Category: Cosmology

Generation(s) of Stars

On By rolcottIn Astronomy: Stellar Science, Cosmology, UncategorizedLeave a comment

“How’re we gonna tell, Mr Moire?”

“Tell what, Jeremy?”

“Those two expanding Universe scenarios. How do we find out whether it’s gonna be the Big Rip or the Big Chill?”

“The Solar System will be recycled long before we’d have firm evidence either way. The weak dark energy we have now is most effective at separating things that are already at a distance. In the Big Rip’s script a brawnier dark energy would show itself first by loosening the gravitational bonds at the largest scale. Galaxies would begin scattering into the voids between the multi‑galactic sheets and filaments we’ve been mapping. Only later would the galaxies themselves release their stars to wander off and dissolve when dark energy gets strong enough to overcome electromagnetism.”

“How soon will we see those things happen?”

“If they happen. Plan on 188 billion years or so, depending on how fast dark energy strengthens. The Rip itself would take about 2 billion years, start to finish. Remember, our Sun will go nova in only five billion years so even the Rip scenario is far, far future. I prefer the slower Chill story where the Cosmological Constant stays constant or at least the w parameter stays on the positive side of minus‑one. Weak dark energy doesn’t mess with large gravitationally‑bound structures. It simply pushes them apart. One by one galaxies and galaxy clusters will disappear beyond the Hubble horizon until our galaxy is the only one in sight. I take comfort in the fact that our observations so far put w so close to minus‑one that we can’t tell if it’s above or below.”

“Why’s that?”

“The closer (w+1) approaches zero, the longer the timeline before we’re alone. We’ll have more time for our stars to complete their life cycles and give rise to new generations of stars.”

“New generations of stars? Wow. Oh, that’s what you meant when you said our Solar System would be recycled.”

“Mm-hm. Think about it. Back when atoms first coalesced after the Big Bang, they were all either hydrogen or helium with just a smidgeon of lithium for flavor. Where did all the other elements come from? Friedmann’s student George Gamow figured that out, along with lots of other stuff. Fascinating guy, interested in just about everything and good at much of it. Born in Odessa USSR, he and his wife tried twice to defect to the West by kayak. They finally made it in 1933 by leveraging his invitation to Brussels and the Solvay Conference on Physics where Einstein and Bohr had their second big debate. By that time Gamow had produced his ‘liquid drop‘ theory of how heavy atomic nuclei decay by spitting out alpha particles and electrons. He built on that theory to explain how stars serve as breeder reactors.”

“I thought breeder reactors are for turning uranium into plutonium for bombs. Did he have anything to do with that?”

“By the start of the war he was a US citizen as well as a top-flight nuclear theorist but they kept him away from the Manhattan Project. That undoubtedly was because of his Soviet background. During the war years he taught university physics, consulted for the Navy, and thought about how stars work. His atom decay work showed that alpha particles could escape from a nucleus by a process a little like water molecules in a droplet bypassing the droplet’s surface tension. For atoms deep inside the Sun, he suggested that his droplet process could work in reverse. He calculated the temperatures and pressures it would take for gravity to force alpha particles or electrons into different kinds of nuclei. The amazing thing was, his calculations worked.”

“Wait — alpha particles? Where’d they come from if the early stars were just hydrogen and helium?”

“An alpha particle is just a helium atom with the electrons stripped off. Anyway, with Gamow leading the way astrophysicists figured out how much of which elements a given star would create by the time it went nova. Those elements became part of the gas‑dust mix that coalesces to become the next generation of stars. We may have gone through 100 such cycles so far.”

“A hundred generations of stars. Wow.”

~~ Rich Olcott

Constant’s Companion

On By rolcottIn CosmologyLeave a comment

“It’s like Mark Twain said, Jeremy — ‘History may not repeat itself, but it rhymes.‘ Newton identified gravity as a force; Einstein proposed the Cosmological Constant. Newton worked the data to develop his Law of Gravity; Friedmann worked Einstein’s theory to devise his model of an exponentially expanding Universe. Newton was uncomfortable with gravity’s ability to act at a distance; Einstein called the Cosmological Constant ‘his greatest blunder.’ The parallels go on.”

“Why didn’t Einstein like the Constant if it explains how the Universe is expanding?”

“It wasn’t supposed to. Expanding Universes weren’t in fashion a century ago when Einstein wrote that paper. At the time everyone including Einstein thought we live in a steady state universe. His first cut at a General Relativity field equation implied a contracting universe so he added a constant term to balance out the contraction even though it made the dynamics look unstable — the Constant had to have just the right value for stability. A decade later Hubble’s data pointed to expansion and Friedman’s equations showed how that can happen.”

