# Naming the place and placing the name

“By the way, Cathleen, is there any rhyme or reason to that three-object object‘s funky name?  I’ve still got it on Old Reliable here.”

PSR J0337+1715

“It’s nothing like funky, Sy, it’s perfectly reasonable and in fact it’s far more informative than a name like ‘Barnard’s Star.’  The ‘PSR‘ part says that the active object, the reason anyone even looked in that system’s direction, is a pulsar.”

“And the numbers?”

“Its location in two parts.  Imagine a 24-hour clockface in the Solar Plane.  The zero hour points to where the Sun is at the Spring equinox.  One o’clock is fifteen degrees east of that, two o’clock is another fifteen degrees eastward and so on until 24 o’clock is back pointing at the Springtime Sun.  Got that?”

“Mm, … yeah.  It’d be like longitudes around the Earth, except the Earth goes around in a day and this clock looks like it measures a year.”

“Careful there, it has nothing to do with time.  It’s just a measure of angle around the celestial equator.  It’s called right ascension.

“How about intermediate angles, like between two and three o’clock?”

“Sixty arc-minutes between hours, sixty arc-seconds between arc-minutes, just like with time.  If you need to you can even go to tenths or hundredths of an arc-second, which divide the circle into … 8,640,000 segments.”

“OK, so if that’s like longitudes, I suppose there’s something like latitudes to go with it?”

“Mm-hm, it’s called declination.  It runs perpendicular to ascension, from plus-90° up top down to 0° at the clockface to minus-90° at the bottom.  Vivian, show Sy Figure 3 from your paper.”“Wait, right ascension in hours-minute-seconds but declination in degrees?”

“Mm-hm.  Blame history.  People have been studying the stars and writing down their locations for a long time.  Some conventions were convenient back in the day and we’re not going to give them up.  So anyway, an object’s J designation with 4-digit numbers tells you which of 13 million directions to look to find it.  Roughly.”

“Roughly?”

“That’s what the ‘J‘ is about.  If the Earth’s rotation were absolutely steady and if the Sun weren’t careening about a moving galaxy, future astronomers could just look at an object’s angular designation and know exactly where to look to find it again.  But it’s not and it does and they won’t.  The Earth’s axis of rotation wobbles in at least three different ways, the Sun’s orbit around the galaxy is anything but regular and so on.  Specialists in astrometry, who measure things to fractions of an arc-second, keep track of time in more ways than you can imagine so we can calculate future positions.  The J-names at least refer back to a specific point in time.  Mostly.  You want your mind bent, look up epoch some day.”

“Plane and ship navigators care, too, right?”

“Not so much.  Earth’s major wobble, for instance, shifts our polar positions only about 40 parts per million per year.  A course you plotted last week from here to Easter Island will get you there next month no problem.”

“Oh, that’d be a challenge.  Once you get away from the Solar System you can’t use the Big Dipper to find the North Star, any of that stuff, because the constellations look different from a different angle.  Get a couple dozen lightyears out, you’ve got a whole different sky.”

“So what do you use instead?”

“I suppose you could use pulsars.  Each one pings at a unique repetition interval and duty cycle so you could recognize it from any angle.  The set of known pulsars would be like landmarks in the galaxy.  If you sent out survey ships, like the old-time navigators who mapped the New World, they could add new pulsars to the database.  When you go someplace, you just triangulate against the pulsars you see and you know where you are.”

If they happen to point towards you! You only ever see 20% of them.  Starquakes and glitches and relativistic distortions mess up the timings.  Poor Xian-sheng goes nuts each time we drop out of warp.

~~ Rich Olcott

# Concerto for Rubber Ruler

An unfamiliar knock at my office door — more of a tap than a knock. “C’mon in, the door’s open.”

“Hi, Maria. No, I’m not busy, just taking care of odds and ends. What can I do for you?”

“I’m doing a paper on Vera Rubin for la profesora. I have the biographical things, like she was usually the only woman in her Astronomy classes and she had to make her own baño at Palomar Observatory because they didn’t have one for señoras, and she never got the Nobel Prize she deserved for discovering dark matter.

“Wait, you have all negatives there.  Her life had positives, too.  What about her many scientific breakthroughs?”

“That’s why I’m here, for the science parts I don’t understand.”

“I’ll do what I can. What’s the first one?”

