Tag: Gravitational waves

A Cosmological Horse Race

On By rolcottIn Astronomy: Multi-messenger, Cosmology, Physics: Einstein, Physics: Electromagnetism, UncategorizedLeave a comment

A crisp Fall day, perfect for a brisk walk around the park. I see why the geese are huddled at the center of the lake — Mr Feder, not their best friend, is on patrol again. Then he spots me. “Hey, Moire, I gotta question!”

“Of course you do, Mr Feder. What is it?”

“Some guy on TV said Einstein proved gravity goes at the speed of light and if the Sun suddenly went away it’d take eight minutes before we went flying off into space. Did Einstein really say that? Why’d he say that? Was the TV guy right? And what would us flying across space feel like?”

“I’ll say this, Mr Feder, you’re true to form. Let’s see… Einstein didn’t quite prove it, the TV fellow was right, and we’d notice being cold and in the dark well before we’d notice we’d left orbit. As to why, that’s a longer story. Walk along with me.”

“Okay, but not too fast. What’s not quite about Einstein’s proving?”

“Physicists like proofs that use dependable mathematical methods to get from experimentally-tested principles, like conservation of energy, to some result they can trust. We’ve been that way since Galileo used experiments to overturn Aristotle’s pure‑thought methodology. When Einstein linked gravity to light the linkage was more like poetry. Beautiful poetry, though.”

“What’s so beautiful about something like that?”

“All the rhymes, Mr Feder, all the rhymes. Both gravity and light get less intense with the square of the distance. Gravity and light have the same kinds of symmetries—”

“What the heck does that mean?”

“If an object or system has symmetry, you can execute certain operations on it yet make no apparent difference. Rotate a square by 90° and it looks just the same. Gravity and light both have spherical symmetry. At a given distance from a source, the field intensity’s the same no matter what direction you are from the source. Because of other symmetries they both obey conservation of momentum and conservation of energy. In the late 1890s researchers found Lorentz symmetry in Maxwell’s equations governing light’s behavior.”

“You’re gonna have to explain that Lorentz thing.”

“Lorentz symmetry has to do with phenomena an observer sees near an object when their speed relative to the object approaches some threshold. Einstein’s Special Relativity theory predicted that gravity would also have Lorentz symmetry. Observations showed he was right.”

“So they both do Lorentz stuff. That makes them the same?”

“Oh, no, completely different physics but they share the same underlying structure. Maxwell’s equations say that light’s threshold is lightspeed.”

“Gravity does lightspeed, too, I suppose.”

“There were arguments about that. Einstein said beauty demands that both use the same threshold. Other people said, ‘Prove it.’ The strongest argument in his favor at the time was rough, indirect, complicated, and had to do with fine details of Earth’s orbit around the Sun. Half a century later pulsar timing data gave us an improved measurement, still indirect and complicated. This one showed gravity’s threshold to be with 0.2% of lightspeed.”

“Anything direct like I could understand it?”

“How about a straight‑up horse race? In 2017, the LIGO facility picked up a gravitational signal that came in at the same time that optical and gamma ray observatories recorded pulses from the same source, a colliding pair of neutron stars in a galaxy 130 million lightyears away. A long track, right?”

“Waves, not horses, but how far apart were the signals?”

“Close enough that the measured speed of gravity is within 10–15 of the speed of light.”

“A photo-finish.”

“Nice pun, Mr Feder. We’re about 8½ light-minutes away from the Sun so we’re also 8½ gravity-minutes from the Sun. As the TV announcer said, if the Sun were to suddenly dematerialize then Earth would lose the Sun’s orbital attraction 8½ minutes later. We as individuals wouldn’t go floating off into space, though. Earth’s gravity would still hold us close as the whole darkened, cooling planet leaves orbit and heads outward.”

“I like it better staying close to home.”

~ Rich Olcott

Fields of Dreams

On By rolcottIn Cosmology, Physics: Quantum Mechanics, Physics: Waves, Uncategorized1 Comment

Vinnie takes a slug of his coffee. “So the gravitational field carries the gravitational wave. I suppose Einstein would blame sound waves on some kind of field?”

I take a slug of mine. “Mm-hm. We techies call it a pressure field. Can’t do solar physics without it. The weather maps you use when plotting up a flight plan — they lay three fields on top of the geography.”

“Lessee — temp, wind … and barometer reading. In the old days I’d use that one to calibrate my altimeter. You say those are fields?”

“In general, if a variable has a value at every point in the region of interest, the complete set of values is a field. Temperature and pressure are the simplest type. Their values are just numbers. Each point in a wind field has both speed and direction, two numbers treated as a single value, so you’ve got a field of vector values.”

“Oh, I know vectors, Sy. I’m a pilot, remember? So you’re saying instead of looking at molecules back‑and‑forthing to make sound waves we step back and look at just the pressure no matter the molecules. Makes things simpler, I can see that. Okay, how about the idea those other guys had?”

