Tag: Richard Feder

Everything Everywhere All at Once

On By rolcottIn Cosmology, UncategorizedLeave a comment

It’s either late Winter or early Spring, the weather can’t make up its mind. The geese don’t seem to approve of my walk around the park’s lake but then I realize it’s not me they object to. “Hey, Moire, wait up, I got a question for you!”

“Good morning, Mr Feder. What can I do for you?”

“This Big Bang thing I been hearing about. How can it make everything from nothing like they say?”

“You’re in good form, Mr Feder, lots of questions buried within a question.”

“Oh yeah? Seems pretty simple to me. How do we even know it happened?”

“Well, there you go, one buried question up already. We have several lines of evidence to support the idea. One of them is the CMB.”

“Complete Monkey Business?”

“Very funny. No, it’s the Cosmic Microwave Background, long‑wavelength light that completely surrounds us. It has the same wavelength profile and the same intensity within a dozen parts per million no matter what direction we look. The best explanation we have for it is that the light is finally arriving here from the Big Bang roughly 14 billion years ago. Well, a couple hundred thousand years after the Bang itself. It took that long for things to cool down enough for electrons and protons to pair up as atoms. The photons had been bouncing around between charged particles but when the charges neutralized each other the photons could roam free.”

“Same in all directions so we’re in the center, huh? The Bang musta been real close‑by.”

“Not really. Astronomers have measured the radiation’s effects on a distant intergalactic dust cloud. The effect is just what we’d expect if the cloud were right here. We’re not in a special location. From everything we can measure, the Bang happened everywhere and all at once.”

“Weird. Hard to see how that can happen.”

“We answered that nearly a century ago when Edwin Hubble discovered that there are other galaxies outside the Milky Way and that they’re in motion.”

“Yeah, I heard about that, too, with everything running away from us.”

“Sorry, no. We’re not that special, remember? On the average, everything’s running away from everything else.”

“Whaddaya mean, ‘on the average‘? Why the wishy-washy?”

“Because things cluster together and swirl around. The Andromeda galaxy is coming straight toward us, for instance, but it won’t get here for 5 billion years. The general trend only shows up when you look at large volumes, say a hundred million lightyears across or bigger. The evidence says yeah, everything’s spreading out.”

“But how can everything be moving away from everything? You run away from something, you gotta be running toward something else.”

“That’d be true if your somethings are all confined in a room whose walls don’t move. The Universe doesn’t work that way. The space between somethings continually grows new space. The volume of the whole assemblage increases.”

“Is that why I just hadda buy new pants?”

“No, that’s just you gaining weight from all that beer and bar food. The electromagnetism that holds your atoms and molecules together is much stronger than what’s driving the expansion. So is the gravitation that holds solar systems and galaxies together. Expansion only gets significant when distances get so large that the inverse square laws diminish both those forces to near zero.”

“What’s this got to do with the CMB?”

“The CMB tells us that the Bang happened everywhere, but expansion says that at early times when stars and galaxies first formed, ‘everywhere‘ was on a much smaller scale than it is now. Imagine having a video of the expansion and playing it backwards. Earendel‘s the farthest star we’ve seen, but if we and it existed 12 billion years ago we’d measure it as being close‑by but still all the way across the observable Universe. Carry that idea the rest of the way. The Big Bang is expansion from a super‑compressed everywhere.”

“Okay, what’s driving the expansion?”

“We don’t know. We call it ‘dark energy‘ but the name’s about all we have for it.”

“Aaaa-HAH! At last something you don’t know!”

“Science is all about finding things we don’t know and working to figure them out.”

~~ Rich Olcott

Astrometers Are Wobble-Watchers

On By rolcottIn Astronomy, UncategorizedLeave a comment

letter A Hi, Sy, what’s going on in Cathleen’s seminar?

You were right, Al.
It’s about exoplanets and how to find them.
Jeremy’s pitching astrometry.
That’s about measuring star locations in the sky.
I’ll fill you in later.

“So that’s my cultural colonialism rant, thanks for listening. On to the real presentation. Maria showed us how to look for exoplanets when they wobble along our line of sight. But what if they wobble perpendicular to that? Careful measurement should show that, right? The ancients thought that holy forces had permanently set the positions of all the stars except for the planets so they didn’t measure that close. Tycho Brahe took meticulous measurements with room‑sized instruments—”

<voice from the back> “Room‑sized? What difference does that make?”

“What if I told you that two stars are 3 millimeters apart in the sky?”

<another voice> “How far out’s your ruler? Sky stuff, you need to talk angles because that’s all you got.”

“Well there you go. That’s why Tycho went for maximum angle‑measuring accuracy. He built a sextant with a 5‑foot radius. He used an entire north‑south wall as a quadrant. His primary instrument was an armillary sphere three yards across.”

