The movie begins in 2050, with the outer-space starship chase.
The time jet is introduced as the first technology of the movie. Ryan Reynolds' character, (Old) Adam, is evading authorities, attempting to steal the spaceship. The capabilities of the time jet are: time travel, voice calls, and signal jamming. Adam receives a transmission from Sorian, who is in the chasing ship. She tells him to surrender but he crashes their tracking signal and escapes. The ship is badly damaged, and Adam uses up the last of its abilities to perform time travel. In this movie, time travel is made possible by traveling through a controlled worm hole.
After the wormhole sequence, the film introduces young Adam in 2022.
Young Adam is sent to the principal's office after he gets beat up by school bullies, and his mom picks him up in a car. The car is presented in parallel to the future capabilities of transportation of time jets, specifically with this scene juxtaposing the opening chase scene, and especially later in the movie during a chase between spaceship and car.
Adam's childhood house is gorgeous! The most noticeable aspect of the home is how interconnected it is with nature. Even with all the advanced technology and appliances inside, it is almost 360º of floor to ceiling windows. It is also situated in a beautiful forest, so trees in every direction. Similar to how this film contrasts time jets with cars, it juxtaposes the modern house with nature, but also somehow blends them beautifully.
After Adam's mom leaves to go on a date with her coworker, Adam is home alone playing a flight simulation game. We know Adam becomes a real pilot in the future, so this game is probably what inspired him and taught him his skills. While we clearly see the positives of virtual reality and video games, we also see a hint of the negatives. Adam's dog, Hawking, is sitting right next to him, looking sad, and Adam pays him no attention. This notion of virtual reality disengaging Adam from the physical world is made more obvious later in the movie [1:11:05] when Adam's father says, "I don't know if I should've built that game for him. Shouldn't he be outside, playing with the rest of the kids? How is he gonna find his place in the world?"
The key to Adam's time jet uses DNA recognition technology––through the contact of a thumb print––to gain access to the vehicle. It was not immediately obvious, but on my second time watching, I noticed a DNA hologram pop up out of the key after young Adam puts his thumb on it. Quite a cool detail since they (both versions of Adam) are the only two (one?) people in the world who can activate the ship with their unique DNA.
Old Adam goes to the store to buy medicine for his wounds, but when he gets there, he has to ask his younger self for cash. Old Adam jokingly says they don't have money in the future but immediately admits he was joking and takes the cash. It is ambiguous whether transactions in the future are entirely digital, or whether old Adam just doesn't carry cash. If the future transactions really are completely digital, then this is one example of problems arising from different levels of technology. In this case, the conflict is caused by different times, but in the real world, technology standards are different for each country. A pottery artisan in India most likely does not accept Apple Pay for example.
When Adam is confronted by Sorian's team of space officers, he is forced to use his lightsaber. An important detail is that he fights them using his fists and martial arts skills for as long as possible, until they hit him to the ground and corner him. Only then does he talk out the lightsaber. It is a powerful weapon, and he knocks out the space officers easily. We later learn that the lightsaber has the ability to disintegrate beings if you hit them solidly across the length of the weapon. Old Adam likely didn't want to kill anyone; furthermore, he may have known one of the first space officers, because they knew his name, saying, "Don't do it Reed!" when he was about to take out the lightsaber. He was responsible with this dangerous technology, only using it when his mission to save the world was in jeopardy.
Laura sacrifices herself to help both Adams escape Sorian's guards and they take her time jet to 2018.
There, they meet Adam's father, Louis, and try to convince him to help them destroy his time travel machine.
The drone is introduced to young Adam as a means to protect old Adam from Sorian's guards when they attempt to raid the Sorian building. It is successful at distracting the guards, in combination with young Adam's piloting skills and old Adam's improvisation to stall the guards. However, when cars start driving toward old Adam to ram him, the drone is not fast enough. For that, Louis saves Adam by ramming his car into the bad guys' cars.
Louis created the arc accelerator and algorithm to produce time travel. We know that it was ultimately successful due to the existence of time jets from the original 2050 timeline. In this new, altered timeline however, Adam and Louis are successful in destroying the machine due to its lack of protection. After a single gunshot to the glass container, the machine begins a meltdown.
The movie ends with both Adams leaving 2018 to return to their respective timelines.
Young Adam sees his mom and learns to appreciate his relationship with her.
Old Adam meets Laura in flight school and the movie ends with them falling in love again.