“Hm? Oh, the other wave carrier idea. Einstein’s gravitational waves are just fine, but the Quantum Field Theorists added a collection of other fields, one for each of the 17 boxes in the Standard Model.”

“Boxes?”

<displaying Old Reliable’s screen> “Here’s the usual graphic. It’s like the chemist’s Periodic Table but goes way below the atomic level. There’s a box each for six kinds of quarks; another half‑dozen for electrons, neutrinos and their kin; four more boxes for mediating electromagnetism and the weak and strong nuclear forces. Finally and at last there’s a box for the famous Higgs boson which isn’t about gravity despite what the pop‑sci press says.”

“What’s in the boxes?”

“Each box holds a list of properties — rest mass, spin, different kinds of charge, and a batch of rules for how to interact with the other thingies.”

“Thingies, Sy? I wouldn’t expect that word from you.”

“I would have said ‘particle‘ but that would violate QFT’s tenets despite the graphic’s headline.”

“Tenets? That word sounds more like you. What’s the problem?”

“That the word ‘particle‘ as we normally use it doesn’t really apply at the quantum field level. Each box names a distinct field that spreads its values and waves all across the Universe. There’s an electron field, a photon field, an up‑quark field, a down‑quark field, and so on. According to QFT, what we’d call a particle is nothing more than a localized peak in its underlying field. Where you find a peak you’ll find all the properties listed in its box. Wherever the field’s value is below its threshold, you find none of them.”

“All or none, huh? I guess that’s where quantum comes in. Wait, that means there could be gazillions of one of them popping up wherever, like maybe a big lump of one kind all right next to each other.”

“No, the rules prevent that. Quarks, for instance, only travel in twos or threes of assorted kinds. The whole job of the gluons is to enforce QFT rules so that, for instance, two up‑quarks and a down‑quark make a proton but only if they have different color charges.”

“Wait, color charge?”

“Not real colors, just quantum values that could as easily have been labeled 1, 2, 3 or A, B, C. There’s also an anti- for each value so the physicists could have used ±1, ±2, ±3, but they didn’t, they used ‘red’ and ‘anti‑red’ and so forth. And ‘color charge‘ is a different property from electric charge. Gluons only interact with color charge, photons only interact with electric charge. The rules are complicated.”

“You said ‘waves.’ Each of these fields can have waves like gravity waves?”

“Absolutely. We can’t draw good pictures of them because they’re 3‑dimensional. And they’re constantly in motion, of course.”

“How fast can those waves travel?”

“The particles are limited to lightspeed or slower; the waves, who knows?”

“Ripples zipping around underneath the quantum threshold could account for entanglement, ya’ know?”

“Maybe.”

~~ Rich Olcott

A Million Times Weaker Than Moonlight

On By rolcottIn Cosmology, Gravitational astronomy, Physics: Waves, UncategorizedLeave a comment

Big Vinnie’s getting downright antsy, which is something to behold. “C’mon, Sy. We get it that sonication ain’t sonification and molecules bumping into each other can carry a sound wave across space if the frequency’s low enough and that can maybe account for galaxies having spiral arms, but you said the Cosmic Hum is a sound, too. That’s a gravity thing, not molecules, right?”

“Not quite what I said, Vinnie. The Hum’s sound‑related, but it’s not ‘sound’ even by our extended definition.”

“Then what’s the connection?”

“Waves.”

“Not frames like always?”

“Not frames, for a change.”

“So it’s waves, but they go though empty space. Can’t happen like sound waves from molecules bumping into each other ’cause molecules are too small to have enough gravity do that when they’re so far apart. What’s carrying the waves?”

“Good question. Einstein figured out one answer. A whole cohort of mid‑20th‑century theoreticians came to a slightly different conclusion.”

“Okay, I’ll bite. What was Einstein’s answer?”

“Relativity, of course. Gravity’s the effect we see from mass deforming nearby space. Moving a mass drives corresponding changes in the shapes of space where it was and where it has moved to. The shape‑changes generate follow‑on gravitational effects that propagate outward over time. Einstein even showed that the gravitational propagation speed is equal to lightspeed.”

“Gimme a sec … Okay, that black hole collision signal LIGO picked up back in 2015, the holes lost a chunk of their combined mass all of a sudden. Quick drop in the gravity thereabouts. You’re saying it took time for the missing gravity strength to get noticed where we’re at. If I remember right, the LIGO people said the event was something like a billion lightyears away so that tells me it happened about a billion years ago and what the LIGO gadget picked up was space waves, right?”

“Right, but it wasn’t just the mass loss, it was the rapid and intense waggles in the gravitational field as those two enormous bodies, each 30 times as massive as the Sun, whirled around each other multiple times per second. The ever‑faster whirling shook the field with a frequency that swept upward to the ‘POP‘ when your mass‑loss happened. LIGO eventually picked up that signal. Einstein would say there’s no ‘action at a distance‘ in the collision‑LIGO interaction, because the objects acted on the gravitational field which acted on the LIGO system.”