<first voice again> “Wait, a sphere, like a big bubble? Why north‑south? What’s a quadrant?”

  • I give him a nudge. “He’s just a kid, Mr Feder. Be nice. One question at a time.”
  • “But I got so many!”

“Think about Tycho’s goal. Like astrometers before him, he wanted to build an accurate map of the heavens. Native Americans a thousand years or more ago carved free‑hand star maps on cave ceilings and turtle shells. Tycho followed the Arabic and Chinese quantitative mapping traditions. There’s two ways to do that. One is to measure and map the visual angles between many pairs of stars. That strategy fails quickly because errors accumulate. Four or five steps along the way you’re plotting the same star in two different locations.”

<Feder’s voice again> “There’s a better way?”

“Yessir. Measure and map each star relative to a standard coordinate system. If your system’s a good one, errors tend to average out. The latitude‑longitude system works well for locating places on Earth. Two thousand years ago the Babylonians used something similar for places in the crystal sphere they thought supported the stars above us. Where the equinoctial Sun rose on the horizon was a special direction. Their buildings celebrated it. Starting from that direction the horizontal angle to a star was its longitude. The star’s latitude was its angle up from the horizon towards the zenith straight above. But those map coordinates don’t work for another part of the world. Astrometers needed something better.”

<Feder again> “So what did they do already?”

“They may or may not have believed the Earth itself is round, but they recognized the Pole Star’s steady position that the rest of the sky revolved around. They also noticed that as each month went by the constellations played ring‑a‑rosie in a plane perpendicular to the north‑south axis. Call that the Plane of The Ecliptic. Pick a star, measure its angle away from the Ecliptic and you’ve got an ecliptic latitude. Measure its angle around the Ecliptic away from a reference star and you’ve got a ecliptic longitude. Tycho’s instruments were designed to measure star coordinates. His quadrant was a 90° bronze arc he embedded in that north‑south wall, let him measure a star’s latitude as it crossed his meridian. His ‘Sphere’ was simply a pair of calibrated metal rings on a gimbal mounting so he could point to target and reference stars and measure the angle between them. If his calibration used degree markings they’d be about 25 millimeters apart. His work was the best of his time but the limit of his accuracy was a few dozen arcseconds.”

“Is that bad?”

“It is if you’re looking for exoplanets by watching for stellar wobble. Maria’s Jupiter example showed the Sun wobbling by 1½ million kilometers. I worked this example with a bigger wobble and a star that would be mid‑range for most of our constellations. Best case, we’d see its image jiggling by about 90 microarcseconds. Tycho’s instruments weren’t good enough for wobbles.”

~~ Rich Olcott

DARTing to A Conclusion

On By rolcottIn Astronomy, Space Travel, Uncategorized2 Comments

The park’s trees are in brilliant Fall colors, the geese in the lake dabble about as I walk past but then, “Hey Moire, I gotta question!”

“Good morning, Mr Feder. What can I do for you?”

“NASA’s DART mission to crash into Diddy’s mos’ asteroid—”

“The asteroid’s name is Didymos, Mr Feder, and DART was programmed to crash into its moon Dimorphos, not into the asteroid itself.”

“Whatever. How’d they know it was gonna hit the sunny side so we could see it? If it hits in the dark, nobody knows what happened. They sent that rocket up nearly a year ago, right? How’d they time that launch just right? Besides, I thought we had Newton’s Laws of Motion and Gravity to figure orbits and forces. Why this big‑dollar experiment to see if a rocket shot would move the thing? Will it hit us?”

“You’re in good form today, Mr Feder.” <unholstering Old Reliable> “Let me pull some facts for you. Ah, Didymos’ distance from the Sun ranges between 1.01 and 2.27 astronomical units. Earth’s at 1.00 AU or 93 million miles, which means that the asteroid’s orbit is 930 000 miles farther out than ours, four times our distance to the Moon. That’s just orbits; Earth is practically always somewhere else than directly under Didymos’ point of closest approach. Mm… also, DART flew outward from Earth’s orbit so if the impact has any effect on the Didymos‑Dimorphos system it’ll be to push things even farther away from the Sun and us. No, I’m not scared, are you?”

“Who me? I’m from Jersey; scare is normal so we just shrug it off. So why the experiment? Newton’s not good enough?”

“Newton’s just fine, but collisions are more complicated than people think. Well, people who’ve never played pool.”

“That’s our national sport in Jersey.”

“Oh, right, so you already know about one variable we can’t be sure of. When the incoming vector doesn’t go through the target’s center of mass it exerts torque on the target.”

“We call that ‘puttin’ English on it.'”

