Shopping The Old Curiosity

“Still got questions, Moire.”

“This’ll be your last shot this year, Mr Feder.  What’s the question?”

“They say a black hole absorbs all the light that falls on it. But the theory of blackbody radiation says a perfect absorber is also a perfect radiator. Emission should be an exact opposite flow to the incoming flow in every direction. Wouldn’t a black hole be shiny like a ball bearing?”Black hole as ball bearing 1
“A perfectly good question, but with crucial imperfections. Let’s start with the definition of a perfect absorber — it’s an object that doesn’t transmit or reflect any light. Super-black, in other words. So by definition it can’t be a mirror.”

“OK, maybe not a mirror, but the black hole has to send out some kind of exact opposite light to balance the arriving light.”

“Yes, but not in the way you think. Blackbody theory does include the assumption that the object is in equilibrium, your ‘exact opposite flow.’ The object must indeed send out as much energy as it receives, otherwise it’d heat up or cool down. But the outbound light doesn’t necessarily have to be at the same frequencies as the inbound light had. In fact, it almost never will.”

“How come not?”

“Because absorption and emission are two different processes and they play by different rules. If we’re including black holes in the discussion there are four different processes. No, five.  Maybe six.”

“I’m listening.”

“Good. Blackbody first. When a photon is absorbed by regular matter, it affects the behavior of some electron in there. Maybe it starts spending more time in a different part of the molecule, maybe it moves faster — one way or another, the electron configuration changes and that pulls the atomic nuclei away from where they were and the object’s atoms wobble differently. So the photon raises the object’s internal kinetic energy, which means raising its temperature, and we’ve got energy absorption, OK?”

“Yeah, and…?”

“At some later time, to keep things in equilibrium that additional energy has to be gotten rid of. But you can’t just paint one bit of energy red, say it’s special and follow it until it’s emitted. The whole molecule or crystal or whatever has excess energy as the result of all the incoming photons. When the total gets high enough, something has to give.  The object emits some photons to get rid of some of the excess. The only thing you can say about the outbound photons is that they generally have a lower energy than the incoming ones.”

“Why’s that?”

“Think of a bucket that’s brim-full and you’re dumping in cupfuls of water. Unless you’re pouring slowly and carefully, the dribbles escaping over the bucket’s rim will generally be many small amounts sloshing out more often than those cupfuls come in.  For light that’s fluorescence.”

“I suppose. What about the black hole?”

“The problem with a black hole is the mystery of what’s inside its event horizon. It probably doesn’t contain matter in the form of electrons and nuclei but we don’t know. There are fundamental reasons why information about what’s inside can’t leak out to us. All we can say is that when a light wave encounters a black hole, it’s trapped by the intense gravity field and its energy increments the black hole’s mass.  The mechanism … who knows?”

“Like I said, it gets absorbed. And gets emitted as Hawking radiation.”

“Sorry, that’s exactly what doesn’t happen. Hawking radiation arises from a different pair of processes. Process 1 generates pairs of virtual particles, which could be photons, electrons or something heavier. That happens at a chaotic but steady rate throughout the Universe.  Usually the particle pairs get back together and annihilate.  However, right next to the black hole’s event horizon there’s Process 2, in which one member of a virtual pair flies inward and the other member flies outward as a piece of Hawking radiation. Neither process even notices incoming photons. That’s not mirroring or even fluorescence.”

“Phooey, it was a neat idea.”

“That it was, but facts.”

~~ Rich Olcott

  • Thanks to lifeisthermal for inspiring this post.
  • Thus endeth a full year of Sy Moire stories.  I hope you enjoyed them.  Here’s to a new year and new ideas for all.
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Three Perils for a Quest(ion), Part 3

“Things are finally slowing down.  You folks got an interesting talk going, mind if I join you?  I got biscotti.”

“Pull up a chair, Eddie.  You know everybody?”

“You and Jeremy, yeah, but the young lady’s new here.”

“I’m Jennie, visiting from England.”

“Pleased to meetcha.  So from what I overheard, we got Jeremy on some kinda Quest to a black hole’s crust.  He’s passed two Perils.  There’s a final one got something to do with a Firewall.”

“One minor correction, Eddie.  He’s not going to a crust, because a black hole doesn’t have one.  Nothing to stand on or crash into, anyway.  He’s headed to its Event Horizon, which is the next best thing.  If you’re headed inward, the Horizon marks the beginning of where it’s physically impossible to get out.”

“Hotel California, eh?”

“You could say that.  The first two Perils had to do with the black hole’s intense gravitational field.  The one ahead has to do with entangled virtual particles.”

“Entangled is the Lucy-and-Ethel thing you said where two particles coordinate instant-like no matter how far apart they are?”

“Good job of overhearing, there, Eddie.  Jeremy, tell him abut virtual particles.”

“Umm, Mr Moire and I talked about a virtual particle snapping into and out of existence in empty space so quickly that the long-time zero average energy isn’t affected.”

“What we didn’t mention then is that when a virtual pair is created, they’re entangled.  Furthermore, they’re anti-particles, which means that each is the opposite of the other — opposite charge, opposite spin, opposite several other things.  Usually they don’t last long — they just meet each other again and annihilate, which is how the average energy stays at zero.  Now think about creating a pair of virtual particles in the black hole’s intense gravitational field where the creation event sends them in opposite directions.”Astronaut and semi-biscotto
“Umm… if they’re on opposite paths then one’s probably headed into the Horizon and the other is outbound. Is the outbound one Hawking radiation?  Hey, if they’re entangled that means the inbound one still has a quantum connection with the one that escaped!”

“Wait on.  If they’re entangled and something happening to one instantaneously affects its twin, but the gravity difference gives each a different rate of time dilation, how does that work then?”

“Paradox, Jennie!  That’s part of what the Firewall is about.  But it gets worse.  You’d think that inbound particle would add mass to the black hole, right?”

“Surely.”

“But it doesn’t.  In fact, it reduces the object’s mass by exactly each particle’s mass.  That ‘long-time zero average energy‘ rule comes into play here.  If the two are separated and can’t annihilate, then one must have positive energy and the other must have negative energy.  Negative energy means negative mass, because of Einstein’s mass-energy equivalence.  The positive-mass twin escapes as Hawking radiation while the negative-mass twin joins the black hole, shrinks it, and by the way, increases its temperature.”

“Surely not, Sy.  Temperature is average kinetic energy.  Adding negative energy to something has to decrease its temperature.”

“Unless the something is a black hole, Jennie.  Hawking showed that a black hole’s temperature is inversely dependent on its mass.  Reduce the mass, raise the temperature, which is why a very small black hole radiates more intensely than a big one.  Chalk up another paradox.”

“Two paradoxes.  Negative mass makes no sense.  I can’t make a pizza with negative cheese.  People would laugh.”

“Right.  Here’s another.  Suppose you drop some highly-structured object, say a diamond, into a black hole.  Sooner or later, much later really, that diamond’s mass-energy will be radiated back out.  But there’s no relationship between the structure that went in and the randomized particles that come out.  Information loss, which is totally forbidden by thermodynamics.  Another paradox.”

“The Firewall resolves all these paradoxes then?”

“Not really, Jennie.  The notion is that there’s this thin layer of insanely intense energetic interactions, the Firewall, just outside of the Event Horizon.  That energy is supposed to break everything apart — entanglements, pre-existing structures, quantum propagators (don’t ask), everything, so what gets through the horizon is mush.  Many physicists think that’s bogus and a cop-out.”

“So no Firewall Peril?”

“Wanna take the chance?”

~~ Rich Olcott