I read in this week's New Scientist magazine that the equations under the general and special theories of relativity with regards time-travel have been solved (for going backwards at least).
Quantum theory, which describes small particles as both waves and matter, yields probabilities on the location of these particles, the particles appearing, in layman's terms, where the waves interfere with each other constructively.
Daniel Greenberger, of New York, and Karl Svozil, of Vienna, solved the equations for waves going backwards in time and found they always interfered destructively. This means the particles do not appear and the conundrum does not arise.
Now although the equations have been soved on paper the results are as yet not entirely useful, for while something may be theoretically possibly, actually being physically possible requires another step. The problem of going backwards implies that particles would have to not appear, does this mean that the particles which make up the individual in question would also not appear as well? Ie would some disappear by travelling backwards in time, and the corollary is if having gone backwards, do they gain particles which may not be their own on the way back?
I for one maintain the time-travel is impossible for one very simple reason. It is impossible to go slower than dead stop. Electrons and sub-atomic particles keep on spinning even at absolute zero, so to stop them and even "send them backwards" is just outside the realms of reality.
Then there is the Douglas Adams that in order for time-travel to be actually possible, in order to avoid the whole-sort-of-general-mish-mash that would arise, time-travel would have to be discovered simultaneously at all points in time in the history of the universe, and we should have by rights already have seen someone.
Unless someone can develop the necessary technology to escape that current space-time dimensions via a time travel device ala a TARDIS, then I doubt whether we'll ever hear (or already have heard of in the past, present, future tense) of a time traveller other than Dr. Who.
oh and BTW happy Bastille Day - start a revolution and chop the head off of French King
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