Month: February 2016

LIGO: Gravity Waves Ain’t Gravitational Waves

On By rolcottIn Astronomy: Techniques, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Foundations of Measurement, Physics: Newton and Gravity, UncategorizedLeave a comment

Sometimes the media get sloppy.  OK, a lot of times, especially when the reporters don’t know what they’re writing about.  Despite many headlines that “LIGO detected gravity waves,” that’s just not so.  In fact, the LIGO team went to a great deal of trouble to ensure that gravity waves didn’t muck up their search for gravitational waves.

Spring2A wave happens in a system when a driving force and a restoring force take turns overshooting an equilibrium point AND the away-from-equilibrium-ness gets communicated around the system.  The system could be a bunch of springs tied together in a squeaky old bedframe, or labor and capital in an economic system, or the network of water molecules forming the ocean surface, or the fibers in the fabric of space (whatever those turn out to be).

If you  were to build a mathematical model of some wavery system you’d have to include those two forces plus quantitative descriptions of the thingies that do the moving and communicating.  If you don’t add anything else, the model will predict motion that cycles forever.  In reality, of course, there’s always something else that lets the system relax into equilibrium.

The something else could be a third force, maybe someone sitting on the bed, or government regulation in an economy, or reactant depletion for a chemical process.  But usually it’s friction of one sort or another — friction drains away energy of motion and converts it to heat.  Inside a spring, for instance, adjacent crystallites of metal rub against each other.  There appears to be very little friction in space — we can see starlight waves that have traveled for billions of years.

Physicists pay attention to waves because there are some general properties that apply to all of them.  For instance, in 1743 Jean-Baptiste le Rond d’Alembert proved there’s a strict relationship between a wave’s peakiness and its time behavior.  Furthermore, Jean-Baptiste Joseph Fourier (pre-Revolutionary France must have been hip-deep in physicist-mathematicians) showed that a wide variety of more-or-less periodic phenomena could be modeled as the sum of waves of differing frequency and amplitude.

Monsieur Fourier’s insight has had an immeasurable impact on our daily lives.  You can thank him any time you hear the word “frequency.”  From broadcast radio and digitally recorded music to time-series-based business forecasting to the mode-locked lasers in a LIGO device — none would exist without Fourier’s reasoning.

Gravity waves happen when a fluid is disturbed and the restoring force is gravity.  We’re talking physicist fluid here, which could be sea water or the atmosphere or solar plasma, anything where the constituent particles aren’t locked in place. Winds or mountain slopes or nuclear explosions push the fluid upwards, gravity pulls it back, and things wobble until friction dissipates that energy.

Gravitational waves are wobbles in gravity itself, or rather, wobbles in the shape of space.  According to General Relativity, mass exerts a tension-like force that squeezes together the spacetime immediately around it.  The more mass, the greater the tension.

Binary BH with AENAn isolated black hole is surrounded by an intense gravitational field and a corresponding compression of spacetime.  A pair of black holes orbiting each other sends out an alternating series of tensions, first high, then extremely high, then high…

Along any given direction from the pair you’d feel a pulsing gravitational field that varied above and below the average force attracting you to the pair.  From a distance and looking down at the orbital plane, if you could see the shape of space you’d see it was distorted by four interlocking spirals of high and low compression, all steadily expanding at the speed of light.

The LIGO team was very aware that the signal of a gravitational wave could be covered up by interfering signals from gravity waves — ocean tides, Earth tides, atmospheric disturbances, janitorial footsteps, you name it.  The design team arrayed each LIGO site with hundreds of “seismometers, accelerometers, microphones, magnetometers, radio receivers, power monitors and a cosmic ray detector.”  As the team processed the LIGO trace they accounted for artifacts that could have come from those sources.

So no, the LIGO team didn’t discover gravity waves, we’ve known about them for a century.  But they did detect the really interesting other kind.

~~ Rich Olcott

Would the CIA want a LIGO?

