Layer Upon Layer

“Excuse me, profesora, you wanted me to come to your office?”

“Yes, Maria. Come in, please. I wanted to have a chat with you before you give your class presentation tomorrow.”

“I am a little nervous about it.”

“I thought you might be. I wanted to help with that. I’ll start by saying that your English language skills have gotten much better than you give yourself credit for. Better yet, you’ll be speaking before friends who want you to succeed. I’m sure you’ll do fine. I think if we go over your material together you’ll be more confident. Come open your laptop on my desk where we can both see it. Now bring up your first slide.”

“Yes, profesora. Already you know that the title of my presentation is ‘The Structure of The Sun.’ I only have one slide, this one, that shows a slice of a star like our Sun.”

“How did the star get that way?”

“It condensed from a galactic gas cloud that was mostly hydrogen. I plan to talk about that with waving of the hands because a good picture of it needs to be in motion and I don’t know how to do that yet.”

“Fair enough, just don’t skip over it. Beginnings are important. Now talk me through your diagram.”

“It starts in the middle ¿see the fusion zone? where protons, that’s hydrogen atoms without their electrons, are squeezed together to release energy and make alpha particles, that’s helium atoms without their electrons. The protons have the same charge so they push each other away, but they are beneath many kilometers of mass that push them together. Also, the temperature is very hot, tens of millions of degrees. Hot atoms move fast, so when the protons are pushed together it happens with enough force and speed .. sorry, I need a word, superar?”


“Thank you. The protons are pushed together with enough force and speed to overcome the charge barrier. The actual reactions are complicated. At the end there is an alpha particle, four times heavier than a proton, and there is much more energy than the overcoming used up. The fusion zone makes heat and the heavy alpha particles fall down into the ash zone. The heat must go somewhere. Already the center is hotter so the new heat goes upward into the radiation zone.”

“And it’s called that because…?”

“Because atom motion is so, mm, frantic?”

“Good word.”

“… So frantic that there’s no moving in the same direction together, no convection like when steam rises over boiling water. Heat can only travel by convection, conduction or radiation. If there is no convection, moving heat must go neighbor‑to‑neighbor by conduction which is collision or by radiation which is photons jumping between atoms again and again until they escape. I have read that one photon’s energy can take 10000 years to cross the radiation zone.”

“So how is the next zone different?”

“It is much higher up from the center, nearly ¾ of the way to the surface. The pressure is 100 times less than in the fusion zone. The atoms have more room to move around together and form winds to carry the heat up by convection. But they can’t only go up, they have to come down, too, and that’s why my drawing has loops.”

“Is there a name for the loops?”

“Oh, yes, they are called Bénard cells and they’re very much like what I see looking into a pot of water just before it boils.”

“What’s the orange above the convection zone?”

“That’s the part of the Sun that we see, the photosphere that emits light in a continuous spectrum. The Fraunhofer lines, the dark lines in the astronomer’s spectrum, are the shadows of atoms high in in the photosphere that absorb only certain colors. I was surprised to learn how narrow the photosphere is, not even 0.02% of the Sun’s radius. Anyway, that’s my presentation, but now I have a question. The Sun’s fuel is hydrogen. The books say when the Sun runs out of fuel it will eject much of its hydrogen mass and collapse to a white dwarf. So it didn’t run out of fuel, yes?”

~~ Rich Olcott

A Match Game

<chirp chirp> “Lab C-324, Susan Kim speaking.”

<hoarsely> “Hi Susan, it’s Sy. Fair warning. The at‑home test I just ran says I’ve got Covid. I’ve had all four shots but it looks like some new variant dodged in anyway. We had coffee together at Al’s yesterday so I wanted to warn you. Better stock up on cough medicine and such.”

“Ooh. Thanks, Sy, sorry to hear that. If it’s any consolation, you’re not alone. About half the lab’s empty today because of Covid. I’m just waiting for this last extraction to complete and then I’m outta here myself. There’s chicken soup going in the slow‑cooker at home.”

“Ah, yes, a Jewish mother’s universal remedy.”

“Korean mothers, too, Sy, except we use more garlic. Chicken soup’s a standard all over the world — soothing, easy on the stomach and loaded with protein.”

“While you’re in wait mode, maybe you could explain something to me.”

“I can try. What is it?”

“How do these tests work? I swabbed my nose, swirled the yuck with the liquid in the little vial and put three drops into the ‘sample port‘ window. In the next few minutes fluid crept across the display window next to the port and I saw dark bars at the T and C markers. What’s that all about?”

“Miracles of modern immunochemistry, Sy, stuff we wouldn’t have been able to execute fifty years ago. What do you know about antibodies?”

