Adam Primaeros (primaeros) wrote,
Adam Primaeros
primaeros

What the hell happened when Cooper went into the black hole?

Not a sex joke. (Not here, anyway.)

This post is my way of getting my head around the climax of Christopher Nolan’s Interstellar, at least in the sense of mathematical manifolds. (Did a lot of geometry in college, and I like thinking visually.) Third-act spoilers abound after the cut.

Okay, let’s get to it. This is the universe, represented as a 2D manifold of space crossed with time.

CoopTime01

The universe doesn’t actually look like a sheet. At least, not to us living on that sheet. It might look like a sheet for entities living in a region with more dimensions than the three of space plus one of time, though.

CoopTime02

This is Cooper heading into a black hole, the latter of which is deforming spacetime as per Einstein’s general relativity with its intense gravitational field.
The movie speaks of “they” who are aiding the Earthlings’ survival in ways such as opening an intergalactic wormhole near Saturn for use as a superhighway to a region with inhabitable planets. The following is how I think “they” did what “they” did to ensure Cooper’s daughter, Murph, succeeds in generating a solid theory of quantum gravity (a real-life physics problem bridging the macrocosmic scale of relativity with the microcosmic realm of quantum physics).

To make this plan work, Cooper needs to be able to travel continuously along a similar spacetime “sheet” to survive and move around, while also being able to affect his original universe in a way not bound by the unidirectionality of time.

CoopTime3

Pulling the sheet past the black hole’s funnel (and giving it a twist) up into itself gives us an intersecting “curve” where Cooper’s entire sense of “space” is equal to the universe’s entire sense of “time”.

The catch here is that “they” need an anchor (explicitly mentioned by Cooper himself in the movie) where a fixed point in the “space” axis is needed so someone can move freely along the cross-section representing all of time, the same way two overlapping planes intersect at a specific line/curve. Said anchor is Murph’s bedroom, then accessible from almost any time it exists.

(Murph’s room, of course, wouldn’t *be* in an absolute point in space at all times, and that part is artistic license… amongst many… other things… in this movie…)

Anyway, now that Cooper is in a position to access his own universe without the limitations of time and its dilation due to relativistic effects, he learns how to (or is instrumental to) literally “poke” at the universe’s spacetime “sheet” and generate little gravity wells.

CoopTime04

Dust queue into lanes, watch hands twitch, books fall, everyone doesn’t die.
Of note: Murph’s success in solving quantum gravity also allows humans to later do this “poking” on their own, as possible precursor to “they” who can manipulate spacetime manifolds willy-vanilly.
When “they” are satisfied the Stable Time Loop of “their” existence has been closed, the tesseract closes in around Cooper and he is ejected back into the universe near the wormhole’s former location near Saturn, relatively unharmed. (He also passes the wormhole highway along the way, hence time-independent cute hand touching with Amelia.)
CoopTime05
Tags: interstellar, manifold, minkowski space
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