On By rolcottIn Astronomy: Techniques, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Electromagnetism, Physics: Fundamentals, Physics: Light and Relativity, UncategorizedLeave a comment

So I was telling a friend about the LIGO announcement, going on about how this new “device” will lead to a whole new kind of astronomy.  He suddenly got a far-away look in his eyes and said, “I wonder how many of these the CIA has.”

The CIA has a forest of antennas, but none of them can do what LIGO does.  That’s because of the physics of how it works, and what it can and cannot detect.  (If you’re new to this topic, please read last week’s post so you’ll be up to speed on what follows.  Oh, and then come back here.)

There are remarkable parallels between electromagnetism and gravity.  The ancients knew about electrostatics — amber rubbed by a piece of cat fur will attract shreds of dry grass.  They certainly knew about gravity, too.  But it wasn’t until 100 years after Newton wrote his Principia that Priestly and then Coulomb found that the electrostatic force law, F = ke·q1·q2 / r2, has the same form as Newton’s Law of Gravity, F = G·m1·m2 / r2. (F is the force between two bodies whose centers are distance r apart, the q‘s are their charges and the m‘s are their masses.)

Jim and AlAlmost a century later, James Clerk Maxwell (the bearded fellow at left) wrote down his electromagnetism equations that explain how light works.  Half a century later, Einstein did the same for gravity.

But interesting as the parallels may be, there are some fundamental differences between the two forces — fundamental enough that not even Einstein was able to tie the two together.

One difference is in their magnitudes.  Consider, for instance, two protons.  Running the numbers, I found that the gravitational force pulling them together is a factor of 1036 smaller than the electrostatic force pushing them apart.  If a physicist wanted to add up all the forces affecting a particular proton, he’d have to get everything else (nuclear strong force, nuclear weak force, electromagnetic, etc.) nailed down to better than one part in 1036 before he could even detect gravity.

But it’s worse — electromagnetism and gravity don’t even have the same shape.

Electromagneticwave3D
Electric (red) and magnetic (blue) fields in a linearly polarized light wave
(graphic from WikiMedia Commons, posted by Lookang and Fu-Kwun Hwang)

A word first about words.  Electrostatics is about pure straight-line-between-centers (longitudinal) attraction and repulsion — that’s Coulomb’s Law.  Electrodynamics is about the cross-wise (transverse) forces exerted by one moving charged particle on the motion of another one.  Those forces are summarized by combining Maxwell’s Equations with the Lorenz Force Law.  A moving charge gives rise to two distinct forces, electric and magnetic, that operate at right angles to each other.  The combined effect is called electromagnetism.

The effect of the electric force is to vibrate a charge along one direction transverse to the wave.  The magnetic force only affects moving charges; it acts to twist their transverse motion to be perpendicular to the wave.  An EM antenna system works by sensing charge flow as electrons move back and forth under the influence of the electric field.

Gravitostatics uses Newton’s Law to calculate longitudinal gravitational interaction between masses.  That works despite gravity’s relative weakness because all the astronomical bodies we know of appear to be electrically neutral — no electrostatic forces get in the way.  A gravimeter senses the strength of the local gravitostatic field.

Maxwell and EinsteinGravitodynamics is completely unlike electrodynamics.  Gravity’s transverse “force” doesn’t act to move a whole mass up and down like Maxwell’s picture at left.  Instead, as shown by Einstein’s picture, gravitational waves stretch and compress while leaving the center of mass in place. I put “force” in quotes because what’s being stretched and compressed is space itself.  See this video for a helpful visualization of a gravitational wave.

LIGO is neither a telescope nor an electromagnetic antenna.  It operates by detecting sudden drastic changes in the disposition of matter within a “small” region.  In LIGO’s Sept 14 observation, 1031 kilograms of black hole suddenly ceased to exist, converted to gravitational waves that spread throughout the Universe.  By comparison, the Hiroshima explosion released the energy of 10-6 kilograms.