“Same thing. If the collision is off‑center some of the incoming projectile’s linear momentum becomes angular momentum in the target object. On a pool table a simple Newtonian model can’t account for frictional torque between spinning balls and the table. The balls don’t go where the model predicts. There’s negligible friction in space, you know, but spin from an off‑center impact would still waste linear momentum and reduce the effect of DART’s impact. But there’s another, bigger variable that we didn’t think much about before we actually touched down on a couple of asteroids.”

“And that is…?”

“Texture. We’re used to thinking of an asteroid as just a solid lump of rock. It was a surprise when Ryugu and Bennu turned out to be loose collections of rocks, pebbles and dust all held together by stickiness and not much gravity. You hit that and surface things just scatter. There’s little effect on the rest of the mass. Until we do the experiment on a particular object we just don’t know whether we’d be able to steer it away from an Earth‑bound orbit.”

“Okay, but what about the sunny‑side thing?”

“Time for more facts.” <tapping on Old Reliable> “Basically, you’re asking what are the odds the moonlet is in eclipse when DART arrives on the scene. Suppose its orbit is in the plane of the ecliptic. Says here Dimorphos’ orbital radius is 1190 meters, which means its orbit is basically a circle 3740 meters long. The thing is approximately a cylinder 200 meters long and 150 meters in diameter. Say the cylinder is pointed along the direction of travel. It occupies (200m/3740m)=5% of its orbit, so there’s a 5% chance it’s dark, 95% chance it’s sunlit.”

“Not a bad bet.”

“The real odds are even better. The asteroid casts a shadow about 800 meters across. Says here the orbital plane is inclined 169° to the ecliptic so the moonlet cycles up and down. At that tilt and 1190 meters from Didymos, 200‑meter Dimorphos dodges the shadow almost completely. No eclipses. DART’s mission ends in sunlight.”

~~ Rich Olcott

  • Thanks to my brother Ken, who asked the question but more nicely.

Footprints in The Glasses

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

I think he sometimes lies in wait for me like a cheetah crouching to ambush prey. No, more like a frog. Today I’m on my daily walk when suddenly — “Hey Moire, I got questions!”

Yeah, more like a frog. “Morning, Mr Feder. Out early today, aren’t you?”

“It’s gonna be hot today so I figured you’d walk the park early. I like it down here by the lake.”

Yup, definitely a frog. “Well, what can I do for you?”

“I’m wearing these new glasses, okay?”

“I can see that. Very … stylish.”

“So I read what you wrote about how light slows down when it goes through stuff and I wonder, does the light slow down enough going through these glasses that I might not see a bus in time? And how does stuff slow down light anyway?”

<drawing Old Reliable from its holster> “That first question is quantitative so let’s gather the numbers. The speed of light in vacuum is about 186 000 miles per second, that’s 300 megameters per second or 300 millimeters per nanosecond. Metric system conversions are kinda fun, aren’t they?”

“Hang on — megameters per second is meters per microsecond, take it down another thousand top and bottom…. I guess that’s okay.”

“Old Reliable doesn’t lie. Alright, your eyeglass lenses look like they’re a couple of millimeters thick. I’ll call it three millimeters to make the numbers pretty. If your lenses were vacuum space a short light pulse would pass through in 0.01 nanosecond, okay?”

“Not that thick, but go on.”

“The slow‑down factor is technically called the refractive index. Old Reliable says that eyeglass refractive indexes typically run about 1.5 so with the slow‑down our light pulse would take 0.015 nanosecond instead of 0.01. Is that enough increase to affect your rection time significantly? Let’s see … Says here that a typical nerve impulse travels at about 50 meters per second. Keeping the numbers pretty I’ll guess that between your eye and the vision centers in the back of your brain is about 2 inches or 5 centimeters. You good with that?”

“Not that short, but anything for pretty numbers. Go on.”

“Five centimeters is 0.05 meters, at 50 meters per second comes to 0.001 second. Slowing down that pulse lengthens your reaction time from 0.001 second to 0.001 000 000 015 second. Not enough of a difference to worry about.”

“But how come it slows at all seeing as I’ve heard it’s mostly empty space between the atoms?”

“There’s empty and there’s empty. You’re thinking of little solar‑system atoms, aren’t you, with particle electrons orbiting the nucleus and what space is left is vacuum. We’ve known for a century that it’s not that way. The electrons aren’t particles, they’re fuzzy blobs, and the volume around them is chock full of lumpy electric field. The incoming lightwave, really an electromagnetic wave, doesn’t see one electron here and another one way over there and free passage in between. Nope, it interacts with the whole field and that’s where the slow‑down happens.”

“Lots of quantum jumps and like that, huh?”

“No quantum jumps unless your glasses are tinted. Mmm… You ever run along the seashore?”

“I’m from Jersey. Of course I have.”

 Time periodicity at a point,
 space periodicity at a moment.