“In her thesis she showed that galaxies are ‘clumped.’  What is that?”

“It means that the galaxies aren’t spread out evenly.  Astronomers at the time believed, I guess on the basis of Occam’s Razor, that galaxies were all the same distance from their neighbors.”

“Occam’s Razor?  Ah, la navaja de Okcam.  Yes, we study that in school — do not assume more than you have to.  But why would evenly be a better assumption than clumpy?”

“At the time she wrote her thesis the dominant idea was that the Big Bang’s initial push would be ‘random’ — every spot in the Universe would have an equal chance of hosting a galaxy.  But she found clusters and voids.  That made astronomers uncomfortable because they couldn’t come up with a mechanism that would make things look that way.  It took twenty years before her observations were accepted.  I’ve long thought part of her problem was that her thesis advisor was George Gamow.  He was a high-powered physicist but not an observational astronomer.  For some people that was sufficient excuse to ignore Rubin’s work.”

“Another excuse.”

“Yes, that, too.”

“But why did she have to discover the clumpy?  You can just look up in the sky and see things that are close to each other.”

“Things that appear to be close together in the sky aren’t necessarily close together in the Universe.  Look out my window.  See the goose flying there?”

“Mmm…  Yes!  I see it.”

“There’s an airplane coming towards it, looks about the same size.  Think they’ll collide?”

“Of course no.  The airplane looks small because it’s far away.”

“But when their paths cross, we see them at the same point in our sky, right?”

“The same height up, yes, and the same compass direction, but they have different distances from us.”

“Mm-hm.  Geometry is why it’s hard to tell whether or not galaxies are clustered.  Two galaxy images might be separated by arc-seconds or less.  The objects themselves could be nearest neighbors or separated by half-a-billion lightyears.  Determining distance is one of the toughest problems in observational astronomy.”

“That’s what Vera Rubin did?  How?”

“In theory, the same way we do today.  In practice, by a lot of painstaking manual work.  She did her work back in the early 1950s, when ‘computer’ was a job title, not a device.  No automation — electronic data recording was a leading-edge research topic.  She had to work with images of spectra spread out on glass plates, several for each galaxy she studied.  Her primary tool, at least in the early days, was a glorified microscope called a measuring engine.  Here’s a picture of her using one.”

“She looks through the eyepiece and then what?”

“She rotates those vernier wheels to move each glass-plate feature on the microscope stage to the eyepiece’s crosshairs.  The verniers give the feature’s x– and y-coordinates to a fraction of a millimeter.  She uses a gear-driven calculating machine to turn galaxy coordinates into sky angles and spectrum coordinates into wavelengths.  The wavelengths, Hubble’s law and more arithmetic give her the galaxy’s distance from us.  More calculations convert her angle-angle-distance coordinates to galactic xy-z-coordinates.  Finally she calculates distances between that galaxy and all the others she’s already done.  After processing a few hundred galaxies, she sees groups of short-distance galaxies in reportable clusters.”

“Wouldn’t a 3-D graphic show them?”

“Not for another 50 years.”

~~ Rich Olcott

# Étude for A Rubber Ruler

93% redder?  How do you figure that, Sy, and what’s it even mean?”

“Simple arithmetic, Vinnie.  Cathleen said that most-distant galaxy is 13 billion lightyears away.  I primed Old Reliable with Hubble’s Constant to turn that distance into expansion velocity and compare it with lightspeed.  Here’s what came up on its screen.”“Whoa, Sy.  Do you read the final chapter of a mystery story before you begin the book?”

“Of course not, Cathleen.  That way you don’t know the players and you miss what the clues mean.”

“Which is the second of Vinnie’s questions.  Let’s take it a step at a time.  I’m sure that’ll make Vinnie happier.”

“It sure will.  First step — what’s a parsec?”

“Just another distance unit, like a mile or kilometer but much bigger.  You know that a lightyear is the distance light travels in an Earth year, right?”

“Right, it’s some huge number of miles.”

“About six trillion miles, 9½ trillion kilometers.  Multiply the kilometers by 3.26 to get parsecs.  And no, I’m not going to explain the term, you can look it up.  Astronomers like the unit, other people put it in the historical-interest category with roods and firkins.”

“Is that weird ‘km/sec/Mparsec’ mix another historical thing?”

