Month: August 2019

Maybe even smaller?

On By rolcottIn Cosmology, Mathematics: Dimensions, Physics: Quantum Mechanics, Uncategorized2 Comments

There’s a sofa in my office. Sometimes it’s used to seat some clients for a consultation, sometimes I use it for a nap. This evening Anne and I are sitting on it, close together, after a meal of Eddie’s Pizza d’amore.

“I’ve been thinking, Sy. I don’t want to use my grow-shrink superpower very much.”

“Fine with me, I like the size you are. Why’d you decide that?”

“I remember Alice saying, ‘Three inches is such a wretched height to be.’ She was thinking about what her cat would do to her at that height. I’m thinking about what an amoeba might do to me if I were down to bacteria-size and I wouldn’t be able to see it coming because I’d be too small to see light. It would be even messier further down.”

“Well, mess is the point of quantum mechanics — all we get is the averages because it’s all chaos at the quantum level. Bohr would say we can’t even talk about what’s down there, but you’d be in the thick of it.”

She shudders delicately, leans in tighter. <long, very friendly pause> “Where’d that weird number come from, Sy?”

“What weird number?”

“Ten-to-the-minus-thirty-fifth. You mentioned it as a possible bottom to the size range.”

“Now you’re asking?”

“I’ve got this new superpower, I need to think about stuff.  Besides, we’ve finished the pizza.”

<sigh> “This conversation reminds me of our elephant adventure.  Oh well.  Umm. It may have started on a cold, wet afternoon. You know, when your head’s just not up to real work so you grab a scratchpad and start doodling? I’ll bet Max Planck was in that state when he started fiddling with universal constants, like the speed of light and his own personal contribution ħ, the quantum of action.”

“He could change their values?”

“No, of course not. But he could combine them in different ways to see what came out. Being a proper physicist he’d make sure the units always came out right. I’m not sure which unit-system he worked in so I’ll just stick with SI units, OK?”

“Why should I argue?”

“No good reason to. So… c is a velocity so its units are meters per second. Planck’s constant ħ is energy times time, which you can write either as joule-seconds or kilogram-meter² per second. He couldn’t just add the numbers together because the units are different. However, he could divide the one by the other so the per-seconds canceled out. That gave him kilogram-meters, which wasn’t particularly interesting. The important step was the next one.”

“Don’t keep me in suspense.”

“He threw Newton’s gravitational constant G into the mix. Its units are meter³ per kilogram per second². ‘Ach, vut a mess,’ he thought, ‘but maybe now ve getting somevere. If I multiply ħ by G the kilograms cancel out und I get meter5 per second³. Now … Ah! Divide by c³ vich is equal to multiplying by second³/meter³ to cancel out all the seconds and ve are left mit chust meter² vich I can take the square root uff. Wunderbar, it is simply a length! How ’bout that?‘”

“Surely he didn’t think ‘how ’bout that?‘”

“Maybe the German equivalent. Anyway, doodling like that is one of the ways researchers get inspirations. This one was so good that √(Għ/c³)=1.6×10-35 meter is now known as the Planck length. That’s where your ten-to-the-minus-thirty-fifth comes from.”

“That’s pretty small. But is it really the bottom?”

“Almost certainly not, for a couple of different reasons. First, although the Planck formula looks like a fundamental limit, it’s not. In the same report Planck re-juggled his constants to define the Planck mass √(ħc/G)=2.2×10-8 kilograms or 22 micrograms. Grains of sand weight less than that. If Planck’s mass isn’t a limit, Planck’s length probably isn’t either. Before you ask, the other reason has to do with relativity and this is not the time for that.”

“Mmm … so if space is quantized, which is where we started, the little bits probably aren’t Planck-sized?”

“Who knows? But my guess is, no, probably much smaller.”

“So I wouldn’t accidentally go out altogether like a candle then. That’s comforting to know.”

My turn to shudder. <another long, friendly pause>.

~~Rich Olcott

Small, yes, but how small?

On By rolcottIn Cosmology, Physics: Quantum Mechanics, UncategorizedLeave a comment

Another quiet summer afternoon in the office. As I’m finishing up some paperwork I hear a fizzing sound I’d not heard in a while. “Hello, Anne, welcome back. Where’ve you been?”

Her white satin looks a bit speckled somehow but her voice still sounds like molten silver. “I’m not sure, Sy. That’s what I’ve come to you about.”

“Tell me about it.”

“Well, after we figured out that I can sort of ‘push’ myself across time and probability variation I realized that the different ‘pushes’ felt like different directions, kind of. When I go backward and forward in time it feels a little like falling backward or forward. Not really, but that’s the best way I can describe it. Moving to a different probability is a little like going left or right. So I wondered, what about up and down?”

“And I gather you tried that.”

“Sure, why not? What good’s a superpower if you don’t know what you can do with it? When I ‘push’ just a little upward thIS HAPPENS.”

“Whoa, watch out for the ceiling fan! Shrink back down again before you break the furniture or something.”

“Oh, I won’t, I’ve learned to be careful when I resize. Good thing I was outside and all by myself the first time I tried it. Took some practice to control how how much my size changes by how light or heavy I ‘pushed’.”

“I think I can see where this is going.”

“Mm-hm, it’s good to know what the limits are, right? I’ve got a pretty good idea of what would happen if I got huge. What I want to know is, what’ll I be getting into if I try ‘pushing’ down as hard as I can?”

“Kinda depends on how far down you go. I’m assuming your retinas scale their sensitivity with your size. When you get bigger do green things look blue and yellow things look green and so forth?”

“Yeah, orange juice had this weird yellow color. Tasted OK, though.”

