Better A Saber Than A Club?

There’s a glass-handled paper-knife on my desk, a reminder of a physics experiment gone very bad back in the day. “Y’know, Vinnie, this knife gives me an idea for another Star Trek weapons technology.”

“What’s that, Sy?”

“Some kinds of wave have another property in addition to frequency, amplitude and phase. What do you know about seismology?”

“Not a whole lot. Uhh … earthquakes … Richter scale … oh, and the Insight lander on Mars has seen a couple dozen marsquakes in the first six months it was looking for them.”

“Cool. Well, where I was going is that earthquakes have three kinds of waves. One’s like a sound wave — it’s called a Pwave or pressure wave and it’s a push-pull motion along the direction the wave is traveling. The second is called an Swave or shear wave. It generates motion in some direction perpendicular to the wave’s path.”

“Not only up-and-down?”

“No, could be any perpendicular direction. Deep in the Earth, rock can slide any which-way. One big difference between the two kinds is that a Pwave travels through both solid and molten rock, but an Swave can’t. Try to apply shearing stress to a fluid and you just stir it around your paddle. The side-to-side shaking isn’t transmitted any further along the wave’s original path. The geophysicists use that difference among other things to map out what’s deep below ground.”

“Parallel and perpendicular should cover all the possibilities. What’s the third kind?”

“It’s about what happens when either kind of deep wave hits the surface. A Pwave will use up most of its energy bouncing things up and down. So will an Swave that’s mostly oriented up-and-down. However, an Swave that’s oriented more-or-less parallel to the surface will shake things side-to-side. That kind’s called a surface wave. It does the most damage and also spreads out more broadly than a P- or Swave that meets the surface with the same energy.”

“This is all very interesting but what does it have to do with Starfleet’s weapons technology? You can’t tell a Romulan captain what direction to come at you from.”

“Of course not, but you can control the polarization angle in your weapon beams.”

“Polarization angle?”

Plane-polarized electromagnetic wave
Electric (E) field is red
Magnetic (B) field is blue
(Image by Loo Kang Wee and
Fu-Kwun Hwang from Wikimedia Commons)

“Yeah. I guess we sort of slid past that point. Any given Swave vibrates in only one direction, but always perpendicular to the wave path. Does that sound familiar?”

“Huh! Yeah, it sounds like polarized light. You still got that light wave movie on Old Reliable?”

“Sure, right here. The red arrow represents the electric part of a light wave. Seismic waves don’t have a magnetic component so the blue arrow’s not a thing for them. The beam is traveling along the y‑axis, and the electric field tries to move electrons up and down in the yz plane. A physicist would say the light beam is planepolarized. Swaves are polarized the same way. See the Enterprise connection?”

“Not yet.”

“Think about the Star Trek force-projection weapons — regular torpedoes, photon torpedoes, ship-mounted phasers, tractor beams, Romulan pulse cannons and the like. They all act like a Pwave, delivering push-pull force along the line of fire. Even if Starfleet’s people develop a shield-shaker that varies a tractor beam’s phase, that’s still just a high-tech version of a club or cannon ball. Beamed Swaves with polarization should be interesting to a Starfleet weapons designer.”

“You may have something. The Bridge crew talks about breaking through someone’s shield. Like you’re using a mace or bludgeon. A polarized wave would be more like an edged knife or saber. Why not rip the shield instead? Those shields are never perfect spheres around a ship. If your beam’s polarization angle happens to match a seam where two shield segments come together — BLOOEY!”

“That’s the idea. And you could jiggle that polarization angle like a jimmy — another way to confuse the opposition’s defense system.”

“I’m picturing a Klingon ship’s butt showing through a rip in its invisibility cloak. Haw!”

~~ Rich Olcott

How To Phase A Foe

“It’s Starfleet’s beams against Klingon shields, Vinnie. I’m saying both are based on wave phenomena.”

“What kind of wave, Sy?”

“Who knows? They’re in the 24th Century, remember. Probably not waves in the weak or strong nuclear force fields — those’d generate nuclear explosions. Could be electromagnetic waves or gravitational waves, could be some fifth or sixth force we haven’t even discovered yet. Whatever, the Enterprise‘s Bridge crew keeps saying ‘frequency’ so it’s got to have some sort of waveishness.”

“OK, you’re sayin’ whatever’s waving, if it’s got frequency, amplitude and phase then we can talk principles for building a weapon system around it. I can see how Geordi’s upping the amplitude of the Enterprise‘s beam weapons would help Worf’s battle job — hit ’em harder, no problem. Jiggling the frequencies … I sort of see that, it’s what they always talk about doing anyway. But you say messing with beam phase can be the kicker. What difference would it make if a peak hits a few milliseconds earlier or later?”