“Not much. I’ve read a little about immunology but I always get the antibodies confused with the antigens and then my understanding goes south.”

“Ignore the ‘anti‘ parts — an antigen is usually a part of something from outside that generates an immune response. As part of the response, cells in your body build antibodies, targeted proteins that stick to specific antigens. Each unique antibody is produced by just a few of your cells. When you’re under a disease attack, your antibodies that match the attacker’s antigens lock onto the attacker to signal your defender cells what needs chewing up. About half‑a‑dozen Nobel Prizes went to researchers who figured out how to get a lab‑grown cell to react to a given antigen and then how to clone enough copies of that cell to make industrial quantities of the corresponding antibody. You follow?”

“So far, so good.”

“One more layer of detail. All antibodies are medium-sized proteins with the same structure like a letter Y. There’s a unique targeting bit at the end of each upper arm. An antigen can be anything — a fragment of protein or carbohydrate, a fatty acid, even some minerals.”

“Wait. If a protein can be an antigen, does that mean that an antibody can be an antigen, too?”

“Indeed, that’s the key for your test kit’s operation. The case holds a strip of porous plastic like filter paper that’s been treated with two narrow colorless stripes and a dot. The T stripe contains immobilized antibody for some fragment of the virus. The C stripe contains immobilized antibody antibody.”

“Hold on — an antibody that targets another antibody like maybe the bottom of the Y?”

“Exactly. That’s the control indicator. The dot holds virus antibodies that can move and they’re linked to tiny particles of gold. Each gold particle is way too small to see, but a bunch of them gathered together looks red‑brown. Okay, you put a few drops of yuckified liquid on top of the dot and the mixture migrates along the porous material. You tell me what happens.”

“Wait, what’s in that liquid?”

“It’s standard pH-buffered saline, keeps the proteins healthy.”

“Hmm. Alright, the dot’s gold‑labeled virus antibody grabs virus in my yuck and swims downstream. The T stripe’s virus antibody snags the virus‑antigen combination particles and I see red‑brown there. Or not, if there’s no virus. Meanwhile, the creeping liquid sweeps other gold‑labeled antibodies, virus‑bound or not, until they hit the C stripe and turn it red‑brown if things are working right. Uhhh, how much gold are we talking about?”

“Colloidal gold particles are typically balls maybe 50 nanometers across. Stripe area’s about 1 mm2, times 50 nanometers, density 19.32 kg/m3, gold’s $55 per gram today … about 5 microcents worth.”

~~ Rich Olcott

In vacuo veritas?

“Let’s see if my notes are complete, Mr Moire. We’re crossed off two possible Universe finales — falling into a Big Crunch or expanding forever while making new matter between the galaxies to keep itself in a steady state. Or the Universe might expand to some critical density and then stay there but we mostly ruled that out because a twitch would push it to either crunching or expanding forever. Einstein’s Cosmological Constant might or might not be dark energy but either way, Friedmann’s equation predicts that the Universe will expand exponentially. Is that all the ways we could end?”

“Of course not, Jeremy. The far distant future’s like anything we humans don’t know much about, we make lots of guesses. Vacuum energy, for instance.”

“Anything to do with getting my roommate off the couch when it’s their turn to do the floors?”

“Very funny, but no. The notion of ‘vacuum‘ has a history. Aristotle said it’s empty space and that’s nothing and you can’t talk about nothing, but of course that’s exactly what he was doing. It wasn’t until Newton’s day that we developed dependable technologies for producing and investigating ‘nothing.’ Turns out that a good vacuum’s hard to find and even outer space is a lot busier than you might think.”

“Yeah, Jim in the Physics lab says he’s working with Ultra‑High Vacuum, a millionth of a millionth of an atmosphere, and the molecules left in the apparatus still cause problems.”

“Wonder how many molecules that is. Time for Old Reliable. <muttering> Avagadro’s Number, 22.4 liters, 10-12 atmospheres … Wow, there’s nearly 30 billion molecules per liter in his rig, a couple hundred times more if he chills it. <scrolling> This Wikipedia article says the solar wind runs only ten thousand protons per liter; interstellar medium’s about a tenth of that. But all those are physical vacuums. Theoretical vacuums are completely empty except they’re sort‑of not.”

“How could they be empty but not? Is that a Schrödinger joke?”

“No, but it does point up how the word has acquired multiple technical meanings. Newton’s concept of a vacuum was basically equivalent to Aristotle’s — simply a space with no matter in it. Two centuries later, Maxwell pointed the way to electric and magnetic fields which meant we needed to define a new vacuum with no such fields. Einstein added his proviso about the speed of light in a vacuum but that was okay. Then along came quantum and strings and several new kinds of vacuum.”