“Uh-huh.  That’s the way Hubble wrote it in 1929.  It makes more sense if you look at it piecewise.  It says for every million parsecs away from us, the outward speed of things in general increases by 70 kilometers per second.”

“That helps, but it mixes old and new units like saying miles per hour per kilometer.  Ugly.  It’d be prettier if you kept all one system, like (pokes at smartphone screen) … about 2.27 km/sec per 1018 kilometers or … about 8 miles an hour per quadrillion miles.  Which ain’t much now that I look at it.”

“Not much, except it adds up over astronomical distances.  The Andromeda galaxy, for instance, is 15×1018 miles away from us, so by your numbers it’d be moving away from us at 120,000 miles per hour.”

“Wait, Cathleen, I thought Andromeda is going to collide with the Milky Way four billion years from now.”

“It is, Sy, and that’s one of the reasons why Hubble’s original number was so far off.  He only looked at about 50 close-by galaxies, some of which are moving toward us and some away.  You only get a view of the general movement when you look at large numbers of galaxies at long distances.  It’s like looking through a window at a snowfall.  If you concentrate on individual flakes you often see one flying upward, even though the fall as a whole is downward.  Andromeda’s 250,000 mph march towards us is against the general expansion.”

“Like if I’m flying a plane and the airspeed indicator says I’m doing 200 but my ground-speed is about 140 then I must be fighting a 60-knot headwind.”

“Exactly, Vinnie.  For Andromeda the ‘headwind’ is the Hubble Flow, that general outward trend.  If Sy’s calculation were valid, which it’s not, then that galaxy 13 billion lightyears from here would indeed be moving further away at  93% of lightspeed.  Someone living in that galaxy could shine a 520-nanometer green laser at us.  At this end we see the beam stretched by 193% to 1000nm.  That’s outside the visible range, well into the near-infrared.  All four visible lines in the hydrogen spectrum would be out there, too.”

“So that’s why ‘old hydrogens’ look different — if they’re far enough away in the Hubble Flow they’re flying away from us so fast all their colors get stretched by the red-shift.”

“Right, Vinnie.”

“Wait, Cathleen, what’s wrong with my calculation?”

“Two things, Sy.  Because the velocities are close to lightspeed, you need to apply a relativistic correction factor.  That velocity ratio Old Reliable reported — call it b.  The proper stretch factor is z=√ [(1+b)/(1–b)].  Relativity takes your 93% stretch down to (taps on laptop keyboard) … about 86%.  The bluest wavelength on hydrogen’s second-down series would be just barely visible in the red at 680nm.”

“What’s the other thing?”

“The Hubble Constant can’t be constant.  Suppose you run the movie backwards.  The Universe shrinks steadily at 70 km/sec/Mparsec.  You hit zero hundreds of millions of years before the Big Bang.”

“The expansion must have started slow and then accelerated.”

“Vaster and faster, eh?”

“Funny, Sy.”

~~ Rich Olcott

# Keep calm and stay close to home

Again with the fizzing sound.  Her white satin still looked good.  A little travel-worn, but on her that looked even better.  Her voice still sounded like molten silver — “Hello.”

“Hello, Anne.  Where you been?”

“You wouldn’t believe.  I don’t believe.  I’ve got to get some control over this.”

“What’s the problem?”

“I never know where I’ll be next.  Or when.  Or even how it’ll look when I get there.  We’ve met before, haven’t we?”

“Yes, we have, and you told me your memory works in circles.  We figured out that when you ‘push,’ you relocate to a reality with a different probability.”

“But it could also be a different time.  Future, past, it’s so confusing.  Sometimes I meet myself and I don’t know whether I’m coming or going.  We never know what to say to each other.  It’s horrible way to be.”

“It sounds awful.  Here, have a tissue.  So, how can I help you?”

“You do theory stuff.  Can you physics a way to let me steer through all this?”

<fizzing sound> Another Anne appeared, next to my file cabinet on the far side of the office.  “Don’t mind me, just passing through.”  <more fizzing>  She flickered away.  My ears itched a little.

“See?  And she always knows more than I do, except when I know more than she does.”

“I’m beginning to get the picture.  Mind if I ask you a few questions?”

“Anything, if it’ll help solve this.”

“When you time-hop, do you use the same kind of ‘push’ feeling that sends you to different probabilities?”

