Time travel was the process of traveling through time, and was done with a time machine.
In 1943, Emmett Brown was working as a professor at the California Institute of Technology. He convinced the president of CalTech, Robert Millikan, to get him an interview with the government for the top secret project for which they were recruiting. After a disastrous interview where he pretended the the house of his landlady was his own, Emmett walked back to his apartment. He was surprised to see Vannevar Bush and J. Robert Oppenheimer there waiting for him. They told him that his unusual method of thinking was exactly what they were looking for, and hired him to work on the Manhattan Project.
While working on the project, Emmett became an expert in the field of nuclear physics. He also was prone to come up with wild hypotheses, which Major General Leslie Groves called "flights of fancy". However, Emmett left a lasting impression on Groves, who believed that if anyone could invent time travel, he could.
On November 5, 1955, Doc Brown came up with the idea of a device that would make time travel possible after slipping and bumping his head while standing on his toilet to hang a clock. The idea came to him in a vision he had after being knocked out. He drew an inverted Y-shape with wires and stated "flux compression". He also performed some mild calculations on the paper.
By the 1960s, Doc utilized his ideas of flux compression to develop a time machine that was capable of sending objects through time, but only during the lifespan of the device. The time machine, known as the temporal field capacitor, was only useful for sending objects into the future. Sending an object even a few minutes into the past caused a buildup of flux energy. If an object was sent any further back than that, the arrival of the object would overheat the capacitor and start an electrical fire.
On October 24, 1962, Leslie Groves and Colonel Lomax visited Doc, on behalf of the United States military, as they were looking for a way to travel back in time to prevent the Cuban Missile Crisis from ever occurring. Doc told them, as he needed funding for his inventions. He later had worries that he could be ushering in an arms race through time, coupled with his regrets about ushering in the nuclear arms race of the Cold War through his participation in the Manhattan Project.
The next day, he wrote himself a letter about his plans, and purposefully sent the letter back several months in the past, to August 1, when he knew that he and his dog, Copernicus, would be safe asleep in his fireproof garage. The Brown family mansion burned down, and the military personnel came and left in the new timeline without ever talking to Doc. Doc used the insurance money to fund the rebuilding of the temporal field capacitor, as well as his future inventions.
The invention of the temporal field capacitor was a necessary step towards the invention of the flux capacitor, which was the device that made time travel possible, as it solved the problem of the excess flux energy when traveling to the past.
The first DeLorean time machine
On October 2, 1982, Marty McFly snuck into Doc's garage to get the interocitor tubes that Doc had purchased under the name of his company, ELB Enterprises. Marty had to solve the riddles of the various traps that Doc had set up to prevent people from entering his garage. Due to Marty's ingenuity, as well as his honesty in admitting that he had sneaked in to get the tubes, Doc hired Marty as his assistant.
This allowed Doc to not have to worry about the care of his garage and his dog, Einstein. He was able to work on experiments in his secret lab. Doc didn't reveal the location to this lab to anyone, including his assistant. He even went to extreme lengths to keep it a secret, registering the building under his birth name, Von Braun.
Doc wanted to use the DeLorean because its stainless steel construction would help with the dispersal of flux energy. In addition, Doc had made a deal with terrorists from Libya. They would steal a box containing plutonium, and in exchange, Doc would build a nuclear weapon for them. Instead, once they gave Doc the plutonium, he sent them a useless shell that simply contained the pinball machine parts.
By 1985, Doc Brown had finished his DeLorean time machine, which was the first time machine capable of transporting living beings through time. It utilized the flux capacitor, as well as a nuclear reactor that used plutonium pellets to generate 1.21 jigowatts of electricity. This allowed it to break the time barrier in what was called temporal displacement. This allowed it to travel along the space-time continuum, bringing the occupant safely to any point in time, but not in space. The original DeLorean time machine could only arrive at the same location from which it departed.
The first successful test of the DeLorean time machine occurred at 1:20:00 am on October 26, 1985 at the Twin Pines Mall. Doc sent Einstein one minute into the future. After the successful test, he planned to travel to 2010. However the libyan terrorists, managed to track Doc down, and shot him.