“Why would we need new definitions? Nothing’s nothing, isn’t it?”

“Not necessarily in theory, and that’s the point. For instance, you might use a Maxwell‑inspired theory to think about how a certain charged object behaves in a certain electromagnetic field. You can’t isolate the field’s effects unless you can add it to a theoretical space containing no objects or electromagnetic fields. Make sense?”

“And that’s a Maxwell vacuum? Seems reasonable. Then what?”

“Quantum theories go in the other direction. They start by assuming that Maxwellian vacuums can’t exist, that space itself continually produces virtual particles from their associated fields.”

“Um, conservation of mass?”

“Valid question. This may feel like dodging, but there’s math and experiment to back it up. What’s really conserved, we think, is mass‑energy. Particles, anti‑particles and energy fluctuations averaging to zero over finite time intervals. A dab of energy concentrated to create a particle’s mass? No problem, because that particle will be annihilated and release its energy equivalent almost immediately. To replace the Maxwellian vacuum, quantum theorists co‑opted the word to refer to a system’s lowest possible quantum state or maybe the lowest possible set of states, depending on which kind of calculation is underway. The cosmology people picked up that notion and that’s when the doom‑saying started.”

“Awright, now we’re getting somewhere. What’s their vacuum like?”

“From what I’ve seen, a tall stack of ‘if‘s and hand‑waving. The idea is that our Universe may not be in the lowest possible quantum state and if so, sometime in the next 188 billion years we could suddenly drop from false to true vacuum, in which case everything goes haywire. I’m not convinced that the Universe even has a quantum state. Don’t panic.”

~~ Rich Olcott

Generation(s) of Stars

“How’re we gonna tell, Mr Moire?”

“Tell what, Jeremy?”

“Those two expanding Universe scenarios. How do we find out whether it’s gonna be the Big Rip or the Big Chill?”

“The Solar System will be recycled long before we’d have firm evidence either way. The weak dark energy we have now is most effective at separating things that are already at a distance. In the Big Rip’s script a brawnier dark energy would show itself first by loosening the gravitational bonds at the largest scale. Galaxies would begin scattering into the voids between the multi‑galactic sheets and filaments we’ve been mapping. Only later would the galaxies themselves release their stars to wander off and dissolve when dark energy gets strong enough to overcome electromagnetism.”

“How soon will we see those things happen?”

“If they happen. Plan on 188 billion years or so, depending on how fast dark energy strengthens. The Rip itself would take about 2 billion years, start to finish. Remember, our Sun will go nova in only five billion years so even the Rip scenario is far, far future. I prefer the slower Chill story where the Cosmological Constant stays constant or at least the w parameter stays on the positive side of minus‑one. Weak dark energy doesn’t mess with large gravitationally‑bound structures. It simply pushes them apart. One by one galaxies and galaxy clusters will disappear beyond the Hubble horizon until our galaxy is the only one in sight. I take comfort in the fact that our observations so far put w so close to minus‑one that we can’t tell if it’s above or below.”

“Why’s that?”

“The closer (w+1) approaches zero, the longer the timeline before we’re alone. We’ll have more time for our stars to complete their life cycles and give rise to new generations of stars.”

“New generations of stars? Wow. Oh, that’s what you meant when you said our Solar System would be recycled.”

“Mm-hm. Think about it. Back when atoms first coalesced after the Big Bang, they were all either hydrogen or helium with just a smidgeon of lithium for flavor. Where did all the other elements come from? Friedmann’s student George Gamow figured that out, along with lots of other stuff. Fascinating guy, interested in just about everything and good at much of it. Born in Odessa USSR, he and his wife tried twice to defect to the West by kayak. They finally made it in 1933 by leveraging his invitation to Brussels and the Solvay Conference on Physics where Einstein and Bohr had their second big debate. By that time Gamow had produced his ‘liquid drop‘ theory of how heavy atomic nuclei decay by spitting out alpha particles and electrons. He built on that theory to explain how stars serve as breeder reactors.”

“I thought breeder reactors are for turning uranium into plutonium for bombs. Did he have anything to do with that?”

“By the start of the war he was a US citizen as well as a top-flight nuclear theorist but they kept him away from the Manhattan Project. That undoubtedly was because of his Soviet background. During the war years he taught university physics, consulted for the Navy, and thought about how stars work. His atom decay work showed that alpha particles could escape from a nucleus by a process a little like water molecules in a droplet bypassing the droplet’s surface tension. For atoms deep inside the Sun, he suggested that his droplet process could work in reverse. He calculated the temperatures and pressures it would take for gravity to force alpha particles or electrons into different kinds of nuclei. The amazing thing was, his calculations worked.”