“Visualize running across hard sand and suddenly you hit a patch of soft sand. You keep your feet oscillating up and down at the same rate, but you make less progress along the beach. Your footprints get closer together, right?”

“Sometimes I fall down. So?”

“Something similar happens with a lightwave. It repeats in time like your foot going up and down and it repeats in space like your footprints in the sand. The wave’s energy changes with repeat time. When light passes through an electric field like the one inside clear, colorless glass, the field doesn’t absorb energy — no change in repeat time. What does happen is the field squeezes the peak‑to‑peak distance. The wave acts like your footprints getting closer together. Less distance divided by the same time means lower speed. The wave slows down inside the glass.”

“Does light ever fall down?”

“Only if its energy quantum matches an absorber’s gap.”

~~ Rich Olcott

The Tops of Time

On By rolcottIn Cosmology, UncategorizedLeave a comment

Mr Feder doesn’t let go of a topic. He’s still stewing about Time. “Moire or somebody said the Big Bang is the Bottom of Time because there wasn’t any time before then. I guess I gotta buy that, but bottoms gotta have tops. What’s the Top of Time?”

“Whoa, Mr Feder, that’s a fuzzy question with a lot of answers, most of which are guesses.”

“No theories?”

“Not really, A few used to be called theories but people started muttering about testability so the theories got downgraded to hypotheses and now they’re guesses except for the ones that’ve been dropped altogether.”

“Like what?”

“Steady State, for one — the idea that Time has no end. That used to be popular, mostly because it was simple. Problem was, Edwin Hubble showed that other galaxies are separate from the Milky Way and in fact they’re receding from us. That clashed with the Cosmological Principle, the idea that on a large scale things are pretty much the same everywhere. Galaxies moving away from each other leave behind empty space that isn’t ‘pretty much the same.’ For the Steady State model to work, new matter would have to spring into existence between the departing galaxies.”

“Nature hates a vacuum, eh?”

“Apparently she doesn’t. Evidence has piled up against the Steady State model and in favor of the Big Bang. We still think the Cosmological Principle is a good assumption, but only on scales bigger than a few hundred million lightyears.”

“So Time has a Top, then.”

“Depends on how you define ‘Top.’ We’re now into Metaphysics territory, where theories come cheap and flimsy. It’s conceivable, for instance, that the Universe curves back onto itself along one or more of its dimensions. If it loops back along the time dimension then we’d be in an oscillating universe that cycles from Big Bang to Big Crunch and back out again. Time would have no Top or Bottom. Crosswise to time, some thinkers like the idea that the Universe circles back along a space dimension. If that’s true and we could see far enough we could inspect the back of our heads.”

“Wait, we’ve got lots of black holes. If their singularities are in the infinite future like you said, that’d stymie the circling.”

“Good point, Vinnie. As I understand the math, connectivity like that is possible if our 4D spacetime is embedded in a ‘bulk‘ with five or more dimensions. But that’s more complicated than I’m willing to accept without at least some evidence which no-one’s shown me yet. The endings of the 2001 and Interstellar movies don’t count.”

“What else you got?”

“What other theories, Mr Feder? How about block universes? Maybe the space dimensions are solid but only part of the time dimension is real. Some people opine that the only reality is ‘NOW,’ an infinitely thin slice of time evolving towards the future. A memory would only be a surviving imprint of things that stopped existing when Time was done with them.”

“I don’t like that one. For one thing, it doesn’t jibe with the ‘everyone’s got their own NOW‘ thing from relativity.”

“Einstein didn’t like it either. The easiest way to reconcile all those different versions of NOW is to assume that they all co‑exist permanently. I call that notion the closed block model. The idea is that all reality — past, present and future — is real and rigid. We perceive time as flowing only because consciousness floats upward along the time coordinate. The Top of Time is way up there, just waiting for us to arrive.”

“Why no sinking downward?”

“Good question, no good answer that I’ve seen. Besides, the closed block model doesn’t allow for free will. I like having free will.”

“Me, too. OK, if there’s closed block, what’s open block?”

“The future doesn’t exist yet. Picture the open block model as our 4D spacetime being a bowl with the Big Bang at the bottom. Time progressively fills the bowl like water. NOW is the Top of Time. Those relativity‑shifted NOWs only show up when we compare records of past observations.”

“Cheap and flimsy, but a pretty picture.”

Adapted from a public domain image,
Credit: NASA/WMAP Science Team

~~ Rich Olcott

Why I Never Know What Time It Is

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

It’s always fun watching Richard Feder (of Fort Lee, NJ) as he puts two and two together. He gets a gleam in his eye and one corner of his mouth twitches. On a good day with the wind behind him I’ve seen his total get as high as 6½. “I wanna get back to that ‘everybody has their own time‘ monkey‑business where if you’re moving fast your clock slows down. What about the stardates on Star Trek? Those guys go zooming through space at all different angles and speeds. How do they keep their calendars in synch?”

