Category: Physics

Bridging A Paradox

On By rolcottIn Physics: Entropy and Thermodynamics, Physics: Gaps, Physics: Quantum Mechanics, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hi, Sy. Vinnie. Hey, I’ve been reading through some of your old stuff—”

“That bored, eh?”

“You know it. Anyhow, something just don’t jibe, ya know?”

“I’m not surprised but I don’t know. Tell me about it.”

“OK, let’s start with your Einstein’s Bubble piece. You got this electron goes up‑and‑down in some other galaxy and sends out a photon and it hits my eye and an atom in there absorbs it and I see the speck of light, right?”

“That’s about the size of it. What’s the problem?”

“I ain’t done yet. OK, the photon can’t give away any energy on the way here ’cause it’s quantum and quantum energy comes in packages. And when it hits my eye I get the whole package, right?”

“Yes, and?”

“And so there’s no energy loss and that means 100% efficient and I thought thermodynamics says you can’t do that.”

“Ah, good point. You’ve just described one version of Loschmidt’s Paradox. A lot of ink has gone into the conflict between quantum mechanics and relativity theory, but Herr Johann Loschmidt found a fundamental conflict between Newtonian mechanics, which is fundamental, and thermodynamics, which is also fundamental. He wasn’t talking photons, of course — it’d be another quarter-century before Planck and Einstein came up with that notion — but his challenge stood on your central issue.”

“Goody for me, so what’s the central issue?”

“Whether or not things can run in reverse. A pendulum that swings from A to B also swings from B to A. Planets go around our Sun counterclockwise, but Newton’s math would be just as accurate if they went clockwise. In all his equations and everything derived from them, you can replace +t with ‑t to make run time backwards and everything looks dandy. That even carries over to quantum mechanics — an excited atom relaxes by emitting a photon that eventually excites another atom, but then the second atom can play the same game by tossing a photon back the other way. That works because photons don’t dissipate their energy.”

“I get your point, Newton-style physics likes things that can back up. So what’s Loschmidt’s beef?”

“Ever see a fire unburn? Down at the microscopic level where atoms and photons live, processes run backwards all the time. Melting and freezing and chemical equilibria depend upon that. Things are different up at the macroscopic level, though — once heat energy gets out or randomness creeps in, processes can’t undo by themselves as Newton would like. That’s why Loschmidt stood the Laws of Thermodynamics up against Newton’s Laws. The paradox isn’t Newton’s fault — the very idea of energy was just being invented in his time and of course atoms and molecules and randomness were still centuries away.”

“Micro, macro, who cares about the difference?”

“The difference is that the micro level is usually a lot simpler than the macro level. We can often use measured or calculated micro‑level properties to predict macro‑level properties. Boltzmann started a whole branch of Physics, Statistical Mechanics, devoted to carrying out that strategy. For instance, if we know enough about what happens when two gas molecules collide we can predict the speed of sound through the gas. Our solid‑state devices depend on macro‑level electric and optical phenomena that depend on micro‑level electron‑atom interactions.”

“Statistical?”

“As in, ‘we don’t know exactly how it’ll go but we can figure the odds…‘ Suppose we’re looking at air molecules and the micro process is a molecule moving. It could go left, right, up, down, towards or away from you like the six sides of a die. Once it’s gone left, what are the odds it’ll reverse course?”

“About 16%, like rolling a die to get a one.”

“You know your odds. Now roll that die again. What’s the odds of snake‑eyes?”

“16% of 16%, that’s like 3 outa 100.”

“There’s a kajillion molecules in the room. Roll the die a kajillion times. What are the odds all the air goes to one wall?”

“So close to zero it ain’t gonna happen.”

“And Boltzmann’s Statistical Mechanics explained why not.”

“Knowing about one molecule predicts a kajillion. Pretty good.”

San Francisco’s Golden Gate Bridge, looking South
Photo by Rich Niewiroski Jr. / CC BY 2.5

~~ Rich Olcott

Breaking Up? Not So Hard

On By rolcottIn Physics: Black Holes and Relativity, UncategorizedLeave a comment

<transcript of smartphone dictation by Sy Moire, hard‑boiled physicist>
Day 173 of self‑isolation….
Perfect weather for a brisk solitary walk, taking the park route….
There’s the geese. No sign of Mr Feder, just as well….

Still thinking about Ms Baird and her plan for generating electric power from a black hole named Lonesome….
Can just hear Vinnie if I ever told him about this which I can’t….
“Hey, Sy, nothin’ gets out of a black hole except gravity, but she’s using Lonesome‘s magnetic field to generate electricity which is electromagnetic. How’s that happen?”
Good question….

Hhmph, that’s one angry squirrel….
Ah, a couple of crows pecking the ground under its tree. Maybe they’re too close to its acorn stash….

