A familiar shadow loomed in from the hallway.
“C’mon in, Vinnie, the door’s open.”
“I brought some sandwiches, Sy.”
“Oh, thanks, Vinnie.”
“Don’t mention it. An’ I got another LIGO issue.”
“Yeah?”
“Ohh, yeah. Now we got that frame thing settled, how does it apply to what you wrote back when? I got a copy here…”
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.
“Ah, I admit I was a bit sloppy there. Tell you what, let’s pretend we’re piloting a pair of space shuttles following separate navigation beams that are straight because that’s what light rays do. So long as we each fly a straight line at constant speed we’re both using the same inertial frame, right?”
“Sure.”
“And if a gravity field suddenly bent your beam to one side, you’d think you’re still flying straight but I’d think you’re headed on a new course, right?”
“Yeah, because now we’d have different inertial frames. I’d think your heading has changed, too.”
“So what does the guy running the beams see?”
“Oh, ground-pounders got their own inertial frame, don’t they? Uhh… He sees me veer off and you stay steady ’cause the gravity field bent only my beam.”
“Right — my shuttle and the earth-bound observer share the same inertial frame, for a while.”
“A while?”
“Forever if the Earth were flat because I’d be flying straight and level, no threat to the shared frame. But the Earth’s not flat. If I want to stay at constant altitude then I’ve got to follow the curve of the surface rather than follow the light beam straight out into space. As soon as I vector downwards I have a different frame than the guy on the ground because he sees I’m not in straight-line motion.”
“It’s starting to get complicated.”
“No worries, this is as bad as it gets. Now, let’s get back to square one and we’re flying along and this time the gravity field compresses your space instead of bending it. What happens? What do you experience?”
“Uhh… I don’t think I’d feel any difference. I’m compressed, the air molecules I breath are compressed, everything gets smaller to scale.”
“Yup. Now what do I see? Do we still have the same inertial frame?”
“Wow. Lessee… I’m still on the beam so no change in direction. Ah! But if my space is compressed, from your frame my miles look shorter. If I keep going the same miles per second by my measure, then you’ll see my speed drop off.”
“Good thinking but there’s even more to it. Einstein showed that space compression and time dilation are two sides of the same phenomenon. When I look at you from my inertial frame, your miles appear to get shorter AND your seconds appear to get longer.”
“My miles per second slow way down from the double whammy, then?”
“Yup, but only in my frame and that other guy’s down on the ground, not in yours.”
“Wait! If my space is compressed, what happens to the space around what got compressed? Doesn’t the compression immediately suck in the rest of the Universe?”
“Einstein’s got that covered, too. He showed that gravity doesn’t act instantaneously. Whenever your space gets compressed, the nearby space stretches to compensate (as seen from an independent frame, of course). The edge of the stretching spreads out at the speed of light. But the stretch deformation gets less intense as it spreads out because it’s only offsetting a limited local compression.”
“OK, let’s get back to LIGO. We got a laser beam going back and forth along each of two perpendicular arms, and that famous gravitational wave hits one arm broadside and the other arm cross-wise. You gonna tell me that’s the same set-up as me and you in the two shuttles?”
“That’s what I’m going to tell you.”
“And the guy on the ground is…”
“The laboratory inertial reference.”
“Eat your sandwich, I gotta think about this.”
(sounds of departing footsteps and closing door)
“Don’t mention it.”
~~ Rich Olcott
“Does the Moon go around the Earth or does the Earth go around the Moon?”
Their common experimental strategy sounds simple enough — compare two beams of light that had traveled along different paths
Of all the wave varieties we’re familiar with, gravitational waves are most similar to (NOT identical with!!) sound waves. A sound wave consists of cycles of compression and expansion like you see in this graphic. Those dots could be particles in a gas (classic “sound waves”) or in a liquid (sonar) or neighboring atoms in a solid (a xylophone or marimba).
Einstein noticed that implication of his Theory of General Relativity and in 1916 predicted that the path of starlight would be bent when it passed close to a heavy object like the Sun. The graphic shows a wave front passing through a static gravitational structure. Two points on the front each progress at one graph-paper increment per step. But the increments don’t match so the front as a whole changes direction. Sure enough, three years after Einstein’s prediction, Eddington observed just that effect while watching a total solar eclipse in the South Atlantic.
We’re being dynamic here, so the simulation has to include the fact that changes in the mass configuration aren’t felt everywhere instantaneously. Einstein showed that space transmits gravitational waves at the speed of light, so I used a scaled “speed of light” in the calculation. You can see how each of the new features expands outward at a steady rate.
The second question is harder. The best the aLIGO team could do was point to a “banana-shaped region” (their words, not mine) that covers about 1% of the sky. The team marshaled a world-wide collaboration of observatories to scan that area (a huge search field by astronomical standards), looking for electromagnetic activities concurrent with the event they’d seen. Nobody saw any. That was part of the evidence that this collision involved two black holes. (If one or both of the objects had been something other than a black hole, the collision would have given off all kinds of photons.)
In contrast, a LIGO facility is (roughly speaking) omni-directional. When a LIGO installation senses a gravitational pulse, it could be coming down from the visible sky or up through the Earth from the other hemisphere — one signal doesn’t carry the “which way?” information. The diagram above shows that situation. (The “chevron” is an image of the LIGO in Hanford WA.) Models based on the signal from that pair of 4-km arms can narrow the source field to a “banana-shaped region,” but there’s still that 180o ambiguity.
The great “if only” is that the VIRGO installation in Italy was not recording data when the Hanford WA and Livingston LA saw that September signal. With three recordings to reconcile, the aLIGO+VIRGO combination would have had enough information to slice that banana and localize the event precisely.
We can investigate things that take longer than an instrument’s characteristic time by making repeated measurements, but we can’t use the instrument to resolve successive events that happen more quickly than that. We also can’t resolve events that take place much closer together than the instrument’s characteristic length.
A 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).
An 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…
Almost 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.
Gravitodynamics 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 
The experiment consists of shooting laser beams out along both arms, then comparing the returned beams.
Hard Science Ain't Hard 