Marty McFly, while trying to outrun the terrorists, accidentally traveled to November 5, 1955, the day that Doc came up with the idea for the flux capacitor. He accidentally prevented the moment that his mother and father fell in love, which made a ripple in space-time, and led to his brother and sister slowly fading out of existence as the ripple caught up to the dates of their birth. Marty, being the youngest, was effected last. Since he was also a time traveler, a time bubble was formed around him when he entered the past, which also temporarily protected him from the ripple effect.
Marty had to convince George McFly to stand up to the high school bully Biff Tannen, in order to convince Lorraine Baines to choose him rather than Biff. The plan succeeded, and on November 12, 1955, the couple fell in love at the Enchantment Under the Sea dance, as they did in the original timeline.
Doc's 1955 counterpart was able to hook a cable up to the clock tower on the Hill Valley Courthouse, which was hit by lightning that night. The lightning rod on the DeLorean hit the cable at the moment of the lightning strike, powering the nuclear reactor and successfully sending Marty back 1985, on the day he left. Marty gave Doc a letter in 1955, warning him of his death.
In the new timeline, Doc wore a bulletproof vest and survived the shooting. Doc left Marty at home that night, and accomplished his original goal, by becoming the first person to travel to the future.
The next morning, Marty woke up to discover that more things had changed in the new timeline. Due to his newfound courage thanks to Marty's guidance, George McFly was a successful writer, and his mom was more confident in herself. Biff no longer rode on George's coat-tails, forcing him to write reports for him to advance his career. Because of this, Biff now ran his own auto detailing business, and George was a client. Marty now owned the 4x4 truck that he had dreamed of owning, and had made plans to go with his girlfriend to the lake.
Doc's trip to the future brought him to August 8, 2015, where he saw two inventions that could improve his DeLorean time machine. The Mr. Fusion nuclear reactor, which was powered by waste, could be used to replace the existing nuclear reactor, as plutonium pellets were hard to come by. In addition, getting a hover conversion would allow the DeLorean to travel more easily, as there would be no need for roads.
He entered the DeLorean in the Hill Valley 1980s Car Expo, and won first place, which entitled him to 10% off a hover conversion at Goldie Wilson Hover Conversion Systems. He searched the internet at the Hill Valley Public Library for prices of valuable items to find out what would be the most valuable investment. Finding what he was searching for, he left the library, entered the date April 18, 1938 into the time circuits, and headed towards his destination.
He arrived two miles outside of Hill Valley, parked the DeLorean behind a billboard advertising Studebakers, and headed into town. At a shop in Courthouse Square, he used one his silver dollar heirlooms for his purchase. He then headed back to the DeLorean, and then traveled back to future.
Once there, he went to Southby's Auction House to sell a near mint first issue of Action Comics for $2,500,000. He then headed back to the DeLorean, where he had stored several more. With his investment, Doc had surmised that he had managed to set him self up financially for life. He then took off in the DeLorean, which had been successfully hover converted and had the Mr. Fusion unit installed.
While in the future, Doc discovered that Marty's son was framed by Griff Tannen for the robbery of the Hill Valley Payroll Substation. This set up a chain of events that led to the imprisonment of Marty's daughter, followed by her suicide while in prison. Doc traveled back to November 13, 1985 to pick up Marty so he could help fix the future for his children.
They traveled to October 21, 2015. Marty posed as his son, and he succeeded in stopping the robbery. Griff Tannen and his gang instead crashed into the Courthouse Mall, after chasing Marty on hoverboards around Courthouse Square, and were arrested.
Biff wasn't sure how to operate the time machine, so he hit the time circuits with his cane. This caused the time circuits to malfunction, and Biff ended up traveling to the past once he reached 88 mph. However, the malfunctioning time circuits sent him farther than possible with the limited amount of digits currently available to input for the year.
Biff found himself in the past, during a time when the land that would be Hill Valley was under the ocean, and dinosaurs roamed the Earth. He encountered a velociraptor, which stole the Blast from the Past bag containing the Grays Sports Almanac. Biff hit the raptor in the head with his cane, retrieved the bag, and traveled forward in time to November 12, 1955.
