Bending the light

One of the coolest (and most misunderstood) parts of science is the use of models.

A model is an artificially-created system that acts like a part of nature that might be inaccessible, difficult, or prohibitively expensive to study.  A great many of the models used by scientists today are sophisticated computer simulations -- these are ubiquitous in climate science, for example -- but they can be a great deal simpler than that.  Two of my students' favorite lab activities were models.  One of them was a "build-a-plant" exercise that turned into a class-wide competition for who could create the most successful species.  The other was a striking simulation of disease transmission where we started with one person who was "sick" (each student had a test tube; all of them were half full of water, but one of them had an odorless, colorless chemical added to it).  During the exercise, the students contacted each other by combining the contents of their tubes.  In any encounter, if both started out "healthy," they stayed that way; if one was "sick," now they both were.  They were allowed to contact as many or as few people as they wanted, and were to keep a list of who they traded with, in order.  Afterwards, we did a chemical test on the contents of the tube to see whose tubes were contaminated, then used the list of trades to see if we could figure out who the index case was.

It never failed to be an eye-opener.  In only five minutes of trades, often half the class got "infected."  The model showed how fast diseases can spread -- even if people were only contacting two or three others, the contaminant spread like wildfire.

In any case, models are powerful tools in science, used to study a wide variety of natural phenomena.  And because of a friend and fellow science aficionado, I now know about a really fascinating one -- a characteristic of certain crystals that is being used as a model to study, of all things, black holes.

[Image licensed under the Creative Commons Ra'ike (de:Benutzer:Ra'ike), Chalcanthite-cured, CC BY-SA 3.0]

The research, which appeared last month in Physical Review A, hinges on the effects that a substance called a photonic crystal has on light.  (We met photonic crystals here only a few weeks ago -- in a brilliant piece of unrelated research regarding why some Roman-era glass has a metallic sheen.)  All crystals have, by definition, a regular, grid-like lattice of atoms, and as light passes through the lattice, it slows down.  This slowing effect happens with all transparent crystals; for example, it's what causes the refraction and internal reflection that make diamonds sparkle.  A researcher named Kyoko Kitamura, of Tohoku University, realized that if light could be made to slow down within a crystal, it should be possible to arrange the molecules in the lattice to force light to bend. 

Well, bending light is exactly what happens near a black hole.  So Kitamura and her team made the intuitive leap that this property could be used to study not only the crystal's interactions with light, but indirectly, to discover more about how light behaves near massive objects.

At this point, it's important to clarify that light is not gravitationally attracted to the immense mass of a black hole -- this is impossible, as photons are massless, so they are immune to the force of gravity (just as particles lacking electrical charge are immune to the electromagnetic force).  What the black hole does is warp the fabric of space, just as a bowling ball on a trampoline warps the membrane downward.  A marble rolling on the trampoline's surface is deflected toward the bowling ball not because the bowling ball is somehow magically attracting the marble, but because the marble is following the shortest path through the curved two-dimensional space it's sitting on.  Light is deflected near a black hole because it's traversing curved space -- in this case, a three-dimensional space that has been warped by the black hole's mass.

[Nota bene: it doesn't take something as massive as a black hole to curve space; you're sitting in curved space right now, warped by the mass of the Earth.  If you throw a ball, its path curves toward the ground for exactly the same reason.  That we are in warped space, subject to the laws of the General Theory of Relativity, is proven every time you use a GPS.  The measurements taken by GPS have to take into account that the ground is nearer to the center of gravity of the Earth than the satellites are, so the warp is higher down here, not only curving space but changing any time measurements (clocks run slower near large masses -- remember Interstellar?).  If GPS didn't take this into account, its estimates of positions would be inaccurate.]

In any case, the fact that photonic crystals can be engineered to interact with light the way a black hole would means we can study the effects of black holes on light without getting near one.  Which is a good thing, considering the difficulty of visiting one, as well as nastiness like event horizons and spaghettification to deal with.

So that's our cool scientific research of the day.  Studies like this always bring to mind the false perception that science is some kind of dry, pedantic exercise.  The reality is that science is one of the most deeply creative of endeavors.  The best science links up realms most of us would never have thought of connecting -- like using crystals to simulate the behavior of black holes.

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Loop-the-loop

Of all the bizarre and fascinating discoveries physicists have made in the last century and a half, I think the one that twists my brain the most is the effect massive objects have on the space around them.

I use the "twists" metaphor deliberately, because the concept -- commonly called "warped space" -- is that anything with mass deforms the space it's in.  You've probably heard the two-dimensional analogy, to a bowling ball sitting on a trampoline and stretching the fabric downward.  If you then roll a marble across the trampoline, it will follow a deflected path.  Not because the bowling ball is mysteriously attracting the marble; the marble is merely following the contours of the space it's traveling through.

