Category: Physics

Energy Is A Shape-shifter

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

Another dinner, another pizza at Eddie’s place. Vinnie wanders over to my table. “Hi, Sy, got a minute?”

“Not doing anything other than eating, Vinnie. What’s on your mind other than the sound of my chewing?”

“At least you keep your mouth closed. No, it’s about this energy thing you’ve gotten back into. I read that enthalpy piece and it’s bothering me.”

“In what way?”

“Well, you said that something’s enthalpy is the energy total of ‘thermal plus Pressure‑Volume plus chemical energy,’ right? I’m trying to fit that together with the potential energy and kinetic energy we talked about a while ago. It’s not working.”

“Deep question for dinner time but worth the effort. Would it help if I told you that the ‘actual versus potential’ notion goes back to Aristotle, the ‘kinetic’ idea came from Newton’s enemy Leibniz, but ‘enthalpy’ wasn’t a word until the 20th century?”

“Not a bit.”

“Didn’t think it would. Here’s another way to look at it. The thinkers prior to the mid‑1700s all looked at lumpy matter — pendulums, rolling balls on a ramp, planets, missiles — either alone or floating in space or colliding with each other. You could in principle calculate kinetic and potential energy for each lump, but that wasn’t enough when the Industrial Revolution came along.”

“What more did they want?”

“Fuel was suddenly for more than cooking and heating the house. Before then, all you needed to know was whether the log pile was stocked better than it was last year. If not, you might have a few chilly early Spring days but you could get past that. Then the Revolution came along. Miners loved Watt’s coal‑fired water‑pump except if you bought one and ran out of coal then the mine flooded. The miners learned that some kinds of coal burned hotter than others. You didn’t need as much of the good kind for a day’s pumping. The demand for a coal‑rating system got the scientists interested, but those lumps of coal weren’t falling or colliding, they just sat there with their heat locked inside. The classical energy quantities didn’t seem to apply so it was time to invent a new kind of energy.”

“That’s how Conservation of Energy works? You just spread the definition out a little?”

“That’s the current status of dark energy, for instance. We know the galaxies are moving apart against gravity so dark energy’s in there to balance the books. We have no good idea why it exists or where it comes from, but we can calculate it. ‘Internal energy’ put the Victorian‑era physicists in the same pickle — ‘atom’ and ‘molecule’ were notions from Greek and Roman times but none of the Victorians seriously believed in them. The notion of chemical bond energy didn’t crop up until the twentieth century. Lacking a good theory, all the Victorians could do was measure and tabulate heat output from different chemical reactions, the data that went into handbooks like the CRC. Naturally they had to invent thermodynamics for doing the energy accountancy.”

“But if it’s just book-balancing, how do you know the energy is real?”

“Because all the different forms of energy convert to each other. Think of a rocket going up to meet the ISS. Some of the rocket fuel’s chemical energy goes into giving the craft gravitational potential energy just getting it up there. At the same time, most of the chemical energy becomes kinetic energy as the craft reaches the 27600 km/h speed it needs to orbit at that altitude.”

<grin> “All?”

“Okay, we haven’t figured out how to harness dark energy. Yet.”

“HAW! Wait, how does enthalpy’s ‘chemical+PV+thermal’ work when the pressure’s zero, like out in space?”

“Then no work was done against an atmosphere up there to make way for the volume. Suppose you suddenly transported a jug of fuel from Earth up to just outside of the ISS. Same amount of fuel, so same amount of chemical energy, right? Same temperature so same thermal component?”

“I suppose.”

“The volume that the jug had occupied on Earth, what happened to it?”

“Suddenly closed in, probably with a little thud.”

“The thud sound’s where the Earth‑side PV energy went. It all balances out.”

~ Rich Olcott

New (Old) Word: Frigorific!

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

A quiet morning at Cal’s Coffee. I’m sipping my morning mud when Susan Kim bustles to my table, mocha latte in hand. “There you are, Sy. I loved your posts in tribute to the well‑thumbed copy of the CRC Handbook on my desk.”

“Glad you enjoyed them.”

“Your Rumford stuff made it even better because I did a class report on him once so I caught your ‘frigorific‘ reference. What do you know about the background to that?”

“Not much. Didn’t sound like a real word when I ran across it.”

“Oh, it’s a real word but it has a technical meaning now that it didn’t in Newton’s time. Back then it was only about making something cold. These days we also use the word for a mixture that maintains a dependable cold temperature. Liquid water and ice, for instance, stays at 0°C as long as there’s still ice in the cold bath. I used to use an ammonium chloride/water frigorific when I needed something down around -15°C. Now of course I use a benchtop refrigerator.”

“Rumford would have liked that. What were the ‘frigorific rays‘ he got all excited about?”