“Like using a towel to pop someone in the locker room. The towel’s just transmi– ulp.”

“An admission of guilt if I ever heard one. Yes, like that, except a towel pop carries all the initial energy to its final destination. Gravitational waves spread their energy across the surface of an expanding sphere. The energy per unit area goes down as the square of the distance.” <keying a calculation on Old Reliable> “Suppose the collision releases 10 solar masses worth of energy, we’re a billion lightyears away, and the ‘POP‘ signal is delivered in a tenth of a second. We’d see a signal power … about a millionth as strong as moonlight.”

“Not much there.”

“Right, which is why LIGO and its kin have been such pernickety instruments to build and run. LIGO’s sensors are mirrors roughly a meter across. You get a million times more power sensitivity if your detector’s diameter is a mile across. That was part of the NANOGrav team’s strategy, but they went much bigger.”

“Yeah, that’s the multi-telescope thing, so NANOGrav faked a receiver the size of the Earth, like the Event Horizon Telescope.”

“Much bigger. Their receiver is the entire Milky Way. Instead of LIGO’s mirrors, NANOGrav’s signal generators are neutron stars a dozen or more miles wide scattered across the galaxy.”

“Gotcha, Sy. Two ways. Neutron stars are billions heavier than a LIGO mirror so they’d be less power‑sensitive, not more. Then, power is about moving stuff closer or farther but if I got you right these space waves don’t really do that anyway, right?”

“Right and right, Vinnie, but not relevant. What NANOGrav’s been watching for is pulsar beams being twitched by a gravitational wave. A waltzing black hole pair should generate years‑long or decades‑long wavelengths. NANOGrav may have found one.”

~~ Rich Olcott

White Noise And Red

On By rolcottIn Gravitational astronomy, UncategorizedLeave a comment

“That point’s kinda weak, Sy. The NANOGrav team says 15 years of pulsar timing data let them hear the Universe humming. What’s the difference if they call it a hum or a rumble or a warble?”

“Not much, Vinnie. Matter of taste and scale, I guess. As a human I think of a ‘hum‘ as something in the auditory range, roughly 60‑120 cycles per second. Whatever these folks have found, it rumbles in years per cycle. Scaled to the Sun’s ten‑billion‑year lifetime I suppose that’d be a supersonic screech.”

“Whatever they’ve found? We don’t know?”

“Not yet, Al. The team likes one hypothesis but it’ll take years to collect enough data for firm support or refutation.”

“In addition to the 15 years‑worth they’ve got already? Why not just add more antennas?”

“What they’re following changes so slowly they need a long baseline to have confidence that jiggles they see are real. Part of this paper is about conclusions the team reached after they stuck a few extra years of old data onto the front of their time series.”

“You can do that?”

“Sure. The series is just a big database, like a spreadsheet with a page for each pulsar and a row on that page for each blink. The row captures the recorded time for the blink’s peak, but also a bunch of other data like measures related to pulse width and asymmetry, the corrected peak time, identifiers for the reporting observatory and reference time standard—”

“Corrected time? Looks suspicious. What did they correct for?”

“Of course you’re suspicious, Vinnie, but so are they and so are other astronomers. You don’t want to make a big announcement like this unless you’ve checked everything for error sources. For instance, Earth moving around the Sun means we’re a little closer to a particular pulsar at one time of year, further away six months later.”

“So you correct the timings to what they’d be at the Sun’s center, right?”

“That’s just for starters. Jupiter and the Sun orbit around their common center of gravity on an 11.8‑year cycle. The researchers had to pull data from the Juno mission to correct for the Sun’s personal waltz. Of course the Solar System is moving relative to the stellar background, another correction. Then maybe the pulsar itself is part of a binary, happens a lot, and it’s probably moving through the sky, too — lots of careful corrections. That’s step one.”

“Then what?”

“Use each pulsar’s corrected timings to build a mathematical model of its idealized behavior. Once you know what’s ‘normal‘, you can start talking about jiggles that deviate from normal.”

“Reminds me of the ephemeris trick — sort of build an artificial pulsar to compare against.”

“Exactly the same idea, Vinnie, and by the way, ephemerides are still used but not to define the length of a second. Step three is statistical analysis: compare all possible deviation histories, every pulsar against every other pulsar.”

“Sounds like a lot of work, even for a computer. So what did they find?”

“Well, what they observed was that the pulsar timings we received weren’t as absolutely regular as they would have been with a static gravitational field. The overall picture resembled fog in a noisy room, waves of every size skittering in every direction and messing up reception. When the researchers broke that picture down by frequency, the waves shorter than 21 months or so added up to just white noise, complete randomness.”