“There’s more than one wave in play. <keys clicking> Here’s a display of the simplest two-beam interaction.”

“I like pictures, but this one’s complicated. Read it out to me.”

“Sure. The bottom line is our base case, a pure sine wave of some sort. We’re looking at how it’s spread out in space. The middle line is the second wave, traveling parallel to the first one. The top line shows the sum of the bottom two at each point in space. That nets out what something at that point would feel from the combined influence of the two waves. See how the bottom two have the same frequency and amplitude?”

“Sure. They’re going in the same direction, right?”

“Either that or exactly the opposite direction, but it doesn’t matter. Time and velocity aren’t in play here, this is just a series of snapshots. When I built this video I said, ‘What will things look like if the second beam is 30° out of phase with the first one? How about 60°?‘ and so on. The wheel shape just labels how out-of-phase they are, OK?”

“Give me a sec. … OK, so when they’re exactly in sync the angle’s zero and … yup, the top line has twice the amplitude of the bottom one. But what happened to the top wave at 180°? Like it’s not there?”

“It’s there, it’s just zero in the region we’re looking at. The two out-of-phase waves cancel each other in that interval. That’s how your noise-cancelling earphones work — an incoming sound wave hits the earphone’s mic and the electronics generate a new sound wave that’s exactly out-of-phase at your ear and all you hear is quiet.”

“I’ve wondered about that. The incoming sound has energy, right, and my phones are using up energy. I know that because my battery runs down. So how come my head doesn’t fry with all that? Where does the energy go?”

“A common question, but it confuses cause and effect. Yes, it looks like the flatline somehow swallows the energy coming from both sides but that’s not what happens. Instead, one side expends energy to counter the other side’s effect. Flatlines signal success, but you generally get it only in a limited region. Suppose these are sound waves, for example, and think about the molecules. When an outside sound source pushes distant molecules toward your ear, that produces a pressure peak coming at you at the speed of sound, right?”

“Yeah, then…”

“Then just as the pressure peak arrives to push local molecules into your ear, your earphone’s speaker acts to pull those same molecules away from it. No net motion at your ear, so no energy expenditure there. The energy’s burned at either end of the transmission path, not at the middle. Don’t worry about your head being fried.”

“Well that’s a relief, but what does this have to do with the Enterprise?”

“Here’s a sketch where I imagined an unfriendly encounter between a Klingon cruiser and the Enterprise after Geordi upgraded it with some phase-sensitive stuff. Two perpendicular force disks peaked right where the Klingon shield troughed. The Klingon’s starboard shield generator just overloaded.”

“That’ll teach ’em.”

“Probably not.”

~~ Rich Olcott

Three Ploys to Face A Foe

Run done, Vinnie and I head upstairs to my office to get out of the windchill. My Starship Enterprise poster reminds me. “Geez, it’s annoying.”

“Now what, Sy?”

“I’ve been binge-watching old Star Trek:Next Generation TV programs and the technobabble’s gotten annoying.”

“What’s the problem this time?”

“Well, whenever the Enterprise gets into a fix where it’s their phaser beam or tractor beam or shields against some new Borg technology or something, Geordi or Worf get busy making adjustments and it’s always the frequency. ‘Modulate to a lower frequency!‘ or ‘Raise the frequency!‘ or even ‘Randomize the frequency!‘ At one point Dr Crusher was fiddling with someone’s ‘biophysical frequency.’ They miss two-thirds of the options, and especially they miss the best one when you’re trying to mess up your opponent’s stuff.”

“Wait, I thought we said frequency’s what waves are all about. There’s more?”

“Oh, yeah. The fact that they’re saying ‘frequency’ says their beams and shields and such are probably based on some kind of wave phenomenon. The good guys should be fiddling with amplitude and phase, too. Especially phase.”

“OK, I’ll bite. What’re those about?”

I poke a few keys on my computer and bring this up on the wall screen.

“OK, we’ve talked about frequency, the distance or time between peaks. Frequency’s the difference between a tuba and a piccolo, between infra-red and X-rays. That top trace is an example of modulating the frequency, somehow varying the carrier wave’s peak-to-peak interval. See the difference between the modulated wave and the dotted lines where it would be if the modulation were turned off?”

“Modulation means changing?”

“Mm-hm. The important thing is that only the piece within the box gets altered.”

“Got it. OK, you’ve labelled the middle line ‘Amplitude‘ and that’s gotta be about peak height because they’re taller inside the modulation box than the dotted line. I’m guessing here, but does the bigger peak mean more energy?”

“Good guess, but it depends on the kind of wave. Sound waves, yup, that’s exactly what’s going on. Light waves are different, because a photon’s energy is is determined by its frequency. You can’t pump up a photon’s amplitude, but you can pump up the number of photons in the beam.”