“Long story but there’s a couple of fun twists. Background first. At the end of the 1700s there was a <grin> heated debate about heat. The phlogiston theory was dead by that time but people still liked the idea that heat was a material fluid. It addressed some chemical puzzles but heat transmission was still mysterious. Everyone knew that a hot object gives off heat by radiation, that the radiation travels in straight lines and that it’s reflected by metal mirrors.”

“Right, the Greeks are supposed to have used huge sun‑focusing mirrors to burn up attacking Roman ships.”

“Maybe. Anyhow, those properties connected heat with light. However, a pane of glass blocks radiated heat, at least until the glass gets hot. People argued this meant heat and light weren’t connected. About 1790 a group of physicists loosely associated with the Academy of Geneva dove into the fray. Rumford was in the group, along with Prévost, Saussure and his student Pictet. They had lots of fun with heat theories and experiments. One of Pictet’s experiments lit Rumford’s fire, so to speak.”

“Good one.”

<smile> “It’s a fairly simple setup that a high school science teacher could do. Pictet hung a concave metallic mirror facing down from the ceiling of a draft‑free room. He placed another concave metallic mirror at floor level immediately beneath it, facing upward. He probably used spherical mirrors which are easy to make, but they could have been elliptical or parabolic sections. Anyhow, he put a thermoscope at the upper mirror’s focal point and a hot object at the lower focal point. Sure enough, the upper focal point got hotter, just as you’d expect.”

“No great surprise, the Greeks would have expected that, too.”

“The surprise happened when he put a cold object in there. The thermoscope’s droplet moved in the cold direction.”

“Wait, like anti‑infrared?”

“That’s the effect. Wave‑theory supporter Rumford took that thought, called it ‘frigorific radiation‘ and ran with it. He constructed a whole thesis around cold waves and heat waves as symmetric partners. He maintained wave intensity, both kinds, increases with temperature difference. Our heat sources are hundreds or thousand of degrees hotter than we are but our cold sources are at most a few dozen degrees colder. By his theory that’s why cold wave phenomena are masked by heat waves.”

“Give me a minute. … Ah, got it. The very meaning of a focal point is that all waves end or start there. A cold object at the sending station emits much less infrared than the warm object did. The thermoscope bulb now gets less than it emits. With less input from below its net energy drops. It chills.”

“Nice, Sy. Now for the other twist. Rumford published his theory in 1805. Herschel had already identified infrared radiation in the Sun’s spectrum in 1800. Two strikes against Herschel, I guess — he was British and he was an astronomer. Continental physicists wouldn’t bother to read his stuff.”

~ Rich Olcott

Rumford’s Boring Story

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

“Okay, Mr Moire, my grandfather’s engineering handbook has Specific Heat tables because Specific Heat measures molecular wabbling. If he’s got them, though, why’s Enthalpy in the handbook, too?”

“Enthalpy’s not my favorite technical term, Jeremy. It’s wound up in a centuries‑old muddle. Nobody back then had a good, crisp notion of energy. Descartes, Leibniz, Newton and a host of German engineers and aristocratic French hobby physicists all recognized that something made motion happen but everyone had their own take on what that was and how to calculate its effects. They used a slew of terms like vis viva, ‘quantity of motion,’ ‘driving force,’ ‘quantity of work,’ a couple of different definitions of ‘momentum‘ — it was a mess. It didn’t help that a lot of the argument went on before Euler’s algebraic notations were widely adopted; technical arguments without math are cumbersome and can get vague and ambiguous. Lots of lovely theories but none of them worked all that well in the real world.”

“Isn’t that usually what happens? I always have problems in the labs.”

“You’re not alone. Centuries ago, Newton’s Laws of Motion and Gravity made good predictions for planets, not so good for artillery trajectories. Gunners always had to throw in correction factors because their missiles fell short. Massachusetts‑born Benjamin Thompson, himself an artilleryman, found part of the reason.”

“Should I know that name?”

“In later years he became Count Rumford. One of those people who get itchy if they’re not creating something. He was particularly interested in heat — how to trap it and how to make it go where you want.”

“Wait, he was an American but he was a Count? I thought that was illegal.”

“Oh, he left the States before they were the States. During the Revolution he organized a Royalist militia in New York and then lit out for Europe. The Bavarians made him a Count after he spent half‑a‑dozen years doing creative things like reorganizing their army, building public works and introducing potato farming. He concocted a nourishing soup for the poor and invented the soup line for serving it up. But all this time his mind was on a then‑central topic of Physics — what is heat?”

“That was the late 1700s? When everyone said heat was some sort of fluid they called ‘caloric‘?”