“I guess Einstein was embarrassed about that, huh, Mr Moire?”

“Well, he’d thought all along that the Constant was mathematically inelegant. Besides, the Constant isn’t just a number or a term in an equation, it’s supposed to represent a real process in operation. Like Newton’s problem with gravity, Einstein couldn’t identify a mechanism to power the Constant.”

“Power it to do what?”

“Think about universal constants, like the speed of light or the electron charge. Doesn’t matter where you are or how fast you’re traveling in which inertial frame, they’ve got the same values. If the Constant is indeed a constant, it contributes equally to cosmological dynamics from every position in space, whether inside a star or millions of lightyears from any galaxy. Every point must exert the same outward force in every direction or there’d be swirling. And it multiplies — every instant of general expansion makes new points in between the old points and they’ll exert the same force, too.”

“That’s what makes it exponential, right?”

“Good insight. It’s a pretty weak force per unit volume, weaker than gravity. We know that because galaxies and galaxy cluster structures maintain integrity even as they’re drifting apart from each other. Even so, a smidgeon of force from each unit volume in space adds up to a lot of force. Multiply force by distance traveled — that’s a huge amount of energy spent against gravity. The big puzzle is, what’s the energy source? Most of the astrophysics community nominates dark energy to power the Cosmological Constant but that’s not much help.”

“As Dr Prather says in class, Mr Moire, ‘You sound tentative. Please expound.‘ Why wouldn’t dark energy be the power source?”

“In Physics we use the word ‘energy‘ with a very specific meaning. Yes, it gets heavy use with sloppy meanings in everything from show business to crystal therapy, but in hard science nearly every serious research program since the 18th Century has entailed quantitative energy accounting. The First Law of Thermodynamics is conservation of energy. Whenever we see something heating up, a chemical reaction running or a force being applied along a distance, physicists automatically think about the energy being expended and where that energy is coming from. Energy’s got to balance out. But the Constant breaks that rule — we have no idea what process provides that energy. Calling the source ‘dark energy‘ just gives it a name without explaining it.”

“Isn’t the missing energy source evidence against Friedmann’s and Einstein’s equations?”

“That’s a tempting option and initially a lot of researchers took it. Unfortunately, it seems that dark energy is a thing. Or maybe a lot of little things. Several different lines of evidence say that the Constant constitutes twice as much mass‑energy as all normal and dark matter combined. Worse yet, as the Universe expands that share will increase.”

“Wait, will the dark energy invade normal matter and break us up?”

“People argue about that. Normal matter’s held together by electromagnetic forces which are 1038 times stronger than gravity, far stronger yet than dark energy. Dark matter’s gravity helps to hold galaxies together, but who knows what holds dark matter together?”

~~ ROlcott

Three Phases of Ever

On By rolcottIn Cosmology, UncategorizedLeave a comment

“So if the Universe isn’t in a steady state and it’s not heading for a Big Crunch, I guess it’s getting bigger forever, huh?”

“Careful, Jeremy, the Universe expansion could maybe reach a stopping point if it happened to hold exactly the right amount of mass‑energy. The expansion could just stop when forces balance out.”

“What forces, Mr Moire? There’s gravity pulling everything together so what’s pushing them apart?”

“That is an excellent question, one that we don’t yet have an answer for. We’re about where Newton was with gravity. There was a lot of observational evidence, he had a name for it and knew how to calculate its effects, but he didn’t know how it worked. That’s us with Einstein’s Cosmological Constant.”

“Observational evidence — we can actually see things accelerate?”

“Not any one object speeding up. Human lifetimes are too short to measure acceleration in galaxies a hundred thousand lightyears across. No, we use the same strategy that Hubble used — measure many galaxies at different distances from us and graph recession speed against distance. During the century since Hubble we’ve greatly improved our estimates of astronomical speeds and distances. Dividing the known speed of light into a galaxy’s measured distance tells us time since it emitted the photons we see. Our findings confirm Hubble’s general conclusion — on average, older photons come from galaxies that fly away faster. Hubble thought that the relation was linear but our fine‑tuned numbers show otherwise. The data says that after the first few seconds the Universe stretched at a steady rate for only the first ⅔ of its life. The stretch has been accelerating since then.”

“Why wasn’t it accelerating since the beginning? Did someone cut in the afterburner?”

