Pete's World

Pete's World is the Doctor's name for the alternate universe that the TARDIS accidentally fell into.

Pete's World is similar to the normal universe, though slightly more advanced. Much of the world's technology is provided by Cybus Industries, a company run by John Lumic. This includes the Zeppelins and EarPods. Politically, Britain became a republic sometime after 1879, which led to the election of a British President, the instigation of a curfew and the banning of alcohol.

History
Much of this worlds history is unknown though it is suspected to mirror our own in nearly all ways bar Britain being a republic, a curfew and banning of alcohol, air travel being dome by airships instead of planes and the introduction of a company called Cybus which apparently sped up that worlds technology to be around 10 or so years ahead of our own.

When The Doctor, Rose Tyler and Mickey Smith accidentally fell into this world Rose discovered that her father was alive in this world and hugely successful where in our world he was dead and never amounted to much, she runs off to find him with The Doctor while Mickey goes to find his grandmother who is dead in our world.

Meanwhile, John Lumic introduces his latest creation a living machine that will be able to save him and upgrade everybody else to what he views as perfection, he has been testing out the technology on homeless people so as not to attract attention but a small group opposing Cybus called The Preachers has noticed and is investigating. He decides to move ahead with the project and sets course for Great Britain.

Once he arrives he plans to test his Cybermen on a party thrown by that worlds version of Pete Tyler and his wife Jackie, the Cybermen invade the party killing many of the guests including the president but The Doctor and Rose along with Pete manage to escape and meet up with Mikey and The Preachers while the Cybermen start to round up the population to turn them into Cybermen using their earpods to control them they capture and "upgrade" that worlds Jackie.

The group who escape formulate a plan to infiltrate and cripple the Cybermen operation which eventually succeeds and the Cybermen begin to shut down and John Lumic dies. Not long after Mickey stays in that world while The Doctor and Rose leave.

Months later, Torchwood One in London began experimenting with a rift which they inadvertently widened to let occupants of both worlds crossover which lead the remaining 5 million Cybermen to cross over to our universe and attack. Knowing a way to close the rift and to get rid of all the Cybermen The Doctor and Rose made a plan to suck the Cybermen into the Void, Rose had decided to stay with The Doctor even though her Mother and Mickey were to remain in the parallel world but there was complications and Rose ended up trapped in the other world without The Doctor and with no way to get back.

Rose was contacted by The Doctor and went to see a projection of him in Bad Wolf Bay as the last crack between worlds closed, she reveled her Mum was pregnant ans she worked for that worlds Torchwood.

Eventually Rose was able to cross back to our world us a transmat device controlled probably from that world's Torchwood, how Torchwood was able to develop ways of crossing over to our world is yet unknown as such technology is highly advanced and the worlds barriers are closed. There world may also be under attack form "The Darkness"

Errors
If the Torchwood in our world was set up by Queen Victoria in response to The Doctor then that means there must have either been a Doctor in that universe, which seems unlikely as such a person has never been mentioned, or something else happened to the Queen to make her develop the institute. Even if the Doctor was not present for those events in this universe the tragedy and paranormal activity could have inspired the creation of Torchwood regardless. The Torchwood of this universe could have also been created under completely different circumstances.

In light of the events in Journey's End, it is possible that this Torchwood was formed in response to the "New Doctor" sent back with Rose. This, however, would require that the event leading to the creation of Torchwood is a point very much fixed in time, and presumably also that the New Doctor creates or finds a method of traveling in space and time. Their Torchwood seems to have a pretty good start on this, based on their ability to send Donna back in Turn Left, so it is absolutely a possibility.

Alternate versions of inhabitants of this universe
Pete Tyler was a successful business-man in this universe, though he had never had any children. He ran Vitex, a subsidiary of Cybus Industries.

Ricky Smith worked with the Preachers and was a wanted criminal. The Preachers were trying to stop Cybus Industries' experiments on the poor, which were actually early attempts to make Cybermen. (DW: Rise of the Cybermen, The Age of Steel) Unfortunately, Ricky died, leaving the Preachers without a leader. Mickey, Ricky's double from the other universe, joined the Preachers, and Jake became the new leader.