“Not everyone, and in fact there were competing theories about caloric — an early version of the particle‑versus‑wave controversy. For a while Rumford even supported the notion that ‘frigorific’ radiation transmitted cold the same way that caloric rays transmitted heat. Whatever, his important contributions were more practical and experimental than theoretical. His redesign of the common fireplace was such an improvement that it took first England and then Europe by storm. Long‑term, though, we remember him for a side observation that he didn’t think important enough to measure properly.”

“Something to do with heat, I’ll bet.”

“Of course. As a wave theory guy, Rumford stood firmly against the ‘caloric is a fluid‘ camp. ‘If heat is material,‘ he reasoned, ‘then a heat‑generating process must eventually run out of caloric.’ He challenged that notion by drilling out a cannon barrel while it was immersed in cold water. A couple of hours of steady grinding brought the water up to boiling. The heating was steady, too, and apparently ‘inexhaustible.’ Better yet, the initial barrel, the cleaned‑out barrel and the drilled‑out shavings all had the same specific heat so no heat had been extracted from anything. He concluded that heat is an aspect of motion, totally contradicting the leading caloric theories and what was left of phlogiston.”

<chuckle> “He was a revolutionary, after all. But what about ‘Enthalpy‘?”

“Here’s an example. Suppose you’ve got a puddle of gasoline, but its temperature is zero kelvins and somehow it’s compressed to zero volume. Add energy to those waggling molecules until the puddle’s at room temperature. Next, push enough atmosphere out of the way to let the puddle expand to its normal size. Pushing the atmosphere takes energy, too — the physicists call that ‘PV work‘ because it’s calculated as the pressure times the volume. The puddle’s enthalpy is its total energy content — thermal plus PV plus the chemical energy you get when it burns.”

~~ Rich Olcott

It’s in The Book

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

A young man’s knock, eager yet a bit hesitant. “Door’s open, Jeremy, c’mon in.”

“Hi, Mr Moire, I’ve got something to show you. It’s from my acheii, my grandfather. He said he didn’t need it any more now he’s retired so he gave it to me. What do you think?”

“Wow, the CRC Handbook of Chemistry And Physics, in the old format, not the 8½×11″ monster. An achievement award, too — my congratulations to your grandfather. Let’s see … over 3000 pages, and that real thin paper you can read through. It’s still got the math tables in front — they moved those to an Appendix by the time I bought my copy. Oooh yeah, lots of data in here, probably represents millions of grad student lab hours. Tech staff, too. And then their bosses spent time checking the work before publishing.”

“Acheii said I’d have to learn a lot before I could use it properly. I see lots of words in there I don’t recognize.” <opens book to a random page> “See, five- and six‑figure values for, what’re Specific Heat and Enthalpy?”

“Your grandfather’s absolutely correct. Much of the data’s extremely specialized. Most techs, including me, have a few personal‑favorite sections they use a lot, never touch the rest of the book. These particular pages, for instance, would be gold for a someone who designs or operates steam‑driven equipment.”

“But what do these numbers mean?”

“Specific Heat is the amount of heat energy you need to put into a certain mass of something in order to raise its temperature by a certain amount. In the early days the Brits, the Scots really, defined the British Thermal Unit as the amount of energy it took to raise the temperature of one pound of liquid water by one degree Fahrenheit. You’d calculate a fuel purchase according to how many BTUs you’d need. Science work these days is metric so these pages tabulate Specific Heat for a substance in joules per gram per °C. Tech in the field moves slow so BTUs are still popular inside the USA and outside the lab.”

“But these tables show different numbers for different temperatures and they’re all for water. Why water? Why isn’t the Specific Heat the same number for every temperature?”

“Water’s important because most power systems use steam or liquid water as the working fluid or coolant. Explaining why heat capacity varies with temperature was one of the triumphs of 19th‑century science. Turns out it’s all about how atomic motion but atoms were a controversial topic at the time. Ostwald, for instance—”

“Who?”

“Wilhelm Ostwald, one of science’s Big Names in the late 1800s. Chemistry back then was mostly about natural product analysis and seeing what reacted with what. Ostwald put his resources into studying chemical processes themselves, things like crystallization and catalysis. He’s regarded as the founder of Physical Chemistry. Even though he invented the mole he steadfastly maintained that atoms and molecules were nothing more than diffraction‑generated illusions. He liked a different theory but that one didn’t work out.”

“Too bad for him.”

“Oh, he won the first Nobel Prize in Chemistry so no problem. Anyway, back to Specific Heat. In terms of its molecules, how do you raise something’s temperature?”

“Um, temperature’s average kinetic energy, so I’d just make the molecules move faster.”

“Well said, except in the quantum world there’s another option. The molecules can’t just waggle any which way. There are rules. Different molecules do different waggles. Some kinds of motion take more energy to excite than others do. Rule 1 is that the high‑energy waggles don’t get to play until the low‑energy ones are engaged. Raising the temperature is a matter of activating more of the high‑energy waggles. Make sense?”