Trekkie and Astronomy fan Al takes the bait. “Artistic license, Mr Feder. The writers can make anything happen, subject to budgets and producer approval. The first Star Trek series, they just used random four‑digit numbers for stardates. That was OK because the network aired the episodes in random order anyway so no‑one cared about story arc continuity. Things were more formal on Captain Picard’s Enterprise, as you’d expect — five‑digit stardates, first digit always ‘4‘ for 24th Century, thousands digit was ‘1‘ for season one, ‘2‘ for season two and so on. Working up the other way, the digit right of the decimal point was tenths of a standard day, the units place counted days within an episode and the tens and hundreds they just picked random numbers.”

“I suppose that’s what they did, but how could they make it work? You guys yammer on about time dilation. Say a ship’s running at Warp Whoop‑de‑doo, relativity should slow its calendar to a crawl. You couldn’t get a whole fleet into battle position when some of the ships had to get started years ahead of time. And that’s just the dilation slow-down, travel time’s on top of that.”

“Travel time measured how, Mr Feder, and from where?”

“Well, there you go, Cathleen, that’s what I’m talking about!”

“You know that Arthur C Clarke quote, ‘Any sufficiently advanced technology is indistinguishable from magic‘? The Enterprise crew’s always communicating with ‘sub‑space radio’, which sure looks like magic to me. They could send sync pulses through there along with chatter. When you drop out of warp space, your clocks catch the pulses and sync up, I suppose.”

“There’s a deeper issue than that, guys.”

“What’s that, Sy?”

“You’re talking like universal time is a thing, which it isn’t. Hasn’t been since Einstein’s Special Relativity used Minkowski’s math to stir space and time together. General Relativity scrambles things even worse, especially close to a strong gravity center. You remember about gravity forcing spacetime to curve, right? The curvature inside a black hole’s event horizon gets so tight that time rotates toward the geometric center. No, I can’t imagine what that looks like, either. The net of it, though, is that a black hole is a funnel into its personal future. Nothing that happens inside one horizon can affect anything inside another one so different holes could even have different time rates. We’ve got something like 25000 or more stellar black holes scattered through the Milky Way, plus that big one in the center, and that’s just one galaxy out of billions. Lots of independent futures out there.”

“What about the past, Sy? I’d think the Big Bang would provide a firm zero for time going forward and it’s been one second per second since then.”

“Nup. Black holes are an extreme case. Any mass slows down time in its vicinity, the closer the slower. That multi‑galaxy gravitational lens that lets us see Earendel? It works because the parts of Earth‑bound light waves closest to the center of mass see more time dilation than the parts farther away and that bends the beam toward our line of sight.”

“Hey, that reminds me of prisms bending light waves.”

“Similar effect, Vinnie, but the geometry’s different. Prisms and conventional lenses change light paths abruptly at their surfaces. Gravitational lenses bend light incrementally along the entire path. Anyhow, time briefly hits light’s brakes wherever it’s near a galaxy cluster, galaxy or anything.”

“So a ship’s clock can fidget depending on what gravity it’s seen recently?”

“Mm-hm. Time does ripples on its ripples. ‘Universal Time‘ is an egregious example of terminology overreach.”

~~ Rich Olcott

Pushing It Too Far

On By rolcottIn Astronomy: Techniques, Cosmology, UncategorizedLeave a comment

It’s like he’s been taking notes. Mr Feder’s got a gleam in his eye and the corner of his mouth is atwitch. “You’re not getting off that easy, Cathleen. You said that Earendell star’s 66 trillion lightyears away. Can’t be, if the Universe’s only 14 billion years old. What’s going on?”

“Oops, did I say trillion? I meant billion, of course, 109 not 1012. A trillion lightyears would be twenty times further than the edge of our observable universe.”

“Hmph. Even with that fix it’s goofy. Sixty-six billion is still what, five times that 14 billion year age you guys keep touting. I thought light couldn’t travel that far in that time.”

“I thought the Universe is 93 billion light years across.”
  ”That’s diameter, and it’s just the observable universe.”
    ”Forty-seven billion radially outward from us.”
      ”None of that jibes with 14 billion years unless ya got stuff goin’ faster than light.”

“Guys, guys, one thing at a time. About that calculation, I literally did it on the back of an envelope, let’s see if it’s still in my purse … Nope, must be on my office desk. Anyhow, distance is the trickiest part of astronomy. The only distance‑related thing we can measure directly is z, that redshift stretch factor. Locate a familiar pattern in an object’s spectrum and see where its wavelength lies relative to the laboratory values. The go‑to pattern is hydrogen’s Lyman series whose longest wavelength is 121 nanometers. If you see the Lyman pattern start at 242 nanometers, you’ve got z=2. The report says that the lens is at z=2.8 and Earendel’s galaxy is at z=6.2. We’d love to tie those back to distance, but it’s not as easy as we’d like.”

