Quartetto for Rubber Ruler

Suddenly Al’s standing at our table.  “Hey guys, I heard you talking about spectroscopy and stuff and figured you could maybe ‘splain something I read.  Here’s some scones and I brought a fresh pot of coffee..”

“Thanks, Al.  What’s the something?  I’m sure Cathleen can ‘splain.”

“Syyy…”

“It’s this article talking about some scientists going down to Australia to use really old light to look for younger light and it’s got something to do with dark matter and I’m confused.”

“You’re talking about the EDGES project, right?”

“Yeah, I’m pretty sure they said ‘EDGES’ in the article.”

“OK, first we need some background on the background, that really old light you mentioned.  The Cosmic Microwave Background is the oldest light in the Universe, photons struggling out of the white-hot plasma fog that dominated most of the first 377,000 years after the Big Bang.”

“Wait a minute, ‘plasma fog’?”

“Mm-hm.  In those early years the Universe was all free electrons and nuclei colliding with photons and each other.  No photon could travel more than a few centimeters before being blocked by some charged particle.  The Universe had to expand and cool down to 4,000K or so before electrons and nuclei could hold together as atoms and the fog could lift.”

“Cathleen showed me an intensity-frequency plot for those suddenly-free photons.  It was a virtually perfect blackbody curve, identical within a couple parts per million everywhere in the sky.  The thing is, the curve corresponds to a temperature of only 2.73K.  Its peak is in the microwave region, hence the CMB moniker, nestled in between far infrared and HF radio.”

“I thought she said that the fog lifted at 4,000K, Sy.  That’s a lot different from 2-whatever.”

Wavelength-stretching, Vinnie, remember?  Universe expansion stretches the photon waves we measure temperatures with, the further the longer just like Hubble said.  The CMB’s the oldest light in the Universe, coming to us from 13.4 billion lightyears away.  The stretch factor is about 1100.”

“Vinnie, that 2.7K blackbody radiation is the background to the story.  Think of it as a spherical shell around the part of the Universe we can see.  There are younger layers inside that shell and older layers beyond it.”

“What could be outside the Universe, Cathleen?”

“Hey, Al, I carefully said, ‘the part of the Universe we can see.’  I’m quite sure that the Universe extends beyond the spatial volume we have access to, but light from out there hasn’t had a chance to get to us yet.  Going outward from our CMB sphere there’s that 337,000-year-deep shell of electron-nucleus fog.  Beyond that, 47,000 years-worth of quark soup and worse, out to the Big Bang itself.  Coming inward from the CMB we see all the things we know of that have to do with atoms.”

“Like galaxies?”

“Well, not immediately, they took a billion years to build up.  First we had to get through the Dark Ages when there weren’t any photons in the visible light range.  We had huge clouds of hydrogen and helium atoms but virtually all of them were in the ground state.  The CMB photons running around were too low-energy to get any chemistry going, much less nuclear processes.  The Universe was dark and cooling until gravitational attraction made clumps of gas dense enough to light up and become stars.  That’s when things got going.”

“How’d that make a difference?”Blackbody spectrum with notch

“A ground state hydrogen atom’s lowest available empty energy level is way above what a CMB photon could supply.  Those Dark Age atoms were essentially transparent to the prevailing electromagnetic radiation.  But when starlight came along it excited some atoms so that they could also absorb CMB light.  See the notch on the long-wavelength side of this blackbody curve?  It marks the shadow of starlit hydrogen clouds against the CMB’s glow.  The notch wavelength indicates when the absorption started.  Its position suggests that some stars lit up as early as 180 million years after the Big Bang.”

“Suggests, huh?”

“Mm-hm.  There are other interpretations.  That’s where the fun comes in, both on the theory side and the get-more-data side.  Like looking at different times.”

“Different times?”

“Every wavelength represents a different stretch factor and a different depth into the past.”

~~ Rich Olcott

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Étude for A Rubber Ruler

93% redder?  How do you figure that, Sy, and what’s it even mean?”