“Like electron shells in an atom, right? Filling the lowest‑energy shells first unless a photon supplies more energy?”

“Exactly, except we’re talking atoms moving within a molecule. Smaller energies, by a factor of 100 or more. My point is, the heat capacity of a substance depends on which waggles activate as the temperature rises. We didn’t understand heat capacity until we applied quantum thinking to the waggles.”

“What about ‘Enthalpy’ then?”

Crystal photo by JJ Harrison

~ Rich Olcott

The Spaghettification Zone

On By rolcottIn Physics: Newton and Gravity, UncategorizedLeave a comment

Vinnie’s still wincing. “That neutron star pulling all the guy’s joints apart — yuckhh! So that’s spaghettification? I thought that was a black hole thing.”

“Yes and no, in that order. Spaghettification’s a tidal phenomenon associated with lopsided gravity fields, black holes or otherwise. You know what causes the tides, of course.”

“Sure, Sy. The Sun pulls up on the water underneath it.”

“That’s not quite it. The Sun’s direct‑line pull on a water molecule is less than a part per million of the Earth’s. What really happens is that the Sun broadly attracts water molecules north‑south east‑west all across the Sun‑side hemisphere. There’s a general movement towards the center of attraction where molecules pile up. The pile‑up’s what we call the tide.”

“What explains the high tide on the other side of the Earth? You can’t claim the Sun pushes it over there.”

“Of course not. It goes back to our lopsided taste of the Sun’s gravitational field. If it weren’t for the Sun’s pull, sea level would be a nice round circle where centrifugal force balances Earth’s gravity. The Sun’s gravity puts its thumb on the scale for the near side, like I said. It’s weaker on the other side, though — balance over there tilts toward the centrifugal force, makes for a far‑side bulge and midnight tides. We get lopsided forces from the moon’s gravity, too. That generates lunar tides. The solar and lunar cycles combine to produce the pattern of tides we experience. But tides can get much stronger. Ever hear of the Roche effect?”

“Can’t say as I have.”

“Imagine the Earth getting closer to the Sun but ignore the heat. What happens?”

Cygnus X-1 Illustration
Credit: NASA, CXC, Melissa Weiss (CXC)

“Sun‑side tides get higher and higher until … the Sun pulls the water away altogether!”

“That’s the idea. In the mid‑1800s Édouard Roche noticed the infinity buried in Newton’s F=GMm/r² equation. He realized that the forces get immense when the center‑to‑center distance, r, gets tiny. ‘Something’s got to give!’ he thought so he worked out the limits. The center‑to‑center force isn’t the critical one. The culprit is the tidal force which arises from the difference in the gravitational strength on either side of an object. When the force difference exceeds the forces holding the object together, it breaks up.”

“Only thing holding the ocean to Earth is gravity.”

“Exactly. Roche’s math applies strictly to objects where gravity’s the major force in play. Things like rubble‑pile asteroids like Bennu and Dimorphos or a black hole sipping the atmosphere off a neighboring blue supergiant star. We relate spaghettification to rubble piles but it can also compete with interatomic electronic forces which are a lot stronger.”

“You’re gonna get quantitative, right?”

“Of course, that’s how I operate.” <tapping on Old Reliable’s screen> “Okay, suppose Niven’s guy Shaffer is approaching some object from far away. I’ve set up tidal force calculations for some interesting cases. Turns out if you know or can estimate an object’s mass and size, you can calculate its density which is key to Roche’s distance where a rubble pile flies apart. You don’t need density for the other thresholds. Spagettification sets in when tidal force is enough to bend a molecule. That’s about 500 newtons per meter, give or take a factor of ten. I estimated the rip‑apart tidal force to be near the tensile strength of the ligaments that hold your bones together. Sound fair?”

“Fair but yucky.”

“Mm‑hm. So here’s the results.”

“What’s with the red numbers?”

“I knew you’d ask that first. Those locations are inside the central object so they make no sense physically. Funny how Niven picked the only object class where stretch and tear effects actually show up.”

“How come there’s blanks under whatever ‘Sgr A*’ is?”

“Astronomer‑ese for ‘Sagittarius A-star,’ the Milky Way’s super‑massive black hole. Can’t properly calculate its density because the volume’s ill‑defined even though we know the Event Horizon’s diameter. Anyhow, look at the huge difference between the Roche radii and the two thresholds that affect chemical bonds.”

“Hey, Niven’s story had Shaffer going down to like 13 miles, about 20 kilometers. He’d’ve been torn apart before he got there.”

“Roughly.”

~~ Rich Olcott

Stretch

On By rolcottIn Physics: Newton and Gravity, Space Travel, Uncategorized2 Comments

It’s a chilly day as I take my favorite elevator up to my office on the Acme Building’s 12th floor. Vinnie’s on my sofa, reading an old paperback. “Morning, Sy. Whaddaya think of Larry Niven?”