“Hey, Sy, I just realized. Your amplitude modulation and frequency modulation must be the AM and FM on my car radio. So in AM radio they sit on the station’s frequency, right, and make a signal by tweaking the amount of power going to the antenna?”

“That’s the basic idea, though engineers chasing efficiency have improved things a lot in the century since they started experimenting with radio. Implementing FM is more complicated so took a few more decades to make that competitive with AM.”

“So what’s the story with, um, ‘phase modulation‘? My radio’s got no PM dial.”

<poking more keys> “Here’s the way I think of a sine wave — it’s what you’d see looking at a mark on the edge of a rolling wheel. The size of the wheel sets the wave’s amplitude, the wheel’s rotation speed sets the wave’s frequency, and the phase is where it is in the rotation cycle. Modulating the phase would be like jerking the wheel back and forth while it’s rotating.”

“So that’s why there’s hiccups in your bottom red Phase line — things don’t match up across a phase shift.. Hmm… I’m still thinking about my radio. AM sound tends to have more static, especially during thunderstorms. That’d be because my radio amplifies any electromagnetic wave amplitudes at the frequency I’d set it for and that includes waves from the lightning. FM sound’s a lot clearer. Is that because frequency shifts don’t happen much?”

“Exactly.”

“PM broadcasts ought to be even safer against noise. How come I never see them?”

“You do. WiFi uses it, precisely because it works well even at extremely low power levels. OK, challenge question — why do you think I think PM would be better than FM against Borg tech?”

“It’d be like in fencing or martial arts. Frequency’s jab, jab, jab, regular-like. Shifting your wave phase would be mixing it up, they wouldn’t know when the next peak’s coming.”

“Yup. Now tell Geordi.”

~~ Rich Olcott

Disentangling 3-D Plaid

Our lake-side jog has slowed to a walk and suddenly Mr Feder swerves off the path to thud onto a park bench. “I’m beat.”

Meanwhile, heavy footsteps from behind on the gravel path and a familiar voice. “Hey, Sy, you guys talking physics?”

“Well, we were, Vinnie. Waves, to be exact, but Feder’s faded and anyway his walk wasn’t fast enough to warm me up.”

“I’ll pace you. What’d I miss?”

“Not a whole lot. So many different kinds of waves but physicists have abstracted them down to a common theme — a pattern that moves through space.”

“Haw — flying plaid.”

“That image would work if each fiber color carried specific values of energy and momentum and the cross-fibers somehow add together and there’s lots of waves coming from all different directions so it’s 3-D.”

“Sounds complicated.”

“As complicated as the sound from a symphony.”

“I prefer dixieland.”

“Same principle. Trumpet, trombone, clarinet, banjo — many layers of harmony but you can choose to tune in on just one line. That’s a clue to how physicists un-complicate waves.”

“How so?”

“Back in the early 19th century, Fourier showed that you can think about any continuous variation stream, no matter how complicated, in terms of a sum of very simple variations called sine waves. You’ve seen pictures of a sine wave — just a series of Ss laid on their sides and linked together head-to-tail.”

“Your basic wiggly line.”

“Mm-hm, except these wiggles are perfectly regular — evenly spaced peaks, all with the same height. The regularity is why sine waves are so popular. Show a physicist something that looks even vaguely periodic and they’ll immediately start thinking sine wave frequencies. Pythagoras did that for sound waves 2500 years ago.”

“Nah, he couldn’t have — he died long before Fourier.”

“Good point. Pythagoras didn’t know about sine waves, but he did figure out how sounds relate to spatial frequencies. Pluck a longer bowstring, get a lower note. Pinch the middle of a vibrating string. The strongest remaining vibration in the string sounds like the note from a string that’s half as long. Pythagoras worked out length relationships for the whole musical scale.”

“You said ‘spacial frequency’ like there’s some other kind.”

“There is, though they’re closely related. Your ear doesn’t sense the space frequency, the distance between peaks. You sense the time between peaks, the time frequency, which is the space frequency, peaks per meter, times how fast the wave travels, meters per second. See how the units work out?”

“Cute. Does that space frequency/time frequency pair-up work for all kinds of waves?”

“Mostly. It doesn’t work for standing waves. Their energy’s trapped between reflectors or some other way and they just march in place. Their time frequency is zero peaks per second whatever their peaks per meter space frequency may be. Interesting effects can happen if the wave velocity changes, say if the wave path crosses from air to water or if there’s drastic temperature changes along the path.”

“Hah! Mirages! Wait, that’s light getting deflected after bouncing off a hot surface into cool air. Does sound do mirages, too?”

“Sure. Our hearing’s not sharp enough to notice sonic deflection by thermal layering in air, but it’s a well-known issue for sonar specialists. Echoes from oceanic cold/warm interfaces play hob with sonar echolocation. I’ll bet dolphins play games with it when the cold layer’s close enough to the surface.”