“Wait — alpha particles? Where’d they come from if the early stars were just hydrogen and helium?”

“An alpha particle is just a helium atom with the electrons stripped off. Anyway, with Gamow leading the way astrophysicists figured out how much of which elements a given star would create by the time it went nova. Those elements became part of the gas‑dust mix that coalesces to become the next generation of stars. We may have gone through 100 such cycles so far.”

“A hundred generations of stars. Wow.”

~~ Rich Olcott

En Route to Spreading Out

“Gee, Mr Moire, if Einstein and Friedmann are right, some day the Universe will expand exponentially and everything dies. Even Dr Mack says that’s a downer.”

“First, it’s not ‘some day,’ it’s already. We’ve got evidence that exponential expansion became the dominant process five billion years ago. The interesting questions are about what happens during the expansion and what the timeline will be. That’s all controlled by a single weird parameter so naturally the parameter’s conventional symbol is w. Each major component of the Universe has its own value of w and they combine to predict the future course of the Universe.”

“Weird sounds like fun. What is it, another difference like the Cosmological Constant minus that mass‑pressure stuff?”

“Good guess, but it’s not a difference, It’s a ratio, between different flavors of energy.”

“Kinetic and potential, I’ll bet.”

“That split seems to be a common theme in Physics, doesn’t it? In this case, you’re almost right if we stretch things. One of the energy flavors is mass, including both normal and dark matter. If you take the long view, every atom of normal matter will sooner or later break down so you can think of it as a packet of potential energy, pent up and waiting for release. Dark matter, who knows? Anyway, w‘s denominator is mass per unit volume. The numerator’s a little trickier. As you guessed, we need something related to kinetic energy and we slide into that sideways.”

“How so?”

“Well, most of the normal matter is very dilute hydrogen which we can treat like a perfect gas. That’s something we’ve got a good theory for. Per unit volume, gas particle kinetic energy is proportional to pressure and that’s what we use for w‘s numerator. Averaged over the volume of space the pressure‑to‑mass ratio w for matter moving at ordinary speeds is effectively zero.”

“Does dark matter follow the same formula?”

“We pretend it does.”

“How about photons? They don’t have mass so that ratio would be infinity.”

“True, but they do carry momentum and it turns out w is simply ⅓ for photons and neutrinos and anything else traveling at relativistic speeds. Then there’s the Cosmological Constant’s w, which is minus‑one. Since the Big Bang we’ve gone from radiation‑dominated to matter‑dominated to Constant‑dominated; the effective w has shifted from somewhat positive to zero and into negative territory. Thanks to the surviving photons and matter, though, we’re still at least slightly above –1.0.”

“What difference does that make?”

“Minus‑one is the boundary between fates for the Universe. More positive than that, gravity and electromagnetism are guaranteed to be stronger than dark energy. Expansion will move gravity‑bound objects farther away from each other, but the galaxies and each galaxy cluster will stay together. The supply of hydrogen that fuels new stars will peter out. Eventually all the stars will gutter out and disappear into the cold dark as they wait for their constituent atoms to decay. The whole process will take something like 1010¹⁰ years.”

“That’s dark, alright, but at least it’ll take a long time. What happens of w is more negative than minus‑one?”

“The Big Rip. If w is more negative than the threshold, dark energy will grow stronger with time. We don’t know of anything that would limit the growth. First dark energy overpowers gravity and allows the galaxies and stars to disperse. Then it overrides the electromagnetism that holds molecules and rocks together. Eventually even the weak and strong nuclear forces will be defeated — no more atoms. Depending on how extreme w is, figure something like 200 billion years, give or take an eon.”

“Wow. But wait, we’ve covered radiation and mass and the Constant and none of them have a w below the threshold. What can have a more negative w?”

“A hypothesis. If there is anything, pretty much all we have is a name, ‘phantom energy,’ which is even more tentative than ‘dark energy.’ People are working to evaluate w with data. Results so far are so close to –1.0 that we can’t tell if it’s above or below the threshold or just teetering on the brink.”

“Two hundred billion years or way more. No worries, hey?”

~~ Rich Olcott

Three Phases of Ever

“So if the Universe isn’t in a steady state and it’s not heading for a Big Crunch, I guess it’s getting bigger forever, huh?”

“Careful, Jeremy, the Universe expansion could maybe reach a stopping point if it happened to hold exactly the right amount of mass‑energy. The expansion could just stop when forces balance out.”

