I've been thinking about time travel lately (and have since picked up the book "The Time Traveler's Wife", good read), and spent a couple free afternoons trying to formulate a good system of time travel for use in RPG settings or in future novels I'll write. Here is where I'm at so far:


Time Travel for the Curtis far-future sci-fi world

Mechanics

Time travel is a teleportation effect where the ability to move through time is an added bonus. How far in space that a traveler can move is determined by how far in time he moves. The space available to move to can be described as a sphere with radius in direct proportion to abs(S - D), where S and D are source and destination times (Exact speed of the sphere's expansion to be determined).

As described below, your reference point is space, not the Earth, and the Earth is already moving very quickly, about 600km/second away from "the origin point". You can think of this as the center of the universe, the location of the big bang, the location of Oa, the Silver City, what have you. Teleporting to the other side of the planet (at the right time of day) can be done by jumping only 15 or so seconds and letting the Earth move for you.

Time travel is accomplished by opening a "Jump bubble" (cooler name to be determined), a sphere that attempts to move all the matter inside it to a destination time and place. If the amount of available energy is not enough to send all the mass to where the bubble is "pointed", then the jump fails and nothing happens. As I know very little about engineering of this nature, I won't attempt to explain just how to point such a bubble.

Matter is not added to the universe through time travel. Energy is converted to matter at the destination time. This implies that the jump bubble turns all the mass from the source time into energy, which would mean a small nuclear explosion in the lab, provided the timeline isn't altered. Conversely, at the destination time, there should be a drop to near absolute zero as all nearby energy is sucked into the new matter. Why neither of these things happens is unknown, but there are many theories, such as the bubble itself is a buffer that spreads the energy/mass transfer out, some extra-dimensional space gets damaged when a jump bubble is active, or we are ripping a hole in space/time that Cthulu will come through and devour us all.

How far in time can you go? Time travel is expensive in energy requirements, so until a portable infinite power supply is available, skipping around in time willy-nilly won't happen. Until then, jumping more than a few years would be prohibitive.


The three laws of time travel:

1 - Time travel trumps causality.
2 - The point in space of "the origin" is a time jump's reference point, Earth is not.
3 - Moving through time costs energy in proportion to mass^2 * (time + distance)^2 + J, where J is the energy required to open a jump bubble. Larger jump bubbles require a negligibly larger J.


1 - Causality:

Like dreams, your experiences in time are real, but they may not be the same experiences as the rest of the world. If a time traveler changes an event that he has a memory of, the event still happened the way he remembers during one iteration through time, but now only he knows that. For example, a survivor of World War III knows that the stirring speach JFK gave to Dallas on November 22, 1963 led to a war which cost millions of lives. He goes back in time and hides out in a book depository and assassinates him before he can give the speech. The time traveler still remembers the speech, and still remembers the war, but in the new timeline, the war is stopped.

Unbeknownst to the time traveler, he has just created a "pit" between 1963 and the time he originated, from which no accurate history can exist. Of course, he is shot and killed by Jack Ruby two days later, so the consequences are not much of an issue for him.

Continuing the above story a little further, fast forward the new timeline to the time the traveler originated from. He now has no motivation to go back in time, even though an alternate timeline version of himself did so in the last "loop". Another traveler says "you know, wouldn't it be nice to go back and stop Kennedy from being assassinated?". She goes back to 1963 and does exactly this. There is some commotion in the book depository and a gunshot. Kennedy is not killed, but the Secret Service convinces him to cancel his speech, and WW3 is hence avoided. Don McLean never writes "American Pie", and as a result the US slowly fades into a non world power.

In the next loop, the two time travelers are never born, because the commotion from the attempted assassination subtly effects the lives of millions of people, and the respective parents of the travelers never meet. A third traveler, however decides that something is amiss when he sees film of the attempted assassins and notices their clothes are anachronistic for the 60s. He goes back in time to just before the struggle to ask everyone what is going on. The original assassin gets a chance to explain, and all the time travelers agree that letting the assassination happen is the best thing.

This pattern continues. Wars break out and are stopped, and progressively more and more people wrestle around in the depository, and then spread out to the grassy knoll, and the loop repeats and the timeline is muddled with changes. Each iteration digs a deeper and deeper pit in the history of the affected time range. A destructive or constructive final solution occurs and prevents time travel from being invented. Constructive and destructive here refer to whether or not the human race continues to exist after the pit solution works itself out. In this case, either the would-be inventor of time travel figures out what must have happened because of his invention, and instead becomes a watch maker, or the Russians see thousands of people appearing in Texas and are scared into launching a nuclear strike that wipes out mankind.

