Ya got potential, kid, but how much?

Dusk at the end of January, not my favorite time of day or year.  I was just closing up the office when I heard a familiar footstep behind me.  “Hi, Vinnie.  What’s up?”

“Energy, Sy.”

“Energy?”

“Energy and LIGO.  Back in flight school we learned all about trading off kinetic energy and potential energy.  When I climb I use up the fuel’s chemical energy to gain gravitational potential energy.  When I dive I convert gravitational potential energy into  kinetic energy ’cause I speed up.  Simple.”

“So how do you think that ties in with LIGO?”

“OK, back when we pretended we was in those two space shuttles (which you sneaky-like used to represent photons in a LIGO) and I got caught in that high-gravity area where space is compressed, we said that in my inertial frame I’m still flying at the same speed but in your inertial frame I’ve slowed down.”

“Yeah, that’s what we worked out.”

“Well, if I’m flying into higher gravity, that’s like diving, right, ’cause I’m going where gravity is stronger like closer to the Earth, so I’m losing gravitational potential energy.  But if I’m slowing down I’ve gotta be losing kinetic energy, too, right?  So how can they both happen?  And how’s it work with photons?”

“Interesting questions, Vinnie, but I’m hungry.  How about some dinner?”shuttle-escape-1

We took the elevator down to Eddie’s pizza joint on the second floor.  I felt heavier already.  We ordered, ate and got down to business.

“OK, Vinnie.  Energy with photons is different than with objects that have mass, so let’s start with the flying-objects case.  How do you calculate gravitational potential energy?”

“Like they taught us in high school, Sy, ‘little g’ times mass times the height, and ‘little g’ is some number I forget.”

“Not a problem, we’ll just suppose that ‘little g’ times your plane’s mass is some convenient number, like 1,000.  So your gravitational potential energy is 1000×height, where the height’s in feet and the unit of energy is … call it a fidget.  OK?”

“Saves having to look up that number.”

sfo-to-den

Vinnie’s route, courtesy of Google Earth

“Fine.  Let’s suppose you’re flying over San Francisco Bay and your radar altimeter reads 20,000 feet.  What’s your gravitational potential energy?”

“Uhh… twenty million fidgets.”

“Great.  You maintain level flight to Denver.  As you pass over the Rockies you notice your altimeter now reads 6,000 feet because of that 14,000-foot mountain you’re flying over.  What’s your gravitational potential energy?”

“Six million fidgets.  Or is it still twenty?”

“Well, if God forbid you were to drop out of the sky, would you hit the ground harder in California or Colorado?”

“California, of course.  I’d fall more than three times as far.”

“So what you really care about isn’t some absolute amount of potential energy, it’s the relative amount of smash you experience if you fall down this far or that far.  ‘Height’ in the formula isn’t some absolute height, it’s height above wherever your floor is.  Make sense?”

“Mm-hm.”

“That’s an essential characteristic of potential energy — electric, gravitational, chemical, you name it.   It’s only potential.  You can’t assign a value without stating the specific transition you’re interested in.  You don’t know voltages in a circuit until you put a resistance between two specific points and meter the current through it.  You don’t know gravitational potential energy until you decide what location you want to compare it with.”

“And I suppose a uranium atom’s nuclear energy is only potential until a nuke or something sets it off.”

“You got the idea.  So, when you flew into that high-gravity compressed-space sector, what happened to your gravitational potential energy?”

“Like I said, it’s like I’m in a dive so I got less, right?”

“Depends on what you’re going to fall onto, doesn’t it?”

“No, wait, it’s definitely less ’cause I gotta use energy to fly back out to flat space.”

“OK, you’re comparing here to far away.  That’s legit.  But where’s that energy go?”

“Ahh, you’re finally getting to the kinetic energy side of my question –”

“Whoa, look at the time!  Got a plane to catch.  We’ll pick this up next week.  Bye.”

“Hey, Sy, your tab! …  Phooey, stuck for it again.”

~~ Rich Olcott

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