"Interstellar" has always been talked about, and with the blessing of Kip Thorne, a Nobel laureate in physics and today's master of general relativity, the scientific nature of this science fiction blockbuster has also been guaranteed. Later in the film, after Murphy receives a Message from his father Cooper, she yells "Finally understood", so what did Murphy finally understand?
In the beginning, blight broke out on the earth, crops gradually went extinct, and humanity was about to face the bad luck of starvation and suffocation. For the sake of the continuation of the human species, one has to look at habitable planets beyond Earth.
However, the closest habitable planet to Earth is also thousands of light-years away, when human aerospace technology could not fly that far. And even if a habitable alien world is found, the giant space station cannot be sent into space, and humans cannot carry out large-scale interstellar migration.
Just when everyone was in trouble, people found wormholes placed "by them" near Saturn. According to Einstein's general theory of relativity, wormholes can fold space-time to connect universes that are very far apart, which is a very special kind of space-time channel.
Professor Brand Sr. realized that this gravitational anomaly would not only allow humans to travel far away in search of habitable alien worlds, but also be used to construct a gravitational equation. If this gravitational equation can be solved, it will be possible to control gravity and send the giant space station into space, thus achieving large-scale interstellar migration. This is a plan to save humanity.
But through in-depth research, the elder Professor Brand only solved half of the equation, and the other half could not be solved. To fully solve the gravitational equation, data inside the black hole is needed so that general relativity and quantum mechanics can be compatible with each other.
However, detecting the interior of a black hole is considered impossible. Black holes are the most extreme gravitational objects in the universe, distorting space to the extreme, trapping light in them. Even if people or detectors can safely enter the black hole and get data, this information cannot be transmitted from the inside of the black hole through electromagnetic waves. The event horizon of a black hole is a one-way channel that allows light to come in and out.
Without knowing what's inside a black hole, the solution to the gravitational equation can't be deduced. Therefore, the old Professor Brand knew that Plan A was not going to work. In the name of Plan A, he secretly implemented Plan B to colonize the alien world.
Still, "they" came out again to help humanity. After Cooper fell into the black hole, he was not destroyed by the black hole, but entered the five-dimensional space-time set by "them". There, Cooper could see every moment in Murphy's room as a child.
Although Cooper obtained the data inside the black hole, he was in five-dimensional space-time and could not use electromagnetic waves to transmit information to low-dimensional space-time. The only way is through gravity, which can span the dimensions of time and space.
In this way, Cooper relayed the black hole message to the Murphy watch as a child. When Murphy grew up, she finally discovered the quantum information from Cooper and successfully solved all the gravitational equations, which is what Murphy shouted "finally understood".
Since then, gravity has become maneuverable, and humans have entered space with the large space station through anti-gravitational technology, eventually avoiding extinction on Earth.