The Tops of Time

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

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

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 Thumbtack in A Needlestack

“What’re the odds?”

“Odds on what, Vinnie?”

“A gazillion galaxies out there, only 41 lensing galaxy clusters, but one of them shows us a singleton star. I mean, what’s special about that star? What are the odds?”

I can’t help it. “Astronomical, Vinnie.”

Cathleen punches my shoulder, hard. “Sy Moire, you be ashamed of yourself. That pun was ancient a century ago. Vinnie, the odds are better than they seem. We didn’t just stumble on Earendel and the Sunrise Arc, we found them in a highly targeted Big Data search for things just like that — objects whose light was extremely stretched and also gravitationally bent in our direction. The Arc’s lensing galaxy cluster has a spherical effect, more or less, so it also acts on light from other far-away objects and sends it in other directions. It even bends an image of our Milky Way towards Earendel’s galaxy.”

“I call weaseling — you used ‘more or less‘.”

“Guilty as charged, Vinnie. A nice, spherical black hole is the simplest case of gravitational lensing — just one mass at the center of its simple light‑bending gravity field. Same thing for a single star like our Sun. Clusters are messy. Tens or hundreds of billion‑star galaxies, scattered at random angles and random positions about their common center of mass. The combined gravity field is lumpy, to say the least. Half of that research paper is devoted to techniques for estimating the field and its effects on light in the region around the Arc.”

“I guess they had to get 3D positions for all the galaxies in the cluster. That’d be a lot of work.”

“It would, Al, but that’s beyond what current technology can do. Instead, they used computer models to do — get this, Sy — curve fitting.”

<chuckle> “Good one, Cathleen.”

“What’s so funny?”

“There’s a well-established scientific technique called ‘curve fitting.’ You graph some data and try to find an equation that does a respectable job of running through or at least near your data points. Newton started it, of course. Putting it in modern terms, he’d plot out some artillery data and say, ‘Hmm, that looks like a parabola H=h+v·t+a·t2. I wonder what values of h, v and a make the H-t curve fit those measurements. Hey, a is always 32 feet per second per second. Cool.’ Or something like that. Anyhow, Cathleen’s joke was that the researchers used curve fitting to fit the Sunrise Arc’s curve, right?”

“They did that, Sy. The underlying physical model, something called ‘caustic optics,’ says that—”

“Caustic like caustic soda? I got burnt by that stuff once.”

Image by Heiner Otterstedt,
under the Creative Commons Attribution-Share Alike 3.0 Unported license

“That’s the old name for sodium hydroxide, Vinnie. It’s a powerful chemical and yeah, it can give you trouble if you’re not careful. That name and caustic optics both come from the Greek word for burning. The optics term goes back to using a lens as a burning glass. See those focused patterns of light next to your water glass? Each pattern is a caustic. The Arc’s lensing cluster’s like any light‑bender, it’s enclosed in a caustic perimeter. Light passing near the perimeter gets split, the two parts going to either side of the perimeter. The Earendel team’s curve‑fitting project asked, ‘Where must the caustic perimeter be to produce these duplicate galaxy images neighboring the Arc?‘ The model even has that bulge from the gravity of a nearby foreground galaxy.”

“And the star?”

“Earendel seems to be smack on top of the perimeter. Any image touching that special line is intensified way beyond what it ought to be given the source’s distance from us. It’s a pretty bright star to begin with, though. Or maybe two stars.”

“Wait, you don’t know?”

“Not yet. This study pushed the boundaries of what Hubble can do for us. We’re going to need JWST‘s infrared instruments to nail things down.”

Al’s in awe. “Wow — that caustic’s sharp enough to pick one star out of a galaxy.”

“Beat the astronomical odds, huh?”

