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I don't believe in Time Travel...not one bit...I don't even believe that particles can either.
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What if that proves to be correct...that you can travel in time, both backwards and forwards, freely. You'll then have to factor that into your hypothesis or abandon it altogether. There's nothing within SR that prevents time travel, so for it to not be real, if you take your hypothesis as correct, then there must be something due to the impedance which counteracts time travel. It seems like your impedance is a one way effect. So, it could be described thermodynamically.