We know a black hole’s only measurable properties are its mass, charge and spin….
And maybe its temperature, thanks to Stephen Hawking….
Its charge is static — hah! cute pun — wouldn’t support continuous electrical generation….
The Event Horizon hides everything inside — we can’t tell if charge moves around in there or even if it’s matter or anti‑matter or something else….
The no‑hair theorem says there’s no landmarks or anything sticking out of the Event Horizon so how do we know the thing’s even spinning?

Ah, we know a black hole’s external structures — the jets, the Ergosphere belt and the accretion disk — rotate because we see red- and blue-shifted radiation from them….
The Ergosphere rotates in lockstep with Lonesome‘s contents because of gravitational frame-dragging….
Probably the disk and the jets do, too, but that’s only a strong maybe….
But why should the Ergosphere’s rotation generate a magnetic field?

How about Newt Barnes’ double‑wheel idea — a belt of charged light‑weight particles inside a belt of opposite‑charged heavy particles all embedded in the Ergosphere and orbiting at the black hole’s spin rate….
Could such a thing exist? Can simple particle collisions really split the charges apart like that?….

OK, fun problem for strolling mental arithmetic. Astronomical “dust” particles are about the size of smoke particles and those are about a micrometer across which is 10‑6 meter so the volume’s about (10‑6)3=10‑18 cubic meter and the density’s sorta close to water at 1 gram per cubic centimeter or a thousand kilograms per cubic meter so the particle mass is about 10‑18×103=10‑15 kilogram. If a that‑size particle collided with something and released just enough kinetic energy to knock off an electron, how fast was it going?

Ionization energy for a hydrogen atom is 13 electronvolts, so let’s go for a collision energy of at least 10 eV. Good old kinetic energy formula is E=½mv² but that’s got to be in joules if we want a speed in meters per second so 10 eV is, lemme think, about 2×10‑18 joules/particle. So v² is 2×2×10‑18/10‑15 which is 4×10‑3 or 40×10‑4, square root of 40 is about 6, so v is about 6×10‑2 or 0.06 meters per second. How’s that compare with typical speeds near Lonesome?

Ms Baird said that Lonesome‘s mass is 1.5 Solar masses and it’s isolated from external gravity and electromagnetic fields. So anything near it is in orbit and we can use the circular orbit formula v²=GM/r….
Dang, don’t remember values for G or M. Have to cheat and look up the Sun’s GM product on Old Reliable….
Ah-hah, 1.3×1020 meters³/second so Lonesome‘s is also near 1020….
A solar‑mass black hole’s half‑diameter is about 3 kilometers so Lonesome‘s would be about 5×103 meters. Say we’re orbiting at twice that so r‘s around 104 meters. Put it together we get v2=1020/104=1016 so v=108 meters/sec….
Everything’s going a billion times faster than 10 eV….
So yeah, no problem getting charged dust particles out there next to Lonesome….

Just look at the color in that tree…
Weird when you think about it. The really good color is summertime chlorophyll green when the trees are soaking up sunlight and turning CO2 into oxygen for us but people get excited about dying leaves that are red or yellow…

Well, now. Lonesome‘s Event Horizon is the no-going-back point on the way to its central singularity which we call infinity because its physics are beyond anything we know. I’ve just closed out another decade of my life, another Event Horizon on my own one‑way path to a singularity…

Hey! Mr Feder! Come ask me a question to get me out of this mood.

Author’s note — Yes, ambient radiation in Lonesome‘s immediate vicinity probably would account for far more ionization than physical impact, but this was a nice exercise in estimation and playing with exponents and applied physical principles.

~~ Rich Olcott

Engineering A Black Hole

On By rolcottIn General: Fun Stuff, Physics: Black Holes and Relativity, Physics: Newton and Gravity, UncategorizedLeave a comment

<bomPAH-dadadadaDEEdah> That weird ringtone on Old Reliable again. Sure enough, the phone function’s caller-ID display says 710‑555‑1701.  “Ms Baird, I presume?”

A computerish voice, aggressive but feminine, with a hint of desperation. “Commander Baird will be with you shortly, Mr Moire. Please hold.”

A moment later, “Hello, Mr Moire.”

“Ms Baird. Congratulations on the promotion.”

“Thank you, Mr Moire. I owe you for that.”

“How so?”

“Your posts about phase-based weaponry got me thinking. I assembled a team, we demonstrated a proof of concept and now Federation ships are being equipped with the Baird‑Prymaat ShieldSaw. Works a treat on Klingon and Romulan shielding. So thank you.”

“My pleasure. Where are you now?”

“I’m on a research ship called the Invigilator. We’re orbiting black hole number 77203 in our catalog. We call it ‘Lonesome‘.”

“Why that name?”

“Because there’s so little other matter in the space nearby. The poor thing barely has an accretion disk.”

“Sounds boring.”