Biff then traveled back to 2015, and dropped the DeLorean off where he left it. However, his actions in the past had caused him to no longer live to be an old man, and he began to fade from existence. Marty and Doc went back to the DeLorean with Jennifer and Einstein, so they could go back to 1985, not knowing that Biff had changed the past.
They found themselves in an alternate reality where Biff controlled Hill Valley, Marty was sent to a boarding school in Switzerland, and Doc was committed to an asylum. Doc found the tip of Biff's cane in the DeLorean, and realized that Biff had stolen the DeLorean to change time. He spotted the almanac in Biff's pocket in an old photograph, and realized that he had taken it from 2015 to the past to make himself rich.
Marty then confronted Biff to find out the moment where he got the almanac. After getting the information, Doc and Marty traveled to November 21, 1955. They had to be careful not to let their younger selves see them, as there were now two versions of both of them in that time period. They were able to successfully get the almanac back and burn it. However, the DeLorean was hit by a bolt of lightning in the air, and sent spinning on its axis up to 88 m.p.h.. Due to the malfunctioning time circuits, it was sent back to January 1, 1885 with Doc inside.
Marty discovered Doc's tombstone. With the help of Doc's 1955 counterpart, he was able to fix the DeLorean, which was sealed up in the Delgado Mine by Doc in 1885. When he traveled back to save Doc, he discovered that Doc fell in love with a woman named Clara Clayton. Doc ultimately ended up saving her life with the hoverboard that Marty had kept from 2015. Marty traveled back to 1985, and the DeLorean was destroyed by a diesel locomotive upon its arrival. Doc and Clara remained in 1885.
Trying to return to the 20th century
Doc was happy in 1885, as his job as the town blacksmith allowed him to conduct scientific experiments, but he didn't have to worry about being tempted with altering the space-time continuum. However, Clara wanted to travel through time. She had seen her mother struggle with fighting her rebellious nature to present herself as a proper 19th century housewife, and she didn't want that life for herself. While Doc had found a happy life in the past, she wondered if she would have been happier in his time period, where she would be allowed by society to pursue her interest in science.
When Doc and Clara had their two sons, Jules and Verne, Clara saw how happy he was reading them stories and telling them tales of his adventures. She didn't want to upset his happiness, but she was becoming less happy herself as time went on, as his stories made her want to travel to the future even more.
In the 1890s, Doc began to become homesick for his own time. He wanted to visit Marty and pick up his dog, Einstein. He began to build a time machine out of a steam locomotive. He was initially unsuccessful with his experiments to generate the amount of electricity needed for time travel. However, he was able to use the technology from the hoverboard that was left behind to create a frictionless dynamo that was able to store multiples of the 1.21 jigowatts needed to power the flux capacitor.
So, he paid some railroad workers to set up 50 yards of track and continued building the train. In 1893, he had deemed the train finished, but feared telling Clara the news. He didn't know that she wanted to travel to the future so badly, and was worried about making her unhappy just to please him.
Clara eventually told Emmett that she knew that he was inventing another time machine, telling him that he couldn't hide anything from her. She said that she would be happy to travel to the future with him and their sons. Doc, feeling his burden being lifted, decided that it was time to attempt to travel back to the future.
On June 12, 1893, the Brown family attempted to travel in the Jules Verne train to 1985. Doc calculated that 50 yards would be enough to reach 88 m.p.h, since he had improved the performance of the presto logs used to heat the boiler of the steam engine. The trip failed however, as the train didn't achieve temporal displacement, and crashed.
Doc had intended to give up his quest for time travel at that point, as he was happy in the 19th century, and didn't want to put his family in unnecessary risk. However, Clara finally told him that she had wanted to travel to the future ever since she found out about the DeLorean time machine. Time travel wasn't just his dream, it was hers too. Jules and Verne also told him that they wanted to go as well. Since his family wanted to travel through time so badly, Doc decided to try another approach towards accomplishing time travel.