“One of the grand old men of hard science fiction. I gather you’re reading something of his there?”

“Yup, been bingeing on his Known Space series. His Neutron Star short story here won a Hugo back in 1967. It’s got so many numbers I wonder how good they are.”

“Probably pretty good. He and Heinlein both enjoyed showing off their celestial mechanics chops. What numbers stick out to you? Wait, what’s the story line again?”

“Story line? Most of Niven’s shorts were puzzles. When he had a good one he’d wrap some hokey story around it. This one, there’s a magical space ship that’s supposed to be invulnerable. Says here nothing can get through the hull, ‘no kind of electromagnetic energy except visible light. No kind of matter, from the smallest subatomic particle to the fastest meteor’ except something reached in and squashed two people to death in the nose of their ship. Our hero Mr Shaeffer’s in a ship just like theirs and has to figure out what the something was before it gets him, too.”

“Ah. What numbers did Niven give us?”

“Shaeffer’s ship was heading towards a neutron star. Lessee… ah, says the star’s mass is 1.3 times the Sun’s, diameter’s about 12 miles, and the ship’s on a fast in‑and‑out orbit, closest approach just a mile above the surface. Oh, and early on he drifts forward like something’s pulling on him but not on the ship. What does that tell you?”

“Enough to solve the puzzle, not enough to check his numbers. Anything about speed?”

“Mmm, he says the ship popped into the system a million miles out and it’d take 12 hours to reach the close‑approach point. The average speed’s just arithmetic, right?”

“Not really. A simple average doesn’t take account of acceleration changes or relativity effects. It’s easier and more accurate to apply conservation of energy. Okay with you if I assume the ship ‘pops into the system’ with zero velocity relative to the star and then free‑falls towards it?”

“That fits with the story, mostly.”

“Good. So right after the pop‑in” <tapping on Old Reliable’s screen> “the ship’s gravitational potential energy is ‑1.08×105 joules/kilogram—”

“Negative?”

“It’s defined as the potential energy Shaeffer’d gave up en route from infinitely far away. At 13 miles from the star’s center, that’s zoomed to ‑8.3×109 J/kg. The potential energy’s converted to kinetic energy ½mv² except we’re talking per kilogram so m is 1.0 and the velocity is —whoa!— 129 thousand kilometers/second. That’s 43% of lightspeed!”

“Well, Shaeffer did see the background stars shift blue even before he got deep into the gravity well. So, how about Niven’s 12‑hour, million‑mile claim?”

“That distance in that time works out to 37 miles per second, way less than lightspeed’s 186 000. Shaeffer was dawdling. You need calculus to figure the actual travel time — integrate 1/v between here and there. Ugly problem to solve manually but Old Reliable’s up to it. Given the appropriate orbit equation and the numbers we’ve worked out so far, Old Reliable says the trip should have taken him about 17 seconds.”

“HAW! I knew something seemed off. Wait, you said you’d solved the puzzle. What’s your answer?”

“Tides. That’s what moved him forward relative to the ship.”

“Yeah, that’s what Niven wrote, but I don’t see why what Shaeffer did saved him.”

“What did Shaeffer do?”

“Spread-eagled himself across a gangway at the ship’s center of gravity.”

“Brilliant — minimized his thickness along the star‑to‑ship line. Gravity’s pull on his sternum wasn’t much different from the pull on his spine. If he’d oriented himself perpendicular to that, his feet would feel a stronger pull than his head would have. Every transverse joint from neck to ankles would crackle or even tear. Talk about chiropractic.”

Vinne winces. “Why does thickness matter?”

“Tidal force reflects how center‑to‑center force changes with distance. Center‑to‑center force rises with 1/r². Tidal force goes up as 1/r³. Cube grows faster than square. Small r, big tides.”

~ Rich Olcott

Competing Curves

On By rolcottIn Mathematics, Physics: Fundamentals, UncategorizedLeave a comment

It’s still October but there’s a distinct taste of oncoming November in the air — grey, gusty with a moist chill as I step into Cal’s coffee shop. “You’re looking a bit grumpy, Cal.”

“Sure am, Sy. Some lady come in here, wanted pumpkin spice. The nerve! I sell good honest high‑quality coffee, special beans and everything, no goofy flavors. You want peppermint or apple brown betty, go down to the mermaid place. Here’s your mugfull, double‑dark as always. By the way, fair warning — Richard Feder’s in town and looking for you. He’s at that corner table.”

“Thanks, Cal.” <sound of footsteps> “Morning, Mr Feder. How’d things go in Fort Lee?

“Nicely, nicely… I got a question, Moire.”

“Of course you do.”