“No, it’s exciting, because it’s so close to a theoretical ideal. It’s like the perfectly flat plane and the frictionless pulley — in real life there are always irregularities that the simple equations can’t account for. For black holes, our only complete solutions assume that the collapsed star is floating in an empty Universe with no impinging gravitational or electromagnetic fields. That doesn’t happen, of course, but Lonesome comes close.”

“But if we understand the theoretical cases and it nearly matches one, why bother with it at all?”

“Engineering reasons.”

“You’re engineering a black hole?”

“In a way, yes. Or at least that’s what we’re working on. We think we have a way to extract power from a black hole. It’ll supply inexhaustible cheap energy for a new Star Fleet anti‑matter factory. “

“I thought the only thing that could escape a black hole’s Event Horizon was Hawking radiation, and it cheats.”

“Gravity escapes honestly. Its intense field generates some unexpected effects. Your physicist Roger Penrose used gravity to explain the polar jets that decorate so many compact objects including black holes. He calculated that if a comet or an atom or something else breakable shatters when it falls into a spinning compact object’s gravitational field, some pieces would be trapped there but under the right conditions other pieces would slingshot outward with more energy than they had going in. In effect, the extra energy would come from the compact object’s angular momentum.”

“And that’s what you’re planning to do? How are you going to trap the expelled pieces?”

“No, that’s not what we’re planning. Too random to be controlled with our current containment field technology. We’re going pure electromagnetic, turning Lonesome into a giant motor‑generator. We know it has a stable magnetic field and it’s spinning rapidly. We’ll start by giving Lonesome some close company. There’s enough junk in its accretion disk for several Neptune‑sized planets. The plan is to use space tugs to haul in the big stuff and Bussard technology for the dust, all to assemble a pair of Ceres-sized planetoids. W’re calling them Pine and Road. We’ll park them in a convenient equatorial orbit in a Lagrange‑stable configuration so Pine, Road and Lonesome stay in a straight line.”

“Someone’s been doing research on old cinema.”

“The Interstellar Movie Database. Anyhow, when the planetoids are out there we string conducting tractor beams between them. If we locate Pine and Road properly, Lonesome’s rotating magnetic field lines will cross the fields at right angles and induce a steady electric current. Power for the anti‑matter synthesizers.”

“Ah, so like Penrose’s process you’re going to drain off some of Lonesome‘s rotational kinetic energy. Won’t it run out?”

“Lonesome‘s mass is half again heavier than your Sun’s, Mr Moire. It’ll spin for a long, long time.”

“Umm … that ‘convenient orbit.’ Lonesome‘s diameter is so small that orbits will be pretty speedy. <calculating quickly with Old Reliable> Even 200 million kilometers away you’d circle Lonesome in less than 15 minutes. Will the magnetic field that far out be strong enough for your purposes?”

“Almost certainly so, but the gravimagnetodynamic equations don’t have exact solutions. We’re not going to know until we get there.”

“That’s how research works, all right. Good luck.”

~~ Rich Olcott

To Swerve And Project

On By rolcottIn Astronomy: Planetary Science, Physics: Light and Relativity, UncategorizedLeave a comment

A crisp Fall dawn, crisp fallen leaves under my feet as I jog the path by the park’s lake.

“Hey! Moire! How about these red sunrises and sunsets? Remind you of Mars?”

“Morning, Mr Feder. Not much, and definitely not dawn or dusk. Those tend more to blue, as a matter of fact.”

“Waitaminnit, Moire. I seen that Brad Pitt Martian movie, him driving hisself all alone across that big plain — the place is blood‑red.”

“Think a minute, Mr Feder. If he was all alone, who was running the cameras?”

“Uhhh, right. Movie. Yeah, they were really on Earth so they could director the lighting and all. But they said they’d scienced the … heck out of it.”

“Oh they did, better than most movies, but artistic license took over in a couple of places. People expect Mars to be red, not mostly clay colored like it really is, so the producers served up red.”

“Wait, I remember the conversation about Earth is blue because of the oceans and Mars is red because of its rusty atmosphere. So what’s with the sky colors?”

“Looking up at sunlight through an atmosphere is very different from looking down at the surface. It all has to do with how what’s in the atmosphere interacts with sunlight. Take Earth’s blue sky, for instance.”

“My favorite color.”

“Sure it is. OK, the Sun’s disk takes up much less than 1% of the sky but that’s enough to give us all our sunlight photons. A fraction of them run into something on the way down to Earth’s surface. What happens depends on how big the something is compared to the photon wavelength. Much larger things, maybe an airplane, completely block the photons and we get a shadow.”

“Obviously.”

“Yeah, but life’s more interesting for smaller somethings. For things like air molecules and dust particles that are much smaller than the the wavelength of visible light, the waves generally swerve around the particle. How much they swerve depends on the wavelength — extreme blue light bends about ten times more than extreme red light for the same scattering particle. So suppose there’s a kid a few miles away from us looking at the sky while we’re looking at it here. There’s a sunbeam with a rainbow‑load of photons headed for the kid, but there are dust particles in the way. Get the picture?”