“No-o, it’s a little different, but not much.”

“We found that you have to ‘push’ harder to get to a less-probable reality.  Is there the same kind of difference between past and future hopping?”

“Now you mention it, yes!  It’s always easier to jump to the future.  I have to struggle sometimes when I get too far ahead of myself.”

“Can you do time and probability together?”

“Hard to say.  When I hop I mostly just try to work out when I am, much less whether things are odd.”

“Give it a shot.  Try a couple of ‘nearby places’ and come back here/now.  Just use tiny ‘pushes.’ I don’t want you to get lost again.”

“Me neither.  OK, here I go.” <prolonged flickering and fizzing> “Is this the right place?  I tried a couple of hops here in your office, and <charming blush> stole some of your papers.  Here.”

“Perfect, Anne, objective evidence is always best.  Let’s see…  Yep, this report is one I finished a week ago, looks OK, and this one … I recognize the name of a client I’ve not yet hooked, but the spelling!  The letter ‘c’ isn’t there at all — ‘rekognize,’ ‘sirkle,’ ‘siense’ — that’s low probability for sure.”

“Actually, it felt like higher probability.”

“Whatever.  One more question.  I gather that most of your hops are more-or-less good ones but every once in a while you drop into a complete surprise, something you’re totally not used to.”

“Uh-huh.”

“I’ll bet the surprises happen when you’re in a jam and do a get me out of here jump.”

“Huh!  I’d not made that connection, but you’re right.”

“I think I’ve got the picture.  When you ‘push,’ you somehow displace yourself on a surface that has two dimensions — time and probability.  You move around in those two dimensions independently from how you move in 3-D space.  I take it you’re comfortable dong that but you want more control over it, right?”

“Mmm, yeah.  It’s kind of my special superpower, you know?  I don’t want to give it up entirely.”

“Good, because I wouldn’t know how to make that happen for you.  Best I can do is give you some strategy coaching, OK?”

“That’d be a big help.”

“Stay calm.”

“That’s it?  Where’s the physics in that?”

“Ever hear of the Drunkard’s Walk?”

“I’ve seen a few.”

“Well, you’re doing one.”

“Beg pardon?”

“It’s math talk for a stepwise process where every step goes in a random direction.  Your problem is that some of the steps are way too big.  Keep the steps small and you’ll stay in familiar territory.”

<molten silver, coming closer> “Like … here?”

“Stay calm.”

~~ Rich Olcott

# Through The Looking Glass, Darkly

The Acme Building is quiet on summer evenings.  I was in my office, using the silence to catch up on paperwork.  Suddenly I heard a fizzing sound.  Naturally I looked around.  She was leaning against the door frame.

White satin looked good on her, and she looked good in it.  A voice like molten silver — “Hello, Mr Moire.”

“Hello yourself.  What can I do for you?”

“I’m open to suggestions, but first you can help me find myself.”

“Excuse me, but you’re right here.  And besides, who are you?”

“Not where I am but when I am.  Anne.”

“You said it right the first time.”

“No, no, my name is Anne.  At the moment.  I think.  Oh, it’s so confusing when your memory works in circles but not very well.  Do you have the time?”

“Well, I was busy, but you’re here and much more interesting.”

“No, I mean, what time is it?”

I showed her my desk clock — date, time, even the phase of the moon.

“Wait — circles?  Time’s one-dimensional.  Clock readings increase or decrease, they don’t go sideways.”

“You don’t know Time as well as I do, Mr Moire.  It’s a lot more complicated than that.  Time can be triangular, haven’t you noticed?”

“Can’t say as I have.”

“That paperwork you’re working on, are you near a deadline?”

“Nah.”

“And given that expanse of time, you feel free to permit distractions.  There are so many distractions.”

“You’re very distracting.”

“Thank you, I guess.  But suppose you had an important deadline coming up tomorrow.   That broad flow of possibilities at the beginning of the project has narrowed to just two — finish or don’t finish.  Your Time has closed in until you.”

“So you’re saying we can think of Time as two-dimensional.  The second dimension being…?”

“I don’t know.  I just go there.  That’s the problem.”

“Hmm… When you do, do you feel like you’re turning left or right?”

