Snake Math
While trying to set up Christmas lights, Jerry falls off the roof. Before he hits the ground, Rick zaps Jerry with a ray that renders him lighter than air for 10 hours, before rendering his shoes heavier than air, thus making Jerry neutrally buoyant and enabling him to jump higher than usual. Rick and Morty depart for an adventure, but their ship breaks down in space. While repairing it outside the ship, Morty is bitten by a snake astronaut which he then kills. Morty tries to atone for the snake’s death by buying another snake from a pet store and sending it to the snake planet; however, the snakes quickly determine that it is not from their world. Soon, a robot snake appears and attacks Morty, before another snake materializes and defends him. More snakes appear in growing numbers to alternately attack or defend the Smiths. Rick explains that Morty’s actions caused the snakes to unite and invent time travel. Rick and Morty travel to the present-day Snake Pentagon to resolve the war, but the snakes have not yet completed their time machine. A future Rick and Morty (who sports a black eye) appear with disguises and a book full of instructions on time travel in the snake language, while also rudely insulting their past selves. Current Rick and Morty travel to 1985 and leave the book at Snake MIT before returning to the present.
To prove the snake equation we must first make the following equivalence for tensor products of the elements [katex]\ket{i}[/katex] and [katex]\bra{j}[/katex]:
[katex] \ket{j}\otimes \bra{j} \equiv \ket{i} \otimes \bra{j} \equiv \ket{i}\bra{j} [/katex]
This is illustrated diagrammatically as 
With this equivalence made, the proof of the snake-equation for the “S” bend is given by
Meanwhile, Jerry loses one of his shoes while attempting to show off his buoyancy, causing him to float away helplessly. Reasoning that he will either survive unassisted or have Rick blamed if he dies, he rejects Rick and Beth’s attempts to help him. With the ray about to wear off as he is high above ground, Jerry prepares to fall to his death when a jet flies by, to which he attaches himself. The plane crashes due to a snake flying into the engine, but Jerry survives. Back on present-day Earth, time-traveling snakes and snake robots are raining down on the planet. Just as Rick planned, the large amount of time travel catches the attention of the Time Cops from “A Rickle in Time”, who travel back in time and kill the first primitive snake to use tools, thus preventing the existence of snake civilization and causing the snakes to disappear. Jerry reveals himself to be on the roof, claiming he was there the whole time, and turns on the Christmas lights before he falls off and breaks his leg. Rick heals Jerry’s leg by 50%, respecting that he got home by himself, but also shuts him out of the house. Rick and Morty look forward to having eggnog, before they are rudely reminded by their smug future selves to make the disguises and time travel travel notes. The future Rick and Morty insult their past selves more before leaving to enjoy eggnog, while the present versions begrudgingly resign to their work while griping about the future versions’s meanness. In the post-credits scene, while waiting to meet their past selves on the snake planet, Morty asks if they are forgetting something. Rick reminds Morty to stay in the car next time, before punching him in the eye.