.  The difficulty is that those two points are causally disconnected; they're far enough apart that light hasn't had time to travel from one to the other, and therefore no mechanism of communication can exist between them.  By our current understanding of information transfer, once causally disconnected, always causally disconnected.  So if something set the initial conditions in point A, how did point B end up with identical conditions if they've never been in contact with each other?  It seems like a ridiculous coincidence.

The other one is the flatness problem, which has to do with the geometry of space-time.  This subject gets complicated fast, and I'm a layperson myself, but as far as I understand it, the gist is this.  The presence of matter warps the fabric of space locally (as per the General Theory of Relativity), but what is its overall geometry?  From studies of such phenomenal as the cosmic microwave background radiation, it seems like the basic geometry of the universe as a whole is perfectly flat.  Once again, there seems to be no particular reason to expect that could occur by accident.

Both these problems are taken care of simultaneously by the inflationary model.  The horizon problem disappears if you assume that in the first tiny fraction of a second after the Big Bang, the entire universe was small enough to be causally connected, but during inflation the space itself expanded so fast that it carried pieces of it away faster than light can travel.  (This is not forbidden by the Theories of Relativity; matter and energy can't exceed the speed of light, but space-time itself is under no such stricture.)  The flatness problem is solved because the inflationary stretching smoothed out any wrinkles and folds that were in space-time at the moment of the Big Bang, just as taking a bunched-up bedsheet and pulling on all four corners flattens it out.

All of this will be facing some serious tests over the next few years as we get better and better at looking out into the far reaches.  Just last week a team at the University of Cambridge published a paper in Nature Astronomy about a new technique to look out so far that what you're seeing is only 378,000 years after the Big Bang.  (I know that may seem like a long time, but it's only 0.003% of the current age of the universe.)  The problem is that prior to this, the universe was filled with a fog of glowing hydrogen atoms, so it was close to opaque.  The new technique involves filtering out the "white noise" from the hydrogen haze, much the way as you can still see the shadows and contours of the landscape on a foggy day.  It's not going to be easy; the signal emitted by the actual objects that were there in the early universe is estimated to be a hundred thousand times weaker than the interference from the glowing fog.

It's mind-blowing.  I've been learning about this stuff for years, but I'm still boggled by it.  If I think about it too hard I'm a little like the poor woman in a video with science vlogger Hank Green, who is trying to wrap her brain around the idea that anywhere you look, if you go out far enough, you're seeing the same point in space (i.e. all spots currently 13.8 billion light years from us were condensed into a single location at the moment of the Big Bang), and seems to be about to have a nervous breakdown from the implications.  (Hat tip to my friend, the amazing author Robert Chazz Chute, for throwing the video my way.)

So think about all this next time you're looking up into a clear night sky.  It's not a bad thing to be reminded periodically how small we are.  The universe is a grand, beautiful, amazing, weird place, and how fortunate we are to be living in at time where we are finally beginning to understand how it works.

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Big brawl over the Big Bang

So apparently, there are a number of people who have their knickers in a twist over the new Cosmos.

The young-Earthers are, predictably, upset with host Neil deGrasse Tyson's repeated mentioning of evolution.  Dan Dewitt, writing for Baptist Press, was perturbed by the whole message, but showed evidence of a severe irony deficiency when he stated that Tyson's Cosmos was "regurgitating... old myths... and proposing theories that have zero physical evidence."

Then we have the climate change deniers, who were torqued by a mention of anthropogenic climate change in each of the first two episodes, with more likely to come.  Jeff Meyer, writing at Brent Bozell's conservative outlet Media Research Center, said, "...deGrasse Tyson chose to take a cheap shot at religious people and claim they don't believe in science, i.e. liberal causes like global warming."

Well, yeah.  Because, largely, they don't.  And climate change is hardly a "liberal cause," unless you accept the idea that in Stephen Colbert's words, "reality has a well-known liberal bias."

Then, we have the people who object to the idea of the Big Bang, which was more or less the topic of the entire first episode.  Elizabeth Mitchell, writing over at the frequently-quoted site Answers in Genesis, had the following to say:

The “observational evidence” [for the Big Bang] to which Tyson refers is not, however, observations that confirm big bang cosmology but interpretations of scientific data that interpret observations within a big bang model of origins. The big bang model is unable to explain many scientific observations, but this is of course not mentioned.

What makes Mitchell's comment even more ludicrous than it would be if read alone is how it appears in juxtaposition with the news from two days ago, in which we find that scientists working in Antarctica have conclusively proven the existence of gravitational waves -- remnants of quantum fluctuations that were created in the first 0.00000000000000000000000000000001 seconds of the universe's existence.  (For those of you who don't want to count, that's 31 zeroes; if you're conversant in scientific notation, it's 10^-32 seconds.)

This map represents nine years' worth of data from the Wilkinson Microwave Anisotropy Probe, which shows minor temperature fluctuations registering in the microwave region of the spectrum -- fluctuations caused by inflation that occurred 13.7 billion years ago.  [image courtesy of NASA, the WMAP team, and the Wikimedia Commons]

I'm sure Mitchell would shriek about "observational" versus "historical" science, and how I wasn't there during the Big Bang to observe what the universe was doing (and given what was happening at the time, I'm damn glad I wasn't).  But keep in mind that the gravitational waves that have been observed were predicted years ago by Andrei Linde, one of the chief architects of inflation theory -- a model of Big Bang cosmology that has now been given a significant leg up over other theories of the early universe.

The synchronicity of Mitchell's snarky little commentary, followed by the triumphal announcement of Linde's vindication, makes me think that if there is a god, he's got quite a wicked sense of humor.  It puts me in mind of a quote from Voltaire: "God is a comedian playing to an audience that is afraid to laugh." And if you want to see something uplifting to counterbalance Mitchell's ignorant criticism, watch this video of Linde being told by physicist Chao-Lin Kuo that the existence of gravitational waves had been proven.  It'll make you smile.

But back to Cosmos.  I do find it heartening that Tyson isn't pussyfooting around on these subjects.  Sagan, partly driven by the fact that the original series was filmed in the 1970s, had to be a little more circumspect about what he said, a little more diplomatic.  Myself, I think Tyson is taking the right approach.  I'm sorry if you don't "believe" in the Big Bang, in evolution, in climate change.  You're wrong.  You can continue to claim that the evidence doesn't exist, or is inconclusive or equivocal.  You're wrong about that, too.  If you'd like to remain ignorant of the reality, that's entirely your prerogative, but you can no longer expect the rest of us to go along with you out of some odd notion that ideas, however ridiculous they are, deserve respect.

Time to play hardball, people.