No knock, the door just opened suddenly.
“Hello, Jeremy. Rule of Three?”
“Huh? No, I was down the hall just now when I saw you go into your office so I knew you hadn’t gotten busy with something yet. Sir. What’s the Rule of Three?”
“Never mind. You’re up here about virtual particles, I guess.”
“Yessir. You said they’re ‘now you might see them, now you probably don’t.’ What’s that about and what do they have to do with abstraction and Einstein’s ‘underlying reality’?”
“What have you heard about Heisenberg’s Uncertainty Principle?”
“Ms Plenum says you can’t know where you are and how fast you’re going.”
“Ms Plenum’s got part of the usual notion but she’s missing the idea of simultaneous precision and a few other things. Turns out you CAN know approximately where you are AND approximately how fast you’re going at a particular moment, but you can’t know both things precisely. There’s going to be some imprecision in both measurements. Think about Coach using a radar gun to track a thrown baseball. How does radar work?”
“It bounces a light beam off of something and measures the light’s round-trip travel time. I suppose it multiplies by the speed of light to convert time to distance.”
“Good. Now how does it get the ball’s speed?”
“Uhh… probably uses two light pulses a certain time apart and calculates the speed as distance difference divided by time difference.”
“Got it in one. Now, suppose that a second after the ball’s thrown the radar says the ball is 61 feet away from the plate and traveling at 92 mph. Air resistance acts to slow the ball’s flight so that 92 is really an average. Maybe it was going 92.1 mph at the first radar pulse and 91.9 mph at the second pulse. So that reported speed has an 0.2 mph range of uncertainty.”
“Oh, and neither of the two pulses caught the ball at exactly 61 feet so that’s uncertain, too, right?”
“There you go. We know the two averages, but each of them has a range. The Uncertainty Principle says that the product of those two ranges has to be greater than Planck’s constant, 10-34 Joule·second. Plugging that Joule-fraction and the mass of an electron into Einstein’s E=mc², we restate the constant as about 10-21 of an electron-second. Those are both teeny numbers — but they’re not zero.”
“So speed and location make an uncertainty pair. Are there others?”
“A few. The most important for this discussion is energy and time.”
“Wait a minute, those two can’t be linked that way.”
“Why not?”
“Well, because … umm … speed is change of location so those two go together, but energy isn’t change of time. Time just … goes, and adding energy won’t make it go faster.”
“As a matter of fact, there are situations where adding energy makes time go slower, but that’s a couple of stories for another day. What we’re talking about here is uncertainty ranges and how they combine. Quantum theory says that if a given particle has a certain energy, give or take an energy range, and it retains that energy for a certain duration, give or take a time range, then the product of the two ranges has to be larger than that same Planck constant. Think about a 1-meter cube of empty space out there somewhere. Got it?
“Sure.”
“Suppose a particle appeared and then vanished somewhere in that cube sometime during a 1-second interval. What’s the longest time that particle could have existed?”
“Easy — one second.”
“How about the shortest time?”
“Zero. Wait, it’d be the smallest possible non-zero time, wouldn’t it?”
“Good catch. So what’s the time uncertainty?”
“One second minus that tiniest bit of time.”
“And what’s the corresponding energy range?”
“That constant number that I forget.”
“10-21 electron-second’s worth. Now let’s pick a shorter interval. What’s the mass range for a particle that appears and disappears sometime during the 10-19 second it takes a photon to cross a hydrogen atom?”
“That’s 10-21 electron-second divided by 10-19 second, so it’d be, like, 0.01 electron.”
“How about 1% of that 10-19 second?”
“Wow — that’d be a whole electron.”
“A whole electron’s worth of uncertainty. But is the electron really there?”
“Probably not, huh?”
“Like I said, ‘Now you probably don’t’.”
~~ Rich Olcott
Hard Science Ain't Hard 