“More like turned one off. The evidence and theory we have so far indicate the Universe has seen a succession of phases dominated by different processes. You’ve probably heard of inflation—”

“Have I? You should see what they want for a burger these days!”

“Not that sort of inflation, but I know how you feel. No, I’m referring to cosmic inflation, very early in the Big Bang sequence, when the Universe expanded by a factor of 1026 within a tiny fraction of a second. It was driven by enormously powerful radiation‑linked effects we don’t understand that finally ran out of steam and let lower‑energy processes take over.”

“How’d that happen?”

“We don’t know. The general principle is that one process so dominates what’s going on in a phase that nothing else matters, until for some reason it stops mattering and we’re in a new phase with a different dominant process. The early Universe was controlled by radiative processes until things cooled off enough for particles to form and persist. That changed the game. Gravity dominated the next 8 billion years. Particles clumped together, atoms then dust then solar systems into larger and larger structures with bigger spaces between them. About 5 billion years ago the game changed again.”

“So early on there weren’t even atoms, huh? Wow. What was the next game‑changer?”

“Thanks to Einstein and Friedmann’s work we’ve got at least a guess.”

“Friedmann?”

“Alexander Friedmann. He was a Russian physicist, used Einstein’s General Relativity results to derive three equations that together model the dynamics of the overall scale of the Universe using just a few estimates for current conditions. His equations give acceleration as the difference of two terms. The positive term is simply proportional to Einstein’s Constant. The negative term depends on both average mass density and pressure. Take a moment to think.”

“Umm… Positive is acceleration, negative is deceleration, density and pressure go down … If the negative term gets smaller than the positive one, acceleration increases, right?”

“It does, and we think the constant term has been increasingly dominant for 5 billion years. Something else to consider — the equation’s result is in terms of scale change divided by current scale. What’s it mean if that ratio’s a positive constant?”

“Change by a constant positive percentage … that’s exponential growth!”

“I thought you’d recognize it. Einstein’s Constant implies the scale of the Universe grows at an exponentially accelerating rate. We’re now in the Cosmological Constant phase.”

In Russian, Aleksandr Aleksandrowitsch Fridman

~~ Rich Olcott

Not Crunch Time

On By rolcottIn Cosmology, UncategorizedLeave a comment

A familiar knock on my office door. “C’mon in, Jeremy, the door’s open.”

“Got a few minutes, Mr Moire?”

The second serious-sounding visitor today. I push my keyboard aside again. “Sure, what’s up?”

“I read your ‘Tops of Time‘ post and then I watched one of Katie Mack’s ‘End of Everything‘ YouTube videos and now I’m confused. And worried.”

“I can understand that. Clearing up the confusion should be easy. Then I’ll do what I can about the worry part, okay?”

“That’d be great, sir.”

“So, imagine an enormous sheet of graph paper, and then imagine Puerto Rico laid down on top of that. You could use the graph paper to describe the latitude and longitude of any place on the island, right?”

“Sure, probably.”

“I happen to know that Playa Jobos is the northernmost point of the island. Does north stop there?”

“Nosir. The island stops there, but north keeps going.”

“Well, there you are.”

“Wait … oh, you’re saying that time by itself keeps going forever but what’s in the Universe might not and that’s what Dr Mack is talking about?”

“That’s the idea. More precisely, the ‘tops‘ I wrote about are different ways that spacetime’s time coordinate could play out in the future, or maybe not. Mack’s ‘end of everything‘ is about the future history of physical stuff laid on top of our mathematical spacetime constructs. Does that clarify things?”

“Mmm, yessir, but what about the ‘maybe not‘ you said?”

“This gets metaphysical, but cosmology often skates on that edge. Descartes and others maintained that space has meaning only when there are separate objects. If there was only one thing in the Universe you’d have nothing to compare sizes against and there’d be no point in measuring distances away from it. That’d be even more the case if there’s nothing. Same thing for time and events. From that perspective, if somehow the Universe emptied out then space and time sort of stop.”

“Just sort‑of stop, like Puerto Rico stops at that Playa place. Really they keep on going, I think, even if no‑one’s there to measure anything.”

“A perfectly reasonable position when there’s no evidence either way. Anyhow, a few of Mack’s scenarios wind up in that situation, right?”

“Umm… there’s the Big Crunch that reverses the Big Bang.”

“That one was popular before we got good data. The idea was that the Big Bang pushed everything apart but eventually gravity will slow outward momentum and pull everything back together again. The notion probably came from humanity’s experience with dirt falling back down after an explosion. The problems with that scheme are that the Big Bang wasn’t an explosion, outward momentum isn’t a thing and besides, we’ve got increasingly good data showing that between‑galaxy distances are getting wider, not shrinking. The last five billion years that’s sped up.”