“A hiss, not a hum. What about the longer waves?”

Fig 1(c) from Agazie, el al (2023).

“Red noise — jiggles heavy‑loaded on longer wavelengths out to the 16‑year maximum their data’s good for so far. But that’s not all. When they plotted jiggle correlation between pulsars separated at different angles across the sky, the curve mostly matched a prediction for the gravitational wave pattern that would be generated by a large number of randomly distributed independent sources.”

“Lots of sources, which would be…?”

“We don’t know. One hypothesis is that they’re pairs of supermassive black holes orbiting each other at the centers of merged galaxies. But I’ve read another paper giving a dozen other explanations. Everyone’s waiting for more data.”

~~ Rich Olcott

Not A Hum, A Rumble

On By rolcottIn Cosmology, Gravitational astronomy, UncategorizedLeave a comment

Vinnie taps on the magazine. “Sy, you’ve done it again. We ask you one question, you spend a lot of time talking about something else entire. They got this article here” <tap> “says the NANOGrav team captured the hum of the Universe. Al and me, we ask you about that and you get us discussing pulsars. Seems to me,” <tap tap> “that if you got a pulsar and the pulses got only a 3% duty cycle they’d sound more like clicks and,” <taptaptaptap> “if it’s a 10 millisecond pulsar that’s a hundred per second and they’d be more like a low‑pitched buzz, nothing like a hum.”

“One more short detour, Vinnie, sorry. Remember when we discussed the VLA, the Very Large Array of radio telescopes in northern New Mexico?”

“Sorta. I do remember visiting the place, out in the desert miles away from anywhere. They’ve got a couple dozen dish antennas each as wide as a four‑lane road, all spread out along railroad tracks. Big dishes for catching weak signals I understand, but I forget why there’s lots of dishes instead of one huge one or how that even works.”

“One reason is simple mechanics. A huge dish would try to sail away in the desert wind. VLA admins even have to safe‑mount those 25‑meter ones when things get gusty. But the real reason goes to how the array works as one big instrument. Here’s a hint — the dishes can be miles apart and lightspeed isn’t infinite.”

“Ah, that joggled my memory. It’s about when a signal comes in from some nova or something, each dish registers it with a slightly different arrival time and then the computers play match‑up games with all the time differences to figure exactly what angle the signal came from, right?”

“Roughly. The VLA’s multi‑dish design is about being able to resolve signal sources that are close together in the sky so yeah, slightly different angles. The Event Horizon Telescope team used the same strategy and a collection of radio dishes all over the world to produce those orange‑ring images of supermassive black holes. NANOGrav and the other Pulsar Timing Arrays sort of the flip the strategy.”

“At last we get to NANOGrav. Wait, they use lots of antennas to send signals to a star?”

“Nothing like that, Al. No, they use just a few antennas but they track the timing of many pulsars. About 70 at last count.”

“But we know what the timing is, to nanoseconds you said.”

“One word, Vinnie. ‘Frames‘.”

“Aw geez, Sy. Again?”

“Mm-hm. In the pulsar’s frame, it’s majestically rotating at a steady pace, tens or hundreds of times per second relative to its neighbors. Its beam proudly announces its presence on an absolutely regular schedule save for a small but steady slow‑down. In our frame, though, things can happen to a pulse as it heads our way.”

“Like what?”

“It might pass through a molecular cloud. We know those exist. Photons in the right wavelength ranges could interact with cloud components. That’d delay them, stretch the pulse, might even create interference between successive pulses. On the theory side, some cosmologists think the Universe may hold objects like cosmic strings or curvature‑induced domain walls that could delay, deflect or otherwise mess up a pulse. The best possibility, though, is that a gravitational wave could cross the path of a pulse en route to us.”

“Why is that a good thing?”

“Because they’d interact to alter that pulse’s timing. Gravitational waves stretch and squeeze time as they squeeze and stretch space. If a wave crosses a traveling pulse, the pulse will get here either early or late depending. Better yet, if we track enough pulsars scattered across the sky we might even see a parade of offset timings as the wave encounters different pulse beams. Hasn’t happened yet, though. The NANOGrav reports so far are about the background variation as waves from everywhere traverse the paths we’re watching.”

“The article says a hum.”

“Hum sounds come in waves per second. The gravitational background happens in waves per decade, such a low frequency even elephants couldn’t hear it.”

“OK, it’s rumble, not a hum. But why either one?”

~~ Rich Olcott

LIGO And NANOGrav

On By rolcottIn Astronomy: Techniques, Gravitational astronomy, Physics: Waves, UncategorizedLeave a comment

Afternoon coffee time, but Al’s place is a little noisier than usual. “Hey, Sy, come here and settle this.”

“Settle what, Al? Hi, Vinnie.”

<waves magazine> “This NANOGrav thing, they claim it’s a brand‑new kind of gravity wave. What’s that about?”