“Those guys will find fun in anything. <pause> So Pythagoras figured sound frequencies playing with a bow. Who did it for light?”

“Who else? Newton, though he didn’t realize it. In his day people thought that light was colorless, that color was a property of objects. Newton used the rainbow images from prisms to show that color belonged to light. But he was a particle guy. He maintained that every color was a different kind of particle. His ideas held sway for over 150 years until Fresnel convinced the science community that lightwaves are a thing and their frequencies determine their color. Among other things Fresnel came up with the math that explained some phenomena that Newton had just handwaved past.”

“Fresnel was more colorful than Newton?”

“Uh-uh. Compared to Newton, Fresnel was pastel.”

~~ Rich Olcott

Wave As You Go By

A winter day, a bit nippy and windy enough to raise scattered whitecaps on the park lake. Apparently neither the geese nor Mr Richard Feder (of Fort Lee, NJ) enjoy that — the geese are standing on the shore and he’s huddled down on a bench as I pass. “Hey Moire, I gotta question.”

“Mr Feder. I’m trying to keep warm. If you want answers you’ll have to jog along.”

“Oh, alright <oof>. OK, watching those waves got me thinking. They keep going because the wind pushes on ’em, right? So what pushes on sound waves and light waves? If something pushes hard enough on a sound wave does it speed up enough to be a light wave?”

“So many questions. Are you sure you’ve got enough wind?”

“Ha, ha. I’ve been working out a little.”

“We’ll see. Well, first, nothing needs to push on a wave once it’s started. They travel on their own momentum.”

“Then why do these waves die away when the wind stops?”

“You’ve got two things going on there, on different time scales. When the wind stops blowing it stops making new waves. Actually, winds rarely stop all at once, they taper off. It looks like waves are dying away but really you just see smaller and smaller waves. Inside a single wave, though, friction takes its toll.”

“Friction? Waves rub against each other? That’s not what’s going on here — they keep their distance unless different groups run crosswise and then they all just keep going.”

Turbulence in a water wave

“Not friction between waves, friction within a wave. There’s a lot of turbulence inside a water wave — the wind piles up surface molecules on one side, gravity and surface tension move the other side’s molecules downward, and the ones inside are pulled in every direction. All that helter-skelter motion randomizes the wave’s momentum and converts the wave’s energy to heat. When that’s gone, the wave’s gone.”

“So how’s sound different from that?”

“Lots of ways. To begin with, wind and gravity move molecules up and down perpendicular to the wave’s direction of travel. Sound waves aren’t affected by gravity. They move molecules back and forth parallel to the wave’s direction.”

“But they still die out, right? Turn to heat and all that?”

“Absolutely, Mr Feder. How fast a wave dies out depends on what heat-conversion processes are in play. In a water wave gravity and surface tension work together to smooth things out. Neither’s active in sound waves. The only way a sound wave can lose energy is through random collisions between molecules that aren’t in sync with the wave. Could be the wave hits a mushy object or maybe it just gets buried in other waves.”

“Like at a football game, when everyone’s shouting but all you hear is the roar.”

“Pretty good example, Mr Feder.”

“So how’s a light wave different?”

“Light waves don’t even need molecules. The electromagnetic field near a particle is the net effect of all the attractions and repulsions it feels from all other charged particles everywhere in the Universe. When some charged particle somewhere moves, that changes the field. The change is transmitted throughout the field as a wave traveling at the speed of light.”

“What makes it die away?”

“It doesn’t. On a dark, clear night your eyes can see stars a quintillion miles away. Astronomers with their instruments can detect objects millions of times further away.”

“No smoothing out? How come?”

“That’s a very deep question, Mr Feder, one that really bothered Einstein. You’d think a photon’s wave would get fainter the further it spreads. In fact, it delivers all its energy to the first charged particle it can interact with, no matter how far it had traveled. Weird, huh?”

“Weird, all right. So we got these three very different things — they start different, they push different, they got different speeds, they die different, but we call them all waves. Why’s that?”

“They’re all waves because they’re all patterns that transmit energy and momentum across space. Physicists have found general rules that apply to the patterns, whatever the wave type. Equations that work for one kind work for many others, too.”

Gravity waves?”

“And gravitational waves.”

~~ Rich Olcott

Should These Three Be Alike?

“What’s all the hubbub in the back room, Al? I’m a little early for my afternoon coffee break and your shop’s usually pretty quiet about now.”

“It’s Cathleen’s Astronomy class, Sy. The department double-booked their seminar room so she asked to use my space until it’s straightened out.”

“Think I’ll eavesdrop.” I slide in just as she’s getting started.

