The Sound of Money

<chirp, chirp> “Moire, here, there’ll be a late-night surcharge for this call.”

“Hiya, Sy, it’s me, Vinnie. Got a minute? I wanna run something past you.”

“Sure, if it’s interesting enough to keep me awake.”

“It’s that Physics-money hobby horse you’ve been riding. I think I’ve got another angle on it for you.”

“Really? Shoot.”

“OK, a while ago you and me and Richard Feder talked about waves and how light waves and sound waves are different because light waves make things go up-and-down while the waves go forward but sound waves go back-and-forth.”

“Transverse waves versus compression waves, uh-huh.”

“Yeah and when you look close at a sound wave what you see is individual molecules don’t travel. What happens is like in a pool game where one ball bumps another ball and it stops but the bumped ball moves forward and the first ball maybe even moves back a little.”

“The compression momentum carries forward even though the particles don’t, right.”

“And that means that sound waves only travel as fast as the air molecules can move back and forth which is a lot slower than light waves which move by shaking the electric field. I got that, but why doesn’t sound move a lot faster in something like iron where the atoms don’t have to move?”

“Oh, it does, something like 200 times faster than in air. There’s a couple of factors in play. It all goes back to Newton —”

“Geez, he had a hand in everything Physics, didn’t he?”

“Except for electromagnetism and nuclear stuff. The available technology was just too primitive to let him experiment in those areas. Anyway, Newton discovered a formula connecting the speed of sound in a medium to its density. Like his Law of Gravity, it worked but he didn’t know why it worked. Also like gravity, we’ve got a better idea now.”

“What’s the better idea?”

“The key notions weren’t even invented until decades after Newton’s Principia was published. The magic words are the particulate nature of matter and intermolecular stiffness.”

“Hah?”

“One at a time. Newton was a particle guy to an extent. He believed that light is made of particles, but he didn’t take the next step to thinking of all matter as being made of particles. But it is, and the particles interact with each other. Think of it as stickiness. How effective the stickiness is depends on the temperature and which molecules you’re talking about. Gas molecules have so much kinetic energy relative to their sticky that they mostly just bounce off each other. In liquids and solids the molecules stay close enough together that the stickiness acts like springs. The springs may be more or less stiff depending on which molecules or ions or atoms are involved.”

“I see where you’re going. Stuff with stiffer springs doesn’t move as much as looser stuff at the same temperature; sound goes faster through a solid than through a liquid or gas. That’s what Newton figured out, huh?”

“No, he just measured and said, basically, ‘here’s the formula.‘ Just like with gravity, he didn’t suggest why the numbers were what they were. <yawn> So, you called with an idea about sound and money physics.”

“Right. Got off the track there, but this was helpful. What got me started was some newscaster saying how the Paycheck Protection Program is dumping money into the economy during the pandemic. My first thought was, ‘Haw, that’s gotta be a splash!‘ Then I imagined this pulse of money sloshing back and forth like a wave and that led me to sound waves and then I kept going. No dollar bill moves around that much, but when people spend them that’s like the compression wave moving out.”

“Interesting idea, Vinnie. From a Physics perspective, the question is, ‘How fast does the wave move?’ It’s another temperature‑versus‑stickiness thing.”

“Yeah, I figure money velocity measures the economy like temperature measures molecule motion. Money velocity goes up with inflation. If the velocity’s high people spend their money because why not.”

“Yup. From the government’s perspective the whole purpose of economic stimulation is getting the cash flowing again. Their problem is locating the money velocity kickover point.”

~~ Rich Olcott

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