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?”
“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.”
“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.”
“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.”
“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
2 thoughts on “Cause, Effect And Time”
So, would explaining why the arrow isn’t a straight line have put you into those metaphysical weeds? Or is that next week’s column? Or is that too far to see yet?
On an unrelated subject, I expect that you are aware of the phenomenon I attribute to this stage of our longevity, of no longer being quite sure of mentally stored factoids one was once sure of. Such as birthdates. September rolls around and I’ve always managed to be sure which was yours and which was Mom’s. But now, not so sure. Yours is first, right? Happy be-early-ed birthday, in case I lose track again by then.
The S-curve is to allow the path between cause and effect to deviate from light’s vertical line. Like that 9-month gestation delay during which Val and I traveled from Boston to Memphis.
And on the unrelated subject, Mom’s came first.
And to a related subject, thanks for the early-ness.