Three Ways To Get Dizzy

<FZzzzzzzzzzzzzzzzzzzzzzzttt!> “Urk … ulp … I need to sit down, quick.”

“Anne? Welcome back, the couch is over there. Goodness, you do look a little green. Can I get you something to drink?”

“A little cool water might help, thanks.”

“Here. Just sit and breathe. That wasn’t your usual fizzing sound when you visit my office. When you’re ready tell me what happened. Must have been an experience, considering some of your other superpower adventures. Where did you ‘push‘ to this time?”

“Well, you know when I push forward I go into the future and when I push backward I go into the past. When I push up or down I get bigger or smaller. You figured out how pushing sideways kicks me to alternate probabilities. And then <shudder> there was that time I found a new direction to push and almost blew up the Earth.”

“Yes, that was a bad one. I’d think you’ve pretty well used up all the directions, though.”

“Not quite. This time I pushed outwards, the same in every direction.”

“Creative. And what happened?”

“Suddenly I was out in deep space, just tumbling in the blackness. There wasn’t an up or down or anything. I couldn’t even tell how big I was. I could see stars way off in the distance or maybe they were galaxies, but they were spinning all crazy. It took me a minute to realize it was me that was spinning, gyrating in several ways at once. It was scary and nauseating but I finally stopped part of it.”

“Floating in space with nothing to kill your angular momentum … how’d you manage to stabilize yourself at all?”

“Using my push superpower, of course. The biggest push resistance is against the past. I pulled pastward from just my shoulders and that stopped my nose‑diving but I was still whirling and cart‑wheeling. I tried to stop that with my feet but that only slowed me down and I was getting dizzy. My white satin had transformed into a spacesuit and I definitely didn’t want to get sick in there so I came home.”

“How’d you do that?”

“Oh, that was simple, I pulled inward. I had to um, zig‑zag? until I got just the right amount.”

“That explains the odd fizzing. I’m glad you got back. Looks like you’re feeling better now.”

“Mostly. Whew! So, Mr Physicist Sy, help me understand it all. <her voice that sounds like molten silver> Please?”

“Well. Um. There’s a couple of ways to go here. I’ll start with degrees of freedom, okay?”

“Whatever you say.”

“Right. You’re used to thinking in straight‑line terms of front/back, left/right and up/down, which makes sense if you’re on a large mostly‑flat surface like on Earth. In mathspeak each of those lines marks an independent degree of freedom because you can move along it without moving along either of the other two.”

“Like in space where I had those three ways to get dizzy.”

“Yup, three rotations at right angles to each other. Boatmen and pilots call them pitch, roll and yaw. Three angular degrees of freedom. Normal space adds three x-y-z straight‑line degrees, but you wouldn’t have been able to move along those unless you brought along a rocket or something. I guess you didn’t, otherwise you could have controlled that spinning.”

“Why would I have carried a rocket when I didn’t know where I was going? Anyhow, my push‑power can drive my straight‑line motion except I didn’t know where I was and that awful spinning had me discombobulated”

“Frankly, I’m glad I don’t know how you feel. Anyhow, if measurable motion is defined along a degree of freedom the measurement is called a coordinate. Simple graphs have an x-coordinate and a y-coordinate. An origin plus almost any three coordinates makes a coordinate system able to locate any point in space. The Cartesian x-y-z system uses three distances or you can have two distances and an angle, that’s cylindrical coordinates, or two angles and one distance and that’s polar coordinates.”

“Three angles?”

“You don’t know where you are.”

<shudder>
 <shudder>

~~ Rich Olcott

‘Twixt A Rock And A Vortex

A chilly late December walk in the park and there’s Vinnie on a lakeside bench, staring at the geese and looking morose. “Hi, Vinnie, why so down on such a bright day?”

“Hi, Sy. I guess you ain’t heard. Frankie’s got the ‘rona.”

Frankie??!? The guys got the constitution of an ox. I don’t think he’s ever been sick in his life.”

“Probably not. Remember when that bug going around last January had everyone coughing for a week? Passed him right by. This time’s different. Three days after he showed a fever, bang, he’s in the hospital.”

“Wow. How’s Emma?”

“She had it first — a week of headaches and coughing. She’s OK now but worried sick. Hospital won’t let her in to see him, of course, which is a good thing I suppose so she can stay home with the kids and their schoolwork.”

“Bummer. We knew it was coming but…”

“Yeah. Makes a difference when it’s someone you know. Hey, do me a favor — throw some science at me, get my mind off this for a while.”

“That’s a big assignment, considering. Let’s see … patient, pandemic … Ah! E pluribus unum and back again.”

“Come again?”

“One of the gaps that stand between Physics and being an exact science.”

“I thought Physics was exact.”

“Good to fifteen decimal places in a few special experiments, but hardly exact. There’s many a slip ‘twixt theory and practice. One of the slips is the gap between kinematic physics, about how separate objects interact, and continuum physics, where you’re looking at one big thing.”

“This is sounding like that Loschmidt guy again.”

“It’s related but bigger. Newton worked on both sides of this one. On the kinematics side there’s billiard balls and planets and such. Assuming no frictional energy loss, Newton’s Three Laws and his Law of Gravity let us calculate exact predictions for their future trajectories … unless you’ve got more than three objects in play. It’s mathematically impossible to write exact predictions for four or more objects unless they start in one of a few special configurations. Newton didn’t do atoms, no surprise, but his work led to Schrödinger’s equation for an exact description of single electron, single nucleus systems. Anything more complicated, all we can do is approximate.”

“Computers. They do a lot with computers.”

“True, but that’s still approximating. Time‑step by time‑step and you never know what might sneak in or out between steps.”

“What’s ‘continuum‘ about then? Q on Star trek?”

“Hardly, we’re talking predictability here. Q’s thing is unpredictability. A physics continuum is a solid or fluid with no relevant internal structure, just an unbroken mass from one edge to the other. Newton showed how to analyze a continuum’s smooth churning by considering the forces that act on an imaginary isolated packet of stuff at various points in there. He basically invented the idea of viscosity as a way to account for friction between a fluid and the walls of the pipe it’s flowing through.”

“Smooth churning, eh? I see a problem.”

“What’s that?”

“The eddies and whirlpools I see when I row — not smooth.”

“Good point. In fact, that’s the point I was getting to. We can use extensions of Newton’s technique to handle a single well‑behaved whirlpool, but in real life big whirlpools throw off smaller ones and they spawn eddies and mini‑vortices and so on, all the way down to atom level. That turns out to be another intractable calculation, just as impossible as the many‑body particle mechanics problem.”

“Ah‑hah! That’s the gap! Newton just did the simple stuff at both ends, stayed away from the middle where things get complicated.”

“Exactly. To his credit, though, he pointed the way for the rest of us.”

“So how can you handle the middle?”

“The same thing that quantum mechanics does — use statistics. That’s if the math expressions are average‑able which sometimes they’re not, and if statistical numbers are good enough for why you’re doing the calculation. Not good enough for weather prediction, for instance — climate is about averages but weather needs specifics.”

“Yeah, like it’s just started to snow which I wasn’t expecting. I’m heading home. See ya, Sy.”

“See ya, Vinnie. … Frankie. … Geez.

~~ Rich Olcott

Three ways to look at things

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.”two-shuttles

“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