Increase the number of dimensions by one, and you've got a basic idea of what this feature of the universe is like.  We live in a three-dimensional space warped into a fourth dimension, and something passing near a massive object (as with the trampoline analogy, the more massive the object, the greater the effect) will follow a curved path.  Possibly, if the "attractor" is big enough, curved into a closed loop -- like the Moon does around the Earth, and the Earth does around the Sun.

Where it gets even weirder is that the degree of deflection of the moving object is dependent on how fast it's going.  Again, the marble provides a good analogy; a fast-moving marble will not alter its trajectory from a straight line very much, while a slow-moving one might actually fall into the "gravity well" of the bowling ball.  The same is true here in three-dimensional space.  This is why there's such a thing as "escape velocity;" the velocity of an object has to be great enough to escape the curvature of the gravity well it's sitting in, and that velocity gets larger as the "attractor" becomes more massive.

With a black hole, the escape velocity is greater than the speed of light.  Put a different way, space around a black hole has been warped so greatly that nothing is moving fast enough to avoid falling in.  Once you get close enough to a black hole to experience that degree of space-time curvature (a point called the "event horizon"), there is no power in the universe that can stop you from falling all the way in and meeting a grim fate called (I kid you not) "spaghettification."

Which, unfortunately, is exactly what it sounds like.

Why this mind-warping topic comes up is because of a paper that appeared this week in Scientific Reports, describing research by Albert Sneppen, a student at the Niels Bohr Institute, looking at what would happen to light as it passed very near -- but not within -- the event horizon of a massive black hole.  Sneppen came up with a mathematical model showing that it creates an effect so bizarre and unmistakable that it is now being proposed as a way of detecting distant black holes.

Suppose between us and a distant galaxy is a large black hole.  The black hole (being black) is invisible; it can only be seen because of how it interacts with the matter and energy around it.  So the light from the galaxy has to pass near the black hole on its voyage to us.  The particles of light that stray too close follow the curvature of space right into the black hole, as you might expect.  The ones that get close, but not too close, are where things are interesting.

Recall that the Earth follows an elliptical path around the Sun because the Sun is warping space enough, and the Earth is moving slowly enough, that the Earth doesn't slingshot away from the Sun (fortunately for us) but remains "captured," following the shortest path through curvature of the space it's in.  So presumably there is a distance around a massive black hole that would have the same property vis-à-vis light; a distance where light speed is exactly right for it to follow the lines of the intensely curved space it's traveling through and describe a circular (or elliptical) path.

So light at that distance would become trapped, circling the black hole forever.  But what about light from the same distant galaxy that is just a leeeeeetle bit farther away?  And a leeeeetle farther than that?  What Sneppen showed is that this effect would cause the light rays from the galaxy passing progressively farther and farther away from the black hole to make a specific number of loops around the black hole before "escaping."  So of the photons of light from the galaxy that end up after that cosmic loop-the-loop heading our way, some (the ones the farthest away from the black hole to start with) would have circled the black hole only once, some twice, some three times, etc.

What this would do is create multiple images of the same galaxy, strung out in a line.

Check out the drawing by Sneppen's collaborator, Peter Laursen, showing the results of the effect:

So there you have it; this morning's reason to feel very, very small.  I don't know about you, but I think the human species can use a little humility these days,  We need to be reminded periodically that we are tiny beings in an enormous universe, one that is so bizarre that it boggles the mind.  Although I have to say it's impressive that we tiny insignificant beings have begun to understand and explain this bizarreness.  As astronomer Carl Sagan put it, "We are a way for the universe to know itself."

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I've loved Neil de Grasse Tyson's brilliant podcast StarTalk for some time.  Tyson's ability to take complex and abstruse theories from astrophysics and make them accessible to the layperson is legendary, as is his animation and sense of humor.

If you've enjoyed it as well, this week's Skeptophilia book-of-the-week is a must-read.  In Cosmic Queries: StarTalk's Guide to Who We Are, How We Got Here, and Where We're Going, Tyson teams up with science writer James Trefil to consider some of the deepest questions there are -- how life on Earth originated, whether it's likely there's life on other planets, whether any life that's out there might be expected to be intelligent, and what the study of physics tells us about the nature of matter, time, and energy.

Just released three months ago, Cosmic Queries will give you the absolute cutting edge of science -- where the questions stand right now.  In a fast-moving scientific world, where books that are five years old are often out-of-date, this fascinating analysis will catch you up to where the scientists stand today, and give you a vision into where we might be headed.  If you're a science aficionado, you need to read this book.

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