Imagine A Skyrocket Inside A Black Hole

Vinnie’s never been a patient man. “We’re still waiting, Sy. What’s the time-cause-effect thing got to do with black holes and information?”

“You’ve got most of the pieces, Vinnie. Put ’em together yourself.”

“Geez, I gotta think? Lessee, what do I know about black holes? Way down inside there’s a huge mass in a teeny singularity space. Gravity’s so intense that relativity theory and quantum mechanics both give up. That can’t be it. Maybe the disk and jets? No, ’cause some holes don’t have them, I think. Gotta be the Event Horizon which is where stuff can’t get out from. How’m I doing, Sy?”

“You’re on the right track. Keep going.”

“Okay, so we just talked about how mass scrambles spacetime, tilts the time axis down to point towards where mass is so axes stop being perpendicular and if you’re near a mass then time moves you even closer to it unless you push away and that’s how gravity works. That’s part of it, right?”

“As rain. So mass and gravity affect time, then what?”

“Ah, Einstein said that cause‑and‑effect runs parallel with time ’cause you can’t have an effect before what caused it. You’re saying that if gravity tilts time, it’ll tilt cause‑and‑effect?”

“So far as we know.”

“That’s a little weasel-ish.”

“Can’t help it. The time‑directed flow of causality is a basic assumption looking for counter‑examples. No‑one’s come up with a good one, though there’s a huge literature of dubious testimonials. Something called a ‘closed timelike curve‘ shows up in some solutions to Einstein’s equations for extreme conditions like near or inside a black hole. Not a practical concern at our present stage of technology — black holes are out of reach and the solutions depend on weird things like matter with negative mass. So anyhow, what happens to causality where gravity tilts time?”

“I see where you’re going. If time’s tilted toward the singularity inside a black hole, than so is cause‑and‑effect. Nothing in there can cause something to happen outside. Hey, bring up that OVR graphics app on Old Reliable, I’ll draw you a picture.”

“Sure.”

“See, way out in space here this circle’s a frame where time, that’s the red line, is perpendicular to the space dimensions, that’s the black line, but it’s way out in space so there’s no gravity and the black line ain’t pointing anywhere in particular. Red line goes from cause in the middle to effect out beyond somewhere. Then inside the black hole here’s a second frame. Its black line is pointing to where the mass is and time is tilted that way too and nothing’s getting away from there.”

“Great. Now add one more frame right on the border of your black hole. Make the black line still point toward the singularity but make the red line tangent to the circle.”

“Like this?”

“Perfect. Now why’d we put it there?”

“You’re saying that somewhere between cause-effect going wherever and cause-effect only going deeper into the black hole there’s a sweet spot where it doesn’t do either?”

“Exactly, and that somewhere is the Event Horizon. Suppose we’re in a mothership and you’re in our shuttlecraft in normal space. You fire off a skyrocket. Both spacecraft see sparks going in every direction. If you dive below an Event Horizon and fire another skyrocket, in your frame you’d see a normal starburst display. If we could check that from the mothership frame, we’d see all the sparks headed inward but we can’t because they’re all headed inward. All the sparkly effects take place closer in.”

“How about lighting a firework on the Horizon?”

“Good luck with that. Mathematically at least, the boundary is infinitely thin.”

“So bottom line, light’s trapped inside the black hole because time doesn’t let the photons have an effect further outward than they started. Do I have that right?”

“For sure. In fact, you can even think of the hole as an infinite number of concentric shells, each carrying a causality sign reading ‘Abandon hope, all ye who enter here‘. So what’s that say about information?”

“Hah, we’re finally there. Got it. Information can generate effects. If time can trap cause‑effect, then it can trap information, too.”

~~ Rich Olcott

Cause, Effect And Time

We’re still at Vinnie’s table by the door of Al’s coffee shop. “Long as we’re talking about black holes, Sy, I read in one of my astronomy magazines that an Event Horizon traps information the same way it traps light. I understand how gravity makes escape velocity for photons go beyond lightspeed, but how does that trap information?”

“Well, to start with, Al, you understand wrong. The whole idea of escape velocity applies to massive objects like rockets that feel the force of gravity. Going up they trade kinetic energy for potential energy; given enough kinetic energy they escape. Photons have zero mass — the only way gravity influences them is by bending the spacetime they fly through.”

“Does the bending also affect information or is that something else?”

Minkowski’s spacetime diagram…

“Fair question, but it’ll take some background to answer it. Good thing I’ve got Old Reliable and my graphics files along. Let’s start with this one. Vinnie’s seen a lot of spacetime graphs like this, Al, but I don’t think you have. Time runs upward, distance runs sideward, okay? Naming a specific time and location specifies an event, just like a calendar entry. Draw a line between two events; the slope is the speed you have to go to get from one to the other.”

“Just the distance, you’re not worrying about direction?”

“Good question. You’re thinking space is 3D and this picture shows only one space dimension. Einstein’s spacetime equations take account of all four dimensions mixing together, which is one reason they’re so hard to solve except in special cases. For where we’re going, distance will be enough, okay?”

“Not gonna argue.”

… compartmentalized by Einstein’s speed limit …

“Now we roll in Einstein’s speed limit. Relativity says that nothing can go faster than light. On a Minkowski diagram like this we draw the lightspeed slope at a 45″ angle. Any physical motion has a slope more vertical than that.”

“Huh?”

“See, Al, you’re going one second per second along time, right? If you’re not making much progress distance‑wise, you don’t do much on Sy’s sideways axis. You move mostly up.”

“Exactly, Vinnie. The bottom and top sections are called ‘timelike‘ because, well, they’re mostly like time.”

“Are the other two sections spacelike?”

“Absolutely. You can’t get from ‘Here & Now‘ to the ‘Too far to see‘ event without going faster than light. Einstein said that’s a no‑no. Suppose that event’s a nova, ‘Now‘ but far away. Astronomers will have to just wait until the nova’s light reaches them at ‘Here‘ but at a later ‘Now.’ Okay, Vinnie, here’s a graphic you haven’t seen yet.”

… and re-interpreted in terms of causality.

“Looks pretty much the same, except for that arrow. What’s cause and effect got to do with time?”

“I don’t want to get into the metaphysical weeds here. There’s a gazillion theories about time — the Universe is expanding and that drives time; entropy always increases and that drives time; time is an emergent property of the underlying structure of the Universe, whatever that means. From an atomic, molecular, mechanical physics point of view, time is the result of causes driving effects. Causes always come first. Your finger bleeds after you cut it, not before. Cause‑effect runs along the time axis. Einstein showed us that cause‑effect can’t travel any faster than lightspeed.”

“That’s a new one. How’d he figure that?”

“Objects move objects to make things happen. They can’t move faster than lightspeed because of the relativity factor.”

“What if the objects are already touching?”

“Your hand and that cup are both made of atoms and it’s really their electric fields that touch. Shifting fields are limited by lightspeed, too.”

“So you’re saying that cause-effect is timelike.”

“Got it in one. Einstein would say causality is not only timelike, but exactly along the time axis. That’s one big reason he was so uncomfortable about action at a distance — a cause ‘Here‘ having an effect ‘There‘ with zero time elapsed would be a horizontal line, pure spacelike, on Minkowski’s graph. Einstein invented the principle of entanglement as a counterexample, thinking it impossible. He’d probably be shocked and distressed to see that today we have experimental proof of entanglement.”

~~ Rich Olcott