“Wait, not an explosion? All the videos show it that way.”

“Chalk it up to artistic license. It’s hard to show everything moving away from everything else without making it look like the viewpoint’s simply diving into a static arrangement. No, an explosion comes out of a center and that’s not the Bang. Remember that huge piece of graph paper? Make it a balloon, tack Puerto Ricos all over it, then pump in some air. There’s no center, but every islander thinks their island is the center and every other island is running away from them. Really, all that’s happening is that the stretching rubber is creating new inter‑island space everywhere.”

“And that’s Universe expansion?”

“Mm-hm. Also known as Hubble Flow. We’ve looked very hard for a center of motion, haven’t found one.”

“If everything’s moving, why isn’t that momentum?”

“It is momentum, but only pairwise. For any two galaxies you can calculate mass times speed same as always. For really distant objects you’ve got to use a relativistic version. Anyway, in the cosmological context you’ve got to ask, momentum relative to what? Everyone has this picture that things came from a common center and will fall back there. The way Hubble expansion works, though, there’s no particular go‑back place.”

“Everything’s speeding up and going everywhere so no Big Crunch then.”

“Not on the original model, anyway.”

~~ Rich Olcott

Time Is Where You Find It

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

A familiar footstep in the hall outside my office, “C’mon in, Vinnie, the door’s open.”

“Got a few minutes, Sy?”

More than just “a minute.” This sounds serious so I push my keyboard aside. “Sure, what’s up?”

“I’ve been thinking about different things, putting ’em together different ways. I came up with something, sorta, that I wanted to run past you before I brought it to one of Cathleen’s ‘Crazy Theories‘ parties.”

“Why, Vinnie, you’re being downright diffident. Spill it.”

“Well, it’s all fuzzy. First part goes way back to years ago when you wrote that there’s zero time between when a photon gets created and when it gets used up. But that means that create and use-up are simultaneous and that goes against Einstein’s ‘No simultaneity‘ thing which I wonder if you couldn’t get around it using time tick signals to sync up two space clocks.”

“That’s quite a mix and I see why you say it’s fuzzy. Would you be surprised if I used the word ‘frame‘ while clarifying it?”

“I’ve known you long enough it wouldn’t surprise me. Go ahead.”

“Let’s start with the synchronization idea. You’re not the first to come up with that suggestion. It can work, but only if the two clocks are flying in formation, exactly parallel course and speed.”

“Hah, that goes back to our first talk with the frame thing. You’re saying the clocks have to share the same frame like me and that other pilot.”

“Exactly. If the ships are zooming along in different inertial frames, each will measure time dilation in the other. How much depends on their relative velocities.”

“Wait, that was another conversation. We were pretending we’re in two spaceships like we’re talking about here and your clock ran slower than mine and my clock ran slower than yours which is weird. You explained it with equations but I’ve never been good with equations. You got a diagram?”

“Better than that, I’ve got a video. It flips back and forth between inertial frames for Enterprise and Voyager. We’ll pretend that they sync their clocks at the point where their tracks cross. I drew the Enterprise timeline vertical because Enterprise doesn’t move in space relative to Enterprise. The white dots are the pings it sends out every second. Meanwhile, Voyager is on a different course with its own timeline so its inertial frame is rotated relative to Enterprise‘s. The gray dots on Voyager‘s track show when that ship receives the Enterprise pings. On the Voyager timeline the pings arrive farther apart than they are on the Enterprise timeline so Voyager perceives that Enterprise is falling farther and farther behind.”

“Gimme a sec … so Voyager says Enterprise‘s timer is going slow, huh?”

“That’s it exactly. Now look at the rotated frame. The pink dots show when Voyager sends out its pings. The gray dots on Enterprise‘s track show when the pings arrive.”

“And Enterprise thinks that Voyager‘s clock is slow, just backwards of the other crew. OK, I see you can’t use sync pulses to match up clocks, but it’s still weird.”

“Which is where Lorentz and Minkowski and Einstein come into the picture. Their basic position was that physical events are real and there should be a way to measure them that doesn’t depend on an observer’s frame of reference. Minkowski’s ‘interval‘ metric qualifies. After converting time and location measurements to intervals, both crews would measure identical spacetime separations. Unfortunately, that wouldn’t help with clock synchronization because spacetime mixes time with space.”

“How about the photons?”