“I been reading your stuff, you had a graph in one post looks just like the graph in a different post. Here, I printed ’em out. What’s up with that?”

“But they plot entirely different things, brightness against distance in one, atom loss against time in the other, completely different equations.”

“Yeah, yeah, but the shapes are the same I don’t care you say they got different equations. Look, they even both go through the same points at x=2 and 4. What’re you trying to pull here?”

“Not pulling anything. Those two curves are similar, yes, but they’re not identical.” <quickly building charts on Old Reliable> “Here, I’ve laid them both on the same axis. For good measure I’ve extended the x‑axis into a second panel with a stretched‑out y‑axis. What do you see?”

“Well, the orange one goes up and stops but it looks like the blue one’s headed for the sky.”

“It is. But where on the x-axis do those things happen?”

“Zero and one. Okay so the blue line squoze in a little.”

“How about out there at the x=8 end? Looks like they’re close, I’ll grant you, but check the y‑values at at the left of the second panel.”

“Uhh… Looks like blue’s four times higher than orange. Then the orange line flattens out but the blue line not so much.”

“Mm‑hm. So they behave differently at that end, too.”

“Yeah, but what about in the middle here” <jabs finger at Old Reliable’s screen> “where they’re real close and even cross over each other a couple times and you could just draw a straight line?”

“You’ve put your finger on something that challenges every theoretician and research experimentalist who works in a quantitative field. How do you connect the dots? Sure, you can eyeball a straight line through observed points sometimes, there are even statistical techniques for locating the best possible straight line, but is a straight line even appropriate? Sometimes it is, sometimes it’s not, and often we don’t know.”

“How can you not know? Everything starts with a straight line, shortest distance between two points, right?”

“Only if they’re the right points. Real observations are always uncertain. Lenses are never perfect, adjustment screws have a little bit of play, detector pixels are larger than a perfect point would be, whatever. Good experimentalists put enormous amounts of time and care into eliminating or at least controlling for every imaginable error source, but perfect measurements just don’t happen.”

“So it’ll be a fuzzy straight line.”

“For some range of ‘fuzzy’, mm‑hm. Now we get into the theory issues. We’ve already seen the simplest one — range of validity. Your straight‑line approximation might be good enough for some purposes in the x‑range between 2 and 4, but things get out of hand outside of that range.”

“Okay, in graphs. But these two curves both look good. Why choose one over the other?”

“That’s where theory and data collude. Sometimes theories tell us what data to look for, sometimes the data challenges us to develop an explanatory theory, sometimes we just try curve after curve until we find one that works across the full range that experiment can reach but we don’t know why. What’s exciting is when we get to use the data to determine which of several competing theories is the correct one. Or least incorrect.”

“I got other ways to get excited.”

“Of course you do.”

~~ Rich Olcott

The Not-so-dangerous Banana

On By rolcottIn Astronomy: Techniques, Physics: Quantum Mechanics, UncategorizedLeave a comment

“Y’know, Cathleen, both our ladders boil down to time. Your Astronomy ladder connects objects at different times in the history of the Universe. My Geology ladder looks back into the Solar System’s history.”

“As an astronomer I normally think of parsecs or lightyear distances but you have a point, Kareem. Edwin Hubble linked astronomical space with time. Come to think of it, my cosmologist colleagues work almost exclusively in the time domain, like ‘T=0 plus a few lumptiseconds.’ Billions of years down to that teeny time interval — how does your time ladder compare?”

“Lumptiseconds out to a hundred trillion times the age of the Universe. I win.”

“C’mon, Kareem.”

“No, really, Sy. My ladder uses isotopes. Every carbon atom has 6 protons in the nucleus, right? Carbon‑12 adds 6 neutrons and it’s stable but another isotope, carbon‑14, has 8 neutrons. It’s radioactive — spits out an electron and becomes stable nitrogen‑14 with 7 and 7. Really heavy isotopes like uranium‑238 spit out alpha particles.”

“Wait, if carbon‑14 spits out an electron doesn’t that make it a carbon ion?”

“Uh‑uh, Cathleen, the electron comes out of the nucleus, not the electron cloud. It’s got a hundred thousand times more energy than a chemical kick could give it. Sy could explain—”

“Nice try, Kareem, this is your geologic time story. Let’s stay with that.”

“If I must. So, the stable isotopes last forever, pretty much, but the radioactive ones are ticking bombs with random detonation times.”

“What’s doing the ticking? Surely there’s no springs or pendulums in there.”

“Quantum, Cathleen. Sy’s trying to stay out of this so I’ll give you my outsider answer. I picture every kind of subatomic particle constantly trying to leave every nucleus, butting their little heads bazillions of times a second against walls set up by the weak and strong nuclear forces. Nearly every try is a bounce‑back, but one success is enough to break the nucleus. Every isotope has its own personal set of parameters for each kind of particle — wall height, wall thickness, something like an internal temperature ruling how hard the particles hit the walls. The ticking is those head‑butts; the randomness comes from quantum’s goofy rules somehow. How’s that, Sy?”