“OK, folks, settle. Last class I challenged you with a question. Venus and Mars both have atmospheres that are dominated by carbon dioxide with a little bit of nitrogen. Earth is right in between them. How come its atmosphere is so different? I gave each of you a piece of that to research. Jeremy, you had the null question. Should we expect Earth’s atmosphere to be about the same as the other two?”

Venus coudtops image by Damia Bouic
JAXA / ISAS / DARTS / Damia Bouic

“I think so, ma’am, on the basis of the protosolar nebula hypothesis. The –“

“Wait a minute, Jeremy. Sy, I saw you sneak in. Jeremy, explain that term to him.”

“Yes’m. Uh, a nebula is a cloud of gas and dust out in space. It could be what got shot out of an exploding star or it could be just a twist in a stream of stuff drifting through the Galaxy. If the twist kinks up, gravity pulls the material on either side of the kink towards the middle and you get a rotating disk. Most of what’s in the disk falls towards its center. The accumulated mass at the center lights up to be a star. Meanwhile, what’s left in the disk keeps most of the original angular momentum but it doesn’t whirl smoothly. There’s going to be local vortices and they attract more stuff and grow up to be planets. That’s what we think happens, anyway.”

“Good summary. So what does that mean for Mars, Venus and the Earth?”

“Their orbits are pretty close together, relative to the disk’s radius, so they ought to have encountered about the same mixture of heavy particles and light ones while they were getting up to size. The light ones would be gas atoms, mostly hydrogen and helium. Half the other atoms are oxygen and they’d react to produce oxides — water, carbon monoxide, grains of silica and iron oxide. And oxygen and nitrogen molecules, of course.”

“Of course. Was gravity the only actor in play there?”

“No-o-o, once the star lit up its photons and solar wind would have pushed against gravity.”

“So three actors. Would photons and solar wind have the same effect? Anybody?”

Silence, until astrophysicist-in-training Newt Barnes speaks up. “No, they’d have different effects. The solar wind is heavy artillery — electrons, protons, alpha particles. They’ll transfer momentum to anything they hit, but they’re more likely to hit a large particle like a dust grain than a small one like an atom. On average, the big particles would be pushed away more.”

“And the photons?”

“A photon is selective — it can only transfer momentum to an atom or molecule that can absorb exactly the photon’s energy. But each kind of atom has its own set of emission and absorption energies. Most light emitted by transitions within hydrogen atoms won’t be absorbed by anything but another hydrogen atom. Same thing for helium. The Sun’s virtually all hydrogen and helium. The photons they emit would move just those disk atoms and leave the heavier stuff in place.”

“That’s only part of the photon story.”

“Oh? Oh, yeah. The Sun’s continuous spectrum. The Sun is hot. Heat jiggles whole ions. Those moving charges produce electromagnetic waves just like charge moving within an atom, but heat-generated waves can have any wavelength and interact with anything. They can bake dust particles and decompose compounds that contain volatile atoms. Then those atoms get swept away in the general rush.”

“Which has the greater effect, solar wind or photons?”

“Hard to say without doing the numbers, but I’d bet on the photons. The metal-and-silicate terrestrial planets are close to the Sun, but the mostly-hydrogen giants are further out.”

“All that said, Jeremy, what’s your conclusion?”

“It sure looks like Earth’s atmosphere should be intermediate between Mars and Venus. How come it’s not?”

~~ Rich Olcott

Fly High, Silver Bird

“TANSTAAFL!” Vinnie’s still unhappy with spacecraft that aren’t rocket-powered. “There Ain’t No Such Thing As A Free Lunch!”

“Ah, good, you’ve read Heinlein. So what’s your problem with Lightsail 2?”

“It can’t work, Sy. Mostly it can’t work. Sails operate fine where there’s air and wind, but there’s none of that in space, just solar wind which if I remember right is just barely not a vacuum.”

Astronomer-in-training Jim speaks up. “You’re right about that, Vinnie. The solar wind’s fast, on the order of a million miles per hour, but it’s only about 10-14 atmospheres. That thin, it’s probably not a significant power source for your sailcraft, Al.”

“I keep telling you folks, it’s not wind-powered, it’s light-powered. There’s oodles of sunlight photons out there!”

“Sure, Al, but photons got zero mass. No mass, no momentum, right?”

Plane-polarized electromagnetic wave in motion
Plane-polarized electromagnetic wave
Electric (E) field is red
Magnetic (B) field is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)

My cue to enter. “Not right, Vinnie. Experimental demonstrations going back more than a century show light exerting pressure. That implies non-zero momentum. On the theory side … you remember when we talked about light waves and the right-hand rule?”

“That was a long time ago, Sy. Remind me.”