“Ah, that’s a misquotation. I didn’t say the time is zero, I said ‘proper time‘ and that’s different. An object’s proper time is measured by its clock in its inertial frame while traveling time t and distance d between two events. Anyone could measure t and d in their inertial frame. Minkowski’s interval is defined as s=√[(ct)²‑d²]. Proper time is s/c. Intuitively I think of s/c as light’s travel time after it’s done traversing distance d. In space, photons always travel at lightspeed so their interval and proper time are always zero.”

“Photon create and use-up aren’t simultaneous then.”

“Only to photons.”

~~ 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

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.

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.

The Bottom of Time

On By rolcottIn Astronomy: Techniques, Cosmology, James Webb Space Telescope, Uncategorized2 Comments

“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

Thinking in Spacetime

On By rolcottIn Cosmology, Mathematics: Dimensions, UncategorizedLeave a comment

The Open Mic session in Al’s coffee shop is still going string. The crowd’s still muttering after Jeremy stuck a pin in Big Mike’s “coincidence” balloon when Jim steps up. Jim’s an Astrophysics post‑doc now so we quiet down expectantly. “Nice try, Mike. Here’s another mind expander to play with. <stepping over to the whiteboard> Folks, I give you … a hypotenuse. ‘That’s just a line,’ you say. Ah, yes, but it’s part of some right triangles like … these. Say three different observers are surveying the line from different locations. Alice finds her distance to point A is 300 meters and her distance to point B is 400. Applying Pythagoras’ Theorem, she figures the A–B distance as 500 meters. We good so far?”

A couple of Jeremy’s groupies look doubtful. Maybe‑an‑Art‑Major shyly raises a hand. “The formula they taught us is a2+b2=c2. And aren’t the x and y supposed to go horizontal and vertical?”

“Whoa, nice questions and important points. In a minute I’m going to use c for the speed of light. It’s confusing to use the same letter for two different purposes. Also, we have to pay them extra for double duty. Anyhow, I’m using d for distance here instead of c, OK? To your next point — Alice, Bob and Carl each have their own horizontal and vertical orientations, but the A–B line doesn’t care who’s looking at it. One of our fundamental principles is that the laws of Physics don’t depend on the observer’s frame of reference. In this situation that means that all three observers should measure the same length. The Pythagorean formula works for all of them, so long as we’re working on a flat plane and no-one’s doing relativistic stuff, OK?”

Tentative nods from the audience.

“Right, so much for flat pictures. Let’s up our game by a dimension. Here’s that same A–B line but it’s in a 3D box. <Maybe‑an‑Art‑Major snorts at Jim’s amateur attempt at perspective.> Fortunately, the Pythagoras formula extends quite nicely to three dimensions. It was fun figuring out why.”

Jeremy yells out. “What about time? Time’s a dimension.”

“For sure, but time’s not a length. You can’t add measurements unless they all have the same units.”

“You could fix that by multiplying time by c. Kilometers per second, times seconds, is a length.” His groupies go “Oooo.”

“Thanks for the bridge to spacetime where we have four coordinates — x, y, z and ct. That makes a big difference because now A and B each have both a where and a when — traveling between them is traveling in space and time. Computationally there’s two paths to follow from here. One is to stick with Pythagoras. Think of a 4D hypercube with our A–B line running between opposite vertices. We’re used to calculating area as x×y and volume as x×y×z so no surprise, the hypercube’s hypervolume is x×y×z×(ct). The square of the A–B line’s length would be b2=(ct)2+d2. Pythagoras would be happy with all of that but Einstein wasn’t. That’s where Alice and Bob and Carl come in again.”

“What do they have to do with it?”

“Carl’s sitting steady here on good green Earth, red‑shifted Alice is flying away at high speed and blue‑shifted Bob is flashing toward us. Because of Lorentz contractions and dilations, they all measure different A–B lengths and durations. Each observer would report a different value for b2. That violates the invariance principle. We need a ruggedized metric able to stand up to that sort of punishment. Einstein’s math professor Hermann Minkowski came up with a good one. First, a little nomenclature. Minkowski was OK with using the word ‘point‘ for a location in xyz space but he used ‘event‘ when time was one of the coordinates.”

“Makes sense, I put events on my calendar.”

“Good strategy. Minkowski’s next step quantified the separation between two events by defining a new metric he called the ‘interval.’ Its formula is very similar to Pythagoras’ formula, with one small change: s2=(ct)2–d2. Alice, Bob and Carl see different distances but they all see the same interval.”

“Minus? Where did that come from?”

~~ Rich Olcott