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