“No turning or moving forward or backward.  Generally I have to … umm… ‘push’ like I’m going uphill, but that only works if there’s a ‘being pushed’ when I get past that.  Otherwise I’m back where I started, whatever that means.”

“What do you see?  What changes during the episode?”

“Little things. <brief fizzing sound.  She … flickered.>  Like ‘over there’ you’re wearing a bright green T-shirt instead of what you’re wearing here.  And you’re using pen-and-paper instead of that laptop.  Green doesn’t suit you.”

“I know, which is why there’s nothing green in my wardrobe, here.  But that gives me an idea.  Did you always have to ‘push’ to get ‘over there’?”

“Usually.”

“Fine.  OK, I’m going to flip this coin.  While it’s in the air, ‘push’ just lightly and come back to tell me which way the coin fell.”

“It’s tails here.  OK, we’re going to do that again but this time ‘push’ much harder.”

<louder fizzing> “That was weird.  Your coin rolled off the desk and landed on edge in a crack in the floor so it’s not heads or tails.”

“AaaHAH!”

“?”

“Your ‘over theres’ have different levels of probability than ‘over here.’  They’re different realities.  Actually, I’ll bet you travel across ranges of probability.  Or tunnel through them, maybe.  That’d why you have to ‘push’ to get past something that’s less probable in order to get to something that’s more probable.  Like getting past a reality where the coin can just hang in the air or fly apart.”

“I’ve done that.  Once I sneezed while ‘pushing’ and wound up sitting at a tea party where the cream and sugar just refused to stir into the tea.  When I ‘pushed’ from there I practically fell into a coffee shop where the coffee was well-behaved.”

“Case closed.  Now I can answer your question.  Spacewise, you’re in my office on the twelfth floor.  Timewise, I just showed you my clock.  As for which reality, you’re in one with a very high probability because, well, you’re here.”

“So provincial.  Oh, Mr Moire, how little you know.” <fizzing>

On the 12th floor of the Acme Building, high above the city, one man still tries to answer the Universe’s persistent questions — Sy Moire, Physics Eye.

~~ Rich Olcott

# Scone but not forgotten

Al grabbed me as I stepped into his coffee shop.  “Sy, you gotta help me!”

“What’s the trouble, Al?”

“It’s Vinnie.  He’s over there, been scribbling on paper napkins all morning.  I’m running out of napkins, Sy!”

I grabbed a cinnamon scone from the rack and a chair at Vinnie’s table.  “What’s keeping you so busy, Vinnie?”  As if I didn’t know.

LIGO, of course.  Every time I think I understand how the machine works something else occurs to me and it slips outa my hands.”

“How about you explain it to me.  Sometimes the best way to find an answer is to describe the problem to someone else.”

(grabbing a napkin near the bottom of one stack) “All right, Sy, I sketched the layout here.  You got these two big L-shaped machines out in the middle of two nowheres 2500 miles apart.  Each L is a pair of steel pipes 2½ miles long.  At the far end of each arm there’s a high-tech stabilized mirror.  Where the two arms meet there’s a laser rigged up to shoot beams down both arms.  There’s also a detector located where the reflected beams join up and cancel each other out unless there’s a gravity wave going past.  Am I good so far?”

“Yeah, that’s pretty much the diagram you see in the books, except it’s gravitational waveGravity waves are something else.”

“Whatever.  So, here’s a sketch of where I was at when I asked you that first question.  See, I copied my original sketch onto another napkin and stretched it a little where the black circle is to show what a gravitational wave would do in stretch phase.  Ignore the little rips.”

“What rips?”

“Uh, thanks.  Anyway, I was thinking the gravitational wave that stretches the x-beam would also stretch the x-pipe so they couldn’t use the light wave to measure the pipe it’s in.  But LIGO works so that’s wrong thinkin’.

“OK, next is for after we talked about inertial frames.  Took me a few tries to get it like I want it and I wound up having to do two sketches, one for each frame.”  He grabbed a couple more napkins from different stacks.

“I didn’t do the yellow wiggles ’cause that got confusing and besides I don’t do wiggly lines so good.  Point is, the space-stretch only shows up in the laboratory inertial frame.  The light waves move with space so they don’t notice the difference, right?”

“Well, I wouldn’t want to put it that way in court, Vinnie, but it’s a pretty good description.”