“Sure, sure, get on with it.”

“So some of the light swerves. The red swerves a little but the blue light swerves ten times as much, enough that it heads straight for us. What color do we see when we look in that direction?”

“Blue, of course.”

“Blue everywhere in the lit‑up sky except when we look straight at the Sun.”

“What about these pretty red sunsets and the red skies over the wildfires?”

“Two different but related phenomena. Sunsets first. An incoming photon with just the right wavelength may simply be absorbed by a molecule. Doesn’t happen often, but there’s lots of molecules. Turns out that oxygen and ozone absorb blue light more strongly than red light. When we’re looking horizontally towards a sunset we’re looking through many more oxygen molecules than when we look vertically. We see the red part of a blue‑filtered version of that swerve rainbow.”

“And the fire skies?”

“The fires released huge amounts of fine smoke particles, just the right size for color‑scattering. Blue light swerves again and again until it’s either absorbed or shot out to space. Red light survives.”

Upper image – Golden Gate Bay under fiery skies, Sept 2020
Lower image – Sunset from Gusev Crater, Mars
Credit: NASA/JPL/Texas A&M/Cornell

“So what’s different about Mars?”

“Three things — Mars dust is different from Earth’s, its atmosphere is a lot thinner, and there’s practically no atmospheric water or oxygen. Rusty Mars dust is the size of smoke particles. With no rain or snow to settle out the dust, it stays aloft all the time. Rust is red because it absorbs blue light and reflects only the red part. With less diffused sunlight, Mars’ sky is basically the black of space overlaid with a red tint. Sunsets are blue‑ish because what blue light there is can travel further.”

“Earth skies are better.”

~~ Rich Olcott

Traffic Control

On By rolcottIn Physics: Fundamentals, Space Travel, UncategorizedLeave a comment

Jeremy Yazzie @jeremyaz
hi @symoire, this is jeremy. ive been reading about the osiris‑rex mission to astrroid bennu and how they’re bringing back a sample – so complicated – fancy robot arm, n2 squirter, air‑cleaner thingy – y not just vacuum the dust or pick up a rock?

Sy Moire @symoire
@jeremyaz – quick answer is that Bennu and OSIRIS-REx are already surrounded by the vacuum of space. Sample collectors can’t suck any harder that that. I’ll email you a more complete answer later

Hi, Sy, can you believe this weather? Temps last week were twice today’s high.

Not to a physicist, Sis.
Those 90s and today’s 45 are just Fahrenheit scale numbers.
Can’t do ratios between them, “twice” does not compute.
I don’t suppose it would help if we went centigrade and said last week’s highs were around 35 and today it’s 5?

No, that’s worse, today’s down by 85% from last week.

Centigrade’s another scale you can’t do ratio arithmetic in. Kelvins is the way to go.
Temp in K tracks the average molecular kinetic energy.
Starts at zero where nothing’s moving and rises in proportion.
Last week’s highs ran around 308 K, today is 278 K.
Today we’re only 10% cooler than last week.

Physicists! Grrrr. However you measure the weather, it still feels cold. No picnic this weekend ;^(

From: Sy Moire <sy@moirestudies.com>
To: Jeremy Yazzie <jeremyaz@college.edu>
Subj: OSIRIS-REx

Jeremy –

OK, now I’m back at the office I’ve got better tech for writing long answers.

First, the “grab a rock” idea has several issues

  • If you pick up a rock, you only have that rock, says nothing about any of its neighbors or the subsurface material it might have smacked into. Dust should be a much better representation of the whole asteroid.
  • The rock might not be willing to be picked up. When the scientists and engineers were planning the OSIRIS‑REx mission, they didn’t know Bennu’s texture — could be one solid rock or a bunch of middle‑size rocks firmly cemented together or a loose “rubble pile” of all‑size rocks and dust held together by gravity alone, or anything in between.
  • Have you ever played one of those arcade games where you try to pick up a toy with a suspended claw gadget and all you’ve got is a couple of control knobs and a button? Picking up a specific rock, even a willing one, is hard when you’re a robot operating 15 light‑minutes away from the home office.

So dust it is, but how to plan dust collection in low gravity when you know nothing about the texture? Something like a whisk broom and dust pan would work unless the surface is too uneven. Something like a drill or disk sander would be good, except to use either one you need a solid footing to work from or else you go spinning one way when the tool spins the other. (That was a problem on the International Space Station.) The Hayabusa2 mission to asteroid Ryugu used a high‑velocity impactor to create dust, but a bad ricochet or shrapnel could kill the OSIRIS‑REx mission. The planners decided that best alternative was puff‑and‑grab.

