sam_738844
Wise Old Owl
Interstellar: 9/10
I believe TARS did not send back equations, but data. Data to solve equations. Almost every equation in Physics depend on constants and variables. Finding them is critical. Data sent by TARS can determine those constants/variables, thereby eliminating incorrect solutions. Lets say you have equation x+y=5. This equation has infinite number of solutions. If you know y then this has only one solution. For constants I can name a few like Planck's Constant etc.
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Nothing can be sent after the SC limit. That IS the blackhole information paradox. The pattern, piece, holder and the instance of the information, these properties will permanently disappear within black-hole. Simply because the curvature of time-space near the horizon is greatly deformed. Speed of information propagation in a forward light-cone is the speed of light, which must be exceeded to escape the gravity field near the singularity. From a potential observer outside the black hole, that information will basically freeze and red-shifted until it is phased out. So any information sent from inside will never actually reach the outside the radius. Even if there is some means to boost the information relatively to the safe zone just out side the SC radius, it will get stuck in the Photon Sphere and will orbit the black hole forever.
The paradox arose after Hawking showed, in 1974-1975, that black holes surrounded by quantum fields actually will radiate particles (“Hawking radiation”) and shrink in size eventually evaporating completely. So where the information inside the black hole does go? if the black hole is gone, where did the it disappear along with the black hole?, that violates quantum theory.
There are more solutions and theories about this than there are hairs in my head. Complementarity, holography and so many string theories and quantum entanglement blah..blah...but bottomline is the TARS plan would never work. It was inevitable that the wormhole theory sticks in the movie for the solution to come.