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