In the end, there will be so many different source histories from all the participants involved that nothing meaningful can be extracted. What was the original history supposed to be? Was it good or bad? Was it a significant historical event, or just a guy trying to go see his ex-girlfriend before they broke up? The original motivation for traveling to that specific time and place will probably be lost, and future history books will just recount "the day when people started appearing out of nowhere".

If all the pit solutions are constructive, pits will tend to solve themselves by delaying the invention of time travel. If so, history may consist of multiple occurrences of pits interrupting normal causality, until time travel is abandoned as a technology.


Handling causality paradoxes

There are three basic time travel paradoxes that are asked by inquisitive people, or appear in fiction, the Grandfather Paradox, the Predestination Paradox, and the Ontological Paradox.

Grandfather Paradox

Can I go back in time and kill my grandfather, since doing that would prevent my birth, and I wouldn't exist to go back in time. Some answers to this paradox involve the universe running interference, e.g., you can go back to meet your grandfather, but every time you try to kill him something gets in the way. The gun jams, he bends over to tie his shoe, etc. Another answer is that time travel sends you to a parallel universe, and you will still exist, but your parallel self will not.

My answer to whether you can kill your grandfather is "sure, why not?". You don't vanish in a puff of logic (thank you, Douglas Adams), and the universe doesn't create coincidences to stop you. You kill him. If you were able to go forward back to the time you started from, the world would have no record of your existence and you would be a stranger. However, it's not likely that you'll be able to go back in time that far anyway, and even less likely that you would be able to get back to your home time.

Causality Paradox

When I'm a young man, someone pulls a gun on me and demands my wallet. A second man jumps from behind a nearby corner and subdues him, saving me from being robbed, and possibly from being killed. Before I can find him to thank him, he is gone. When I invent time travel, I decide to go back and thank the man. When I get there, however, I see that there is no man hiding behind the corner, and knowing what is about to happen to my past self, I myself leap out and subdue the robber.

This is an example of a causality paradox. I wouldn't have gone back in time to that point if there was no one to thank. Many examples of this appear in fiction. Bill and Ted have to remember to go back and drop a trash can on their pursuers' heads. Harry Potter has to save himself by casting the spell to drive off the ghosty whatnots from across the lake. Kyle Reese goes back and fathers John Connor, which he never would have done if John Connor didn't already exist. Approximately one out of every 6 episodes of every Star Trek spinoff has some variation of this as well.

It's all bunk. If you wouldn't have gone back unless you had already gone back, then you won't go back. This would be another example of the universe throwing coincidental causal interference, which it doesn't do.

Ontological Paradox

Similar to the Causality Paradox is the Ontological Paradox. A good example of this is the Christopher Reeve/Jane Seymour movie "Somewhere in time". An old lady visits a playwright and presses a pocketwatch into his hand, saying "Come back to me". He ends up time traveling back to her time (1912) and gives her the pocketwatch. Where did the watch come from?

Another example involves naming: In The Terminator, who gave John Connor his name? Kyle Reese returns to 1980 and says "Your son, John Connor, sent me from the future," or some such. Sarah Connor says later in the movie "at least I know what to call him now."

This type of thing is also bunk. The pocketwatch was never made by anyone, and hence doesn't exist. Nobody gave John Connor his name, which is fine, because nobody fathered him either. I have an alternate solution, at the bottom of this article, which almost makes the Terminator movies consistent with my theory of time.


2 - Vector:

Earth is not a frame of reference for time travel, the "origin point", described above, is. When you move in space/time, you do not automatically move to the place the Earth will be/was at that time, you start out at the same space you started in, moving the same direction at the same speed. The Earth will be in a different place on its orbit around the sun. The sun will be in a different place as the galaxy continues to rotate. The galaxy will be in a different place since it is still screaming away from the big bang. The effect that moves you through time costs more energy to place you back near the Earth.

It is necessary to arrive in space near Earth and then navigate to the surface, for two reasons. First, the Earth's vector will not match yours when you appear in the destination time, which means that on arrival the Earth would be either moving into you at greater than terminal velocity, or away from you at greater than escape velocity. Second, the exact place you arrive is imprecise, due to the lack of a good quantum gravity theory or global solution to N-body equations.