So why not an astronautical Roomba that just sucks in the dust? The thing about vacuum is that it’s a place where gas molecules aren’t. Suppose you’re a gas molecule. You’re surrounded by your buddies, all in motion and bouncing off of each other like on a crowded 3‑D dance floor. You stay more‑or‑less in place because you’re being hit more‑or‑less equally from every direction. Suddenly there’s a vacuum to one side. You’re not hit as much over there so that’s the direction you and a bunch of your buddies move. If you encounter a dust particle, it picks up your momentum and moves toward the emptiness where it could be trapped in somebody’s filter.

The planners decided to capture dust particles by entraining them in a flow of gas molecules through a filter. To make gas flow you need more gas on one side then the other. Gas molecules being few and far between in space, the obvious place to put your pusher gas is inside the filter. Hence the nitrogen squirt technique and the “air‑cleaner thingy.”

— Sy

Diagram of TAGSAM in operation
Adapted from asteroidmission.org/?attachment_id=1699
Credit: University of Arizona

~~ Rich Olcott

Free Energy, or Not

On By rolcottIn Cosmology, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

From: Richard Feder <rmfeder@fortleenj.com>
To: Sy Moire <sy@moirestudies.com>
Subj: Questions

What’s this about “free energy”? Is that energy that’s free to move around anywhere? Or maybe the vacuum energy that this guy said is in the vacuum of space that will transform the earth into a wonderful world of everything for free for everybody forever once we figure out how to handle the force fields and pull energy out of them?

From: Sy Moire <sy@moirestudies.com>
To: Richard Feder <rmfeder@fortleenj.com>
Subj: Re: Questions

Well, Mr Feder, as usual you have a lot of questions all rolled up together. I’ll try to take one at a time.

It’s clear you already know that to make something happen you need energy. Not a very substantial definition, but then energy is an abstract thing it took humanity a couple of hundred years to get our minds around and we’re still learning.

Physics has several more formal definitions for “energy,” all clustered around the ability to exert force to move something and/or heat something up. The “and/or” is the kicker, because it turns out you can’t do just the moving. As one statement of the Second Law of Thermodynamics puts it, “There are no perfectly efficient processes.”

For example, when your car’s engine burns a few drops of gasoline in the cylinder, the liquid becomes a 22000‑times larger volume of hot gas that pushes the piston down in its power stroke to move the car forward. In the process, though, the engine heats up (wasted energy), gases exiting the cylinder are much hotter than air temperature (more wasted energy) and there’s friction‑generated heat all through the drive train (even more waste). Improving the drive train’s lubrication can reduce friction, but there’s no way to stop energy loss into heated-up combustion product molecules.

Two hundred years of effort haven’t uncovered a usable loophole in the Second Law. However, we have been able to quantify it. Especially for practically important chemical reactions, like burning gasoline, scientists can calculate how much energy the reaction product molecules will retain as heat. The energy available to do work is what’s left.

For historical reasons, the “available to do work” part is called “free energy.” Not free like running about like ball lightning, but free in the sense of not being bound up in jiggling heated‑up molecules.

Vacuum energy is just the opposite of free — it’s bound up in the structure of space itself. We’ve known for a century that atoms waggle back and forth within their molecules. Those vibrations give rise to the infrared spectra we use for remote temperature sensing and for studying planetary atmospheres. One of the basic results of quantum mechanics is that there’s a minimum amount of motion, called zero‑point vibration, that would persist even if the molecule were frozen to absolute zero temperature.

There are other kinds of zero‑point motion. We know of two phenomena, the Casimir effect and the Lamb shift, that can be explained by assuming that the electric field and other force fields “vibrate” at the ultramicroscopic scale even in the absence of matter. Not vibrations like going up and down, but like getting more and less intense. It’s possible that the same “vibrations” spark radioactive decay and some kinds of light emission.

Visualize space being marked off with a mesh of cubes. In each cube one or more fields more‑or‑less periodically intensify and then relax. The variation strength and timing are unpredictable. Neighboring squares may or may not sync up and that’s unpredictable, too.

The activity is all governed by yet another Heisenberg’s Uncertainty Principle trade‑off. The stronger the intensification, the less certain we can be about when or where the next one will happen.

What we can say is that whether you look at a large volume of space (even an atom is ultramicroscopicly huge) or a long period of time (a second might as well be a millennium), on the average the intensity is zero. All our energy‑using techniques involve channeling energy from a high‑potential source to a low‑potential sink. Vacuum energy sources are everywhere but so are the sinks and they all flit around. Catching lightning in a jar was easy by comparison.

Regards,
Sy Moire.