After seeing a Steam tricycle driver driving a Serpollet steam tricycle, Doc decided to use one as a time machine. He used the flux capacitor and the time circuits from the prototype Jules Verne Train. He then donned a diving suit to protect himself from the the stresses of space-time and the temperature variation. He successfully traveled to 2035 from August 13, 1893. While there, he had planned to pick up everything he needed to complete the Jules Verne Train.
The Jules Verne train
Later in the 1890s, Doc was able to successfully complete the Jules Verne train. He traveled to some point in the 1980s and picked up Einstein, then traveled to October 27, 1985. There, the Brown family met up with Marty McFly and Jennifer Parker in the most likely place that they might be at that given time, the site of the DeLorean's destruction. He introduced his family, and gave Marty the picture that was taken in 1885 of Marty and Doc in front of the clock that had yet to be installed in the Hill Valley Courthouse.
When the Brown family began to live part time in the 20th century, they brought the Jules Verne train with them. It had the ability for spatial displacement, which allowed it to travel to any location in any time period.
The temporal duplicate DeLorean
On May 14, 1986, a DeLorean time machine arrived at Doc's garage, six months after Doc's original DeLorean was destroyed. This DeLorean was a temporal duplicate, which had been created when the original DeLorean was hit by lightning in 1955. While the original DeLorean was sent seventy years in the past, the temporal duplicate DeLorean was sent seventy years into the future. Doc traveled to the future and discovered that DeLorean. He was able to get it back from Griff Tannen before he caused damage to the time stream.
As it was an exact duplicate of the original DeLorean, it had all the additions that the original DeLorean had when it was hit by lightning in 1955. It also had some additions that Doc had made since then, including an automatic retrieval system which would send the DeLorean to the future to retrieve Marty in the event that Doc didn't use the DeLorean for an extended period of time.
Marty played a tape of Doc explaining this feature, and realized that Doc was in trouble. He traveled to June 13, 1931 to rescue Doc. Things didn't go as planned, and Doc was erased from time due to Marty accidentally causing a young Emmett to fall in love with and marry Edna Strickland. Doc never created the time machine, so he wasn't able to get the rejuvenation treatments that extended his life.
Marty was able to convince the alternate Doc from this timeline to repair the time machine. This Doc, who went by the name Citizen Brown, traveled back to 1931 with Marty to try to fix the timeline. As they arrived at a later date then they had intended, Citizen Brown repaired the time circuits of this DeLorean, which were unstable. He used flux emitters to calibrate the time circuits to ensure that the DeLorean arrived at the right time.
When Marty proved that Edna was the arsonist who burned down the Hill Valley speakeasy, the timeline was repaired. Young Emmett never married Edna, so Citizen Brown faded from existence. Edna Strickland stole the DeLorean and accidentally headed into the past, while trying to avoid Officer Danny Parker. Marty gave young Emmett a newspaper clipping from 1986 and told him not to look at it until he was awarded the key to the city. At that point, Doc arrived in 1931, as he had received the key and then understood who had given him the newspaper clipping. This Doc had arrived in a different DeLorean, which was from the new timeline, so it didn't contain the modifications that Citizen Brown had made.
Once Hill Valley faded from existence, they realized that Edna Strickland had seriously damaged the time stream at some time in the past. Marty's great grandfather William McFly, told them about an old woman named Mary Pickford, who he thought would know about the town that used to be there.
It turns out that Mary Pickford was actually Edna Strickland, who had traveled back to 1876 and accidentally burned down the town when she tried to set fire to the Palace Saloon. After she gave them the date of the arson, Marty and Doc traveled to July 17, 1876 to stop her. Doc used flux overrides to control the flux emitters on Edna's DeLorean. They were able to remotely control her DeLorean, accelerating to 88 mph before that DeLorean faded from existence once the time bubble protecting it popped and time caught up with itself.
The new DeLorean
In 1991, Doc Brown built a new DeLorean. This DeLorean had many improvements, including audio activation of the time circuits, and spatial displacement, which, like the Jules Verne train, allowed it to travel to any place on Earth at any time period. This DeLorean also had the ability to transform into a suitcase, which prevented it from being stolen and allowed it to hidden more easily.