Chart by Sjlegg, licensed under CC S-A 3.0 unported

“Good enough for jazz, Kareem. Carry on.”

“Right. So every kind of radioisotope is characterized by what kinds of particle it emits, how much energy each kind has after busting through a wall, and how often that happens in a given sample size. And the isotope’s chemistry, of course, which is the same as every other isotope that has the same number of protons. The general rule is that the stable isotopes have maybe a few more neutrons than protons but nearly every element has some unstable isotopes. The ones with too many neutrons, like carbon‑14, emit electrons as beta particles. They go up a square in the Periodic Table. Too few and they drop down by emitting a positron.”

“All those radioactive stand‑ins for normal atoms. Sounds ghastly. Why are we still here and not all burnt up?”

“First, when one of these atoms decays by itself it’s a lot of energy for that one atom, but the energy spreads out as heat across many atoms. Unless a bunch of atoms crumble at about the same time, there’s only a tiny bit of general heating. The major biological danger from radioactivity comes from spit‑out particles breaking protein or DNA molecules.”

“Mutated, not burnt.”

“Mm‑hm. Second, the radioactives are generally rare relative to their stable siblings. In many cases that’s because the bad guys, like aluminum‑26, have had time to decay to near‑zero. That banana you’re eating has about half a gram of potassium atoms but only 0.012% are unstable potassium‑40. Third, an isotope with a long half‑life doesn’t lose many atoms per unit time. A kilogram of tellurium‑128, for instance, loses 2000 atoms per year. The potassium‑40 in your banana has a half‑life of nearly 2 million years. Overall, it releases only about 1300 beta particles per second producing less than a nanowatt of heat‑you‑up power. Not to worry.”

“Two million years? How do you measure something that slow?”

~~ Rich Olcott

Mushy stuff

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

“Amanda! Amanda! Amanda!”

“All right, everyone, settle down for our final Crazy Theorist. Jim, you’re up.”

“Thanks, Cathleen. To be honest I’m a little uncomfortable because what I’ve prepared looks like a follow-on to Newt’s idea but we didn’t plan it that way. This is about something I’ve been puzzling over. Like Newt said, black holes have mass, which is what everyone pays attention to, and charge, which is mostly unimportant, and spin. Spin’s what I’ve been pondering. We’ve all got this picture of a perfect black sphere, so how do we know it’s spinning?”

Voice from the back of the room — “Maybe it’s got lumps or something on it.”

“Nope. The No-hair Theorem says the event horizon is mathematically smooth, no distinguishing marks or tattoos. Question, Jeremy?”

“Yessir. Suppose an asteroid or something falls in. Time dilation makes it look like it’s going slower and slower as it gets close to the event horizon, right? Wouldn’t the stuck asteroid be a marker to track the black hole’s rotation?”

“Excellent question.” <Several of Jeremy’s groupies go, “Oooh.”> “Two things to pay attention to here. First, if we can see the asteroid, it’s not yet inside the horizon so it wouldn’t be a direct marker. Beyond that, the hole’s rotation drags nearby spacetime around with it in the ergosphere, that pumpkin‑shaped region surrounding the event horizon except at the rotational poles. As soon as the asteroid penetrates the ergosphere it gets dragged along. From our perspective the asteroid spirals in instead of dropping straight. What with time dilation, if the hole’s spinning fast enough we could even see multiple images of the same asteroid at different levels approaching the horizon.”

Jeremy and all his groupies go, “Oooh.”

“Anyhow, astronomical observation has given us lots of evidence that black holes do spin. I’ve been pondering what’s spinning in there. Most people seem to think that once an object crosses the event horizon it becomes quantum mush. There’d be this great mass of mush spinning like a ball. In fact, that was Schwarzchild’s model for his non-rotating black hole — a simple sphere of incompressible fluid that has the same density throughout, even at the central singularity.”

VBOR — “Boring!”

“Well yeah, but it might be correct, especially if spaghettification and the Firewall act to grind everything down to subatomic particles on the way in. But I got a different idea when I started thinking about what happened to those two black holes that LIGO heard collide in 2015. It just didn’t seem reasonable that both of those objects, each dozens of solar masses in size, would get mushed in the few seconds it took to collide. Question, Vinnie?”

“Yeah, nice talk so far. Hey, Sy and me, we talked a while ago about you can’t have a black hole inside another black hole, right, Sy?”

“That’s not quite what I said, Vinnie. What I proved was that after two black holes collide they can’t both still be black holes inside the big one. That’s different and I don’t think that’s where Jim’s going with this.”