“What forces, Mr Moire? There’s gravity pulling everything together so what’s pushing them apart?”

“That is an excellent question, one that we don’t yet have an answer for. We’re about where Newton was with gravity. There was a lot of observational evidence, he had a name for it and knew how to calculate its effects, but he didn’t know how it worked. That’s us with Einstein’s Cosmological Constant.”

“Observational evidence — we can actually see things accelerate?”

“Not any one object speeding up. Human lifetimes are too short to measure acceleration in galaxies a hundred thousand lightyears across. No, we use the same strategy that Hubble used — measure many galaxies at different distances from us and graph recession speed against distance. During the century since Hubble we’ve greatly improved our estimates of astronomical speeds and distances. Dividing the known speed of light into a galaxy’s measured distance tells us time since it emitted the photons we see. Our findings confirm Hubble’s general conclusion — on average, older photons come from galaxies that fly away faster. Hubble thought that the relation was linear but our fine‑tuned numbers show otherwise. The data says that after the first few seconds the Universe stretched at a steady rate for only the first ⅔ of its life. The stretch has been accelerating since then.”

“Why wasn’t it accelerating since the beginning? Did someone cut in the afterburner?”

“More like turned one off. The evidence and theory we have so far indicate the Universe has seen a succession of phases dominated by different processes. You’ve probably heard of inflation—”

“Have I? You should see what they want for a burger these days!”

“Not that sort of inflation, but I know how you feel. No, I’m referring to cosmic inflation, very early in the Big Bang sequence, when the Universe expanded by a factor of 1026 within a tiny fraction of a second. It was driven by enormously powerful radiation‑linked effects we don’t understand that finally ran out of steam and let lower‑energy processes take over.”

“How’d that happen?”

“We don’t know. The general principle is that one process so dominates what’s going on in a phase that nothing else matters, until for some reason it stops mattering and we’re in a new phase with a different dominant process. The early Universe was controlled by radiative processes until things cooled off enough for particles to form and persist. That changed the game. Gravity dominated the next 8 billion years. Particles clumped together, atoms then dust then solar systems into larger and larger structures with bigger spaces between them. About 5 billion years ago the game changed again.”

“So early on there weren’t even atoms, huh? Wow. What was the next game‑changer?”

“Thanks to Einstein and Friedmann’s work we’ve got at least a guess.”


“Alexander Friedmann. He was a Russian physicist, used Einstein’s General Relativity results to derive three equations that together model the dynamics of the overall scale of the Universe using just a few estimates for current conditions. His equations give acceleration as the difference of two terms. The positive term is simply proportional to Einstein’s Constant. The negative term depends on both average mass density and pressure. Take a moment to think.”

“Umm… Positive is acceleration, negative is deceleration, density and pressure go down … If the negative term gets smaller than the positive one, acceleration increases, right?”

“It does, and we think the constant term has been increasingly dominant for 5 billion years. Something else to consider — the equation’s result is in terms of scale change divided by current scale. What’s it mean if that ratio’s a positive constant?”

“Change by a constant positive percentage … that’s exponential growth!”

“I thought you’d recognize it. Einstein’s Constant implies the scale of the Universe grows at an exponentially accelerating rate. We’re now in the Cosmological Constant phase.”

In Russian, Aleksandr Aleksandrowitsch Fridman

~~ Rich Olcott

Not Crunch Time

A familiar knock on my office door. “C’mon in, Jeremy, the door’s open.”

“Got a few minutes, Mr Moire?”

The second serious-sounding visitor today. I push my keyboard aside again. “Sure, what’s up?”

“I read your ‘Tops of Time‘ post and then I watched one of Katie Mack’s End of Everything‘ YouTube videos and now I’m confused. And worried.”

“I can understand that. Clearing up the confusion should be easy. Then I’ll do what I can about the worry part, okay?”

“That’d be great, sir.”

“So, imagine an enormous sheet of graph paper, and then imagine Puerto Rico laid down on top of that. You could use the graph paper to describe the latitude and longitude of any place on the island, right?”

“Sure, probably.”

“I happen to know that Playa Jobos is the northernmost point of the island. Does north stop there?”

“Nosir. The island stops there, but north keeps going.”

“Well, there you are.”

“Wait … oh, you’re saying that time by itself keeps going forever but what’s in the Universe might not and that’s what Dr Mack is talking about?”

“That’s the idea. More precisely, the ‘tops‘ I wrote about are different ways that spacetime’s time coordinate could play out in the future, or maybe not. Mack’s ‘end of everything‘ is about the future history of physical stuff laid on top of our mathematical spacetime constructs. Does that clarify things?”