~~ Rich Olcott

Too Many Schrödingers

On By rolcottIn Uncategorized, Cosmology, Physics: Quantum Mechanics, Crazy TheoriesLeave a comment

Cathleen takes back control of the conference software. “Thanks, Jim. OK, the final contestant in our online Crazy Theories contest is the winner of our last face-to-face event where she told us why Spock and horseshoe crabs both have green blood. You’re up, Amanda.”

“Thanks, and hello out there. I can’t believe Jim and I are both talking about parallel universes. It’s almost like we’re thinking in parallel, right?”

<Jim’s mic is muted so he makes gagging motions>

“We need some prep work before I can talk about the Multiverse. I’m gonna start with this heat map of North America at a particular time. Hot in the Texas panhandle, cool in British Columbia, no surprise. You can do a lot with a heat map — pick a latitude and longitude, it tells you the relative temperature. Do some arithmetic on the all numbers and you can get average temperature, highs and lows, front strength in degrees per mile, lots of stuff like that.

“You build this kind of map by doing a lot of individual measurements. If you’re lucky you can summarize those measurements with a function, a compact mathematical expression that does the same job — pick a latitude and longitude, it tells you the value. Three nice things about functions — they take up a lot less space than a map, you can use straightforward mathematical operations on them so getting statistics is less work than with a map, and you can form superpositions by adding functions together.”

Cathleen interrupts. “Amanda, there’s a question in the chat box. ‘Can you give an example of superposition?’“

“Sure. You can superpose simple sine‑wave functions to describe chords for sound waves or blended colors for light waves, for instance.

“Now when we get to really small‑scale thingies, we need quantum calculations. The question is, what do quantum calculations tell us? That’s been argued about for a hundred years because the values they generate are iffy superpositions. Twenty percent of this, eighty percent of that. Everybody’s heard of that poor cat in Schrödinger’s box.

“Many researchers say the quantum values are relative probabilities for observing different results in an experiment — but most of them carefully avoid worrying about why the answers aren’t always the same. Einstein wanted to know what Bohr was averaging over to get his averages. Bohr said it doesn’t matter, the percentages are the only things we can know about the system and it’s useless to speculate further.

“Hugh Everett thought bigger. He suggested that the correct quantum function for an observation should include experiment and experimenter. He took that a step further by showing that a proper quantum function would need to include anyone watching the experimenter and so on. In fact, he proposed, maybe there’s just one quantum function for the entire Universe. That would have some interesting implications.

“Remember Schrödinger’s catbox with two possible experimental results? Everett would say that his universal quantum function contains a superposition of two component sub-functions — happy Schrödinger with a live kitty and sad Schrödinger with a disposal problem. Each Schrödinger would be quite certain that he’d seen the definite result of a purely random operation. Two Schrödingers in parallel universes going forward.

“But in fact there’d be way more than two. When Schrödinger’s eye absorbs a photon, or maybe doesn’t, that generates another pair of universes. So do the quantum events that occur as his nerve cells fire, or don’t. Each Schrödinger moves into the future embedded in a dense bundle of parallel universes.”

Cathleen interrupts. “Another question. ‘What about conservation of mass?‘”

“Good question, whoever asked that. Everett doesn’t address that explicitly in his thesis, but I think he assumed the usual superposition math. That always includes a fix‑up step so that the sum of all the pieces adds up to unity. Half a Schrödinger mass on one track and half on the other. Even as each of them splits again and again and again the total is still only one Schrödinger‑mass. There’s other interpretation — each Schrödinger’s universe would be independent of the others so there’s no summing‑up to generate a conservation‑of‑mass problem. Your choice.

“Everett traded quantum weirdness for a weird Universe. Not much of a trade-off, I think.”

~~ Rich Olcott

The Sound of Money

On By rolcottIn Physics: Money, Physics: Waves, UncategorizedLeave a comment

<chirp, chirp> “Moire, here, there’ll be a late-night surcharge for this call.”

“Hiya, Sy, it’s me, Vinnie. Got a minute? I wanna run something past you.”

“Sure, if it’s interesting enough to keep me awake.”

“It’s that Physics-money hobby horse you’ve been riding. I think I’ve got another angle on it for you.”

“Really? Shoot.”

“OK, a while ago you and me and Richard Feder talked about waves and how light waves and sound waves are different because light waves make things go up-and-down while the waves go forward but sound waves go back-and-forth.”

“Transverse waves versus compression waves, uh-huh.”

“Yeah and when you look close at a sound wave what you see is individual molecules don’t travel. What happens is like in a pool game where one ball bumps another ball and it stops but the bumped ball moves forward and the first ball maybe even moves back a little.”

“The compression momentum carries forward even though the particles don’t, right.”

“And that means that sound waves only travel as fast as the air molecules can move back and forth which is a lot slower than light waves which move by shaking the electric field. I got that, but why doesn’t sound move a lot faster in something like iron where the atoms don’t have to move?”

“Oh, it does, something like 200 times faster than in air. There’s a couple of factors in play. It all goes back to Newton —”

“Geez, he had a hand in everything Physics, didn’t he?”