“Right, Mr Moire. I’m not claiming that our two colliders retain their black hole identities. My crazy theory is that each one persists as a high‑density nubbin in an ocean of mush and the nubbins continue to orbit in there as gravity propels them towards the singularity.”

VBOR —”Orbit? Like they just keep that dance going after the collision?”

“Sure. What we can see of their collision is an interaction between the two event horizons and all the external structures. From the outside, we’d see a large part of each object’s mass eternally inbound, locked into the time dilation just above the joined horizon. From the infalling mass perspective, though, the nubbins are still far apart. They collide farther in and farther into the future. The event horizon collision is in their past, and each nubbin still has a lot of angular momentum to stir into the mush. Spin is stirred-up mush.”

Cathleen’s back at the mic. “Well, there you have it. Amanda’s male-pattern baldness theory, Newt’s hyper‑planetary gear, Kareem’s purple snowball or Jim’s mush. Who wins the Ceremonial Broom?”

The claque responds — “Amanda! Amanda! Amanda!”

~ Rich Olcott

A Great Big Mesh

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

Cal has my coffee mug filled as soon as I step into his shop. “Get to the back room quick, Sy. Cathleen’s got another Crazy Theories seminar going back there.”

So I do. First thing I hear is Amanda finishing her turn at the mic. “And that’s why humans evolved male pattern baldness.”

A furor of “Amanda! Amanda! Amanda!” then Cathleen regains control. “Thank you, Amanda. Next up — Newt Barnes. What’s your Crazy Theory, Newt?”

“Crazy idea, not a theory, but I like it. Everybody’s heard of black holes, right?”

<general nodding>

“And we’ve all heard that nothing can leave a black hole, not even light.”

<more nodding>

“Well in fact that’s mostly not true. There’s so much confusion about black holes. We’ve known about a black hole’s event horizon and its internal mass since the 1920s. It took years for us to realize that the central mass could wrap a shiny accretion disk around itself, and an ergosphere, and maybe spit out jets. So, close outside the Event Horizon there’s a lot of light‑emitting structure, right?”

<A bit less nodding, but still.>

“Right. So I’ll skip in past a few controversial layers and get down to the famously black event horizon. Why’s it black?”

Voice from the back of the room — “Because photons can’t get out because escape velocity’s faster than lightspeed.”

“That’s the answer I expected, but it’s also one of the confusing parts. You’re right, the horizon marks the level where outward‑bound massy particles can’t escape. The escape velocity equation depends on trading off kinetic and gravitational potential energy. Any particle with mass would have to convert an impossible amount of kinetic energy into gravitational potential energy to get through the barrier. But zero‑mass particles, photons and such, are pure kinetic energy. They aren’t bound by a gravitational potential so escape velocity trade‑offs simply don’t apply. There’s a deeper reason photons also can’t get out.”

VBOR — “So what’s trapping them?”

“Time. It traps photons and any kind of information. The other thing about the Event Horizon is, it’s the level where spacetime is so bent around that the time‑coordinate is just on the verge of pointing inward. Once you’re inside that boundary the cause‑and‑effect arrow of time is against you. Whatever direction you point your flashlight, its beam will emerge in your future and that’s away from the horizon. Trying to send a signal outside would be like sending it into your past, which you can’t do. Nothing gets away from a black hole except…”

“Except?”

“Roger Penrose found a loophole and I may have found another one. There’s something that Wheeler called the No-Hair Theorem. It says that the Event Horizon hides everything inside it except for its mass, electric charge and angular momentum.”

“How do those get out?”

“They don’t get out so much as serve as backdrop for all the drama in the rest of the structure. If you know the mass, for instance, you can calculate its temperature and the Horizon’s diameter and a collection of other properties.”

Cathleen senses a teachable moment and breaks in. “Talk about charge and spin, Newt.”

“I was going there, Cathleen. Kerr and company’s equations take account of both of those. Turns out the attractive forces between opposite charges are so much stronger than gravity that it’s hard for an object in space to build up a significant amount of either kind of charge without getting neutralized almost immediately. Kind of ironic that the Coulomb force, far stronger than gravity, generates net energy contributions that are much smaller than the gravity‑based ones. Spin, though, that’s where the loopholes are. Penrose figured out how particles from the accretion disk could dip into the black hole’s spinning ergosphere, steal some of its energy, and stream up to power the jets.”

VBOR — “What’s your loophole then?”

“Speed contrast between layers. The black hole mass is spinning at a great rate, dragging nearby spacetime and the ergosphere and the accretion disk around with it. But the layers go slower as you move outward. Station a turbine generator like an idler gear between any two layers and you’re pulling power from the black hole’s spin.”

Silence … then, “Amanda! Amanda! Amanda!”

~ Rich Olcott