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The Big Picture

'Have you ever heard of Plato, Aristotle, Socrates? Morons.' -- Vizzini from "The Princess Bride"

Wednesday, April 05, 2006

Finally, some science!


I would like to discuss something in the category of Philosophy of Science. The reason, I will keep to myself for the moment. The topic is time travel and the "grandfather paradox". Briefly, the paradox is:
Suppose a person is able to travel through time, he goes back in time and kills his grandfather before he ever met his wife (the grandmother). Now if the grandfather never fathered any children, so the traveler's parents would never have given birth to him. Then the traveler would never have existed to go back in time and kill his grandfather. Ensuring that the grandfather would not die and could therefore have children, allowing the man to be born and go back and kill his grandfather -- starting the cycle all over again.

This is known as an infinite causality loop -- and defies logic, as there is now no way to know which event happened "first" -- was the traveler born first, giving him the opportunity to go back in time, or was he never born, giving the grandfather the opportunity to have children? So the loop continues on for infinity in both directions – the paradox.

You can read all the known solutions at Wikipedia, but the one I'd like to discuss is the most plausible answer (of course, presuming time travel is technologically possible), that of relative timelines. That is the option that concerns me in this post.

The basic idea is that there is no feedback from the future into the past – causes cannot create effects before the cause happens. That is, the timeline does not affect objects (or people) "out of their natural timeframe".

Let us demonstrate this with the grandfather paradox. I will use a fictional person nicknamed 'Hefe' as our time traveler. First the information necessary: we will refer to times (years) with the designation a, b, c (a being, chronologically the oldest event and c being the current year); events with the designation A, B, C (A being the event of interest occurring in a, etc); and altered events (historical events changed by the time traveler) or times, designated by a prime ('), e.g. changing event A yields a new event A' and time b becomes b' etc. (by definition a remains a because the change occurred after a). The exact moment in time that the change takes place will be designated by an asterisk in the time frame it occurs, in time a, when we make a change, the time is referred to as a*. By definition then, a occurs before a*, and a remains a, but then b becomes b’ etc.

Also, concerning Hefe, he was born in 1970 (now on referred to as b) and traveled back in time from 2006 (now referred to as c). His birth is B, and his entering the time machine is C. The grandfather's meeting his wife was in 1940, a, and is designated as A.

So just before C the timeline looks like this:
a (A happens) -> b (B happens) -> c (C has not yet happened)

Now let's watch Hefe travel through time and kill his grandfather:
a (A) -> b (B) -> c (C = he transverses time back to a) ->
a ->a* (A') -> b' (B') -> c' (C')

a* is the time at which Hefe shoots his grandfather
A' is his grandmother never marrying his grandfather
B' is Hefe never being born, in the new timeline b'
C' is Hefe never traveling back in time at new timeline c'
<------------- is time travel back in time

We clearly have the paradox because there is no way for C' to lead to a*. That is to say C, not C’, is the cause of a*. But the question is, what happened to Hefe in a'? This is the key to solving the paradox. Hefe is now at a’, just after a*. Again turning to what we know to be real: Matter just doesn't disappear: and future event C' won't happen for 66 years! That is to say an effect cannot precede its cause. Using this knowledge, the paradox cannot occur. Thus Hefe is still living (and existing) just after a* in time a'. He is free to get back into his time machine and attempt to travel back to his native time c -- only he will arrive in c' instead. There no one knows Hefe, as he never existed (remember B' took place at b’, 36 years ago, not B). So Hefe would now be alive and wholly existing in time c' but all his memories and experiences would still be from b through c. If we refer to this time as d and his returning, event D, we have the new timeline:
a* -> a’ (A’) ->-> d (D)

Where ->-> denotes time travel forward, skipping b’ and c’
Note: d and D neither have a prime because there was no original d and D in the initial timeline, and so only one d and D, and they are in the alternative timeline of c’.

When we look at time from this perspective of cause and effect, there is now no paradox, because the event that started the paradox was C, only has an effect in d (and that effect is D). From the perspective of a (or a’), neither C nor C' will happen for 66 years and thus cannot possibly have an effect on A at time a*. What this means is that a* happens because of C, but a* also occurred 66 years earlier than c' thus, C' is irrelevant – the new C’ cannot change a* and Hefe is still from C, not C’ and still operating at a*. The other way to see it is that C’ cannot change C and Hefe is from C so he cannot just vanish.

