The PhoneWave (Name subject to change) is one of the inventions of the Future Gadget Laboratory (Future Gadget No. 8). With it, you can send messages to the past, known as D-Mail.
The PhoneWave would serve as the basis for the much more advanced Time Leap Machine.
Initially, the lab wanted to create a microwave that could be controlled remotely using a mobile phone. The timer (in seconds) was added and Daru changed the direction of rotation of the microwave plate to the opposite (i.e., clockwise) and switched control to the computer, connected a mobile phone (like a receiver) to the microwave itself, the time was sent from the mobile phone through a program configured to the phone number connected to the microwave. After that, laboratory members noticed the strange effect of the device: bananas placed in it, instead of being heated, became green and watery, like a gel (hence the name gelbana, “gel banana”). When they didn’t put inside the whole bunch, but a banana torn from it, the gel banana as a result of the device turned out to be attached to the bunch left on the table. Analysis of gel bananas under a microscope showed that they are changed at the molecular level, the molecules having been forcibly ripped apart.
The first PhoneWave was created by the Future Gadget Lab in 2010. Capable of sending short messages to the past via text, this machine served as the basis for SERN's time machine, and proved instrumental in switching timelines between Alpha and Beta worldlines, but was destroyed on the Beta Attractor Field and the Steins Gate worldline not long after creation.
A variant of the PhoneWave was created by Hashida Itaru and Hiyajo Maho later on in the Beta Attractor Field. This variant was designed to replicate the original's functions and was eventually upgraded with increased data transmission. It was used to send a video message to Okabe Rintarou, to be seen after his first failed attempt to rescue Kurisu.
The PhoneWave works on the principle that the microwaves are amplified by the cell phone’s emissions, causing the air molecules in the microwave to clash at light speeds, creating mini black holes that would normally immediately disappear; however, the cathode rays from the 42" CRT below the lab add angular velocity to the black holes, making them stable Kerr black holes, which allow things to ignore the laws of space and time and travel back to the past. The gelification is caused by the objects being compressed and reconstituted, though it ignores data since data has no mass or volume, instead curtailing anything over 36 bytes of data.
The idea for the PhoneWave and D-Mail was originally called the “tachyonic antitelephone” and was developed by Albert Einstein in 1907 as a thought experiment about a communications device that would send messages back in time, in a paper by Einstein titled “On the relativity principle and the conclusions drawn from it” (or “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen” in the original German). In 1910, Albert Einstein and Arnold Sommerfeld described this hypothetical device as something “to telegraph into the past”. In 1917, Richard Chace Tolman came up with this same thought experiment independently, giving the paradox it causes a name, Tolman’s paradox (as Einstein has many other paradoxes associated with him already). The name “tachyonic antitelephone” for it was later coined by Gregory Benford many years later. Einstein’s original idea involves faster-than-light signals transmitted by particles that move faster than light speed called tachyons, which would transmit messages back in time between 2 telegraphs using Morse code.
The purpose of this thought experiment was for Einstein to prove that faster-than-light speed is impossible because it would violate causality, a form of time paradox. This was part of Albert Einstein’s efforts to try to spread the idea of his theory of special relativity. Einstein had not yet achieved his greatest theoretical breakthrough, general relativity, which he finally figured out in 1915, but this was part of the work leading up to it, as the “tachyonic antitelephone” paradox logically proved that the speed of light was the cosmic speed limit, at least if one assumes that time paradoxes that violate causality are contradictions that cannot be resolved and that proof by contradiction is logically valid. Kurisu Makise discusses Tachyon theory as one of 11 scientific theories for potential time travel early in Steins;Gate, and uses the same logic as Einstein against it, as well as some other arguments of her own.
The PhoneWave averts a paradox with D-Mail because it does not use tachyons but instead Kerr black holes, according to the Kerr black hole theory of time travel, and because the Attractor Field theory of the Science Adventure Series allows for paradox-free sending of messages into the past, through the principle of world lines, which is similar to the many-worlds interpretation of quantum physics developed by Hugh Everett III, who proposed the many-worlds interpretation in 1957. There are several differences between the Attractor Field theory and the many-worlds interpretation, the most important one being the existence of Attractor Fields and World Line Convergence.
Originally, the PhoneWave, through its D-Mail function, is able to send text messages or pager messages back in time to cell phones or pagers, although it is limited to sending 36 bytes, and messages longer than 12 bytes get split up, with 13-24 byte messages getting split into 2 and 25-36 byte messages getting split into 3. Messages longer than 36 bytes are split into 3, with only the first 36 bytes being transmitted and bytes 37 and later not being transmitted.
Later on, it is upgraded into the Time Leap Machine, able to send the memories stored in the hippocampus in the human brain back in time, using the Large Hadron Collider to compress the enormous memory data of the hippocampus down to only 36 bytes. This is done using Kurisu Makise’s theoretical knowledge from her thesis about Visual Rebuilding and other things she knows regarding neuroscience and physics, along with Itaru Hashida’s technical knowledge regarding hacking into SERN, coding the software, and designing the hardware.
The PhoneWave only works when the 42" CRT in the Braun Tube Workshop is on, even after being upgraded into the Time Leap Machine, since the cathode rays from the 42" CRT are just right for stabilizing the miniature black holes of the PhoneWave into stable Kerr black holes, allowing data to be sent through. It is still not able to do physical time travel without gelification, as demonstrated by the gel bananas as well as chicken tenders that Mayuri Shiina put in the PhoneWave which were not only refrozen but also gelified just like the bananas. This is because it still cannot produce naked singularities, an even more stable form of Kerr black holes where the event horizon completely disappears, which are needed to safely do physical time travel of human beings or anything else that is larger than an atom, since even molecules are ripped apart by the PhoneWave.
However, since data does not have any size or mass, it is not subject to the same limitations as physical objects, and it can be sent back in time in the form of electromagnetic waves, which, in wave-partical duality, are equivalent to photons, which are massless point particles that travel at the speed of light. Since photons have no mass or size, they are safe from being gelified, and the fact that they are in wave rather than particle form also helps too, since that way the electromagnetic waves from a phone can be fused with the microwave rays from the microwave (which is the process that actually produces the black holes in the first place).