To summarize, there are now three theories in my mind of how time travel might work.
First, you have the theory of time somewhat presented in the MiniMonthly- the idea that time is just a pathway through a series of parallel universes. In this context, if one was to time travel, they would be leaping out of the normal pathway and following some other pathway which the time machine somehow sets up for them. It could be as similar or as dissimilar to the original pathway as you can imagine- and likely in ways you can't. In this theory, paradoxes are commonplace and nearly anything is possible. This is what I call the Parallel Universe Theory of Time Travel.
Second, you have the theory of time as shown in at least a couple different movies- a theory that states that time cannot be changed or altered even if time travel becomes possible. This theory's major claim is that certain paradoxes will not happen because they cannot happen. The typical example is the traveler killing his grandfather. If traveler does so then traveler cannot exist and if traveler cannot exist then grandfather cannot be killed, but if not killed then traveler exists, etc etc. According to this theory, the moment you existed, you have no choice but to exist. You cannot change that fact now. Even traveling back in time will not let you change anything because anything you change, you already did change. In some ways this theory means that you really don't have a choice in your future. But look at it this way: there will be only one future because you will do only one thing. But you still did it. You chose the route you will/would go down and everything happened that way and everything is kept in one nice neat line of cause and effect. Everything is fixed in a straight line and nothing is able to deviate from that. This is what I call the Static Time Theory (or sometimes "Fixed Theory") of Time Travel.
Finally, we have a third theory that offers a mutable version of time which has your standard timelines, only they are allowed to be manipulated in some interesting ways. It took several glances before I finally understood what the zigzag-filled diagram that keeps being displayed all over the site was supposed to represent. Read the primer on time to help make sense of it all. Basically, the theory goes something like this. Time is a sequence of free-will and cause-effect lines which progress forward slowly, as we observe it. If someone travels to the future, they don't affect the timeline at all. If someone travels backwards in time, however, they *destroy* that timeline (presumably all the way to the point where they traveled), and the timeline gets _replaced_ by a new one where the traveler has appeared. Depending on the result of this new timeline, several things can happen. If the new timeline ends up not affecting the things that caused it to come into existence (the exact same traveler traveling back to the exact same spot in the exact same way), then there are no paradoxes and time is able to continue on down a new timeline. If the new timeline ends up causing the original timeline, then time gets stuck in an infinite loop, alternating from one event to the other and unable to go anywhere new (though the viewers in the loop supposedly would not be able to tell when they are stuck in an infinite loop). If the new timeline does something else and still allows the traveler to return, just in some other manner or state, then a second N-jump occurs and may continue to occur in a sawtooth pattern, which may theoretically go on forever, or may eventually snap to either an N-jump or an infinite loop. I'm not clear on what the theory says will happen if the new timeline ends up destroying the time machine or making no traveler go back in time, but I suppose it could easily be either the regular N-jump with time proceeding onward, or else time is destroyed and a sawtooth snap may or may not occur. It's possible I have the entire theory mixed up in some way, too. In any case, this theory is sometimes called the Replacement Theory of Time Travel.
What follows is some nitpicking and thoughts evoked by reading about this last theory; it will make the most sense if you are reading/have read the website given above.
A Primer on Time
Why in an N-jump does the future get destroyed? Don't all those people that the Traveler leaves behind still have their own free wills and their own timelines?
Why in an infinity loop does the fact that the Traveler not travel back destroy the future of the CD timeline? Won't Traveler and younger Traveler just live on in peace following the future of the CD timeline?
In the Two Brothers scenario:
Why couldn't the time machine take you to a future you created but with yourself replacing the self that supposedly would have lived all those years? You apply a grim view, although admittedly logical, but if the machine can travel into the future, and it can somehow distinguish between all the possible futures from that point, it should be possible to find the future where you have happy memories and still developed a time machine- perhaps even meeting yourself and telling yourself to do it- or absorbing and taking over yourself, the time machine somehow matching closely related matter and lifeforce and replacing it with yourself- or it could even just move you to a future where the time in-between didn't even have to happen- everything just jumped forward and is only left in your mind as a history that you erased. Also, traveling to another universe is according to the theory really time travel- since we are all moving through different universes as we plod slowly forward in time- if you subscribe to the parallel dimension theory then you easily answer the problem of scientists never getting results by supposing that the time machine (or perhaps more accurately parallel dimension traveling/jumping machine) could easily send the cube to a dimension where we are all the same and the scientists receive the cube and make the recordings and travel down the series of parallel universes in which the scientists will send the cube back to themselves and then life goes on- having infinite parallel dimensions at your disposal means you can have as successful or as unsuccessful an experiment as you could ever imagine- no matter what type it is or what kind of travel it may be trying to do.
Parallel dimensions theory issues:
If there are so many cool parallel dimensions.. why hasn't any of them tried to contact us? Are we that boring? Do they have to leave us undisturbed? Are there any real ways to direct or affect our path through the dimensions? Are we somehow stuck in rules of cause and effect and there's no way for other dimensions to affect that? Or perhaps we are all running rampant all the time through all the different dimensions and we just don't know it because there are so many of us for every possible dimension? Maybe we do jump to other pathways but as soon as we do we are changed to having the memories of that pathway and even if we go and come back, we don't know it because we came back to the pathway where we don't have those memories? Maybe we are sensitive to certain other pathways and that's why you get things like fate or destiny.. like the man who meets his future wife and has an irrational notion that he is going to marry her.
