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 62 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-freakin-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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After the collapse

When you start looking into black holes, there's a lot to be fascinated by.

As you probably know, a black hole is one type of collapsed star.  The ultimate fate of a star depends on its initial mass.  When the collapse begins at the end of a star's life, it continues until it meets a force strong enough to counteract the gravitational pull of its mass.  In low-mass stars like the Sun, that oppositional force is the mutual repulsion of the negatively-charged electrons in its constituent atoms.  This leaves a dense, white-hot blob called a white dwarf, slowly radiating its heat away and cooling.  More massive stars -- between ten and twenty-five solar masses -- have such a high gravitational pull that once they start collapsing the electrostatic repulsion is insufficient to stop it.  The electrons are forced into the nuclei, resulting in a neutron star, a stellar core so dense that a matchbox-sized chunk of its matter would weigh three billion tons.

Above twenty-five solar masses, however, even the neutron degeneracy pressure isn't enough to halt the collapse.  Supergiant stars continue to collapse, warping space into a closed form that even light can't escape.

This is the origin of a black hole.

[Image is in the Public Domain courtesy of NASA/JPL]

Black holes are seriously odd beasts.  Let's start with what we can infer from the upshot of Einstein's General Theory of Relativity, that gravitational fields and accelerated frames of reference are indistinguishable.  (To clarify with an easy example; if you were in a box with no windows, and were being accelerated at a rate of 9.8 m/s^2, you would have no way of knowing you weren't simply in Earth's gravitational field.)  So as weird as it sounds, the same relativistic weirdness would occur in a powerful gravitational field as occurs when you move at a high velocity; time would slow down, mass increase, and so on.  You might recall this from the movie Interstellar.  The crew of a spaceship stranded on a planet orbiting a black hole experiences time dilation -- while a year passes for them, a hundred years passes for people out in the more ordinary reaches of the universe.

This is only the start of the weirdness, though.  You may have heard about spaghettification -- yes, that's really what it's called -- when an object falls into a black hole.  Usually the example given is an astronaut, but that kind of seems cruel; spaghettification would be as unpleasant as it sounds.  What happens is that the falling object would be ripped apart by tidal forces.  A tidal force occurs when one part of an object experiences a different gravitational pull than another part of the same object, and the result is that the object is stretched.

There actually is a tidal force on your own body right now; assuming you're not doing a headstand, your feet are closer to the Earth's center of mass, so they're being pulled a little harder than your head is.  The difference is so small that we're unaware of it.  But with an object near a black hole, the gradient of gravitational pull is so large that when the object gets close -- how close depends on the black hole's mass -- the tidal forces rip it apart, stretching it in a thin filament of matter (thus the "spaghetti" in "spaghettification").

The reason all this comes up is a paper published this week in Monthly Notices of the Royal Astronomical Society that contains observational data of a star getting sucked into a black hole and spaghettified.  "When an unlucky star wanders too close to a supermassive black hole in the centre of a galaxy, the extreme gravitational pull of the black hole shreds the star into thin streams of material," said study co-author Thomas Wevers, a European Southern Observatory Fellow in Santiago, Chile, in an interview with Science Daily.  "As some of the thin strands of stellar material fall into the black hole during this spaghettification process, a bright flare of energy is released, which we can detect."

That's not the only reason that black holes were in the news last week.  In a paper in Nature Communications Physics, scientists describe their observations of a rare event -- the merger of two black holes.  When this happens, the coalescence causes such a powerful shift in the warped gravitational field surrounding it that it sends ripples out through the fabric of space.  These gravitational waves travel outward from their source at the speed of light, and the ones from something as cataclysmic as a black hole merger are so powerful they can be detected here on Earth, thousands of light years away.

"The pitch and amplitude of the signal increases as the two black holes orbit around their mutual center of mass, faster and faster as they approach each other," said Juan Calderón Bustillo, of the University of Hong Kong.  "After the collision, the final remnant black hole emits a signal with a constant pitch and decaying amplitude -- like the sound of a bell being struck."

So that's our excursion into the bizarre and counterintuitive world of collapsed stars.  The whole thing makes me realize what a violent and hostile place much of the universe is, and glad we're relatively safe down here on our comfortable little planet orbiting an ordinary star in the outer spiral arms of an ordinary galaxy.

Boring as it can seem sometimes, it beats being spaghettified by a significant margin.

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This week's Skeptophilia book recommendation is brand new, and is as elegiac as it is inspiring -- David Attenborough's A Life on Our Planet: My Witness Statement and a Vision for the Future.

Attenborough is a familiar name, face, and (especially) voice to those of us who love nature documentaries.  Through series such as Our Planet, Life on Earth, and Planet Earth, he has brought into our homes the beauty of nature -- and its desperate fragility.

At 93, Attenborough's A Life on Our Planet is a fitting coda to his lifelong quest to spark wonder in our minds at the beauty that surrounds us, but at the same time wake us up to the perils of what we're doing to it.  His message isn't all doom and gloom; despite it all, he remains hopeful, and firm in his conviction that we can reverse our course and save what's left of the biodiversity of the Earth.  It's a poignant and evocative work -- something everyone who has been inspired by Attenborough for decades should put on their reading list.

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