“Does it really say, ‘gravity wave‘? Let me see that. … <sigh> Press release journalism at its finest. ‘Gravity waves’ and ‘gravitational waves’ are two entirely different things.”

“I kinda remember you wrote about that, but it was so long ago I forget how they’re different.”

“Gravity waves happen in a fluid, like air or the ocean. Some disturbance, like a heat spike or an underwater landslide, pushes part of the fluid upward relative to a center of gravity. Gravity acts to pull that part down again but in the meantime the fluid’s own internal forces spread the initial up‑shift outwards. Adjacent fluid segments pull each other up and down and that’s a gravity wave. The whole process keeps going until friction dissipates the energy.”

“Gravitational waves don’t do that?”

“No, because gravitational waves temporarily modify the shape of space itself. The center doesn’t go up and down, it…” <showing a file on Old Reliable> “Here, see for yourself what happens. It’s called quadrupolar distortion. Mind you, the effects are tiny percentagewise which is why the LIGO apparatus had to be built kilometer‑scale in order to measure sub‑femtometer variations. The LIGO engineers took serious precautions to prevent gravity waves from masquerading as gravitational waves.”

“Alright, so now we’ve almost got used to LIGO machines catching these waves from colliding black holes and such. How are NANOGrav waves different?”

“Is infrared light different from visible light?”

“The Hubble sees visible but the Webb sees infrared.”

“Figures you’d have that cold, Al. What I think Sy’s getting at is they’re both electromagnetic even though we only see one of them. You’re gonna say the same for these new gravitational waves, right, Sy?”

“Got it in one, Vinnie. There’s only one electromagnetic field in the Universe but lots of waves running through it. Visible light is about moving charge between energy levels in atoms or molecules which is how the visual proteins in our eyes pick it up. Infrared can’t excite electrons. It can only waggle molecule parts which is why we feel it as heat. Same way, there’s only one gravitational field but lots of waves running through it. The LIGO devices are tuned to pick up drastic changes like the <ahem> massive energy release from a black hole collision.”

“You said ‘tuned‘. Gravitational waves got frequencies?”

“Sure. And just like light, high frequencies reflect high‑energy processes. LIGO detects waves in the kilohertz range, thousands of peaks per second. NANOGrav’s detection range is sub‑nanohertz, where one cycle can take years to complete. Amazingly low energy.”

“How can they detect anything that slow?”

“With really good clocks and a great deal of patience. The new reports are based on fifteen years of data, half a billion seconds counted out in nanoseconds.”

“Hey, wait a minute. LIGO’s only half‑a‑dozen years old. Where’d they get the extra data from, the future?”

“Of course not. Do you remember us working out how LIGO works? The center sends out a laser pulse along two perpendicular arms, then compares the two travel times when the pulse is reflected back. Light’s distance‑per‑time is constant, right? When a passing gravitational wave squeezes space along one arm, the pulse in that arm completes its round trip faster. The two times don’t match any more and everyone gets excited.”

“Sounds familiar.”

“Good. NANOGrav also uses a timing‑based strategy, but it depends on pulsars instead of lasers. Before you ask, a pulsar is a rotating neutron star that blasts a beam of electromagnetic radiation. What makes it a pulsar is that the beam points away from the rotation axis. We only catch a pulse when the beam points straight at us like a lighthouse or airport beacon. Radio and X‑ray observatories have been watching these beasts for half a century but it’s only in the past 15 years that our clocks have gotten good enough to register timing hiccups when a gravitational wave passes between us and a pulsar.”

~ Rich Olcott

A Three-dog Night Would Be So Cool

On By rolcottIn Astronomy: Multi-messenger, Astronomy: Techniques, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Light and Relativity, UncategorizedLeave a comment

“So we’ve got three fundamentally different messengers from the stars, Mr Feder.  The past couple of years have given us several encouraging instances of receiving two messengers from the same event.  If we ever receive all three messengers from the same event, that might give us what we need to solve the biggest problem in modern physics.”

“That’s a pretty deep statement, Moire.  Care to unpack it?  The geese here would love to hear about it.”

“Lakeside is a good place for thoughts like this.  The first messenger was photons.  We’ve been observing starlight photons for tens of thousand of years.  Tycho Brahe and Galileo took it to a new level a few centuries ago with their careful observation, precision measurements and Galileo’s telescope.”

“That’s done us pretty good, huh?”

“Oh sure, we’ve charted the heavens and how things move, what we can see of them.  But our charts imply there’s much we can’t see.  Photons only interact with electric charge.  Except for flat-out getting absorbed if the wavelength is right, photons don’t care about electrically neutral material and especially they don’t care about dark matter.”

“So that’s why we’re interested in the other messengers.”

