Time Travel has been in works of Science Fiction such as Gene Roddenberry's Star Trek and HGWells' The Time Machine for a very long time. But Theoretical Physicists such as Albert Einstein, Niels Bohr, Stephen Hawking and many others have theorized and debated the possibilities of real Time Travel for almost as long.
In a Time Travel Thought Experiment, participants could make the assumption that Time Travel will eventually be possible and that scientists will be looking for historical elements of support for their experiments. Put another way, if I am personally going to be successful in sending information backward in time, to myself, next year, then what do I need to do this year to be ready to receive that information? If receiving the information is technologically easier than sending it, perhaps I can conquer the easier issue first, by making for future selves a Time Travel Sandbox which can be a place and time which will be safe for conducting time travel experiments.
So what might be needed in order for me to receive this information? Well probably quite a lot of things:
An agreed upon medium of information exchange. This medium would be selected based upon a best guess of what methods would be most easily accomplished by future scientists. Rather than simply listen for any communication from the future, we might have to actually specify it. And yet we would not be able to specify the results. Fortunately Quantum Physics gives us several methods why which we might request to know the result of an experiment that can only be known after its observation.
We might hope to utilize communication with the lowest possible energy requirements - Assuming that we are the creators of the technology that succeeds one day in Time Travel, we may as well make it easy on ourselves when we finally attempt to communicate with our own past. That means the method should require as little energy as possible, and communicate information as that is highly credible.
A set of rules may need to be designed as an experimental environment. This would be some set of controls to minimize the risk of any actual experiments. For example, if future scientists sent back information that Time Travel was impossible, and that we must immediately abandon the idea, and if we were to believe them, then immediately a potential paradox is created. We would need to avoid paradoxes or situations that had the potential to create them.
There would have to be a fairly reliable way for future researchers to be made aware of the methods of the experiment.
A list of assumptions would have to be developed. For example, that Time Travel Paradoxes are solvable or avoidable.
A list of issues would have to be maintained until the critical issues with a particular methodology were resolved.
Goals and scope for such an experiment would have to be defined.
The intent of such a Thought Experiment is to hasten the development of technology that does not yet exist, by speculating about some of the historical needs of such experimentation and filling those needs now. Scientists participating in a Time Travel Thought Experiment by attempting to address these issues could be considered to be colleagues of their future counterparts who will be the actual Time Travelers in the future.
Methods of a Time Travel Thought Experiment might overlap or be similar to the Search For Extraterrestrial Intelligence Project (SETI) and might even use data collected by SETI. Most certainly the exact methods will be a matter of collaboration using something like Wiki Wiki.
Ideas for sending information backward in time:
A signal fired at a wormhole
Challenges
Finding one
Finding one where the time difference between the two blackholes is useful
Receiving information out of the other side of the Worm Hole. If time-separated Worm Holes are an extremely common occurrence of nature, and future Time Travelers find one connected to our current Space Time, it would only be a matter of being prepared to receive information from it. Finding this Worm Hole could be a result of finding the information signal emanating from it. This however would provide information to future Time Travelers about the existence of this Worm Hole and thus might create Time Travel Paradoxes before any truly useful information is even sent.
Given Hawkings Evaporation, it might be possible that Worm Holes could be infinitely small and exist anywhere. However, this might be subject to a period of time longer than the age of the Known Universe, unless information could be preserved through multiple self-repeating Big Bangs. Or unless very old shrinking Black Holes could pass through Worm Holes and thus move backward in time into the younger universe.
Perhaps one assumption is that no real Time Travel (even of only information) is possible without inherently creating Time Travel Paradoxes, and perhaps this is the ONLY reason that backward time Time Travel is not possible.
An assumption could be made that backward Time Travel does not create any greater number of paradoxes than forward Time Travel, and thus would be equally possible. Many Worlds could be required specifically to resolve all possible paradoxes.
See also Grand Unified Theory, Quantum Mechanics, General Relativity, Space Time, Time Travel, Time Travelers
Assume Many Worlds is true, i.e., going back in time to kill Hitler does not change your original timeline T1 (or timepoint - where one is travelling from) but creates a new one where perhaps WWII does not occur, T2. Then since one could travel from T1->T0, if she could return from T0->T1, might it not be possible to go from T0->T2 instead (and stay there), effectively seeming to the traveller/observer that her timeline was changed?
The physics of Warp Drive technology applies to Time Travel - it may be feasible
to warp Space Time as a bubble around a vehicle using Exotic Matter, without creating or having to find Worm Holes.
See hcs.harvard.edu 
If you have a Worm Hole that connects one part of space to another distant part (e.g. through a higher-dimensional "fold"), it's possible to turn it into a time machine. Just put one "end" of the Worm Hole on a ship that goes near the speed of light for a few years. Due to Time Dilation, time will slow down for the moving end with respect to the stationary end. Thus you have constructed a time machine. Going through the end that was stationary will transport you to the past. This design has the limitation that you can't travel back to before the machine was built.
-- Alan Balkany
If we assume that the universe EVER allowed the natural OR artificial occurrence of a Worm Hole, then according to Hawking's radiation these would eventually evaporate to an incredibly small mass. They should then be able to become small enough to pass backward in time through another Worm Hole.
We may not presently be able to send information backward in time, but we certainly can send information FORWARD in time, to a time when we ourselves are more capable of fulfilling a request for a Worm Hole-based experiment. Perhaps, as this page suggests, we can make some useful requests of our own future scientists.
For another intriguing point, let's suppose in a 6 years, in 2010, we begin to construct a time traveling Worm Hole (A) by by accelerating one of its Black Holes at near the speed of light for 5 years. By 2015 we would then have Worm Hole A in which one end was (supposedly) in the year 2010 or so, and the other end in the year 2015. Let's suppose that we then construct Worm Hole B which connects the years 2015 and 2020.
What happens if we send the early end of Worm Hole B backward in time through Worm Hole A. It's early connecting point would then be in 2010, 5 years before it's creation! -- Faron Moore
You're ignoring Nivens Law Of Time Travel.
Actually Nivens Law Of Time Travel simply supposes that a universe in which backward Time Travel is possible, looks exactly the same as one in which such a feat is not possible. In other words, "if X then likely never X". The creation of any law which states that "if X then not X" is simply a restructuring of the Epimonides Paradox. Unfortunately, any such supposition cannot be used to produce logical statements in a confined universe. The Many Worlds view proposed above seems to be the only way to deal with this sort of problem.
What about our ability to modify the meaning of events which have occurred in the past? For example, the Historical Significance of an event cannot be fully determined without relating future events to that original event from the past. Take the problem of a secret. The significance of the secret depends both upon its actual content as well as whether it is eventually revealed or lost. There is no way to know for sure which type of significance will exist. Only the eventual full realization and application of the information can resolve its significance. (Can the value of information ever be fully resolved?) The interest in the idea of backward Time Travel, stems from the mysteriously indominable hope that "mistakes" (though undefined) could somehow be corrected at a future time (by someone "out there") when there exists improved technological capacity, wisdom, historical insight and perhaps emotional fortitude to deal with the situation.
See original on c2.com