Adapted from a public-domain image.
Credit: Science: NASA / ESA / Brian Welch (JHU) / Dan Coe (STScI); Image processing: NASA / ESA / Alyssa Pagan (STScI)

~~ Rich Olcott

A Needle in A Needlestack

“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

When The Stars Are Aligned Right

Cathleen and I are chatting when Vinnie bursts into the coffee shop waving a newspaper. “New news, guys, they’ve just announced Hubble spotted the farthest‑away star. How about that? Think what JWST will be able to do!”

Cathleen raises an eyebrow. “Sounds like press release science. What else do they say?”

“Not a whole lot. Lessee… These guys went through old Hubble data and found a piece of an Einstein ring which I don’t know what that is and partway along the ring is a star and somehow they figured out it’s 50 times heavier than the Sun and 12 billion years old and it’s the farthest star they’ve ever seen and that’s why NASA’s all excited.”

“Do you believe all that?”

“Maybe the NASA PR people do?”

“Maybe. I just read the technical paper behind that announcement. The authors themselves aren’t absolutely sure. The paper’s loaded with supporting evidence and ‘how we did it‘ details but it’s also loaded with caveats. The text includes a string of alternative explanations for their observations, winding up with a typical ‘we await further evidence from JWST‘ statement. Reads a lot more like real science. Besides, we’ve already seen more distant stars but they’re all jumbled together inside their very distant galaxies.”

“Unpack it for me. Start with what’s an Einstein ring?”

“It’s a gravitational lensing effect. Sy, does Old Reliable still have a copy of that graphic you did about gravitational lensing?”

“That was years ago. Let me check… Uh‑huh, here it is.”

“Thanks. Vinnie, you know how a prism changes light’s direction.”

“Sy and me, we talked about how a prism bends light when light crosses from air to glass or the other way ’cause of the different speed it goes in each material. Uhh, if I remember right the light bends toward the slower speed, and you get more bend with shorter wavelengths.”

“Bingo, Vinnie. Gravitational lensing also bends light, but the resemblance ends there. The light’s just going through empty space, not different media. What varies is the shape of spacetime itself. Say an object approaches a heavy mass. Because of relativity the space it moves through appears compressed and its time is dilated. Compressed distance divided by dilated time means reduced velocity. Parts of a spread‑out lightwave closest to the mass slow down more than parts further way so the whole wave bends toward the heavy mass. Okay?”

“Hold on. Umm, so in your picture light coming towards us from that galaxy doesn’t get blocked by that black thingy, the light bends around it on both sides and focuses in on us?”

“Exactly. Now carry it further. The diagram cuts a flat 2D slice along round 3D spatial reality. Those yellow lines really are cones. Three‑sixty degrees around the black blob, the galaxy’s light bends by the same amount towards the line between us and the blob. Your Einstein ring is a cut across the cone, assuming that the galaxy, the blob and Earth are all exactly on the same straight line. If the galaxy’s off‑center the picture isn’t as pretty — you only get part of a ring, like those red arcs in Sy’s diagram.”

“A galactic rainbow. That ought to be awesome!”

“Well it would be, but there’s another difference between prisms and blobs. Rainbows happen because prisms and raindrops bend short‑wavelength colors more than longer ones, like you said. Gravitational lensing doesn’t care about wavelength. Wavelengths do shift as light traverses a gravitational well but the outbound red shift cancels the inbound blue shift.. Where gravity generates an Einstein ring, all wavelengths bend through the same angle. Which is a good thing for bleeding‑edge astronomy researchers.”

“Why’s that, Cathleen?”

“If the effect were wavelength‑dependent we’d have aberration, the astronomer’s nemesis. Images would be smeared out. As it is, all the photons from a point hit the same spot on the sensor and we’ve got something to see.”

“Tell him about amplification, Cathleen.”

“Good point, Sy. Each galactic star emits light in every direction. In effect, the blob collects light over its entire surface area and concentrates that light along the focal line. We get the brightest image when the stars are aligned right.”

~~ Rich Olcott

Now And Then And There

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.”

