Determining your universe's Time Travel Paradigm

Question

How might the occupants of any given universe identify which (if any) of the many proposed Time Travel Paradigms govern their potential use of time travel? By "Time Travel Paradigms" I refer to the proposed solutions to paradoxes attributed to traveling backwards in time, such as:

1. Anything done while in the past will be revealed to have already occured in the past, before the time travel was attempted.
2. The moment you arrive in the past, the timelines fork and you now exist in an alternate timeline.
3. You simply can't.

My question is less about how the person travelling back in time would recognize the rules of time travel in their universe, but how that person (presumabley a scientist of sorts) would be able to decidedly prove that the universe works in that particular, definable way to the general/scientific public.

It would seem that the bare minimum would be the ability to travel back in time again and again, while producing the same results each time. Then, of course, multiple sources would need to independently verify the accuracy of these results by going back in time themselves. All in all, it would add up to quite a bit of time traveling with uncertain consequences.

Additionally, it seems that certain methods would be difficult to discern from others. For example, considering the two examples I listed above, assume I traveled back in time in an attempt to kill Hitler. I fail, and return to the present. Nothing is noticeably different, but I have no real proof whether my assassination attempt happened in the previous history of my universe (the first supposition above), or if my act split the timelines and I now exist in a very, very similar alternate timeline (second supposition).

Answer 1

Travel back in time five minutes and say hello to your past self.

If you remember meeting yourself before you left, you have paradigm one.

If you don't remember meeting yourself before you left, you have paradigm two.

If you walked out of the time machine without time travelling, you have paradigm three.

Answer 2

If you have a time machine, you can easily distinguish versions 1 and 2 by actively trying to create a time paradox. In universe 1, you will inevitably fail to do so, even if it can only be avoided by the most strange coincidences. You may actually be able to win the lottery by forcing a paradox if you don't. In universe 2, if you go back yourself, you'll find that you can change the past, but if you send something (or someone) back into the past to change things but don't travel yourself, then you'll find that the past has not changed.

Universe 3 will be identified by you not being able to build a time machine. But of course, that cannot be an absolute proof, as you might just not have found the way to do it. However, the moment you've got a working time machine, universe 3 is disproved.

Answer 3

Although Samuel's answer is succinct, it is not entirely accurate. You already realize it, but it is worth repeating that for some situations the three possibilities are indistinguishable. For instance, if you travel back in time and produce an alternate timeline, from the point of the original timeline the result is identical to the proposition that time travel is impossible - any attempt simply causes the traveler to disappear. Likewise, if changes are propagated forward, all sorts of unintended historical effects are produced. Larry Niven's Law of Time Travel suggests that for this situation the only "stable" history is one in which some combination of historical accident results in time travel "never" being invented. Finally, of course, version 2 is indistinguishable from version 1 in the new timeline.

With that said, establishing the existence of time travel to any desired degree of confidence is fairly easy. You simply tell an investigator to walk to the room next door and pick up the locked metal box which he will find there. Three days later, tell him to open it and observe that it contains that day's paper, which you bought that morning, then put in a box and travelled back 3 days to place in the room. By being careful with your transport arrangements you can prevent paradox or closed loops. Repeating the process repeatedly will establish your bona fides to any desired degree of reliability, although the amount of care required to avoid the investigator cheating will be considerable. The second time you do this, the investigator is going to be tempted to open the box early and use the prescience he gains. There are ways around this, such as encrypting the box's contents and supplying the key on the day the box is to be opened, but this can produce some very tricky details to get right to both sides' satisfaction, and is very similar to the problem of transmitting encrypted data without getting spoofed by an opponent.

Note - in looking over the preceding comments, I find that I am in agreement with Cort Ammon concerning "decidedly prove", although my phrasing about degrees of confidence was made without consideration of his objection. Science doesn't work by proving things, but repeated confirmation can be "close enough for all practical purposes". As in, take a gymnasium, and line up 100 teenage girls on one wall, and 100 teenage boys on the facing wall. Have each group walk half-way toward the center each time a bell rings. Theoretically, the two groups will never meet, but after a relatively small number of bells they will be close enough for all practical purposes.