@TM:
For example, traveling back further back in time we would open ourselves to many different paradoxes. What would happen if I traveled back in time to killed my father, heaven forbid?
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Time no longer follows a straight line but branches off into many different universes.
To the second: That’s probaly what is called the Many-worlds-theory, first mentioned by Everett and Wheeler. This actually would allow time travel without paradoxa: If you travel backwards, you will not end up in the “world” that you actually came from. You could kill your father there, and never be born in that world, but still you will be born in yours.
But there are other things which are opposing time travel:
Anyone, as a living being, consists of matter. Matter and Energy are equivalent. Now suddenly (as you travel backwards) the universe lends itself energy from the future? I think the conservation of energy (or any other conservation laws) ís the most powerful argument against time travel.
Another example: We believe (and have good reason to do so), that the overall universe is electronically neutral: same amount of positve and negative charges.
Now, (after having splitted a H atom) if you take with you (going back in time) a single electron, and leave the proton “in the future”, you violate that law for some time.
I grow more and more opposed to time travel :)