Time and tide

I don't know if you've had the experience of running into a relatively straightforward concept that your brain just doesn't seem to be able to wrap itself around.

One such idea for me is the explanation for tides.  I've gone through it over and over, starting in high school physics, and I keep having to go back and revisit it because I think I've got it and then my brain goes, "...wait, what?" and I have to look it up again.

The sticking point has always been why there are two high tides on opposite sides of the Earth.  I get that the water on the side of the Earth facing the Moon experiences the Moon's extra gravitational attraction and is pulled away from the Earth's surface, creating a bulge.  But why is there a bulge on the side facing away from the Moon?

Now that I'm 64 and have gone over it approximately 482 times, I think I've finally got it.  Which is more than I can say for Bill O'Reilly:

So, let's see if I can prove Mr. O'Reilly wrong.

Consider three points on the Earth: A (on the surface, facing the Moon), B (at the center of the Earth), and C (on the surface, opposite the Moon).  Then ask yourself what the difference is in the pull of the Moon on those three points.

Isaac Newton showed that the force of gravity is proportional to two things -- the masses of the objects involved, and the inverse square of the distance between them.  The second part is what's important here.  Because A, B, and C are all different distances from the Moon, they experience a difference in the gravitational attraction they experience.  A is pulled hardest and C the least, with B in the middle.

This means that the Earth is stretched.  Everything experiences these tidal forces, but water, which is freer to move, responds far more than land does.  At point A, the water is pulled toward the Moon, and experiences a high tide.  (That's the obvious part.)  The less obvious part is that because points B and C are subject to a difference in the gravitational attraction, the net effect is to pull them apart -- so from our perspective on the Earth's surface, the water at C pulls away and upward, so there's a high tide there, as well.

There's practically no limit to how big these forces can get.  On the Earth, they're fairly small, although sometimes phenomena like a seiche (a standing wave in a partially-enclosed body of water) can amplify the effect and create situations like what happens in the Bay of Fundy, Nova Scotia, where the difference in the water level between high and low tide can be as much as sixteen meters.

But out in space, you can find systems where the masses and distances combine to create tidal forces that are, to put it in scientific terms, abso-fucking-lutely enormous.  This, in fact, is why the whole subject comes up today; the discovery of a binary system in the Large Magellanic Cloud made up of a supergiant with a mass thirty-five times that of the Sun, and a smaller (but still giant) companion ten times the mass of the Sun.  They're close enough that they orbit their common center of gravity about once a month.  And the combination of the huge masses and close proximity creates tidal bulges about three million kilometers tall.

That's over three times the diameter of the Sun.

You think the people living along the Bay of Fundy have it bad.

Artist's conception of the system in the Large Magellanic Cloud [Illustration by Melissa Weiss of NASA/Chandra X-Ray Observatory/Center for Astrophysics]

And that's not even as extreme as tidal forces can get.  If you were unfortunate enough to fall feet-first into a black hole, you would undergo what physicists call -- I'm not making this up -- spaghettification.  The tidal forces are so huge that they're even significant across a small distance like that between your head and your feet, so you'd be stretched along your vertical axis and compressed along your horizontal one.  Put more bluntly, you'd be squished like a tube of toothpaste, ultimately comprising the same volume as before but a much greater length.

It would not be pleasant.

Be that as it may, I think I've finally got the explanation for tides locked down.  We'll see how long it lasts.

At least I'm pretty sure I'm still ahead of Bill O'Reilly.

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A celestial do-si-do

A common -- although, as it turns out, completely understandable -- error is to say that the Earth and other planets orbit the Sun.

No, I'm not recommending a return to the geocentric model, where the Earth is at the center of the universe and everything orbits around it in perfect circles, as decreed by the Almighty at the moment of creation (which, of course, was six thousand years ago).  The inaccuracy I'm referring to is much smaller than that -- but is still significant.

Instead of saying "the planets orbit the Sun," the more precise way to state it is that the planets and the Sun all orbit their common center of gravity.  Newton's Third Law describes how every force exerted creates an equal and opposite force -- so just as the Sun is pulling on the Earth, the Earth is pulling on the Sun.  The result is that both are in a dance around the system's center of gravity.  Given the Sun's vastly larger mass, their mutual center of gravity is well inside the Sun, so to say "the Earth orbits the Sun" is a sufficiently close approximation to account for what we observe on a daily basis.

The effect is big enough, though, that this is one of the ways that exoplanets have been discovered -- mostly in nearby systems, where it's easier to see.  A star with an unseen companion gets pulled around as they orbit their common center of gravity, so from our perspective it looks like the star has a slight wobble.  As the wobble is bigger if the planet has a larger mass, this technique has been used mostly to find exoplanets that are gas giants, like Jupiter and Saturn, which are big enough to sling their host star around more effectively.

Sometimes, though, looking for a stellar wobble results in discovering something else -- an invisible object much too massive to be a planet, in a celestial do-si-do with a star.

That was the subject of a paper published this week in The Open Journal of Astrophysics, describing research led by Kareem El-Badry of Caltech.  The team found 21 stars with heavy but invisible companions, which from their size appear to be neutron stars, the collapsed, ultra-dense cores left behind by giant stars after they exhaust their fuel.

The curious thing is that prior to the formation of a neutron star, the giant star went supernova -- so why didn't that colossal explosion completely blow away the Sun-like star it's paired with?  The simple answer is we don't know.  "We still do not have a complete model for how these binaries form," El-Badry said.  "In principle, the progenitor to the neutron star should have become huge and interacted with the solar-type star during its late-stage evolution.  The huge star would have knocked the little star around, likely temporarily engulfing it.  Later, the neutron star progenitor would have exploded in a supernova, which, according to models, should have unbound the binary systems, sending the neutron stars and Sun-like stars careening in opposite directions...  The discovery of these new systems shows that at least some binaries survive these cataclysmic processes even though models cannot yet fully explain how."

If El-Badry et al.'s research bears up, it will be the first time neutron stars have been detected purely by their gravitational effects.

So that's today's cool news from science.  A stellar dance between a Sun-like star and a collapsed, super-dense neutron star.  And I love that El-Badry ends with the words, "... models cannot yet fully explain how."  Focus on the word "yet."  These are the sorts of things that push science forward -- some unexplained observation that makes scientists scratch their heads.  As Isaac Asimov put it, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!', but '... that's funny.'"

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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.

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