Seismometers do a fine job of detecting nuclear explosions.  Hey, CIA, they’re a lot cheaper than LIGO.

~~ Rich Olcott

LIGO, a new kind of astronomy

On By rolcottIn Astronomy: Techniques, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Fundamentals, UncategorizedLeave a comment

Like thousands of physics geeks around the world, I was glued to the tube Thursday morning for the big LIGO (Laser Interferometer Gravitational-Wave Observatory) announcement.  As I watched the for-the-public videos (this is a good one), I was puzzled by one aspect of the LIGO setup.  The de-puzzling explanation spotlit just how different gravitational astronomy will be from what we’re used to.

There are two LIGO installations, 2500 miles apart, one near New Orleans and the other near Seattle.  Each one looks like a big L with steel-pipe arms 4 kilometers long.  By the way, both arms are evacuated to eliminate some sources of interference and a modest theoretical consideration.

LIGO3The experiment consists of shooting laser beams out along both arms, then comparing the returned beams.

Some background: Einstein conquered an apparent relativity paradox.  If Ethel on vehicle A is speeding (like, just shy of light-speed speeding) past Fred on vehicle B, Fred sees that Ethel’s yardstick appears to be shorter than his own yardstick.  Meanwhile, Ethel is quite sure that Fred’s yardstick is the shorter one.

Einstein explained that both observations are valid.  Fred and Ethel can agree with each other but only after each takes proper account of their relative motion.  “Proper account” is a calculation called the Lorenz transformation.   What Fred (for instance) should do is divide what he thinks is the length of Ethel’s yardstick by √[1-(v/c)²] to get her “proper” length.  (Her relative velocity is v, and c is the speed of light.)

Suppose Fred’s standing in the lab and Ethel’s riding a laser beam.  Here’s the puzzle: wouldn’t the same Fred/Ethel logic apply to LIGO?  Wouldn’t the same yardstick distortion affect both the interferometer apparatus and the laser beams?

Well, no, for two reasons.  First, the Lorenz effect doesn’t even apply, because the back-and-forth reflected laser beams are standing waves.  That means nothing is actually traveling.  Put another way, if Ethel rode that light wave she’d be standing as still as Fred.

The other reason is that the experiment is less about distance traveled and more about time of flight.

Suppose you’re one of a pair of photons (no, entanglement doesn’t enter into the game) that simultaneously traverse the interferometer’s beam-splitter mirror.  Your buddy goes down one arm, strikes the far-end mirror and comes back to the detector.  You take the same trip, but use the other arm.

The beam lengths are carefully adjusted so that under normal circumstances, when the two of you reach the detector you’re out of step.   You peak when your buddy troughs and vice-versa.  The waves cancel and the detector sees no light.

Now a gravitational wave passes by (red arcs in the diagram).  In general, the wave will affect the two arms differently.  In the optimal case, the wave front hits one arm broadside but cuts across the perpendicular one.  Suppose the wave is in a space-compression phase when it hits.  The broadside arm, beam AND apparatus, is shortened relative to the other one which barely sees the wave at all.

The local speed of light (miles per second) in a vacuum is constant.  Where space is compressed, the miles per second don’t change but the miles get smaller.  The light wave slows down relative to the uncompressed laboratory reference frame.  As a result, your buddy in the compressed arm takes just a leetle longer than you do to complete his trip to the detector.  Now the two of you are in-step.  The detector sees light, there is great rejoicing and Kip Thorne gets his Nobel Prize.

But the other wonderful thing is, LIGO and neutrino astronomy are humanity’s first fundamentally new ways to investigate our off-planet Universe.  Ever since Galileo trained his crude telescope on Jupiter the astronomers have been using electromagnetic radiation for that purpose – first visible light, then infra-red and radio waves.  In 1964 we added microwave astronomy to the list.  Later on we put up satellites that gave us the UV and gamma-ray skies.