“So the light waves bop along at 186,000 miles per second in their frame, but from the machine’s perspective those are stretched miles so the guy running the machine thinks those photons are faster than the ones in the other pipe.  And that difference in speed gets the yellow lines out of phase with the blue ones and the detector rings a bell or something, right?”

“It’s even better than that.” I reached for another napkin, caught Al’s eye on me and grabbed an envelope from my coat pocket instead. “Remember how a gravitational wave works in two directions perpendicular to the wave’s line of travel?”

“Yeah, so?”

“So at the same moment that the wave is stretching space in the x-direction, it’s squeezing space in the y-direction.  LIGO’s detection scheme monitors the difference between the two returning beams.  As I’ve drawn it here using the detector’s inertial frame, the x-beam is going fast AND the y-beam is going slow so the detector sees twice the phase difference. A few milliseconds later they’ll switch because the x-direction will get squeezed while the y-direction gets stretched.  And yeah, a bell does ring but only after some computers munch on the data and subtract out environmental stuff like temperature swings and earthquakes and the janitor’s footsteps.”

“Uh-huh, I think I got it.” Turning in his chair, “Hey, Al, bring Sy here another scone, on me.  And put the one he’s got on my tab, too.”

“Thanks, Vinnie.”

“Don’t mention it.”

~~ Rich Olcott

# A Matter of Perspective

As I stepped off the escalator by the luggage carousel a hand came down heavy on my shoulder.

“Keep movin’, I gotchur bag.”

That’s Vinnie, always the surprises.  I didn’t bother to ask how he knew which flight I came in on.  What came next was also no surprise.

“You owe me for the pizza.  Now about that kinetic energy –”

“Hold that thought ’til we get to my office where I can draw diagrams.”

We got my car out of the lot, drove to the Acme Building and took the elevator to 12.

As my computer booted up I asked, “When we talked about potential energy, did we ever mention inertial frames?”

“Come to think of it, no, we didn’t.  How come?”

“Because they’ve got nothing to do with potential energy.  Gravitational and electrical potentials are all about intensity at one location in space relative to other locations in space.  The potentials are static so long as the configuration is static.  If something in the region changes, like maybe a mass moves or the charge on one object increases, then the potential field adjusts to suit.”

“Right, kinetic energy’s got to do with things that move, like its name says.  I get that.  But how does it play into LIGO?”

“Let’s stick with our spacecraft example for a bit.  I’ve been out of town for a while, so a quick review’s in order.  Objects that travel in straight lines and constant speed with respect to each other share the same inertial frame.  Masses wrinkle the shape of space.  The paths light rays take are always the shortest possible paths, so we say a light ray shows us what a straight line is.

“In our story, we’re flying a pair of space shuttles using identical speed settings along different light-ray navigation beams.  Suddenly you encounter a region of space that’s compressed, maybe by a nearby mass or maybe by a passing gravitational wave.

“That compressed space separates our inertial frames.  In your inertial frame there’s no effect — you’re still following your nav beam and the miles per second you measure hasn’t changed.  However, from my inertial frame you’ve slowed down because the space you’re traveling through is compressed relative to mine.  Does all that ring a bell?”

“Pretty much the way I remember it. Now what?”

“Do you remember the formula for kinetic energy?”

“Give me a sec… mass times the square of the velocity.”

“Uh-huh.  Mind you, ‘velocity’ is the combination of speed and direction but velocity-squared is just a number.  So, your kinetic energy depends in a nice, simple way on speed.  What happened to your kinetic energy when you encountered that gravity well?”

“Ah, now I see where you’re going.  In my frame my speed doesn’t change so I don’t gain or lose kinetic energy.  In your frame you see me slow down so you figure me as losing kinetic energy.”

“But the Conservation of Energy rule holds across the Universe.  Where’d your kinetic energy go?”

“Does your frame see me gaining potential energy somehow that I don’t see in mine?”

“Nice try, but that’s not it.  We’ve already seen that potential energy doesn’t depend on frames.  What made our frames diverge in the first place?”

“That gravity field curving the space I’d flown into.  Hey, action-reaction!  If the curved space slowed me down, did I speed it up?”

“Now we’re getting there.  No, you didn’t speed up space, ’cause space doesn’t work that way — the miles don’t go anywhere.  But your kinetic energy (that I can see and you can’t) did act to change the spatial curvature (that I can see and you can’t).  I suspect the curvature flattened out, but the math to check that is beyond me.”

