|MadSci Network: Physics|
I am not sure where the routet to Alternative Timelines or Time Travel comes from in Physics. Certainly this idea is not allowed in Relativity. In fact Relativity was designed to expressly forbid Time Travel and parts of the Universe being different to other parts. That is, Alternate Realities and Timelines. Our reality is one where we do not see these things and so they are thought not to occur. The argument goes like this, if it is possible it should occur. We have no evidence for alternative realities/timelines and so they do not exist. It is a simplistic argument but matches day to day experience. It is possible the idea comes from the view of the Universe Quantum Mechanics gives us. Very briefly, in Quantum Mechanics observables, things, no longer have a definite existence. We talk instead about their `probability density' and its `decomposed wave functions'. This is explained through the famous Schrodinger's Cat "Gedankenexperiment" (thought experiment). The idea is that if you are not observing a thing, it exists in all possible states, a probability density. When you do the observation the object assumes a particular state, its wave-function collapses or decomposes.
This has lead to a new interpretation of Quantum Mechanics called the Many-Worlds Interpretation. It is not generally accepted amongst Physicists but does have a few leading proponents. The argument used is what happens to the other states when an observation is made. The Many-Worlders argue that each possible state creates a new, alternative, universe. So, every second of every day there are billions of slightly different universes being created as Particles decide to adopt one state rather than another. This can also mean is that there is an alternative me that decided NOT to answer your question, or get this morning or have that last cup of coffee, or go to work or have cheese for lunch. It is my feeling that such a Universe is inherently impossible. It requires the conservation of energy to be broken as whole new universes are being continually created.
To answer your question quickly, there is no evidence that alternative timelines exist. And if they did, how would we know of them. So for all practicable purposes, they do not.
As to the application of Physics to Human Consciousness and decision making, I refer you to the works of Jack Sarfatti. He has a uniquely different approach to applying Quantum Mechanics to consciousness. A good starting point can be found here. There are many pages on the Web that reference Jack Sarfatti. There follow a few Web Pages on the Many-Worlds idea you may find interesting. A word of warning, they are all highly technical.
Remarks on Many Worlds Interpretation A unique perspective on the many-worlds interpretation Many-Worlds FAQ
I hope this goes part way to answering your question as this is outside the domain of standard Physics and more about MetaPhysics which I am not an expert in.
There is another theory I just remembered that postulated that many Universes could exist if multiple Big-Bangs had occurred, or are continuing to occur. I can not remember the details but it was in an issue of Scientific American or Astronomy last year.
Try the links in the MadSci Library for more information on Physics.