“It’s like radar guns, right? The bigger the stretch, the faster away from us — you should make an equation outta that.”

“They have, Mr Feder, but Doppler’s simple linear relationship is only good for small z, near zero. If z‘s greater than 0.1 or so, relativity’s in play and things get complicated.”

“Wait, the Hubble constant ties distance to speed. That was Hubble’s other big discovery. Old Reliable here says it’s something like 70 kilometers per second for every megaparsec distance. What’s that in normal language? <tapping keys> Whoa, so for every lightyear additional distance, things fly away from us about an inch per second faster. That’s not much.”

“True, Sy, but remember we’re talking distant, barely observable galaxies that are billions of lightyears away. Billions of inches add up. Like with the Doppler calculation, you get startling numbers if you push a simple linear relation like this too far. As an extreme example, your Hubble rule says that light from a galaxy 15 billion lightyears away will never reach us because Hubble Flow moves them away faster than photons fly toward us. We don’t know if that’s true. We think Hubble’s number changes with time. Researchers have built a bucketful of different expansion models for how that can happen; each of them makes different predictions. I’m sure my 66 came from one of those. Anyhow, most people nowadays don’t call it the Hubble constant, it’s the Hubble parameter.”

“Sixty-six or forty-seven or whatever, those diameters still don’t jibe with how long the light’s had a chance to travel.”

“Sy, care to take this? It’s more in your field than mine.”

“Sure, Cathleen. The ‘edge of the observable universe‘ isn’t a shell with a fixed diameter, it simply marks the take-off points for the oldest photons to reach us so far. Suppose Earendel sent us a photon about 13 billion years ago. The JWST caught it last night, but in those 13 billion years the universe expanded enough to insert twenty or thirty billion lightyears of new space between between here and Earendel. The edge is now that much farther away than when the photon’s journey started. A year from now we’ll be seeing photons that are another year older, but the stars they came from will have flown even farther away. Make sense?”

“A two-way stretch.”

“You could say that.”

~~ Rich Olcott

  • Thanks to my brother Neil, who pointed out the error and asked the question.

A Needle in A Needlestack

On By rolcottIn Astronomy: Techniques, James Webb Space Telescope, UncategorizedLeave a comment

“How’d they find that far-away star, Cathleen? Seems like you’d have to know just where to point your telescope.”

“It’s worse than that, Al, first you’ve got to find that telescope, or more precisely, its lens. We can’t simply swing a black hole or galaxy cluster into position for a good look at something interesting. No, we have to discover lensing objects that magnify good stuff beyond them. The good news is that some of those are out there, but the bad news is that the sky is cluttered with far more objects that don’t play the game we want. This research team appears to have hit paydirt but they did it with humungous power shovels and heavy‑duty panning techniques.”

“Impressive metaphor, Cathleen. Could you un‑metaphor it for us?”

“Sure, Sy. The power shovels are Hubble and Spitzer, both of which piled up beaucoodles of data from decades of infrared observing time.”

“I thought Hubble was designed for visible and UV surveillance.”

“It is, mostly, but since 2009 its instrument suite included WFC3, a camera that’s sensitive out to 1700 nanometers and covers a square 2 arcminutes on a side. That’s a lot, by big‑telescope astronomy standards.”

“Wait, arcminutes?”

“That’s right, Mr Feder. We astronomers have trouble with distances but we’re good at measuring angles. The Moon’s about a degree across. One degree is sixty arcminutes, next step down is sixty arcseconds per arcminute. After that we go semi‑metric, milliarcseconds and so forth. One WFC3 pixel records a patch of sky 130 milliarcseconds across. JWST‘s NIRCam instrument has a resolution twice as sharp. Anyway, Hubble‘s 1700‑nanometer limit is plenty good enough to pick up 120‑nanometer hydrogen light that’s been stretched out by a factor of z=2.8. Distance and stretch correlate; the lens that highlighted Earendel and its Sunrise Arc for NASA and Vinnie is that far away.”

“How far away?”

“It’s tricky to answer that. The spectra we see let us measure an object’s z‑factor, which by way of the Doppler effect tells us how fast the object is moving away. Hubble’s constant ties that to distance, sort of. My convenient rule of thumb is that an object whose z is near 2 is running away at 80% of lightspeed and on the average is about 55 trillion lightyears from us but don’t quote me because relativity complicates matters. Using the same dicey calculation I estimated the lens and Earendel velocities at 87% and 96% of lightspeed, which would put their ‘proper distances‘ around 60 and 66 trillion lightyears away. And no, I’m not going to go into ‘proper distance‘ versus ‘comoving distance‘.”

