Meanwhile, back at the office

Closing time.  Anne and I stroll from Al’s coffee shop back to the Acme Building.  It’s a clear night with at least 4,500 stars, but Anne’s looking at the velvet black between them.

“What you said, Sy, about the Universe not obeying Conservation of Energy — tell me more about that.”

“Aaa-hmmm … OK.  You’ve heard about the Universe expanding, right?”

“Ye-es, but I don’t know why that happens.”

“Neither do the scientists, but there’s pretty firm evidence that it’s happening, if only at the longest scales.  Stars within galaxies get closer together as they radiate away their gravitational energy.  But the galaxies themselves are getting further apart, as far out as we can measure.”

“What’s that got to do with Conservation of Energy?”

“Well, galaxies have mass so they should be drawn together by gravity the way that gravity pulls stars together inside galaxies.  But that’s not what’s happening.  Something’s actively pushing galaxies or galaxy clusters away from each other.  Giving the something a name like ‘dark energy‘ is just an accounting gimmick to pretend the First Law is still in effect at very large distances — we don’t know the energy source for the pushing, or even if there is one.  There’s a separate set of observations we attribute to a ‘dark energy‘ that may or may not have the same underlying cause.  That’s what I was talking about.”Fading white satin

We’re at the Acme Building.  I flash my badge to get us past Security and into the elevator.  As I reach out to press the ’12’ button she puts her hand on my arm.  “Sy, I want to see if I understand this entropy-elephant thing.  You said entropy started as an accounting gimmick, to help engineers keep track of fuel energy escaping into the surroundings.  Energy absorbed at one temperature they called the environment’s heat capacity.  Total energy absorbed over a range of temperatures, divided by the difference in temperature, they called change in entropy.”

The elevator lets us out on my floor and we walk to door 1217.  “You’ve got it right so far, Anne.  Then what?”

“Then the chemists realized that you can predict how lots of systems will work from only knowing a certain set of properties for the beginning and end states.  Pressure, volume, chemical composition, whatever, but also entropy.  But except for simple gases they couldn’t predict heat capacity or entropy, only measure it.”

My key lets us in.  She leans back against the door frame.  “That’s where your physicists come in, Sy.  They learned that heat in a substance is actually the kinetic energy of its molecules.  Gas molecules can move around, but that motion’s constrained in liquids and even more constrained in solids.  Going from solid to liquid and from liquid to gas absorbs heat energy in breaking those constraints.  That absorbed heat appears as increased entropy.”

She’s lounging against my filing cabinet.  “The other way that substances absorb heat is for parts of molecules to rotate and vibrate relative to other parts.  But there are levels.  Some vibrations excite easier than others, and many rotations are even easier.  In a cold material only some motions are active.  Rising temperature puts more kinds of motion into play.  Heat energy spreads across more and more sub-molecular absorbers.”

She’s perched on the edge of my desk.  “Here’s where entropy as possibility-counting shows up.  More heat, more possibilities, more entropy.  Now we can do arithmetic and prediction instead of measuring.  Anything you can count possibilities for you can think about defining an entropy for, like information bits or black holes or socks.  But it’ll be a different entropy, with its own rules and its own range of validity.  … And…”Riding the Elephant

She’s looming directly over me.  Her dark eyes are huge.

“And…?”

When we first met, Sy, you asked what you could do for me.  You’ve helped me see that when I travel across time and probability I’m riding the Entropy Elephant.  I’d like to show my appreciation.  Can you think of a possibility?”

A dark night, in a city that knows how to keep its secrets.  On the 12th floor of the Acme Building, one man still tries to answer the Universe’s persistent questions — Sy Moire, Physics Eye.

~~ Rich Olcott

Advertisements

Gentle pressure in the dark

“C’mon in, the door’s open.”

Vinnie clomps in and he opens the conversation with, “I don’t believe that stuff you wrote about LIGO.  It can’t possibly work the way they say.”

“Well, sir, would you mind telling me why you have a problem with those posts?”  I’m being real polite, because Vinnie’s a smart guy and reads books.  Besides, he’s Vinnie.

