The parallel and divergent dimensions theories are repeatedly presented as "this is how time travel really works", and the response is given that this is a very interesting theory--but it's not time travel.
This illustration may explain why.
You had a brother. He was two years younger than you, and you were always very close growing up. However, when you were a high school sophomore, your brother contracted a rare, debilitating, and fatal disease, and it was clear that your time together in this life was limited.
You gave up your dreams of becoming an architect, and instead picked up more biology, went on to college and into medical research. In ten years, you managed to devise a cure for that disease, a medicine which would have saved your brother's life.
It's too late, though. Your brother died mere months prior to the development. Besides, it would have required more years of testing before the FDA would have approved human trials, and the drug is only truly effective if administered in the early stages. Your brother has died; there's nothing you can do about it.
The stubbornness that caused you to press on and develop this cure so swiftly won't let you accept this. You return to graduate school, pick up the needed background, and earn a doctorate in physics. Then you assemble a research team, get grant funding, and devise a method of traveling to the past. You build your machine, a mere ten years after you began your researches in the field, a mere twenty years after your brother was diagnosed with this dread disease. Still wanting to recover your lost brother, you take the cure, samples, formula, research information, and travel back thirty years. You know who the leaders are in several pharmaceutical companies, and you arrange for one of them to take on the testing and approval of the drug. All is going well; you return to the future, the time you left.
But to which future have you returned? The parallel dimensions theory proposes that there are now two futures--the one you know, and the one you have created. What is the history of the world when you return to your own time?
Most theorists preferring this theory maintain that you can only return to the future you created; therefore, we'll examine the minority view first, that you return to the world you left.
It is a given of the Parallel Dimensions Theory that you can't change your own past. Thus if you return to the world from which you departed, you will find it unchanged.
That means all your labor has been vain. Your brother died a decade ago, and neither your medicine nor your time machine was able to save him. Everything that drove you to do this has failed. Your brother is dead.
Proponents of this theory will say that certainly this is so; it's not a problem. However, consider this: there is no evidence that time travel works, but your own claim to have been in the past--a claim that is unverifiable, because nothing you did in the past was ever done. Your project is shut down; you lose your funding, no one publishes your papers, and no one is interested in giving you another job. Time travel doesn't work, the science headlines say. You cannot travel to the past. As Al in Quantum Leap addressing the Senate Committee, you have not even a scrap of evidence that your time travels are anything other than your fanciful stories told to get more funding, and you don't even have the faint hope that your changes to history will work their way through to the present and save your project. You were never in the past--the real past, the only past that any normal person means when they say "the past". You were in another universe which was remarkably similar to this one, but that's not the same thing.
As mentioned, the majority of those who support the Parallel Dimensions theory believe that if you return to the future after traveling to the past, you will always arrive in the universe you created. Let us look at the history of this other world.
You delivered your wonder drug to the pharmaceutical company, and since they didn't have to spend a fortune in development they went forward with testing. The drug proved itself in early tests, and was approved for clinical trials, and by the end of the decade was in common use. Thus when your brother got sick, the doctor said how very fortunate he was. Ten years ago what he had would have been fatal, but today there's a wonderful treatment for it, and he should recover fully. He does so.
Of course, he's not exactly your brother. There's a fifteen-year-old version of you in high school when he's diagnosed, hoping one day to be an architect. His brother contracts some disease which was once serious, but now is easily cured. He's happy for his brother, and for the wonders of modern science; but he's got none of the motivation which so controlled your life. He goes on to study architecture, and becomes a great architect. He travels all over the world, designing buildings, monuments, cities, airports, bridges, and so many other structures; and he comes home regularly to see his brother, whom he is only dimly aware how fortunate he is to have. By the time he's thirty-five, and his brother thirty-three, he is known around the world for his architectural skills.
By the time you were thirty-five, your brother had been dead a decade, you had developed a cure for a killer disease and a cogent theory of time travel, and left for the past. You know nothing about architecture, but what you knew as an interested high school student.