“Let’s get back to your metaphor, Cathleen. I get that Hubble and Spitzer and such generated a ton of data. What’s the panning part about?”

“Well, in the old days it would have been hired hands and graduate students spending years peering at dots on photographic plates. These days it’s computers, thank Heaven. The research team used a series of programs to filter their digital data. The software had to decide which dots are stars or noise specks and which are galaxies or arcs. Then it picked out the reddest red galaxy images, then clusters of galaxy images at the same redness level that are near each other in space, then clusters with arcs around them. I said that WFC3 covers a square 2 arcminutes on a side, remember? The sky, both hemispheres, contains almost 2½ million squares like that, although the surveys didn’t get all of them. Anyhow, after burning through cubic acres of computer time the team found 41 deep red lensing clusters.”

“Only 41.”

“Yup.”

We ponder that for a minute, then Vinnie pipes up. “Wait, the dots are in color?”

“No, but these images are generally taken through a filter that transmits only a known narrow wavelength range, infrared or whatever. Using relative dot intensity at several different wavelengths you can create ‘false color‘ images. When you find something, you know where to point spectroscopic tools to be sure you’ve found the good stuff.”

“Like a star shining less than a billion years after the Big Bang.”

“Paydirt.”

Image adapted from NASA and STScI

~~ Rich Olcott

Now And Then And There

On By rolcottIn Cosmology, James Webb Space Telescope, Physics: Light and Relativity, UncategorizedLeave a comment

Still at our table in Al’s otherwise empty coffee shop. We’re leading up to how Physics scrambled ‘Now‘ when a bell dings behind the counter. Al dashes over there. Meanwhile, Cathleen scribbles on a paper napkin with her colored pencils. She adds two red lines just as Al comes back with a plate of scones. “Here, Sy, if you’re going to talk Minkowski space this might be useful.”

“Hah, you’re right, Cathleen, this is perfect. Thanks, Al, I’ll have a strawberry one. Mmm, I love ’em fresh like this. OK, guys, take a look at Cathleen’s graphy artwork.”

“So? It’s the tile floor here.”

“Not even close, Mr Feder. Check the labels. The up‑and‑down label is ‘Time’ with later as higher. The diagram covers the period we’ve been sitting here. ‘Now‘ moves up, ‘Here’ goes side‑to‑side. ‘Table‘ and ‘Oven‘, different points in space, are two parallel lines. They’re lines because they both exist during this time period. They’re vertical because neither one moves from its relative spatial position. Okay?”

“Go on, Moire.”
  ”Makes sense to me, Sy.”

“Good. ‘Bell‘ marks an event, a specific point in spacetime. In this case it’s the moment when we here at the table heard the bell. I said ‘spacetime‘ because we’re treating space and time as a combined thing. Okay?”

“Go on, Moire.”
  ”Makes sense to me, Sy.”

“So then Al went to the oven and came back to the table. He traveled a distance, took some time to do that. Distance divided by time equals velocity. ‘Table‘ has zero velocity and its line is vertical. Al’s line would tilt down more if he went faster, okay?”

“Mmmm, got it, Sy.”
  ”Cute how you draw the come-back label backwards, lady. Go on, Moire.”

“I do my best, Mr Feder.”

“Fine, you’ve got the basic ideas. Now imagine all around us there’s graph paper like this — except there’s no paper and it’s a 4‑dimensional grid to account for motion in three spatial dimensions while time proceeds. Al left and returned to the same space point so his spacetime interval is just the time difference. If two events differ in time AND place there’s special arithmetic for calculating the interval.”

“So where’s that get us, Moire?”

“It got 18th and 19th Century Physics very far, indeed. Newton and everyone after him made great progress using math based on a nice stable rectangular space grid crossed with an orderly time line. Then Lorentz and Poincaré and Einstein came along.”

“Who’s Poincaré?”

“The foremost mathematician of nineteenth Century France. A mine safety engineer most days and a wide‑ranging thinker the rest of the time — did bleeding‑edge work in many branches of physics and math, even invented a few branches of his own. He put Lorentz’s relativity work on a firm mathematical footing, set the spacetime and gravity stage for Minkowsky and Einstein. All that and a long list of academic and governmental appointments but somehow he found the time to have four kids.”

Simultaneity Animation by “Acdx”
licensed under Creative Commons Attribution-Share Alike 4.0 International.

“A ball of fire, huh? So what’d he do to Newton’s jungle gym?”