“I’m good with your story about how Michelson’s interferometer worked and why there’s no æther.  Makes sense, how the waves mess up when they’re outta step.  Like my platoon had to walk funny when we crossed a bridge.  But the gravity wave thing makes no sense.  When a wave goes by maybe it fiddles space but it can’t change where the LIGO mirrors are.”

“Gravitational wave,” I murmur, but speak up with, “What makes you think that space can move but not the mirrors?”

“I seen how dark energy spreads galaxies apart but they don’t get any bigger.  Same thing must happen in the LIGO machine.”

“Not the same, Vinnie.  I’ll show you the numbers.”

“Ah, geez, don’t do calculus at me.”de-vs-gravity

“No, just arithmetic we can do on a spreadsheet.” I fire up the laptop and start poking in  astronomical (both senses) numbers.  “Suppose we compare what happens when two galaxies face each other in intergalactic space, with what happens when two stars face each other inside a galaxy.  The Milky Way’s my favorite galaxy and the Sun’s my favorite star.  Can we work with those?”

“Yeah, why not?”

“OK, we’ll need a couple of mass numbers.  The Sun’s mass is… (sound of keys clicking as I query Wikipedia) … 2×1030 kilograms, and the Milky Way has (more key clicks) about 1012 stars.  Let’s pretend they’re all the Sun’s size so the galaxy’s mass is (2×1030)×1012 = 2×1042 kg. Cute how that works, multiplying numbers by adding exponents, eh?”

“Cute, yeah, cute.”  He’s getting a little impatient.

“Next step is the sizes.  The Milky Way’s radius is 10×104 lightyears, give or take..  At 1016 meters per lightyear, we can say it’s got a radius of 5×1020 meters.  You remember the formula for the area of a circle?”

“Sure, it’s πr2.” I told you Vinnie’s smart.

“Right, so the Milky Way’s area is 25π×1040 m2.  Meanwhile, the Sun’s radius is 1.4×109 m and its cross-sectional area must be 2π×1018 m2.  Are you with me?”

“Yeah, but what’re we doing playing with areas?  Newton’s gravity equations just talk about distances between centers.”  I told you Vinnie’s smart.

“OK, we’ll do gravity first.  Suppose we’ve got our Milky Way facing another Milky Way an average inter-galactic distance away.  That’s about 60 galaxy radii,  about 300×1020 meters.  The average distance between stars in the Milky Way is about 4 lightyears or 4×1016 meters.  (I can see he’s hooked so I take a risk)  You’re so smart, what’s that Newton equation?”

Force or potential energy?”

“Alright, I’m impressed.  Let’s go for force.”

“Force equals Newton’s G times the product of the masses divided by the square of the distance.”

“Full credit, Vinnie.  G is about 7×10-11 newton-meter²/kilogram², so we’ve got a gravity force of (typing rapidly) (7×10-11)×(2×1042)×(2×1042)/(300×1020)² = 3.1×1029 N for the galaxies, and (7×10-11)×(2×1030)×(2×1030)/(4×1016)² = 1.75×1017 N for the stars.  Capeesh?”

“Yeah, yeah.  Get on with it.”

“Now for dark energy.  We don’t know what it is, but theory says it somehow exerts a steady pressure that pushes everything away from everything.  That outward pressure’s exerted here in the office, out in space, everywhere.  Pressure is force per unit area, which is why we calculated areas.

“But the pressure’s really, really weak.  Last I saw, the estimate’s on the order of 10-9 N/m².  So our Milky Way is pushed away from that other one by a force of (10-9)×(25π×1040) ≈ 1031 N, and our Sun is pushed away from that other star by a force of (10-9)×(2π×1018) ≈ 1010 N with rounding.  Here, look at the spreadsheet summary…”

 Force, newtons Between Galaxies Between stars
Gravity 3.1×1029 1.75×1017
Dark energy 1031 1010
Ratio 3.1×10-2 17.5×106

“So gravity’s force pulling stars together is 18 million times stronger than dark energy’s pressure pushing them apart.  That’s why the galaxies aren’t expanding.”

“Gotta go.”

(sound of door-slam )

“Don’t mention it.”

~~ Rich Olcott