“… Ah, I still have the diagram on Old Reliable. See here? The light wave is coming out of the screen and its electric field moves electrons vertically. Meanwhile, the magnetic field perpendicular to the electric field twists moving charges to scoot them along a helical path. So there’s your momentum, in the interaction between the two fields. The wave’s combined action delivers force to whatever it hits, giving it momentum in the wave’s direction of travel. No photons in this picture.”

Astrophysicist-in-training Newt Barnes dives in. “When you think photons and electrons, Vinnie, think Einstein. His Nobel prize was for his explanation of the photoelectric effect. Think about some really high-speed particle flying through space. I’m watching it from Earth and you’re watching it from a spaceship moving along with it so we’ve each got our own frame of reference.”

“Frames, awright! Sy and me, we’ve talked about them a lot. When you say ‘high-speed’ you’re talking near light-speed, right?”

“Of course, because that’s when relativity gets significant. If we each measure the particle’s speed, do we get the same answer?”

“Nope, because you on Earth would see me and the particle moving through compressed space and dilated time so the speed I’d measure would be more than the speed you’d measure.”

“Mm-hm. And using ENewton=mv² you’d assign it a larger energy than I would. We need a relativistic version of Newton’s formula. Einstein said that rest mass is what it is, independent of the observer’s frame, and we should calculate energy from EEinstein²=(pc)²+(mc²)², where p is the momentum. If the momentum is zero because the velocity is zero, we get the familiar EEinstein=mc² equation.”

“I see where you’re going, Newt. If you got no mass OR energy then you got nothing at all. But if something’s got zero mass but non-zero energy like a photon does, then it’s got to have momentum from p=EEinstein/c.”

“You got it, Vinnie. So either way you look at it, wave or particle, light carries momentum and can power Lightsail 2.”

Lightsail 2 flying over Earth, against a yellow background
Adapted from image by Josh Spradling / The Planetary Society

“Question is, can sunlight give it enough momentum to get anywhere?”

“Now you’re getting quantitative. Sy, start up Old Reliable again.”

“OK, Newt, now what?”

“How much power can Lightsail 2 harvest from the Sun? That’ll be the solar constant in joules per second per square meter, times the sail’s area, 32 square meters, times a 90% efficiency factor.”

“Got it — 39.2 kilojoules per second.”

“That’s the supply, now for the demand. Lightsail 2 masses 5 kilograms and starts at 720 kilometers up. Ask Old Reliable to use the standard circular orbit equations to see how long it would take to harvest enough energy to raise the craft to another orbit 200 kilometers higher.”

“Combining potential and kinetic energies, I get 3.85 megajoules between orbits. That’s only 98 seconds-worth. I’m ignoring atmospheric drag and such, but net-net, Lightsail 2‘s got joules to burn.”

“Case closed, Vinnie.”

~~ Rich Olcott

Fierce Roaring Beast

A darkish day calls for a fresh scone so I head for Al’s coffee shop. Cathleen’s there with some of her Astronomy students. Al’s at their table instead of his usual place behind the cash register. “So what’s going on with these FRBs?”

She plays it cool. “Which FRBs, Al? Fixed Rate Bonds? Failure Review Boards? Flexible Reed Baskets?”

Jim, next to her, joins in. “Feedback Reverb Buffers? Forged Razor Blades?
Fennel Root Beer?”

I give it a shot. “Freely Rolling Boulders? Flashing Rapiers and Broadswords? Fragile Reality Boundary?”

“C’mon, guys. Fast Radio Bursts. Somebody said they’re the hottest thing in Astronomy.”

Cathleen, ever the teacher, gives in. “Well, they’re right, Al. We’ve only known about them since 2007 and they’re among the most mystifying objects we’ve found out there. Apparently they’re scattered randomly in galaxies all over the sky. They release immense amounts of energy in incredibly short periods of time.”

“I’ll say.” Vinnie’s joins the conversation from the next table. “Sy and me, we been talking about using the speed of light to measure stuff. When I read that those radio blasts from somewhere last just a millisecond or so, I thought, ‘Whatever makes that blast happen, the signal to keep it going can’t travel above lightspeed. From one side to the other must be closer than light can travel in a millisecond. That’s only 186 miles. We got asteroids bigger than that!'”

“300 kilometers in metric.” Jim’s back in. “I’ve played with that idea, too. The 70 FRBs reported so far all lasted about a millisecond within a factor of 3 either way — maybe that’s telling us something. The fastest way to get lots of energy is a matter-antimatter annihilation that completely converts mass to energy by E=mc².  Antimatter’s awfully rare 13 billion years after the Big Bang, but suppose there’s still a half-kilogram pebble out there a couple galaxies away and it hits a hunk of normal matter. The annihilation destroys a full kilogram; the energy release is 1017 joules. If the event takes one millisecond that’s 1020 watts of power.”

