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

Think globally, act locally. Electrons do.

“Watcha, Johnnie, you sure ‘at particle’s inna box?”
“O’course ’tis, Jennie!  Why wouldn’t it be?”
“Me Mam sez particles can tunnel outta boxes ’cause they’re waves.”

“Can’t be both, Jessie.”


Double slit experiment
The double-slit experiment.
An electron beam travels from the source at left to a display screen. In between there’s a barrier with two narrow slits.

Maybe it can.

Nobel-winning (1965) physicist Richard Feynman said the double-slit experiment (diagrammed here) embodies the “central mystery” of Quantum Mechanics.

When the bottom slit is covered the display screen shows just what you’d expect — a bright area  opposite the top slit.

When both slits are open, the screen shows a banded pattern you see with waves.  Where a peak in a top-slit wave meets a peak in the bottom-slit wave, the screen shines brightly.  Where a peak meets a trough the two waves cancel and the screen is dark.  Overall there’s a series of stripes.  So electrons are waves, right?

But wait.  If we throttle the beam current way down, the display shows individual speckles where each electron hits.  So the electrons are particles, right?

Now for the spooky part.  If both slits are open to a throttled beam those singleton speckles don’t cluster behind the slits as you’d expect particles to do.  A speckle may appear anywhere on the screen, even in an apparently blocked-off region.  What’s more, when you send out many electrons one-by-one their individual hits cluster exactly where the bright stripes were when the beam was running full-on.

It’s as though each electron becomes a wave that goes through both slits, interferes with itself, and then goes back to being a particle!

By the way, this experiment isn’t a freak observation.  It’s been repeated with the same results many times, not just with electrons but also with light (photons), atoms, and even massive molecules like buckyballs (fullerene spheres that contain 60 carbon atoms).  In each case, the results indicate that the whatevers have a dual character — as a localized particle AND as a wave that reacts to the global environment.

Physicists have been arguing the “Which is it?” question ever since Louis-Victor-Pierre-Raymond, the 7th Duc de Broglie, raised it in his 1924 PhD Thesis (for which he received a Nobel Prize in 1929 — not bad for a beginner).  He showed that any moving “particle” comes along with a “wave” whose peak-to-peak wavelength is inversely proportional to the particle’s mass times its velocity.  The longer the wavelength, the less well you know where the thing is.

I just had to put numbers to de Broglie’s equation.  With Newton in mind, I measured one of the apples in my kitchen.  To scale everything, I assumed each object moved by one of its diameters per second.  (OK, I cheated for the electron — modern physics says it’s just a point, so I used a not-really-valid classical calculation to get something to work with.)

“Particle” Mass, kilograms Diameter, meters Wavelength, meters Wavelength, diameters
Apple 0.2 0.07 7.1×10-33 1.0×10-31
Buckyball 1.2×10-24 1.0×10-9 0.083 8.3×10+7
Hydrogen atom 1.7×10-27 1.0×10-10 600 6.0×10+12
Electron 9.1×10-31 3.0×10-17 3.7×10+12 1.2×10+29

That apple has a wave far smaller than any of its hydrogen atoms so I’ll have no trouble grabbing it for a bite.  Anything tinier than a small virus is spread way out unless it’s moving pretty fast, as in a beam apparatus.  For instance, an electron going at 1% of light-speed has a wavelength only a nanometer wide.

Different physicists have taken different positions on the “particle or wave?” question.  Duc de Broglie claimed that both exist — particles are real and they travel where their waves tell them to.  Bohr and Heisenberg went the opposite route, saying that the wave’s not real, it’s only a mathematical device for calculating relative probabilities for measuring this or that value.  Furthermore, the particle doesn’t exist as such until a measurement determines its location or momentum.  Einstein and Schrödinger liked particles.  Feynman and Dirac just threw up their hands and calculated.

Which brings us to the other kind of quantum spookiness — “entanglement.”  In fact, Einstein actually used the word spukhafte (German for “spooky”) in a discussion of the notion.  He really didn’t like it and for good reason — entanglement rudely collides with his own Theory of Relativity.  But that’s another story.

~~ Rich Olcott