You travel back to the future, to the year when you were thirty-five, and go to find your brother, the one whose life you saved. Yet he is not your brother; or perhaps more precisely, you are not his brother. His brother is an architect, world famous in that field. His brother knows nothing of medicine, pharmacology, physics, or time travel. You're an impostor; you're not even all that good an impostor. You know nothing that either your brother or his brother have done over the past twenty years. You are unfamiliar with the fields of study his brother pursued. Given the very different lives you've led--yours constantly cooped up in labs, his often on construction sites--you probably don't even look much alike. Sure, you've got the same DNA and fingerprints, but do you really want to push the issue that far? (Not even clones have the same fingerprints, although they share DNA.) You are not this person's brother. You're a stranger, and you will always be a stranger.
Meanwhile, back in your own world, your brother died. You did not save your brother; you saved someone else's brother.
What's worse, now you've died. Oh, you don't realize it--you're still alive as far as you know. But you stepped into that quantum leap accelerator and vanished, and there was never another trace of you anywhere in time or space. You never appeared in the past; nothing you were going to do to leave your mark in the past was done; you never returned. You will be reported killed in a failed time travel experiment. The experiment will be labeled a failure, and shut down. It will be remembered as a famed folly, with your name attached. The conclusion for all the world will be that time travel doesn't work.
All of this is rather fanciful, and shows up many of the problems with Parallel Dimension Theory. In the end, no matter what happens, those of us at the starting point will believe time travel is impossible, and will give it up. It doesn't work, because traveling to another universe is not time travel.
But the story just told will never happen, even if Parallel Dimension Theory is true. The world doesn't work that way.
It makes for wonderful fiction to imagine the lone inventor working in his lab to create the next great discovery; and I would not minimize the work of lone inventors. They are, however, mainly a nineteenth century phenomenon. Dr. Frankenstein's search for the secret of life, Dr. Jeckyl's effort to unlock his inner self, Alexander Hartdegen's invention of the time machine--these are all the works of wealthy nineteenth century self-financed aristocratic inventors, of which the nineteenth century offered many. Today's inventors don't discover science; they apply it as technology. Science is advanced in large, well-funded laboratories by teams of researchers working under the guidance of a few who have a proven track record of successful research and careful experimentation. No one is going to build a time machine and assume that it works without testing it; no one is going to suddenly leap back in time, any more than we sent people into space before we were certain we could send empty space capsules up there.
The first time traveler would not be human; it would not be animal, nor even vegetable. It would be a carefully crafted chunk of material, a very pure element, most likely carbon but a number of elemental metals also commend themselves. It would be crafted precisely, probably a cube or possibly a sphere of specific dimensions and mass. It would be sent back a very short temporal distance, probably mere minutes. But it would never arrive in the past, and so all experimentation would grind to a halt over this one problem.
You see, everything that is said of the consequences of sending a human back in time must equally be true of the consequences of sending a cubic centimeter of carbon back in time. Time travel can't work one way for people and a different way for things. And until it has been demonstrated that a block of pure carbon can be reliably moved from the present to the past, no one is going to allow a human being, nor even an earthworm, to make a trip in any such machine.
The ultimate problem with parallel dimension theory is that if it works it can't be demonstrated. Thus time travel dead-ends under this theory, as no one can know whether those who vanish are in another physical world, or have merely had their atoms scattered across the cosmos.
Parallel Dimension theory is interesting, but it's not time travel. It isn't time travel unless the traveler arrives in his own past. That means he can impact his own life; and that means we need a theory that addresses what happens when someone impacts his own life. The theory of this site does that; it says you can change the past, but be careful how you do it because that's a very dangerous power.
Both the Parallel Dimension and the Fixed Time theory seem to start from the assumption that the past cannot be changed, and so to look for a way to make time travel possible without changing the past. Parallel Dimension theory does this by saying you aren't in your own past; that in essence says that when you travel to the past, you don't travel to the past but actually do something else. What, though, if you do travel to the past? What if the past can be changed? What if the assumption is false? Most theorists see only the two theories, and think it is a choice between being unable to control your own actions on the one hand (a consequence of the Fixed Time theory) and being unable to reach your own past on the other (the meaning of the Parallel Dimensions theory). It is not a choice between those two options. There is a third possibility for time travel which permits people to change their own past, and addresses the consequences thereof.