“How’s that stand up against the power we receive in an FRB signal, Jim?”

“That’s the thing, Sy, we don’t have a good handle on distances. We know how much power our antennas picked up, but power reception drops as the square of the source distance and we don’t know how far away these things are. If your distance estimate is off by a factor of 10 your estimate of emitted power is wrong by a factor of 100.”

“Ballpark us.”

<sigh> “For a conservative estimate, say that next-nearest-neighbor galaxy is something like 1021 kilometers away. When the signal finally hits us those watts have been spread over a 1021-kilometer sphere. Its area is something like 1049 square meters so the signal’s power density would be around 10-29 watts per square meter. I know what you’re going to ask, Cathleen. Assuming the radio-telescope observations used a one-gigahertz bandwidth, the 0.3-to-30-Jansky signals they’ve recorded are about a million million times stronger than my pebble can account for. Further-away collisions would give even smaller signals.”

Looking around at her students, “Good self-checking, Jim, but for the sake of argument, guys, what other evidence do we have to rule out Jim’s hypothesis? Greg?”

“Mmm… spectra? A collision like Jim described ought to shine all across the spectrum, from radio on up through gamma rays. But we don’t seem to get any of that.”

“Terry, if the object’s very far away wouldn’t its shorter wavelengths be red-shifted by the Hubble Flow?”

“Sure, but the furthest-away one we’ve tagged so far is nearer than z=0.2. Wavelengths have been stretched by 20% or less. Blue light would shift down to green or yellow at most.”

“Fran?”

“We ought to get even bigger flashes from antimatter rocks and asteroids. But all the signals have about the same strength within a factor of 100.”

“I got an evidence.”

“Yes, Vinnie?”

“That collision wouldn’t’a had a chance to get started. First contact, blooie! the gases and radiation and stuff push the rest of the pieces apart and kill the yield. That’s one of the problems the A-bomb guys had to solve.”

Al’s been eaves-dropping, of course. “Hey, guys. Fresh Raisin Bread, on the house.”

~~ Rich Olcott

Friendly Resting Behemoths

Trombones And Echoes

Vinnie’s fiddling with his Pizza Eddie’s pizza crumbs. “Hey, Sy, so we got the time standard switched over from that faked 1900 Sun to counting lightwave peaks in a laser beam. I understand why that’s more precise ’cause it’s a counting measure, and it’s repeatable and portable ’cause they can set up a time laser on Mars or wherever that uses the same identical kinds of atoms to do the frequency stuff. All this talk I hear about spacetime, I’m thinkin’ space is linked to time, right? So are they doing smart stuff like that for measuring space?”

“They did in 1960, Vinnie. Before that the meter was defined to be the distance between two carefully positioned scratches on a platinum-iridium bar that was lovingly preserved in a Paris basement vault. In 1960 they went to a new standard. Here, I’ll bring it up on Old Reliable. By the way, it’s spelled m-e-t-e-r stateside, but it’s the same thing.”

“Mmm… Something goofy there. Look at the number. You’ve been going on about how a counted standard is more precise than one that depends on ratios. How can you count 0.73 of a cycle?”

“You can’t, of course, but suppose you look at 100 meters. Then you’d be looking at an even 165,076,373 of them, OK?”

“Sorta, but now you’re counting 165 million peaks. That’s a lot to ask even a grad student to do, if you can trust him.”

“He won’t have to. Twenty-three years later they went to this better definition.”

“Wait, that depends on how accurate we can measure the speed of light. We get more accurate, the number changes. Doesn’t that get us into the ‘different king, different foot-size’ hassle?”

“Quite the contrary. It locks down the size of the unit. Suppose we develop technology that’s good to another half-dozen digits of precision. Then we just tack half-a-dozen zeroes onto that fraction’s denominator after its decimal point. Einstein said that the speed of light is the same everywhere in the Universe. Defining the meter in terms of lightspeed gives us the same kind of good-everywhere metric for space that the atomic clocks give us for time.”

“I suppose, but that doesn’t really get us past that crazy-high count problem.”

“Actually, we’ve got three different strategies for different length scales. For long distances we just use time-of-flight. Pick someplace far away and bounce a laser pulse off of it. Use an atomic clock to measure the round-trip time. Take half that, divide by the defined speed of light and you’ve got the distance in meters. Accuracy is limited only by the clock’s resolution and the pulse’s duration. The Moon’s about a quarter-million miles away which would be about 2½ seconds round-trip. We’ve put reflectors up there that astronomers can track to within a few millimeters.”

“Fine, but when distances get smaller you don’t have as many clock-ticks to work with. Then what do you do?”

“You go to something that doesn’t depend on clock-ticks but is still connected to that constant speed of light. Here, this video on Old Reliable ought to give you a clue.”