“Right. So when you get smaller the colors you perceive will shift the other way, to shorter wavelengths — at first, yellow things will look red, blue things will look yellow and you’ll see ultraviolet as blue. When you get a thousand times smaller than normal, most things will look black because there’s not much X-ray illumination unless you’re close to a badly-shielded Crookes tube.”

“Good thing this ‘push’ ability also gave me some kind of extra feel-sense that’s not sight. Sometimes when I try to ‘push’ it ‘feels’ blocked until I move around a little. After the ‘push’ I see a wall or something I would have jumped into.”

“That’s a relief. I was wondering how you’d navigate when you’re a million times smaller than normal, at the single-cell level, or a million times smaller than that when you’d be atom-sized.”

“Then what comes?”

“Mmm… one more factor of a thousand would get you down to about the size of an atomic nucleus, but below that things get real fuzzy. It’s hard to get experimental data in the sub-nuclear size range because any photon with a wavelength that short is essentially an extremely-high-energy gamma ray, better at blowing nuclei apart than measuring them. Theory says you’d encounter nuclei as roiling balls of protons and neutrons, but each of those is a trio of quarks which may or may not be composed of even smaller things.”

“Is that the end of small?”

“Maybe not. Some physicists think space is quantized at scales near 10—35 meter. If they’re wrong then there’s no end.”

“Quantized?”

“Quantized means something is measured out in whole numbers. Electric charge is quantized, for instance, because you can have one electron, two electrons, and so on, but you can’t have 1½ electrons. Some physicists think it’s possible that space itself is quantized. The basic idea is to somehow label each point in space with its own set of whole numbers.  There’d be no vacant space between points, just like there’s no whole number between two adjacent whole numbers.”

“So how small can I get?”

“Darned if I know.”

~~ Rich Olcott

Thanks to Jerry Mirelli for his thoughts that inspired this post and the next.

Fly High, Silver Bird

On By rolcottIn Physics: Light and Relativity, Space Travel, UncategorizedLeave a comment

“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

Sail On, Silver Bird

On By rolcottIn Physics: Light and Relativity, Space Travel, UncategorizedLeave a comment

Big excitement in Al’s coffee shop. “What’s the fuss, Al?”

“Lightsail 2, Sy. The Planetary Society’s Sun-powered spacecraft. Ten years of work and some luck and it’s up there, way above Hubble and the ISS, boosting itself higher every day and using no fuel to do it. Is that cool or what?”

“Sun-powered? Like with a huge set of solar panels and an electric engine?”

“No, that’s the thing. It’s got a couple of little panels to power its electronics and all, but propulsion is all direct from the Sun and that doesn’t stop. Steady as she goes, Skipper, Earth to Mars in weeks, not months. Woo-hoo!”

Image by Josh Spradling / The Planetary Society

Never the rah-rah type, Big Vinnie throws shade from his usual table by the door. “It didn’t get there by itself, Al. SpaceX’s Falcon Heavy rocket did the hard work, getting Lightsail 2 and about 20 other thingies up to orbit. Takes a lot of thrust to get out of Earth’s gravity well. Chemical rockets can do that, puny little ion drives and lightsails can’t.”

“Yeah, Vinnie, but those ‘puny’ guys could lead us to a totally different travel strategy.” A voice from the crowd, astrophysicist-in-training Newt Barnes. “Your big brawny rocket has to burn a lot of delta-v just to boost its own fuel. That’s a problem.”

Al looks puzzled. “Delta-v?”

“It’s how you figure rocket propellant, Al. With a car you think about miles per gallon because if you take your foot off the gas you eventually stop. In space you just keep going with whatever momentum you’ve got. What’s important is how much you can change momentum — speed up, slow down, change direction — and that depends on the propellant you’re using and the engine you’re putting it through. All you’ve got is what’s in the tanks.”

Al still looks puzzled. I fill in the connection. “Delta means difference, Al, and v is velocity which covers both speed and direction so delta-v means — “

“Got it, Sy. So Vinnie likes big hardware but bigger makes for harder to get off the ground and Newt’s suggesting there’s a limit somewhere.”

“Yup, it’s gotten to the point that the SpaceX people chase an extra few percent performance by chilling their propellants so they can cram more into the size tanks they use. I don’t know what the limit is but we may be getting close.”

Newt’s back in. “Which is where strategy comes in, Vinnie. Up to now we’re mostly using a ballistic strategy to get to off-Earth destinations, treating the vehicle like a projectile that gets all its momentum at the beginning of the trip. But there’s really three phases to the trip, right? You climb out of a gravity well, you travel to your target, and maybe you make a controlled landing you hope. With the ballistic strategy you burn your fuel in phase one while you’re getting yourself into a transfer orbit. Then you coast on momentum through phase two.”

“You got a better strategy?”

“In some ways, yeah. How about applying continuous acceleration throughout phase two instead of just coasting? The Dawn spacecraft, for example, was rocket-launched out of Earth’s gravity well but used a xenon-ion engine in continuous-burn mode to get to Mars and then on to Vesta and Ceres. Worked just fine.”

“But they’re such low-thrust –“

“Hey, Vinnie, taking a long time to build up speed’s no problem when you’re on a long trip anyway. Dawn‘s motor averaged 1.8 kilometer per second of delta-v — that works out to … about 4,000 miles per hour of increased speed for every hour you keep the motor running. Adds up.”

“OK, I’ll give you the ion motor’s more efficient than a chemical system, but still, you need that xenon reaction mass to get your delta-v. You still gotta boost it up out of the well. All you’re doing with that strategy is extend the limit.”

Al dives back in. “That’s the beauty of Lightsail, guys. No delta-v at all. Just put it up there and light-pressure from the Sun provides the energy. Look, I got this slick video that shows how it works.”

Video courtesy of The Planetary Society.

~~ Rich Olcott