Relating Time Travel and Prophecies
Although it might be that future time travel experiments will take place with results in our past, we might not be able to relate corresponding events to time travel.
Imagine the possibility that we have seen the results of time travel experiments, but describe what we see as something else: ghosts, spirits, angels, apparitions, demonic possessions, prophecies, dreams, lost souls messages from god, and messages from the death, Wicca board movements you name it.
Most of the above terms describe unexplained events that could point to a non-physical form of time travel. Some of these events like ghosts, spirits, Wicca board movements and messages from the death have not had much impact on history. These events might point at the existence of a spiritual world where some kind of presence intents to communicate with us. However the existence of such a spiritual world has never been proven.
If time travel is going to be invented it is likely that one of the flavors will be a non-physical form, allowing time travelers to re-live the past with little risk of interfering or interaction. Such form of time travel might be relatively inoffensive and might therefore happen frequently. You would expect that such experiments might cause many unexplained observations like the ones mentioned earlier.
To confirm that time travel has taken place we should start looking for events that undoubtedly indicate a relationship with the future. If we cannot find reasonable indications that time travel experiments have taken place, it might mean that the technology will not be invented.
What is an indication that an experiment has taken place? One of the unique capabilities of this technology is that the traveler knows the future of the people he visits. This visitor can therefore give true predictions. True prophecy is an event that cannot be explained by any contemporary technology. It makes it the ideal candidate that we should look for that might indicate that time travel exist.
One of the problems with prophecies is that they get clamed (confiscated). Religions claim many prophecies as Gods word. Some claim that prophecy is the primary test of divine authorship and that biblical prophecies show the supernatural origin of the bible.
It seems that we are scrambling for the same events. Prophecies are being mentioned as proof for the supernatural origin of the bible, while we might want to proof time travel through the existence of true prophecy. But since prophecies have been claimed does that mean that we have to proof religions to be wrong? Does it make God a time traveler?
If the technology ever gets invented it could be used to prove and explain almost anything, all mystifying events in past and present could be explained in such a way that they seem to relate to the technology of time travel.