Since the milky way is moving at an estimated 600km/s, a traveler's arrival will start in deep space even if only traveling a few hours in time. Traveling a week or two would put the traveler well outside the solar system. This causes the energy requirements to send a traveler far through time to be astronomically higher if he wants to get back to Earth. Also, unless AI exists, or spaceships are remarkably easy to fly, it also culls the list of potential time travelers to a more manageable number. This will allow causal pits to work themselves out quicker, as after several iterations, no one in a timeline will be qualified to pilot a ship.

Time travel could produce interesting possibilities for space exploration. Calculating that an object of interest (planet, comet, etc.) was two years ago where the Earth is right now, a traveler could go back in time two years to check it out, and radio his findings back to Earth, and make the slow trek back home. Energy requirements will make using this trick to colonize another planet close to impossible, as more mass is geometrically more energy to move.

3 - Energy:

Since thousands of people from the future didn't appear in Texas in 1963, does this mean that time travel isn't possible? Not necessarily. According to my energy requirement equation above, every moment that goes by makes it geometrically harder to travel back to 1963. The power requirements to send even a low-mass child back more than 5 years would be astronomical. If time travel isn't invented until 2300, then 1963 is off limits.

Since the vector problem above requires much more energy to transport both a traveler and his ship, it will not be possible for the traveler to initiate a second trip. He couldn't take with him the energy needed, and the time travel equipment, as the combined mass would make the energy requirements too high for an initial trip. In far future fiction, however, this problem may be solved by lightweight time travel equipment and infinite power supplies.


In defense of the Terminator series:

I think the Terminator series has not truly broken any of the causality paradoxes listed in item 1, but instead describes a world stuck in a causal feedback loop attempting to work itself out. Consider:

Timeline 1: Sarah Connor meets a hunky man in 1981 and they have a kid, and name him John. Sarah ends up training herself and her son in military stuff, and John goes on to lead the rebellion against the machines. The machines send back a Terminator to 1980 to stop all this. At exactly the same moment, Kyle Reese also goes back to 1980.

Timeline 2: The Terminator and Kyle Reese both interrupt Sarah's meeting of the hunky man. Kyle fathers a new John. The Terminator is destroyed, except his hand is left behind. Skynet, inc. finds the hand, and uses it to accelerate research, and Skynet ends up able to produce even better robots, like the bad guy from Terminator 2. The new John beats Skynet, and reprograms an Arnie to go back in time to 1990... at the exact same moment as the liquid metal robot goes through the portal to kill young John.

Timeline 3: Time happens like Timeline 2 until 1990. Then Liquid metal guy and Arnie 2 arrive, and in the course of duking it out, the main technician from Skynet, inc. decides that he doesn't want to be the cause of the end of the world, and quits. As a result, Skynet is delayed a little, and ends up being able to make a robot cooler than Arnie, but not as cool as liquid metal guy. Arnie 3 kills John during the machine wars because John now has an emotional attachment to the Arnie line and let his guard down. John's wife then defeats Skynet, and reprograms Arnie 3 to go back to 2000... at the exact moment that the chick robot goes back to kill 20 something John.

Timeline 4: Time happens like Timeline 2 until 1990, and Timeline 3 until 2000. Robots duke it out until they are both killed, and John is warned that Arnie 3 will try to kill him. In this timeline, unless Terminator 4 is in the works, John will live, and will hopefully destroy the time machine before Skynet can use it to cause more havoc. Time travel will have been destroyed as a technology, and the characters will have dug themselves out of the pit.

Why don't they need spaceships to fly back down to Earth? Why all the exact moment jumps? Why are all the jumps spaced out in 10 year increments? Well, in the Terminator world, time travel only works on living tissue exteriors, so spaceships are out. As for all the exact moment jumps and 10 year increments, these are the rare matches in vectors of the Earth when you start, and the Earth when you arrive, that would be spaced out far apart in time, and require jumping at a precise moment. It is likely that they entered their respective chambers at different times, and only the jumps occurred simultaneously. These vector matches would be the only times where a jump would be possible, otherwise, as indicated above in the "Vector" section, the travelers would be crushed by the Earth or fly from the ground out into space.

Why not go back even further and kill Sarah's mother, or back to the same time multiple times? The first question is easy, it costs too much energy (also, you may remember that in T1, Sarah's mother does, in fact, get killed). For the second question, there could be vector problems for multiple arrival spots, which sounds a little far fetched, even when we're suspending our disbelief. Instead, let's attribute that to machine overconfidence and the perceived need for stealth.