The Time Leap Machine is a modified version of the Future Gadget #8: the PhoneWave (Name subject to change) that appears in Steins;Gate. It is capable of sending people’s memories into the past, i.e., time leaping, which is different from physical time travel. Its name, the Time Leap Machine, is a reference to The Girl Who Leapt Through Time, a classic piece of Japanese literature that was later made into a movie.
The Time Leap Machine of the Alpha Attractor Field that most of Steins;Gate takes place in was built by Kurisu Makise, and based on her research into how memories are stored in the hippocampus part of the brain. It also relies on Visual Rebuilding technology that was developed in the 1990s at Viktor Chondria University for scanning information from people’s brains using electromagnetic waves, and also beaming information into people’s brains using electromagnetic waves. This same Visual Rebuilding technology played a major part in an earlier game in the Science Adventure Series, Chaos;Head. It relies on a special headset to scan the brain of the person doing the time leap, and someone can only leap back in time to a time when they had their cell phone with them.
Furthermore, it relies on SERN’s Large Hadron Collider to compress all of the data in the human memory into a small enough size to be equivalent to a D-Mail. After that, it relies on similar principles to D-Mail to be sent back in time. The compressed memory data from the hippocampus automatically decompresses upon arrival in the past, using software Itaru Hashida wrote. The person’s past self will hear their phone ring and bring it up near their face, and then the phone will beam the electromagnetic waves full of their future memories directly into their hippocampus, transferring their memories back in time.
The longest increment of time it is safe to jump back is 48 hours, and it is only possible for someone to jump back into their own past brain, not somebody else’s, because every brain is unique and a different brain would be incompatible. Also, because the brain changes over time, the amount that a brain changes by in a period longer than 48 hours means that the same brain of the same person might not be compatible if a time leap is attempted that is longer than that, which could potentially lead to brain damage and in the worst case scenario, turn the person into a vegetable who is brain-dead.
A more likely way things can fail is that the person might not have their phone with them, their phone might be off, or they might fail to answer their phone, in which case the time leap would not occur, but at least there would not be any brain damage. If things fail in this way, nothing at all happens.
Just like a D-mail, a time leap alters what world line someone is in, it jumps back to an earlier point in time in the current world line, thus creating a new worldline from the point of arrival. However, according to Suzuha, time leap can only change divergence by 0.000001% in most cases. Due to World Line Convergence, many events that occur in a given world line are fixed and cannot be altered by someone using the Time Leap Machine, in fact, a lot more events than the amount that are fixed in a given Attractor Field, since every Attractor Field has many world lines in it.
Ultimately, the Time Leap Machine, while useful, is not as powerful as D-Mail, since D-Mail is capable of changing world lines and can even change to a different Attractor Field under the right circumstances. However, the Time Leap Machine is easier to control than D-Mail, since the effects of D-Mails are unpredictable, but using the Time Leap Machine, someone can get to know how a world line turns out very well and use this to gather information, with their memories intact, in order to know exactly what D-Mail to send in order to achieve the desired outcome.
Using both time leaping and D-Mail together, someone can navigate between different world lines and find a way to achieve the world line they want. In Rintaro Okabe’s case, since he is the main person using the Time Leap Machine, his goal is what he calls the Steins Gate world line, with divergence number 1.048596. In the Steins Gate world line, it is possible for Okabe to save both Mayuri Shiina and Kurisu Makise, as well as avoiding both SERN’s dystopia (the result the Alpha Attractor Field converges on) and World War III (the result the Beta Attractor Field converges on), since the Steins Gate world line is under the influence of both Alpha and Beta attractor fields and not part of either one.
Other characters besides Okabe use the Time Leap Machine too. In various different world lines, Luka Urushibara, Kurisu Makise, and Nae Tennouji have also used the Time Leap Machine; in Luka and Nae’s cases, this happened in the parts of the Steins;Gate visual novel, while in Kurisu’s case, this happened in Steins;Gate: The Movie - Load Region of Déjà vu. Rintaro Okabe is the Time Leap Machine’s main user, though, using it in many different world lines, rather than in just one world line each like those other characters.
Given enough time, energy, and equipment, it would be possible to upgrade the Time Leap Machine so that it is possible to jump back longer amounts of time than just 48 hours. This occurs in Steins;Gate 0, where an upgraded Time Leap Machine, the Time Leap Machine of the Beta Attractor Field (which was not built by Kurisu, but instead by Itaru Hashida and Maho Hiyajo) is able to jump back in time up to 2 weeks safely after Maho figures out a way to upgrade it to make these longer time leaps back in time.
So in the Alpha Attractor Field as well as the Steins Gate world line, the Time Leap Machine is made by Kurisu Makise, who is alive to do the work, while in the Beta Attractor Field, it is made by Itaru Hashida and Maho Hiyajo using Kurisu’s work as a basis, as Kurisu dies before having a chance to become a Lab Mem in the Beta Attractor Field.