“Except for electromagnetism and nuclear stuff. The available technology was just too primitive to let him experiment in those areas. Anyway, Newton discovered a formula connecting the speed of sound in a medium to its density. Like his Law of Gravity, it worked but he didn’t know why it worked. Also like gravity, we’ve got a better idea now.”

“What’s the better idea?”

“The key notions weren’t even invented until decades after Newton’s Principia was published. The magic words are the particulate nature of matter and intermolecular stiffness.”

“Hah?”

“One at a time. Newton was a particle guy to an extent. He believed that light is made of particles, but he didn’t take the next step to thinking of all matter as being made of particles. But it is, and the particles interact with each other. Think of it as stickiness. How effective the stickiness is depends on the temperature and which molecules you’re talking about. Gas molecules have so much kinetic energy relative to their sticky that they mostly just bounce off each other. In liquids and solids the molecules stay close enough together that the stickiness acts like springs. The springs may be more or less stiff depending on which molecules or ions or atoms are involved.”

“I see where you’re going. Stuff with stiffer springs doesn’t move as much as looser stuff at the same temperature; sound goes faster through a solid than through a liquid or gas. That’s what Newton figured out, huh?”

“No, he just measured and said, basically, ‘here’s the formula.‘ Just like with gravity, he didn’t suggest why the numbers were what they were. <yawn> So, you called with an idea about sound and money physics.”

“Right. Got off the track there, but this was helpful. What got me started was some newscaster saying how the Paycheck Protection Program is dumping money into the economy during the pandemic. My first thought was, ‘Haw, that’s gotta be a splash!‘ Then I imagined this pulse of money sloshing back and forth like a wave and that led me to sound waves and then I kept going. No dollar bill moves around that much, but when people spend them that’s like the compression wave moving out.”

“Interesting idea, Vinnie. From a Physics perspective, the question is, ‘How fast does the wave move?’ It’s another temperature‑versus‑stickiness thing.”

“Yeah, I figure money velocity measures the economy like temperature measures molecule motion. Money velocity goes up with inflation. If the velocity’s high people spend their money because why not.”

“Yup. From the government’s perspective the whole purpose of economic stimulation is getting the cash flowing again. Their problem is locating the money velocity kickover point.”

~~ Rich Olcott

Spare Change And Silly Putty

On By rolcottIn Physics: Money, UncategorizedLeave a comment

“Ok, Sy, you said Pascal explained the ‘water seeks its level‘ thing before Newton got a chance to. Newton was so smart, though — how’d Pascal beat him to it?”

“Pass me a strawberry scone, Al, and I’ll tell you why.”

“Anything for free food, eh, Sy? Alright, here.”

“Oferpitysake, Al, add it to my tab like always. Too much hassle putting on this face mask just to walk from my car to the scones. Pascal had a 20‑year head start — did his hydrostatics work when Newton wasn’t even in his teens. Unfortunately, Pascal died when Newton was only half-way through college. Whoa, if only Pascal had been alive and productive in France while Newton was in his science years in England and Leibniz was churning at everything in northern Germany. What advances might they have made arguing with each other? Where would our Math and Physics be today?”

“They didn’t like each other?”

“Newton didn’t like anybody. He and Leibniz feuded for decades over who invented calculus. Pascal and Leibniz probably would have gotten along fine — Leibniz could make nice with everyone except Newton. Come to think of it, Newton and Pascal had a lot in common. Newton was a preemie and Pascal was seriously ill for the first year of his life, never got much better. Newton wrote his first formal paper at 22; Pascal publicly proved that vacuums exist by creating some when he was 24. On the flip side, Pascal was 33 when he presented his studies of what we now call the Pascal Triangle but Newton waited until he was 44 to publish his Principia. And each of them spent much of the final quarter of his life on religious, even mystical matters.”

“So did Newton and Pascal both do much about money and water?”

“Not about the combination, though both had a lot to do about each one. Newton was Master of England’s Royal Mint and spent much of his time in office chasing down counterfeiters. Pascal wasn’t a gambler but Fermat was and the two of them teamed up to invent the probability theories that power today’s gaming, finance and insurance industries. So there’s that. Pascal and Newton both pioneered the science of fluids but from different perspectives. Pascal looked at static situations — comparing atmospheric pressure at two different altitudes, that sort of thing. Newton, as usual, studied change — in this case how fluids flow.”

“Pour water into a pipe and it pours out the other end. What’s to study?”