“Mmm, yessir, but what about the ‘maybe not‘ you said?”

“This gets metaphysical, but cosmology often skates on that edge. Descartes and others maintained that space has meaning only when there are separate objects. If there was only one thing in the Universe you’d have nothing to compare sizes against and there’d be no point in measuring distances away from it. That’d be even more the case if there’s nothing. Same thing for time and events. From that perspective, if somehow the Universe emptied out then space and time sort of stop.”

“Just sort‑of stop, like Puerto Rico stops at that Playa place. Really they keep on going, I think, even if no‑one’s there to measure anything.”

“A perfectly reasonable position when there’s no evidence either way. Anyhow, a few of Mack’s scenarios wind up in that situation, right?”

“Umm… there’s the Big Crunch that reverses the Big Bang.”

“That one was popular before we got good data. The idea was that the Big Bang pushed everything apart but eventually gravity will slow outward momentum and pull everything back together again. The notion probably came from humanity’s experience with dirt falling back down after an explosion. The problems with that scheme are that the Big Bang wasn’t an explosion, outward momentum isn’t a thing and besides, we’ve got increasingly good data showing that between‑galaxy distances are getting wider, not shrinking. The last five billion years that’s sped up.”

“Wait, not an explosion? All the videos show it that way.”

“Chalk it up to artistic license. It’s hard to show everything moving away from everything else without making it look like the viewpoint’s simply diving into a static arrangement. No, an explosion comes out of a center and that’s not the Bang. Remember that huge piece of graph paper? Make it a balloon, tack Puerto Ricos all over it, then pump in some air. There’s no center, but every islander thinks their island is the center and every other island is running away from them. Really, all that’s happening is that the stretching rubber is creating new inter‑island space everywhere.”

“And that’s Universe expansion?”

“Mm-hm. Also known as Hubble Flow. We’ve looked very hard for a center of motion, haven’t found one.”

“If everything’s moving, why isn’t that momentum?”

“It is momentum, but only pairwise. For any two galaxies you can calculate mass times speed same as always. For really distant objects you’ve got to use a relativistic version. Anyway, in the cosmological context you’ve got to ask, momentum relative to what? Everyone has this picture that things came from a common center and will fall back there. The way Hubble expansion works, though, there’s no particular go‑back place.”

“Everything’s speeding up and going everywhere so no Big Crunch then.”

“Not on the original model, anyway.”

~~ Rich Olcott

Time Is Where You Find It

A familiar footstep in the hall outside my office, “C’mon in, Vinnie, the door’s open.”

“Got a few minutes, Sy?”

More than just “a minute.” This sounds serious so I push my keyboard aside. “Sure, what’s up?”

“I’ve been thinking about different things, putting ’em together different ways. I came up with something, sorta, that I wanted to run past you before I brought it to one of Cathleen’s ‘Crazy Theories‘ parties.”

“Why, Vinnie, you’re being downright diffident. Spill it.”

“Well, it’s all fuzzy. First part goes way back to years ago when you wrote that there’s zero time between when a photon gets created and when it gets used up. But that means that create and use-up are simultaneous and that goes against Einstein’s ‘No simultaneity‘ thing which I wonder if you couldn’t get around it using time tick signals to sync up two space clocks.”

“That’s quite a mix and I see why you say it’s fuzzy. Would you be surprised if I used the word ‘frame‘ while clarifying it?”

“I’ve known you long enough it wouldn’t surprise me. Go ahead.”

“Let’s start with the synchronization idea. You’re not the first to come up with that suggestion. It can work, but only if the two clocks are flying in formation, exactly parallel course and speed.”

“Hah, that goes back to our first talk with the frame thing. You’re saying the clocks have to share the same frame like me and that other pilot.”

“Exactly. If the ships are zooming along in different inertial frames, each will measure time dilation in the other. How much depends on their relative velocities.”

“Wait, that was another conversation. We were pretending we’re in two spaceships like we’re talking about here and your clock ran slower than mine and my clock ran slower than yours which is weird. You explained it with equations but I’ve never been good with equations. You got a diagram?”

“Better than that, I’ve got a video. It flips back and forth between inertial frames for Enterprise and Voyager. We’ll pretend that they sync their clocks at the point where their tracks cross. I drew the Enterprise timeline vertical because Enterprise doesn’t move in space relative to Enterprise. The white dots are the pings it sends out every second. Meanwhile, Voyager is on a different course with its own timeline so its inertial frame is rotated relative to Enterprise‘s. The gray dots on Voyager‘s track show when that ship receives the Enterprise pings. On the Voyager timeline the pings arrive farther apart than they are on the Enterprise timeline so Voyager perceives that Enterprise is falling farther and farther behind.”