“OK, the speed which is a constant is the number of peaks that’s the frequency times the distance between them that’s the wavelength. If I know a wavelength then arithmetic gets me the frequency and vice-versa. Fine, but how do I get either one of them?”

“How do you tune a trombone?”

“Huh? I suppose you just move the slide until you get the note you want.”

“Yup, if a musician has good ear training and good muscle memory they can set the trombone’s resonant tube length to play the right frequency. Table-top laser distance measurements use the same principle. A laser has a resonant cavity between two mirrors. Setting the mirror-to-mirror distance determines the laser’s output. When you match the cavity length to something you want to measure, the laser beam frequency tells you the distance. At smaller scales you use interference techniques to compare wavelengths.”

Vinnie gets a gleam in his eye. “Time-of-flight measurement, eh?” He flicks a pizza crumb across the room.

In a flash Eddie’s standing over our table. “Hey, hotshot, do that again and you’re outta here!”

“Speed of light, Sy?”

“Pretty close, Vinnie.”

~~ Rich Olcott

For the VLA, Timing Is Everything

Eddie’s pizza is especially tasty after a long walk down a stairwell. Vinnie and I are polishing off the last of our crumbs when he says, “OK, so we got these incredibly accurate clocks. Two questions. What do we use them for besides sending out those BBC pips, and what do they have to do with the new kilogram standard?”

“Pips? Oh, the top-of-the-hour radio station beeps we used to depend upon to set our watches. Kept us all up-to-the-minute, us and the trains and planes — but we don’t need 10-digit accuracy for that. What we do get from high-quality time signals is the ability to create distributed instruments.”

“Distributed instruments?”

“Ones with pieces in different places. You know about the Jansky Very Large Array, that huge multi-dish radio telescope in New Mexico?”

Karl G. Jansky Very Large Array, photo by Mihaiscanu
via Wikimedia Commons licensed under Creative Commons

“Been there. Nice folks in Pie Town up the road.”

“Did you look around?”

“Of course. What I didn’t understand is why they got 27 dishes and they’re all pointed the same direction. You’d think one would be enough for looking at something.”

“Ah, that’s the thing. All of them together make one telescope.”

<sets smartphone to calculator mode> “Lessee … dish is 25 meters across, πD2/4, 27 dishes, convert square meters to… Geez, 3¼ acres! A single dish that size would be a bear to keep steady in the wind down there. No wonder they split it up.”

“That was one concern, but the total area’s not as important as the distance between the pairs.”

“Why’s that even relevant?”

“Because radio telescopes don’t work the way that optical ones do. No lens or mirror, just a big dish that accepts whatever comes in along a narrow beam of radio waves.”

“How narrow?”

“About the size of the full Moon.”

“That can cover a lot of stars and galaxies.”

“It sure can, which is why early radio astronomy was pretty low-resolution. Astronomers needed a way to pick out the signals from individual objects within that field of view. Turns out two eyes are better than one.”

“3D vision?”

“Kinda related, but not really. Our two eyes give us 3D vision because each eye provides a slightly different picture of close-by objects, say, less than about 5 yards away. For everything further, one eye’s view is no different from the other’s. You’d get the same effect if distant things were painted on a flat background, which is how come a movie set backdrop still looks real.”

“You’re saying that the stars are so far away that each dish gets the same picture.”

“Yeah.”

“So why have more than one?”

“They don’t get the picture at the same time. With an atomic clock you can take account of when each signal arrives at each dish. Here’s a diagram I did up on Old Reliable. It’s way out of scale but it makes the point, I think. We’ve got two dishes at the bottom here, and those purple dots are two galaxies. Each dish sees them on top of each other and can’t distinguish which one sent that peaky signal. What’s important is, the dish on the right receives the signal later. See that red bar? That’s the additional path length the signal has to travel to reach the second dish.”

“Can’t be much later, light travels pretty fast.”

“About 30 centimeters per nanosecond, which adds up. When the VLA dishes are fully spread out, the longest dish-to-dish distance is about 36 kilometers which is about 120 microseconds as the photon flies. That’s over a million ticks on the cesium clock – no problem tracking the differences.”

“Same picture a little bit later. Doesn’t seem worth the trouble.”

“What makes it worth the trouble is what you can learn from the total space-time pattern after you combine the signals mathematically. Under good conditions the VLA can resolve signals from separate objects only 40 milliarcseconds apart, about 1/45000 the diameter of the Moon. That’s less than the width of a dime seen from 50 miles away.”

“The time pattern is how the dishes act like a single spread-around telescope, huh? Without the high-precision time data, they’re just duplicates?”

“Atomic clocks let us see the Universe.”

~~ Rich Olcott