The astronomers have been incredibly ingenious in wringing information out of every photon, but when you look back it’s all photons.  Gravitational astronomy offers a whole new path to new phenomena.  Who knows what we’ll see.

~~ Rich Olcott

Smoke and a mirror

On By rolcottIn General: Fun Stuff, Physics: Fundamentals, Uncategorized1 Comment

Etna jellyfish pairGrammie always grimaced when Grampie lit up one of his cigars inside the house.  We kids grinned though because he’d soon be blowing smoke rings for us.  Great fun to try poking a finger into the center, but we quickly learned that the ring itself vanished if we touched it.

My grandfather can’t take credit for the smoke ring on the left — it was “blown” by Mt Etna.  Looks very like the jellyfish on the right, doesn’t it?  When I see two such similar structures, I always wonder if the resemblance comes from the same physics phenomenon.

This one does — the physics area is Fluid Dynamics, and the phenomenon is a vortex ring. We need to get a little technical and abstract here: to a physicist a fluid is anything that’s composed of particles that don’t have a fixed spatial relationship to each other. Liquid water is a fluid, of course (its molecules can slide past each other) and so is air.  The sun’s ionized protons and electrons comprise a fluid, and so can a mob of people and so can vehicle traffic (if it’s moving at all).  You can use Fluid Dynamics to analyze motion when the individual particles are numerous and small relative to the volume in question.

Ring x-section
Adapted from a NOAA page

You get a vortex whenever you have two distinct fluids in contact but moving at sufficiently different velocities.  (Remember that “velocity” includes both speed and direction.)  When Grampie let out that little puff of air (with some smoke in it), his fast-moving breath collided with the still air around him.  When the still air didn’t get out of the way, his breath curled back toward him.  The smoke collected in the dark gray areas in this diagram.

That curl is the essence of vorticity and turbulence.  The general underlying rule is “faster curls toward slower,” just like that skater video in my previous post.  Suppose fluid is flowing through a pipe.  Layers next to the outside surface move slowly whereas the bulk material near the center moves quickly.  If the bulk is going fast enough, the speed difference will generate many little whorls against the circumference, converting pump energy to turbulence and heat.  The plant operator might complain about “back pressure” because the fluid isn’t flowing as rapidly as expected from the applied pressure.

But Grampie didn’t puff into a pipe (he’s a cigar man, right?), he puffed into the open air.  Those curls weren’t just at the top and bottom of his breath, they formed a complete circle all around his mouth.  If his puff didn’t come out perfectly straight, the smoke had a twist to it and circulated along that circle, the way Etna’s ring seems to be doing (note the words In and Out buried in the diagram’s gray blobs).  When a vortex closes its loop like that, you’ve got a vortex ring.

A vortex ring is a peculiar beast because it seems to have a life of its own, independent of the surrounding medium.  Grampie’s little puff of vortical air usually retained its integrity and carried its smoke particles for several feet before energy loss or little fingers broke up the circulation.

To show just how special vortex rings are, consider the jellyfish.  Until I ran across this article, I’d thought that jellyfish used jet propulsion like octopuses and squids do — squirt water out one way to move the other way.  Not the case.  Jellyfish do something much more sophisticated, something that makes them possibly “the most energy-efficient animals in the world.”

jellyfish vortices

Thanks to a very nice piece of biophysics detective work (read the paper, it’s cool, no equations), we now know that a jellyfish doesn’t just squirt.  Rather, it relaxes its single ring of muscle tissue to open wide.  That motion pulls in a pre-existing vortex ring that pushes against the bell.  On the power stroke, the jellyfish contracts its bell to push water out (OK, that’s a squirt) and create another vortex ring rolling in the opposite direction.  In effect, the jellyfish continually builds and climbs a ladder of vortex rings.

Vortex rings are encapsulated angular momentum, potentially in play at any size in any medium.