“Gimme a sec … so Voyager says Enterprise‘s timer is going slow, huh?”

“That’s it exactly. Now look at the rotated frame. The pink dots show when Voyager sends out its pings. The gray dots on Enterprise‘s track show when the pings arrive.”

“And Enterprise thinks that Voyager‘s clock is slow, just backwards of the other crew. OK, I see you can’t use sync pulses to match up clocks, but it’s still weird.”

“Which is where Lorentz and Minkowski and Einstein come into the picture. Their basic position was that physical events are real and there should be a way to measure them that doesn’t depend on an observer’s frame of reference. Minkowski’s ‘interval‘ metric qualifies. After converting time and location measurements to intervals, both crews would measure identical spacetime separations. Unfortunately, that wouldn’t help with clock synchronization because spacetime mixes time with space.”

“How about the photons?”

“Ah, that’s a misquotation. I didn’t say the time is zero, I said ‘proper time‘ and that’s different. An object’s proper time is measured by its clock in its inertial frame while traveling time t and distance d between two events. Anyone could measure t and d in their inertial frame. Minkowski’s interval is defined as s=[(ct)²‑d²]. Proper time is s/c. Intuitively I think of s/c as light’s travel time after it’s done traversing distance d. In space, photons always travel at lightspeed so their interval and proper time are always zero.”

“Photon create and use-up aren’t simultaneous then.”

“Only to photons.”

~~ Rich Olcott

The Threshold of Stuffiness

<chirp chirp> “Moire here.”

“Hi, Sy, it’s Susan Kim. I read your humidifier piece and I’ve got your answer for you.”

“Answer? I didn’t know I’d asked a question.”

“Sure you did. You worked out that your humidifier mostly keeps your office at 45% relative humidity by moisturizing incoming air that’s a lot drier than that. As a chemist I like how you brought in moles to check your numbers. Anyway, you wondered how to figure the incoming airflow. I’ve got your answer. It’s a scaling problem.”

“Mineral scaling? No, I don’t think so. The unit’s mostly white plastic so I wouldn’t see any scaling, but it seems to be working fine. I’ve been using de-ionized water and following the instructions to rinse the tank with vinegar every week or so.”

“Nope, not that kind of scale, Sy. You’ve got a good estimate from a small sample and you wondered how to scale it up, is all.”

“Sample? How’d I take a sample?”

“You gave us the numbers. Your office is 1200 cubic feet, right, and it took 88 milliliters of water to raise the relative humidity to where you wanted it, right, and the humidifier used a 1000 milliliters of water to keep it there for a day, right? Well, then. If one roomful of air requires 88 milliliters, then a thousand milliliters would humidify (1000/88)=11.4 room changes per day.”

“Is that a good number?”

“I knew you’d ask. According to the ventilation guidelines I looked up, ‘Buildings occupied by people typically need between 5 and 10 cubic feet per minute per person of fresh air ventilation.‘ You’re getting 11.4 roomfuls per day, times your office volume of 1200 cubic feet, divided by 1440 minutes per day. That comes to 9.5 cubic feet per minute. On the button if you’re alone, a little bit shy if you’ve got a client or somebody in there. I’d say your building’s architect did a pretty good job.”

“I like the place, except for when the elevators act up. All that figuring must have you thirsty. Meet me at Al’s and I’ll buy you a mocha latte.”

“Sounds like a plan.”

“Hi, folks. Saw you coming so I drew your usuals, mocha latte for Susan, black mud for Sy. Did I guess right?”

“Al, you make mocha lattes better than anybody.”

“Thanks, Susan, I do my best. Go on, take a table.”

“Susan, I was thinking while I walked over here. My cousin Crystal doesn’t like to wear those N95 virus masks because she says they make her short of breath. Her theory is that they trap her exhaled CO2 and those molecules get in the way of the O2 molecules she wants to breathe in. What does chemistry say to that theory?”

“Hmm. Well, we can make some estimates. N95 filtration is designed to block 95% of all particles larger than 300 nanometers. A couple thousand CO2 molecules could march abreast through a mesh opening that size no problem. An O2 molecule is about the same size. Both kinds are so small they never contact the mesh material so there’s essentially zero likelihood of differential effect.”

“So exhaled CO2 isn’t preferentially concentrated. Good. How about the crowd‑out idea?”

“Give me a second. <tapping on phone> Not supported by the numbers, Sy. There’s one CO2 for every 525 O2‘s in fresh air. Exhaled air is poorer in O2, richer in CO2, but even there oxygen has a 4‑to‑1 dominance.”