“Exactly.  Even electrically neutral things have mass and interact with the gravitational field.  You remember the big news a few years ago, when our brand-new LIGO instruments caught a gravitational wave signal from a couple of black holes in collision.  Black holes don’t give off photons, so the gravitational wave messenger was our only way of learning about that event.”

“No lightwave signal at all?”

“Well, there was a report of a possible gamma-ray flare in that patch of sky, but it was borderline-detectable.  No observatory using lower-energy light saw anything there.  So, no.”

“You’re gonna tell me and the geese about some two-messenger event now, right?”

“That’s where I’m going, Mr Feder.  Photons first.  Astronomers have been wondering for decades about where short, high-energy gamma-ray bursts come from.  They seem to happen randomly in time and space.  About a year ago the Fermi satellite’s gamma-ray telescope detected one of those bursts and sent out an automated ‘Look HERE’ alert to other observatories.  Unfortunately, Fermi‘s resolution isn’t wonderful so its email pointed to a pretty large patch of sky.  Meanwhile back on Earth and within a couple of seconds of Fermi‘s moment, the LIGO instruments caught an unusual gravitational wave signal that ran about a hundred times slower than the black-hole signals they’d seen.  Another automated ‘Look HERE’ alert went out.  This one pointed to a small portion of that same patch of sky.  Two messengers.”

“Did anyone find anything?”

“Seventy other observatories scrutinized the overlap region at every wavelength known to Man.  They found a kilonova, an explosion of light and matter a thousand times brighter than typical novae.  The gravitational wave evidence indicated a collision between two neutron stars, something that had never before been recorded.  Photon evidence from the spewed-out cloud identified a dozen heavy elements theoreticians hadn’t been able to track to an origin.  Timing details in the signals gave cosmologists an independent path to resolving a problem with the Hubble Constant.  And now we know where those short gamma-ray bursts come from.”

“Pretty good for a two-messenger event.  Got another story like that?”

“A good one.  This one’s neutrinos and photons, and the neutrinos came in first.  One neutrino.”

“One neutrino?”

“Yup, but it was a special one, a super-high-powered neutrino whose incoming path our IceCube observatory could get a good fix on.  IceCube sent out its own automated ‘Look HERE’ alert.  The Fermi team picked up the alert and got real excited because the alert’s coordinates matched the location of a known and studied gamma-ray source.  Not a short-burster, but a flaring blazar.  That neutrino’s extreme energy is evidence for blazars being one of the long-sought sources of cosmic rays.”

“Puzzle solved, maybe.  Now what you said about a three-messenger signal?”grebe messenger pairs“Gravitational waves are relativity effects and neutrinos are quantum mechanical.  Physicists have been struggling for a century to bridge those two domains.  Evidence from a three-messenger event could provide the final clues.”

“I’ll bet the geese enjoyed hearing all that.”

“They’re grebes, Mr Feder.”

~~ Rich Olcott

Gravity’s Real Rainbow

On By rolcottIn Astronomy: Multi-messenger, Astronomy: Stellar Science, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Waves, UncategorizedLeave a comment

Some people are born to scones, some have scones thrust upon them.  As I stepped into his coffee shop this morning, Al was loading a fresh batch onto the rack.  “Hey, Sy, try one of these.”

“Uhh … not really my taste.  You got any cinnamon ones ready?”

“Not much for cheddar-habañero, huh?  I’m doing them for the hipster trade,” waving towards all the fedoras on the room.  “Here ya go.  Oh, Vinnie’s waiting for you.”

I navigated to the table bearing a pile of crumpled yellow paper, pulled up a chair.  “Morning, Vinnie, how’s the yellow writing tablet working out for you?”

“Better’n the paper napkins, but it’s nearly used up.”

“What problem are you working on now?”

“OK, I’m still on LIGO and still on that energy question I posed way back — how do I figure the energy of a photon when a gravitational wave hits it in a LIGO?  You had me flying that space shuttle to explain frames and such, but kept putting off photons.”

“Can’t argue with that, Vinnie, but there’s a reason.  Photons are different from atoms and such because they’ve got zero mass.  Not just nearly massless like neutrinos, but exactly zero.  So — do you remember Newton’s formula for momentum?”

“Yeah, momentum is mass times the velocity.”

“Right, so what’s the momentum of a photon?”

“Uhh, zero times speed-of-light.  But that’s still zero.”

“Yup.  But there’s lots of experimental data to show that photons do carry non-zero momentum.  Among other things, light shining on an an electrode in a vacuum tube knocks electrons out of it and lets an electric current flow through the tube.  Compton got his Nobel prize for that 1923 demonstration of the photoelectric effect, and Einstein got his for explaining it.”

“So then where’s the momentum come from and how do you figure it?”

“Where it comes from is a long heavy-math story, but calculating it is simple.  Remember those Greek letters for calculating waves?”

(starts a fresh sheet of note paper) “Uhh… this (writes λ) is lambda is wavelength and this (writes ν) is nu is cycles per second.”