“Measuring how fast it pours and how that’s affected by the pressure and the pipe and what’s being poured. Newton explored the motion of fluids in exhausting detail in Book II of his Principia. As you’d expect, he found that the flow rate of water or any of the other fluids he investigated rises with the pressure and with the cross-sectional area of the pipe. Being Newton, though, he also also considered forces that resist flow. Think about it — the pipe itself doesn’t move and neither does the layer of fluid right next to the pipe’s walls. The flow rate ramps up from zero at the walls to full-on at the center of the pipe. The ramp-up rate depends on the fluid’s viscosity, another concept that Newton discovered or invented depending on how you look at it. Viscosity measures the drag force the slower layers exert on their faster neighbors. Fluids like molasses are viscous because their molecules are really good at grabbing onto molecules in the layers next door.”

“Where’s money fit into this picture?”

“I’m getting to that. Newton thought that each kind of fluid had its own viscosity, always the same. Not quite — temperature makes a difference and there’s non‑Newtonian materials like Silly Putty whose viscosity depends on how fast you yank on them. But the weirdest non‑Newtonian fluid is ultra‑low‑temperature liquid helium. It’s a superfluid and has zero viscosity. The helium atoms experience absolutely no drag from their neighbors and can sneak through the tiniest cracks. Money does the same, right? Each dime and dollar flows with no drag from its cousins.”

“Money’s a superfluid?”

“Yup. Think how it leaks out of your pocket.”

“Uh-huh. … Hey, Sy, about that tab…”

~~ Rich Olcott

A Turn to The Urn

On By rolcottIn Physics: Money, UncategorizedLeave a comment

Working under social distancing rules, Al’s selling coffee from a drive-up cart in front of his shop — urns, paper cups, everything at arms length. No cash register, credit or debit transactions only. “Give me my usual, Al. I miss the mugs; your brews just don’t taste the same in paper.”

“I know, Sy, but what can you do? Say, I’ve been reading your stuff with the sort‑of overlaps between Physics and Economics. Beyond your usual orbital? <heh, heh>”

“Very funny, Al. Yeah, a little, but it’s giving me some new perspectives on old ground.”

“Oh, yeah? What’s next?”

“Fluid mechanics, for instance. Ever notice how many money terms relate to water? ‘Cash flow,’ of course, but there’s also ‘liquidity,’ ‘frozen assets,’ ‘drowning in debt,’ a long list, so I decided to chase that metaphor, see how well it holds up. There’s a lot of Physics on your coffee cart, for instance.”

“Well, it’s heavy, I’ll tell you that.”

“Sure, but how about that glass tube that tells you how full the urn is? The Egyptians were using the principle thousands of years ago but Pascal put it on a firm theoretical basis before Newton got a chance to.”

“There’s theory in that thing?”

“Sure. There’s a pipe from the urn to the little tube, right, so all the liquid is connected. Pascal proved that the pressure on every little packet of fluid anywhere in a connected system has to be the same, otherwise fluid would flow to wherever the pressure is least and even things out. Pressure at the bottom of any skinny vertical column comes from atmospheric pressure plus the pull of gravity on the liquid in that column. It takes 33 feet of water to balance normal atmospheric pressure. For columns the size of your urn gravity’s contribution is less than 3% of atmospheric so the atmosphere rules. Pressure on the tube is the same as pressure on the urn so the two have to be at the same height. When the urn’s low, the tube’s low because Physics.”

“Cool, though when you look at it that way it seems obvious.”

“The good explanations often are. It takes a Pascal or a Newton to make it obvious.”

“So what’s this got to do with Economics?”

“Pascal’s principle supplied a fundamental assumption about how market‑based systems are supposed to work. Not with water, but with money — and instead of pressure there’s profit potential. The idea is that just like water will flow everywhere in a connected system until the pressure is equalized, money will flow everywhere in an economy until no‑one thinks they can make more profit in one place than in another. It’s more complicated than your coffee urn, though.”

“I expect so — lots more opportunities.”

“Well, yes, but the force‑equivalent is more complicated, too. Gravity and atmospheric pressure both exert force in the same direction. When you’re considering an investment, what do you think about?”

“The net profit, of course — how much I could make against what it’ll cost me to get in.”

“How about risk?”

“Three guesses why I’m doing this no-cash. I know what you mean though — like what if this electric cord overheats and burns the place down. Not likely, I checked the wire gauge and the circuit box.”

“Good strategy — look at all the things that can go wrong and address what you can control. But there’s uncontrolables, right? From an Economics perspective, you need to put each risk in money terms. Take the likelihood that something bad will happen, multiply by the monetary loss if it does happen and you get monetary risk you’ve got to figure against that expected net profit. My point is that the Economics version of Pascal’s principle has to take account of forces that pull money towards an investment option AND forces that push money away.”

“Two-way stretch, huh?”

“Absolutely. Take a look at a stock or bond prospectus some day. You’ll see risk categories you’ve never even heard of. Bond analysts have a field day with that kind of stuff. Their job is to calculate likely growth and cash yield against likely risk and come up with a price.”

“Risky business.”

“Always the joker, Al.”

~~ Rich Olcott