“But if the mask traps exhaled air…”

“Right. The key number is the retention ratio, what fraction of an exhaled breath the mask holds back. A typical exhale runs about 500 milliliters, could be half that if you’ve got lung trouble, twice or more if you’re working hard. This mask looks about 300 milliliters just sitting on the table, but there’s probably only 100 milliliters of space when I’m wearing it. It’s just arithmetic to get the O2/CO2 ratio for each breathing mode, see?”

“Looks good.”

“Even a shallow breather still gets 79 times more O2 than CO2. Blocking just doesn’t happen.”

“I’ll tell Crys.”

~ Rich Olcott

It’s The Heat AND The Humidity

<from the casebook of Sy Moire, Consulting Physicist> Monday. Weather sunny, warm for this time of year. Dry, bad effects on nose and throat at wake‑up time. Bought a room humidifier Friday at Big Box — up‑scale, 4‑liter reservoir, ultrasonic but silent, WiFi‑enabled etc. Long way from the jug with boiler tube my folks used to use. WiFi’s a sneaky way to avoid building a remote control — just use the customer’s smart phone. Guess that keeps the price down.

Good news is, phone app does graphs of relative humidity against time. Had it in measure-only mode in office Monday night, baseline wobbled in the 32-36% range. Bad news is, when the device is running on Automatic it works toward a 45% target but had trouble getting near that high on its maiden effort on Saturday. Wondered, how much water would it have to send into the room to hit the target?

Start with the numbers. “45%” is forty‑five percent of what? Surely not some arbitrary maximum. Weather guy talks about relative humidity so, relative to what? Searched a little in the internet. All the sources say RH is a ratio of ratios, something over maximum something. “Something” is water vapor mass per unit volume or else water vapor mass per total gas mass in the same volume. Clouds, fog, raindrops and snowflakes don’t count. Then things get fuzzy. Some sources say the maximum is “saturation” which is just a tautology. The most precise definition says “the partial pressure of water in air over a large flat surface of pure water under laboratory conditions” <shudder>.

Doing engineer stuff here so keep it simple. Found a chart of water vapor content at 100% humidity at different temperatures. Will go with that. No surprise, the warmer the air, the more water mass it can hold before fogging up. I’m comfortable around 68°F which is 20°C. The chart says 100% saturated 20°C air holds 17.3 grams of water per cubic meter. 45% of that is 7.8 and 30% is 5.3. Need to know how many cubic meters in the office.

OK, measured the room as 10’×15′ with an 8′ ceiling. Ignore the space the furniture takes up. Total volume is 1200 cubic feet. Old Reliable says that’s 34 cubic meters. If the room’s at 100% humidity its air holds
  (34 m3)×(17.3 g/m3)
   = 588 grams of water.
At 1000 grams per liter that’s 0.588 liter or about a pint. Suppose humidifier starts when the room’s at 30% humidity. For a 15% bump to 45% the gadget has to vaporize
  (34 m3)×(17.3 g/m3)×(0.45-0.30)
   = 88 g = 88 milliliters.

Wow, that’s only about 6 tablespoons. Does that number even make sense? OK, air is about 80% N2, molecular weight 28. The other 20% is mostly O2, molecular weight 32. The average is near 29. Basic chem class stuff — at Earth‑typical room temp and pressure, a 22.4‑liter chunk of air has a mass near 29 grams, so office’s roomful of air would mass
  (29g/mole)×(1 mole/22.4 liters)
   ×(1000 liters/m3)×(34 m3/room)
    = 44 kilograms
The 588-gram number says that it’d get foggy in here if the moisture content ever got much above (588 g)/(44000 g) = 1.3% by mass, which sounds reasonable.

88 milliliters ain’t much, so how come the unit used up a liter of water in just one day?

Ah-hah. Air’s not sitting still. Ventilation system continually brings in low‑humidity outside air. Plus, clients complain in the wintertime about cold drafts leaking in around the door, transom and windows. If it weren’t for air shuttling in and out, we’d use up all the oxygen in here — that isn’t happening. Wonder how to calculate that flow. Bottom line is, humidifier doesn’t moisten what’s in the room so much as it loads up what comes in dry.

Problem — evaporating water cools air, Old Reliable says 2256 kilojoules per kilogram. 88 grams won’t have much effect, but a liter/day is a kilogram/day. An hour is 1/24 of a day. 1/24 liter means 94 kilojoules per hour of cooling. Air heat capacity is 1 kilojoule/(kilogram oC). (94 kJ/44 kg air)=2.1 degrees per hour. Suddenly I feel chilly.

~~ Rich Olcott