“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

Now And Then

“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

The Bottom of Time

“Cathleen, one of my Astronomy magazines had an article, claimed that James Webb Space Telescope can see back to the Big Bang. That doesn’t seem right, right?”

“You’re right, Al, it’s not quite right. By our present state of knowledge JWST‘s infrared perspective goes back only 98% of the way to the Bang. Not quite the Bottom of Time, but close.”

“Whaddaya mean, ‘Bottom of Time‘? I’ve heard people talking about how weird it musta been before the Big Bang. And how can JWST see back in time anyway? Telescopes look across space, not time.”

“So many questions, Mr Feder, and some hiding behind others. That’s his usual mode, Cathleen. Care to tag-team?”

“You’re on, Sy. Well, Mr Feder. The ‘look back in time‘ part comes from light not traveling infinitely fast. We’ve known that for three centuries, ever since Rømer—”

“Roamer?”

“Ole Rømer, a Danish scientist who lived in Newson’s time. Everyone knew that Jupiter’s innermost large moon Io had a dependably regular orbit, circling Jupiter every 49½ hours like clockwork. Rømer was an astronomer when he wasn’t tutoring the French King’s son or being Copenhagen’s equivalent of Public Safety Commissioner. He watched Io closely, kept notes on exactly when she ducked behind Jupiter and when she reappeared on the other side. His observed timings weren’t quite regular, generally off by a few minutes. Funny thing was, the irregularities correlated with the Earth‑Jupiter distance — up to 3½ minutes earlier than expected when Earth in its orbit was closest to Jupiter, similarly late when they were far apart. There was a lot of argument about how that could be, but Rømer, Huygens, even Newton, all agreed that the best explanation was that we only see Io’s passage events after light has taken its time to travel from there to here.”

“Seems reasonable. Why should people argue about that?”

“The major sticking point was the speed that Huygens calculated from Rømer’s data. We now know it’s 186000 miles or 300000 kilometers or one lightsecond per second. Different ways of stating the same quantity. Huygens came up with a somewhat smaller number but still. The establishment pundits had been okay with light transmission being instantaneous. Given definite numbers, though, they had trouble accepting the idea that anything physical could go that fast.”

“Tag, my turn. Flip that distance per time ratio upside down — for every additional lightsecond of distance we’re looking at events happening one second farther into the past. That’s the key to JWST‘s view into the long‑ago. Al, you got that JWST‘s infrared capabilities will beat Hubble‘s vis‑UV ones for distance. Unless there’s something seriously wrong with Einstein’s assumption that lightspeed’s an absolute constant throughout spacetime, we expect JWST to give us visibility to the oldest free photons in the Universe, just 379000 years upward from the Big Bang.”

“Wait, I heard weaseling there. Free photons? Like you gotta pay for the others?”

“Ha, ha, Mr Feder. During those first 379000‑or‑so years, we think the Universe was so hot and so dense that no photon’s wave had much of a chance to spread out before it encountered a charged something and got absorbed. At last, things cooled down enough for atoms to form and stay in one piece. Atoms are neutral. Quantum rules restrict their interaction to only photons that have certain wavelengths. The rest of the photons, and there’s a huge number of them, were free to roam the expanding Universe until they happen to find a suitable absorber. Maybe someone’s eye or if we’re lucky, a sensor on JWST or some other telescope.”

Thanks for this to George Derenburger

“What about before the 300‑and‑something thousand years? Like, before Year Zero? Musta been weird, huh?”

“Well, there’s a problem with that question. You’re assuming there was a Year Minus‑One, but that’s just not the case.”

“Why not? Arithmetic works that way.”

“But the Universe doesn’t. Stephen Hawking came up with a good way to think about it. What on Earth is south of the South Pole?”

“Eeayahh … nope. Can’t get any further south than that.”

“Well, there you are, so to speak. Time’s bottom is Year Zero and you can’t get any further down than that. We think.”

~~ Rich Olcott