“Lemme think…  Right, so back to my original question — what I wasn’t getting was how I could lose both kinetic energy AND potential energy flying into that compressed space.  Lessee if I got this right.  We both see I lost potential energy ’cause I’ve got less than back in flat space.  But only you see that my kinetic energy changed the curvature that only you see.  Good?”

“Good.”

(sound of footsteps)

(sound of door)

“Don’t mention it.”

~~ Rich Olcott

# 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?”

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.”

“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

# A Defective Story

It was an interesting knock at my office door — aggressive but feminine, with a hint of desperation.

“C’mon in, the door’s open.”

She wore a business suit that must have cost a month’s rent.  It fit her like it had been sewn on, and she had all the right sizes.  There was a button missing from the left sleeve.  On the other hand her left lapel bore a Star Trek badge, Security Section.

“What can I do for you, Miss…?”

“My name’s Victoria Baird, Mr Moire.  I’m CEO of ADastra, ‘media relations for the stars.’  I’ve been reading your posts, put two and two together, and thought I’d better drop in.”

“Well, it’s nice to know I’ve got readers.  Which posts caught your attention?”

“Several of them, but mostly this one,” pointing to a Web page on her smartphone.  It was my Breathing Space video.  “You show how gravitational waves fluctuate as they polarize local space.  They induce varying curvatures in different directions.  Curved space is mass, Mr Moire, but this curvature moves at lightspeed.  Hadn’t you noticed that?”

“It crossed my mind, yes, but when I thought about surfing a gravitational wave like ocean surfers do, I realized you’d have to get up to the wave’s speed to ride it.”

“There’s more.  Are you familiar with that one-man starcraft that Ambassador Spock used in the 2009 Star Trek film?  The ship with the rotating after-section?”

“I did see ‘Baby Star Trek,’ yes.”

“Did you know that the starcraft’s official design designation is Jellyfish?”

“Well, it is.  And you’ve written about Earth jellyfish, haven’t you, Mr Moire, and how their propulsion system is so efficient?”

I was getting a little tired of her aggressive questions, so I challenged her with one of my own.  “And you see a connection?”

“I do, and that’s why you have to help me, Mr Moire.  Can I trust you?”

“Secrets are my business, Miss Baird.  Uncovering them or covering them up, it’s all the same to me.”

“Maybe I need to let my hair down.”  She removed her cloche cap and her pointed ears sprang free.  “I need you to get me back to my crew.”

“Can’t you just call them on that communicator badge?”

“This is costume jewelry.  The spectrum here on Earth is so crowded that my real badge is useless at long range.  I’ve been looking for subtle signals in the media.  I thought your posts were just such a signal … but I can see you’re a local.”

“Guilty as charged.  I take it the connection you saw resembled the signal you sought?”

“Yes.  You’ve published two of the essential principles of the LaForge Drive.  The first was your displays of spatial curvature in motion.  The second was your description of how jellyfish move by stepping along a ladder of seawater vortices.

“That’s what the LaForge Drive does, Mr Moire.  The counter-rotating blades are an osmium-hassium alloy, the densest substance known, and under tremendous compression.  Together their mass creates a complex pilot wave in the gravity field.  The spacecraft surfs on that waveform the way a jellyfish surfs on the eddies it creates.

“The wave’s phase velocity exceeds lightspeed by some enormous factor we’ve never been able to measure.  In fact, I’m here on Earth because I was on a research cruise to find if there’s a limit.  We … ran into a problem and I’m part of an away team sent to procure … something we need.”

“That trope’s been done to death, Miss Baird.  And besides, that design wouldn’t be practical.  What’s your real story?”

“What do you mean it’s not practical?”

“You can’t steer.  Pilot waves follow the most intense local spatial curvature, which means the craft will always home like a torpedo on the nearest large mass.”

Suddenly that badge chirped.  “We’ve recovered the detonator, Lieutenant.  Have you kept him from looking out the window?”

“Yes, his eyes have been on me the whole time.  Ready for beam-up.  Goodbye, Mr Moire, that was fun.”

Her form began to shimmer, twinkle … and disappeared.

“Don’t mention it.”

~~ 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?”

“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?”

“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.”

“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