~~ Rich Olcott

The Force(s) of Geometry

On By rolcottIn Mathematics, Physics: Fundamentals, UncategorizedLeave a comment

There’s a lot more to Geometry than congruent triangles.  Geometry can generate hurricanes and slam you to the floor.

It all starts (of course) with Newton.  His three laws boil down to

Effect is to Cause as Change of Motion is to Force.

They successfully account for the physical movement of pretty much everything bigger than an atom.  But sometimes the forces are a bit weird and it takes Geometry to understand them.

Side forceFor instance, suppose Fred and Ethel collaborate on a narwhale research project.  Fred is based in San Diego CA and Ethel works out of Norfolk VA. They fly to meet their research vessel at the North Pole. Fred’s plane follows the green track, Ethel’s plane follows the yellow one.  At the start of the trip, they’re on parallel paths going straight north (the dotted lines).  After a few hours, though, Ethel notices the two planes pulling closer together.

Ethel calls on her Newton knowledge to explain the phenomenon.  “It can’t be Earth’s gravity moving us together, because that force points down to Earth’s center and this is a sideways motion.  Our planes each weigh about 2000 kilograms and we’re still 2,000 kilometers apart.  By Newton’s F = G m1m2/r2 equation, the gravitational force between us should be (6.7×10-11 N m2/kg2) x (2000 kg) x (2000 kg) / (2,000 m)2 = 6.7×10-11 newtons, way too small to account for our speed of approach.  Both planes were electrically grounded when we fueled up, so we’re both carrying a neutral electric charge and it can’t be an electrostatic force.  If it were magnetic my compass would be going nuts and it’s not.  Woo-hoo, I’ve discovered a new kind of force!”

See what I did there?  Fred and Ethel would have stayed a constant distance apart if Earth were a cylinder.  Parallel lines running up a cylinder never meet.  But Earth is a sphere, not a cylinder.  Any pair of lines on a sphere must meet, sooner or later.  Ethel’s “sideways force” is a product of Geometry.

Sandy
Images extracted from NOAA’s SOS Explorer app, available from sos.noaa.gov

Hurricanes, too.  This video shows a day in the life of Hurricane Sandy.  Weather geeks will find several interesting details there, but for now just notice the centers of  counter-clockwise rotation (the one off the Florida coast is Sandy).  Storm centers in the Northern Hemisphere virtually always spin counterclockwise.  Funny thing is, in the Southern Hemisphere those centers go clockwise instead.

The difference has to do with angular momentum.  We could get all formal vector math here, but the easy way is to consider how fast the air is moving in different parts of the world.

We’ve all seen at least one ice show act where skaters form a spinning line. The last skater to join up (usually it’s a short girl) has to push like mad to catch the end of that moving line and everyone applauds her success. Meanwhile the tall girl at the center of the line is barely moving except to fend off dizziness.

YellowknifeThe line rotates as a unit — every skater completes a 360o rotation in the same time. Similarly, everywhere on Earth a day lasts for exactly 24 hours.

Skaters at the end of the line must skate faster than those further in because they have to cover a greater distance in the same amount of time.  The same geometry applies to Earth’s atmosphere.  The Earth is 25,000 miles around at the equator but only 12,500 miles around near the latitude of Whitehorse, Canada.  By and large, a blob of air at the equator must move twice as fast as a blob at 60o north.

chain 2Now suppose our speedy skater hits a slushy patch of ice.  Her end of the line is slowed down, so what happens to the rest of the line?  It deforms — there’s a new center of rotation that forces the entire line to curl around towards the slow spot.  Similarly, that blob near the Equator in the split-Earth diagram curls in the direction of the slower-moving air to its north, which is counter-clockwise.

In the Southern hemisphere, “slower” is southward and clockwise.

If not for Geometry (those differing circle sizes), we wouldn’t have hurricanes.  Or gravity — but that’s another story.

~~ Rich Olcott