Breathing Space

It was December, it was cold, no surprise.  I unlocked my office door, stepped in and there was Vinnie, standing at the window.  He turned to me, shrugged a little and said, “Morning, Sy.”  That’s Vinnie for you.

“Morning, Vinnie.  What got you onto the streets this early?”

“I ain’t on the streets, I’m up here where it’s warm and you can answer my LIGO question.”

“And what’s that?”

“I read your post about gravitational waves, how they stretch and compress space.  What the heck does that even mean?”

gravwave

An array of coordinate systems
floating in a zero-gravity environment,
each depicting a local x, y, and z axis

“Funny thing, I just saw a paper by Professor Saulson at Syracuse that does a nice job on that.  Imagine a boxful of something real light but sparkly, like shiny dust grains.  If there’s no gravitational field nearby you can arrange rows of those grains in a nice, neat cubical array out there in empty space.  Put ’em, oh, exactly a mile apart in the x, y, and z directions.  They’re going to serve as markers for the coordinate system, OK?”

“I suppose.”

“Now it’s important that these grains are in free-fall, not connected to each other and too light to attract each other but all in the same inertial frame.  The whole array may be standing still in the Universe, whatever that means, or it could be heading somewhere at a steady speed, but it’s not accelerating in whole or in part.  If you shine a ray of light along any row, you’ll see every grain in that row and they’ll all look like they’re standing still, right?”

“I suppose.”

“OK, now a gravitational wave passes by.  You remember how they operate?”

“Yeah, but remind me.”

(sigh)  “Gravity can act in two ways.  The gravitational attraction that Newton identified acts along the line connecting the two objects acting on each other.  That longitudinal force doesn’t vary with time unless the object masses change or their distance changes.  We good so far?”
long-and-transverse-grav
“Sure.”

“Gravity can also act transverse to that line under certain circumstances.  Suppose we here on Earth observe two black holes orbiting each other.  The line I’m talking about is the one that runs from us to the center of their orbit.  As each black hole circles that center, its gravitational field moves along with it.  The net effect is that the combined gravitational field varies perpendicular to our line of sight.  Make sense?”

“Gimme a sec…  OK, I can see that.  So now what?”

“So now that variation also gets transmitted to us in the gravitational wave.  We can ignore longitudinal compression and stretching along our sight line.  The black holes are so far away from us that if we plug the distance variation into Newton’s F=m1m2/r² equation the force variation is way too small to measure with current technology.

“The good news is that we can measure the off-axis variation because of the shape of the wave’s off-axis component.  It doesn’t move space up-and-down.  Instead, it compresses in one direction while it stretches perpendicular to that, and then the actions reverse.  For instance, if the wave is traveling along the z-axis, we’d see stretching follow compression along the x-axis at the same time as we’d see compression following stretching along the y-axis.”

gravwave-2“Squeeze in two sides, pop out the other two, eh?”

“Exactly.  You can see how that affects our grain array in this video I just happen to have cued up.  See how the up-down and left-right coordinates close in and spread out separately as the wave passes by?”

“Does this have anything to do with that ‘expansion of the Universe’ thing?”

“Well, the gravitational waves don’t, so far as we know, but the notion of expanding the distance between coordinate markers is exactly what we think is going on with that phenomenon.  It’s not like putting more frosting on the outside of a cake, it’s squirting more filling between the layers.  That cosmological pressure we discussed puts more distance between the markers we call galaxies.”

“Um-hmm.  Stay warm.”

(sound of departing footsteps and door closing)

“Don’t mention it.”

~~ Rich Olcott

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