“Vinnie, you never cease to impress.  OK, a photon’s momentum is proportional to its frequency.  Here’s the formula: p=h·ν/c.  If we plug in the E=h·ν equation we played with last week we get another equation for momentum, this one with no Greek in it:  p=E/c.  Would you suppose that E represents total energy, kinetic energy or potential energy?”

“Momentum’s all about movement, right, so I vote for kinetic energy.”

“Bingo.  How about gravity?”

“That’s potential energy ’cause it depends on where you’re comparing it to.”

light-in-a-gravity-well“OK, back when we started this whole conversation you began by telling me how you trade off gravitational potential energy for increased kinetic energy when you dive your airplane.  Walk us through how that’d work for a photon, OK?  Start with the photon’s inertial frame.”

“That’s easy.  The photon’s feeling no forces, not even gravitational, ’cause it’s just following the curves in space, right, so there’s no change in momentum so its kinetic energy is constant.  Your equation there says that it won’t see a change in frequency.  Wavelength, either, from the λ=c/ν equation ’cause in its frame there’s no space compression so the speed of light’s always the same.”

“Bravo!  Now, for our Earth-bound inertial frame…?”

“Lessee… OK, we see the photon dropping into a gravity well so it’s got to be losing gravitational potential energy.  That means its kinetic energy has to increase ’cause it’s not giving up energy to anything else.  Only way it can do that is to increase its momentum.  Your equation there says that means its frequency will increase.  Umm, or the local speed of light gets squinched which means the wavelength gets shorter.  Or both.  Anyway, that means we see the light get bluer?”

“Vinnie, we’ll make a physicist of you yet.  You’re absolutely right — looking from the outside at that beam of photons encountering a more intense gravity field we’d see a gravitational blue-shift.  When they leave the field, it’s a red-shift.”

“Keeping track of frames does make a difference.”

Al yelled over, “Like using tablet paper instead of paper napkins.”

~~ Rich Olcott

LIGO and lambda and photons, oh my!

On By rolcottIn Astronomy: Multi-messenger, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Light and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

I was walking my daily constitutional when Al waved me into his coffee shop.  “Sy, he’s at it again with the paper napkins.  Do something!”

I looked over.  There was Vinnie at his table, barricaded behind a pile of crumpled-up paper.  I grabbed a chair.

“Morning, Vinnie.  Having fun?”

“Greek letters.  Why’d they have to use Greek letters?”

The question was both rhetorical and derivative so I ignored it.  There were opened books under the barricade — upper-level physics texts.  “How come you’re chasing through those books?”

“I wanted to follow up on how LIGO operates with photons after we talked about all that space shuttle stuff.  But geez, Sy!”

“You’re a brave man, Vinnie.  So,  which letters are giving you trouble?”

“These two, that look kinda like each other upside down.” He pointed to one equation, λ=c/ν.

“Ah, wavelength equals the speed of light divided by the frequency.”

“How do you do that?”

“Some of those symbols go way back.  You just get used to them.  Most of them make sense when you learn the names for the letters — lambda (λ) is the peak-to-peak length of a lightwave, and nu (ν) is the number of peaks per second.  If it makes you feel any better, I’ve yet to meet a physicist who can write a zeta (ζ) — they generally just draw a squiggle and move on.”

“And there’s this other equation,” pointing to E=h·ν.  “What’s that about?”

“Good eye.  You just picked two equations that are fundamental to LIGO’s operation.  If a lightwave has frequency ν, the equations tell us two things about it — its energy is h·ν (h is Planck’s constant, 6.6×10-34 Joule-seconds), and its wavelength is c/ν (c is the speed of light).  For instance, yellow light has a frequency near 520×1012/sec.  One photon carries 3.8×10-40 Joules of energy.  Not much, but it adds up when a light beam contains lots of photons.  The same photon has a wavelength near 580×10-9 meters traveling through free space.”

“So what happens when one of those photons is in a LIGO beam?  Won’t a gravitational wave’s stretch-and-squeeze action mess up its wave?”

paper-napkin-waveI smoothed out one of Vinnie’s crumpled napkins. As I folded it into pleats and scooted it along the table I said, “Doesn’t mess up the wave so much as change the way we think about it.  We’re used to graphing out a spatial wave as an up-and-down pattern like this that moves through time, right?”

“That’s a lousy-looking wave.”

time-and-space-and-napkin
As the napkin moves through space,
the upper graph shows the height of its edge
above the observation point.

“It’s a paper napkin, f’pitysake, and I’m making a point here. Watch close.  If you monitor a particular point along the wave’s path in space and track how that point moves in time, you get the same profile except we draw it along the t-axis instead of along a space-axis.  See?”

“Hey, the time profile is the space profile going backwards.  Oh, right, it’s goin’ into the past ’cause it’s a memory.”