From the Spreadsheet example:
"Let's expand our spreadsheet a bit. Let us suppose that B1 is the beginning of a new decade. B2 is the next event. Just as the value of A2 is dependent on the value of A1, so the value of B2 is dependent on the value of B1. What is the value of B1? Its value is in flux; it is constantly changing. B2 cannot have a value, because it cannot derive a value from B1. This is different from A1, which is situated in the chain such that, from its perspective, the value of B1 is momentarily stable. B1 only changes after (sequentially) A1 changes. B2 cannot proceed from B1 because it's outside the loop."
This is more of the reasoning for why the future gets destroyed, but I just don't see it. If you can claim that in the infinite loop A1 can momentarily get a stable value from B1, then there is no reason that B2 can't also do so. It's true that B1 in a way points back to A1 and I definitely agree that there is a loop which can be defined. A1 could have easily been left out of the loop if it was A3 or A4 that decided to point to B1. This shortens the loop from the front. Likewise, A100 could have been left out if B1 had decided to point to A98-98 instead. This shortens the loop from the back. My point is that even though you have a loop, it's not like you have to limit yourself to just that loop. There are entrance points and exit points and you can start forming double loops and complex knots and everything. If you want to just focus on one loop, fine, but there's no reason that things outside the loop can't have stuff happen to them as well.
From The Uncaused Cause:
"The entire theory is at this point founded on the fact that those who propose it have no alternative. Thus they make a completely unjustified leap in logic, and get themselves into trouble.
"It is possible, they observe, that the collision between the ball and itself could conceivably knock it on course for the entrance to the wormhole. Since it is possible that it would do this, and since we can't imagine or explain what would happen to time if the ball did not enter the wormhole, that must be what happens. The ball coming out of the wormhole which collides with itself will always knock itself into the wormhole."
This is good stuff. Definitely it makes sense logically that just because something could always happen to fit into place, it doesn't mean that it always will. But, consider- mightn't you be doing this with the "destroys time" issue?
"The answer to that is that the ball will never go into the wormhole.
An event whose occurrence is dependent upon its own occurrence cannot occur. That's just simple."
No, that's just your opinion. There could be other explanations. We want to ask where the cause originally came from, but what if it is just that it came from nowhere? Maybe rules like conservation of matter can be broken, and rules like cause and effect can be bent. We can still travel through a nice and orderly sequence of causes and effects with something being introduced that seemingly has no cause (it just _is_), or has its cause in the future. That being said, I can see it from your point of view. Your opinion that "uncaused events just cannot happen, that's not the way it works" is definitely plausible. But the idea that "the ball reentering the hole in a different way just cannot happen, that's not the way it works" seems just as plausible as well.
The Response (in Mass Suicide and the Grandfather Paradox):
"Something will go wrong. After all, they argue, clearly you are alive, so clearly you have already failed to kill your grandfather.
"This sounds so reasonable. After all, they aren't saying that I can't do it, only that I won't. I have failed, so I will fail. We don't know what will go wrong, but something will go wrong."
To better represent the concept, you should probably state this a little differently. I would put, "they aren't saying that I can't try to do it, only that, in the end, I didn't."
Here are some other thoughts about fixed time that include free will and the future. According to my view of the fixed time theory, when you go and try to make the paradox happen, you exercise your free will, but in a way it is meaningless, because you know the end result already. Yet, in other ways, it is not so meaningless, because really, you don't know the end result for sure- you know you still exist somehow, but you don't know for sure that how you came to exist matches how you really came to exist, which may be revealed by your attempt. Also you don't know any of the history from where you are to where you make the attempt. You choose (and chose) to make that as interesting or as uninteresting as you like.
God by Another Name (in Mass Suicide and the Grandfather Paradox):
Reading your first paragraph, I can't help but think, "of course they get offended." You bring in theology when all that they are stating is a theory. I can't speak for all of them, especially those that mistakenly claim it's Nature, but I think I can describe their view more eloquently or concisely than what you seem to have received so far.
Perhaps the most direct and pointed way to show you why their theory does not call upon some intelligent presence is to change the next three paragraphs from an argument against fixed time theory to an argument against gravity.
Gravity, as you have probably been taught, is a _law_. It's just what happens. There's no intelligence making sure that whenever any apple is loosed from a tree that it falls towards the largest body of mass near it rather than away. There was no claim in Einstein's theories that Nature or some other presence caused time to pass slowly for things moving at high speeds. The theory was that it just _does_. Later the theory was proven correct. It could have been proven false.
If you make this argument against fixed time theory, you make it against _all of science_. Perhaps from the view of someone studying theology, this is a valid argument and it could definitely be said that from a certain view point one may claim that all science is really just a religion. However it makes little sense to me to call out one theory as suddenly ascribing the way things work as due to something other than just "the way things work", when you likely would not claim the same for the average mathematical theory. To illustrate it from a separate tack, I would say that it makes as little sense as would claiming that you believe time cannot go on after the A-B timeline of an N-jump (and is destroyed and reformed) because some deity checked and made sure it happened that way.
All of that being said, the next three paragraphs after that are strong and make a lot of sense to me. Just because it might seem like we can't alter history, we should definitely not let that stop ourselves from fully pursuing the truth of the matter and doing everything reasonable within our power to alter it in some small way in the cause of science. The final paragraph of this section also makes sense as well.
What do you think? Do you have defenses or support for any of these theories? Do you know of or have others you can share? Can you answer any of the questions posed herein?