“Simple arithmetic, Vinnie.  Cathleen said that most-distant galaxy is 13 billion lightyears away.  I primed Old Reliable with Hubble’s Constant to turn that distance into expansion velocity and compare it with lightspeed.  Here’s what came up on its screen.”Old Reliable z calculation“Whoa, Sy.  Do you read the final chapter of a mystery story before you begin the book?”

“Of course not, Cathleen.  That way you don’t know the players and you miss what the clues mean.”

“Which is the second of Vinnie’s questions.  Let’s take it a step at a time.  I’m sure that’ll make Vinnie happier.”

“It sure will.  First step — what’s a parsec?”

“Just another distance unit, like a mile or kilometer but much bigger.  You know that a lightyear is the distance light travels in an Earth year, right?”

“Right, it’s some huge number of miles.”

“About six trillion miles, 9½ trillion kilometers.  Multiply the kilometers by 3.26 to get parsecs.  And no, I’m not going to explain the term, you can look it up.  Astronomers like the unit, other people put it in the historical-interest category with roods and firkins.”

“Is that weird ‘km/sec/Mparsec’ mix another historical thing?”

“Uh-huh.  That’s the way Hubble wrote it in 1929.  It makes more sense if you look at it piecewise.  It says for every million parsecs away from us, the outward speed of things in general increases by 70 kilometers per second.”

“That helps, but it mixes old and new units like saying miles per hour per kilometer.  Ugly.  It’d be prettier if you kept all one system, like (pokes at smartphone screen) … about 2.27 km/sec per 1018 kilometers or … about 8 miles an hour per quadrillion miles.  Which ain’t much now that I look at it.”

“Not much, except it adds up over astronomical distances.  The Andromeda galaxy, for instance, is 15×1018 miles away from us, so by your numbers it’d be moving away from us at 120,000 miles per hour.”

“Wait, Cathleen, I thought Andromeda is going to collide with the Milky Way four billion years from now.”

Opposing motion in a starfield“It is, Sy, and that’s one of the reasons why Hubble’s original number was so far off.  He only looked at about 50 close-by galaxies, some of which are moving toward us and some away.  You only get a view of the general movement when you look at large numbers of galaxies at long distances.  It’s like looking through a window at a snowfall.  If you concentrate on individual flakes you often see one flying upward, even though the fall as a whole is downward.  Andromeda’s 250,000 mph march towards us is against the general expansion.”

“Like if I’m flying a plane and the airspeed indicator says I’m doing 200 but my ground-speed is about 140 then I must be fighting a 60-knot headwind.”

“Exactly, Vinnie.  For Andromeda the ‘headwind’ is the Hubble Flow, that general outward trend.  If Sy’s calculation were valid, which it’s not, then that galaxy 13 billion lightyears from here would indeed be moving further away at  93% of lightspeed.  Someone living in that galaxy could shine a 520-nanometer green laser at us.  At this end we see the beam stretched by 193% to 1000nm.  That’s outside the visible range, well into the near-infrared.  All four visible lines in the hydrogen spectrum would be out there, too.”

“So that’s why ‘old hydrogens’ look different — if they’re far enough away in the Hubble Flow they’re flying away from us so fast all their colors get stretched by the red-shift.”

“Right, Vinnie.”

“Wait, Cathleen, what’s wrong with my calculation?”

“Two things, Sy.  Because the velocities are close to lightspeed, you need to apply a relativistic correction factor.  That velocity ratio Old Reliable reported — call it b.  The proper stretch factor is z=√ [(1+b)/(1–b)].  Relativity takes your 93% stretch down to (taps on laptop keyboard) … about 86%.  The bluest wavelength on hydrogen’s second-down series would be just barely visible in the red at 680nm.”

“What’s the other thing?”Ruler in perspective

“The Hubble Constant can’t be constant.  Suppose you run the movie backwards.  The Universe shrinks steadily at 70 km/sec/Mparsec.  You hit zero hundreds of millions of years before the Big Bang.”

“The expansion must have started slow and then accelerated.”

“Vaster and faster, eh?”

“Funny, Sy.”

~~ Rich Olcott