“That’s one of those things that people miss.  If you only draw sine waves, they’re the same in either direction.  The important point is that although timewaves and spacewaves have the same shape, they’ve got different meanings.  The timewave is directly connected to the wave’s energy by that E equation.  The spacewave is indirectly connected, because your other equation there scales it by the local speed of light.”

“Come again?  Local speed of light?  I thought it was 186,000 miles per second everywhere.”

“It is, but some of those miles are shorter than others.  Near a heavy mass, for instance, or in the compression phase of a gravitational wave, or inside a transparent material.  If you’re traveling in the lightwave’s inertial frame, you see no variation.  But if you’re watching from an independent inertial frame, you see the lightwave hit a slow patch.  Distance per cycle gets shorter.  Like that lambda-nu equation says, when c gets smaller the wavelength decreases.”

Al walked over.  “Gotcha a present, Vinnie.  Here’s a pad of yellow writing paper.  No more napkins, OK?”

“Uhh, thanks.”

“Don’t mention it.”

~~ Rich Olcott

Scone but not forgotten

On By rolcottIn Gravitational astronomy, Physics: Black Holes and Relativity, Uncategorized3 Comments

Al grabbed me as I stepped into his coffee shop.  “Sy, you gotta help me!”

“What’s the trouble, Al?”

“It’s Vinnie.  He’s over there, been scribbling on paper napkins all morning.  I’m running out of napkins, Sy!”

I grabbed a cinnamon scone from the rack and a chair at Vinnie’s table.  “What’s keeping you so busy, Vinnie?”  As if I didn’t know.

“LIGO, of course.  Every time I think I understand how the machine works something else occurs to me and it slips outa my hands.”

“How about you explain it to me.  Sometimes the best way to find an answer is to describe the problem to someone else.”

Interferometer 1
Vinnie’s paper napkin

(grabbing a napkin near the bottom of one stack) “All right, Sy, I sketched the layout here.  You got these two big L-shaped machines out in the middle of two nowheres 2500 miles apart.  Each L is a pair of steel pipes 2½ miles long.  At the far end of each arm there’s a high-tech stabilized mirror.  Where the two arms meet there’s a laser rigged up to shoot beams down both arms.  There’s also a detector located where the reflected beams join up and cancel each other out unless there’s a gravity wave going past.  Am I good so far?”

“Yeah, that’s pretty much the diagram you see in the books, except it’s gravitational wave.  Gravity waves are something else.”

interferometer-4
Paper napkin

“Whatever.  So, here’s a sketch of where I was at when I asked you that first question.  See, I copied my original sketch onto another napkin and stretched it a little where the black circle is to show what a gravitational wave would do in stretch phase.  Ignore the little rips.”

“What rips?”

“Uh, thanks.  Anyway, I was thinking the gravitational wave that stretches the x-beam would also stretch the x-pipe so they couldn’t use the light wave to measure the pipe it’s in.  But LIGO works so that’s wrong thinkin’.

“OK, next is for after we talked about inertial frames.  Took me a few tries to get it like I want it and I wound up having to do two sketches, one for each frame.”  He grabbed a couple more napkins from different stacks.

interferometer-5lp
Paper napkins and

“I didn’t do the yellow wiggles ’cause that got confusing and besides I don’t do wiggly lines so good.  Point is, the space-stretch only shows up in the laboratory inertial frame.  The light waves move with space so they don’t notice the difference, right?”

“Well, I wouldn’t want to put it that way in court, Vinnie, but it’s a pretty good description.”

“So the light waves bop along at 186,000 miles per second in their frame, but from the machine’s perspective those are stretched miles so the guy running the machine thinks those photons are faster than the ones in the other pipe.  And that difference in speed gets the yellow lines out of phase with the blue ones and the detector rings a bell or something, right?”

“It’s even better than that.” I reached for another napkin, caught Al’s eye on me and grabbed an envelope from my coat pocket instead. “Remember how a gravitational wave works in two directions perpendicular to the wave’s line of travel?”

interferometer-5d
On the back of an envelope

“Yeah, so?”

“So at the same moment that the wave is stretching space in the x-direction, it’s squeezing space in the y-direction.  LIGO’s detection scheme monitors the difference between the two returning beams.  As I’ve drawn it here using the detector’s inertial frame, the x-beam is going fast AND the y-beam is going slow so the detector sees twice the phase difference. A few milliseconds later they’ll switch because the x-direction will get squeezed while the y-direction gets stretched.  And yeah, a bell does ring but only after some computers munch on the data and subtract out environmental stuff like temperature swings and earthquakes and the janitor’s footsteps.”

“Uh-huh, I think I got it.” Turning in his chair, “Hey, Al, bring Sy here another scone, on me.  And put the one he’s got on my tab, too.”

“Thanks, Vinnie.”

“Don’t mention it.”

~~ Rich Olcott