By 1991, Doc improved upon the temporal field capacitor with the remote control mail delivery time machine, which could send objects through time, beyond the lifespan of the device. When the Brown family were visiting the Pyramids of Giza in Egypt in 1000 BCE, a spear damaged the flux capacitor of the Jules Verne train. The time train was sent to 1692 in Salem, Massachusetts. Doc used the remote control mail delivery time machine to send a scratch and listen postcard to 1991 to let Marty know the situation.
Marty used the new DeLorean to travel back to September 23, 1692 with a spare flux capacitor. He crashed in a lake, and another addition that Doc made to the new DeLorean was revealed when an inflatable device was automatically triggered, bringing the DeLorean back to the surface. After several days, Doc was able to repair the train, and they were able to take both the Jules Verne train and the new DeLorean time machine back to 1991.
The 8-passenger DeLorean
The 8-passenger DeLorean was faster, more energy efficient, a convertible, and was equipped with a sub-ether time-tracking scanner.
It was originally planned to be used to send Doc's time travel volunteers one day into the future, but instead was used to bump Biff Tannen after he stole another DeLorean time machine, which sent both cars from the primeval Hill Valley back to 1991.
Time travel without a machine
When Doc was stranded in 1885, he had come up with a plan to travel without a time machine. He devised an idea for a time parachute, in which a person would ascend in a balloon to a distance of half a mile, and then would be released from the balloon. The person would fall at a rate of 35 feet per second per second, and would reach 88 m.p.h. between four and five seconds. Since the time circuits and flux capacitor are connected to the parachute, the person, who would be protected from the rigors of space-time and the temperature variation by wearing a protective suit, would travel through time. The time traveler would then pull the ripcord of the parachute once they traveled through time, and arrive safely on the ground in that time period.
After traveling from 1991 to August 5, 1926, Jules Brown devised a similar plan. His father, who was a child at the time, was going to be in a barrel going over the Upper Yosemite Falls while movie producer D.W. Tannen filmed it. To keep his father safe, Verne Brown took his place in the barrel, and Jules put a spare flux capacitor inside. As Doc had improved time travel at that point to allow for travel through both space and time, once the barrel reached 88 m.p.h., it was sent safely towards land.
Blue DeLorean time machine
On May 15th, 1986, a future version of Marty appeared in a blue DeLorean time machine. Apart from the color, this car was identical to the original DeLorean, including having the ability to fly.
Black DeLorean time machine
Shortly after the blue DeLorean arrived, another future version of Marty appeared in a black DeLorean time machine. The black DeLorean was identical to the original DeLorean, except it was black in color and had fire decals on each door. Interestingly, the wheels of this car did not appear to rotate while it was in flight, instead remaining as they would on a regular car.
Unspecified DeLorean time machines
Doc used a DeLorean time machine several times after he returned from 1885. It's unknown which time machine was used in these instances, but since they appeared similar to the original DeLorean, they were likely either the temporal duplicate DeLorean or a new time machine.
On May 15th, 1986, a future version of Marty arrived outside Doc's garage in a DeLorean time machine.
In 1988, Doc traveled to Orlando, Florida on May 1, 1990 to visit Universal Studios Florida. He was able to have an experience beyond that of usual theme park visitors, as he was able to actively participate in the rides.
In 1991, Biff stowed away in a DeLorean time machine when the scientists from the Institute of Technology traveled to 1955. Biff stole this time machine and traveled to the future and the past, while being pursued by time travel volunteers in an 8-passenger DeLorean remotely piloted by Doc Brown.
Doc traveled to 2045 or beyond, where he witnessed the devastation caused by a nuclear holocaust which was accidentally triggered by an overload of the Mr. Fusion network by a signal sent out by Griff Tannen's ThingMeme social media application. Doc successfully traveled from 2015 to an unknown point the past to prevent the the Mr. Fusion, hover conversion, food hydrator and self-tying shoes from being available by 2015.