“Turned its steel rod framework into jello. Remember how Cathleen’s Minkowski diagram connected slope with velocity? Einstein showed how Lorentz’s relativity factor sets a speed limit for our Universe. On the diagram, that’d be a minimum slope. Going vertical is okay, that’s standing still in space. Going horizontal isn’t, because that’d be instantaneous travel. This animation tells the ‘Now‘ story better than words can.”

“Whah?”
  ”Whah?”

“We’re looking down on three space travelers and three events. Speeds below lightspeed are within the gray hourglass shape. The white line perpendicular to each traveler’s time line is their personal ‘Now‘. The travelers go at different velocities relative to us so their slopes and ‘Now‘ lines are different. From our point of view, time goes straight up. One traveler is sitting still relative to us so its timeline is marked ‘v=0‘ and parallels ours. We and the v=0 traveler see events A, B and C happening simultaneously. The other travelers don’t agree. ‘Simultaneous‘ is an illusion.”

~~ Rich Olcott

Hyperbolic plane image by Murdock Grewar,
licensed under Creative Commons Attribution-Share Alike 4.0 International.

Now And Then

On By rolcottIn James Webb Space Telescope, Mathematics, Physics: Light and Relativity, UncategorizedLeave a comment

“Alright, I suppose there’s no going down below the Universe’s Year Zero, but what about the other direction? Do you physics guys have a handle on Time’s Top?”

“That’d be Cosmology, Mr Feder. We physicists avoid theorizing about stuff we can’t check against data. Well, except for string theory. The far past leaves clues that astronomers like Cathleen can gather. Sad to say, though, we barely have a handle on Now.”

Cathleen grins. Al and Mr Feder go, “Whaaat?”

“No, really. One of Einstein’s insights was that two observers randomly and independently flying through space won’t be able to agree on whether two external events occurred simultaneously. They can’t even agree on what time it is now.”

“Oh, yeah, I know about that. I’ve read about how the GPS system needs to make corrections to account for what relativity does to the satellite timings.”

“You’re right, Al, but that’s a different issue. Some of that relativistic correction has to do with space compression because of Earth’s mass. The simultaneity problem is strictly about rapid motion and geometry.”

“Wait — geometry?”

“Relativistic geometry, which is a bit different from the kind that Descartes built.”

“Whoa, Sy, slow down there. Descartes was the ‘I think therefore I am‘ guy, right? What’s that got to do with geometry?”

“I guess I got a little ahead of myself there, didn’t I? OK. Yeah, Al, same Descartes. Grew up Catholic in France, was a professional mercenary soldier in the Thirty Years War, wound up fighting first on the Catholic French side and later on fought on the Protestant Dutch side but cross‑over was common, both directions. He realized he was in an ostensibly religious war that was really about who ruled over whom. That may have had something to do with him becoming a professional philosopher who rejected all religious dogmas in favor of what he could learn solely from logic and his own senses. That’s where his famous mantra came from — he started by proving to himself that he existed.”

“Logic led to geometry, I suppose.”

“Indeed, but a new kind, one that required a few innovations that Descartes developed. On the one hand, mathematicians traditionally expressed algebraic problems in words and some of them were doozies, like saying ‘the zenzizenzizenzic‘ where we’d just say x8. We got that simple but <ahem> powerful notation from Descartes. On the geometry side, he’d ditch all the confusing line-ending markers in a diagram like this one. Instead, he’d label the whole line representing a known quantity with a front-of-the-alphabet letter like a or b or c. A line representing an unknown quantity would get its label from the alphabet-trailers like x, y and z. Then he used the same character conventions and his new power notation to write and manipulate algebraic expressions. Those notational inventions were foundational for his bridge between algebraic and geometrical problems. Draw your problem with lines and curves, transform it to algebraic equations, solve that problem exactly, transform it back to geometry and you’re done. Or vice-versa.”

The mesolabe instrument (in red).

“That goes back to Descartes, huh?”

“Mm-hm. His big innovation, though, arose from a borrow from an early Greek gadget called a mesolabe. He proposed an idealized version that would let someone break a line into exact fractions or compare a length against a unit length. That broke the rules of classical Geometry but setting his mesolabe’s Y‑angle to 90° prompted him to name points by their distance along the x– and y‑axes. That’s the nub of the Cartesian coordinate system — a rectangular grid of numbered straight lines that go on forever. Graph paper, right? Wrap the grid around the Earth and you’ve got latitudes and longitudes. Add more numbered grid lines perpendicular to either grid and you’ve got z‑axis coordinates. Three coordinates let you name any point in space. Newton and all the physicists who came after him until the dawn of the 20th Century assumed Descartes’ nice, stable coordinate system.”

“20th Century — that’s when Einstein came on the scene. He broke that system?”

“Sure did. You’ve heard about bent space?”

“Who hasn’t?”

“Well, fasten your seat belts, it’s going to be a fun ride.”

~~ Rich Olcott