In less symbolic terms, we are dealing with two types of timelines, independent of each other, the main timeline which was altered from its natural course by time travel and involves everything but Hefe, and the independent timeline of Hefe, who never experienced the altered timeline, because he was born in the original and his timeline only involves him. By analogy, consider a two-lane highway. The path of the road itself traces out one timeline. Now add a car to that highway, the path of the car traces out an independent path from the road, but one which happens to coincide with the road's path – their two timelines are coincident. The road eventually forks, and the car takes the right fork. But the driver of the car realizes he wants to be on the other fork, so he backs up and begins to travel down the left fork. Now the path of the car is significantly different from the path of the road, the road always did have two forks and still does, but the first time the car backed up, diverging from the path of the road. That demonstrates that while the car and the road generally follow the same path, they are independent, and the path of the road does not change simply because the car changed.

Applying this analogy to Hefe, Hefe is originally following down the highway just like everyone and everything else (there is now much traffic on the road, not just one car). At the fork, all the traffic, including Hefe, takes the right fork. At some point down that fork, Hefe decides he needed to go down the left fork and backs up (gets in his time machine and travels backwards in time). This time he takes the left fork (he shoots his grandfather). Only now all the other traffic now follows him down the left fork instead of taking the right fork. On this fork Hefe never backs up, but keeps on driving. So now we see that on this fork there was no point where Hefe backed up, yet traffic kept going as if nothing happened from just prior to the fork – they never realize they initially took the right fork. So we can visualize the solution to the paradox and how it is avoided by employing two independent timelines, which are coincident, but can diverge through time travel. The paradox disappears because everyone, including Hefe, begin traveling the alternate fork, never realizing that the initial fork taken every, in fact, was taken. We see Hefe’s actions, and how he simply travels down a new fork along with everything else

We have now grasped the intricacies of how there are no infinite causal loops, using facts at hand and rational thought. We can safely say that this solution makes much more sense because an infinite loop with no beginning and end defies logic (thus is a paradox), but by employing a simple construct like independent, yet coincident, timelines, and the logic that future events cannot affect past events (in other words, the effect cannot precede the cause) we have solved the paradox of time travel.

But are we done yet? Have we fixed everything in this paradox? Let's consider Hefe's time line more carefully now. We now know that the main timeline never loops (the cause and effect problem), it simply shifts to a new fork; Hefe’s timeline seems to loop though, as he backed up and ‘relived’ a, a*, b (now b’), c (now c’). It was a loop because past events did change. That seems intuitively correct, but it is not. The reason is that the rules must be the same for all timelines, even for Hefe’s coincident timeline, future events cannot affect past events. Hefe’s timeline still says that a future cause had an effect in the past. In other words, Hefe's timeline could not have looped back either – that at c, C couldn’t cause A’ at time a* because a* still happens long before c (66 years before). This leaves us with one option: Hefe's timeline was always moving forward even if it was moving backwards in relation to the main timeline. C happened before A which happened before A', not the other way around! More importantly, a happened, then a*, and finally c. So now we have a new paradox to deal with. We realize that our timeline actually looks like this:
a (C) -> a*(A) ->-> c(A')

We see that we now have things all messed up. There must be a third independent timeline from the two we have postulated thus far. A "master" timeline if you will. This timeline functions differently (even though, it too, must obey the same rules) in that it must be unalterable -- absolute. The way to visualize it would be to stretch out the main timeline and Hefe's timeline and place them according to cause and effect instead of chronologically. What we get then is this:
a(A) -> b(B) -> c(C) -> d'(A) -> d*'(A') -> e'(B') -> f'(C') -> g(D)

a is now the same original time just prior to the arrival of Hefe (just before a*)
b,c are the initial times that occurred in the original timeline
d’ is now the former a only now Hefe has arrived in the ‘past’
d*’ is now the former a* but comes after d’ instead of a
e’ is now the former b’ and represents the alternate timeline where Hefe was not born (B’)
f’ is the former c’ and is the time when C’ occurs (which is Hefe not existing to travel back in time)
g is the former d which had no analogue in the original timeline because it never happened

Our time traveler, Hefe, could either have lived through the interceding years (d*’, e’, f’), or got back in his time machine and 'skipped' forward to g(D). Let us assume he went ahead and travel into the future, to time g, and now call event D his reentry into the new main timeline.

What we have accomplished is to break time into two independent components: its real chronological component (consisting of both the main timeline and Hefe’s timeline), the sequence of times, a, b, c etc; and a cause-effect component which doesn't sequence events in time, but rather by causes preceding effects. This is a very important realization. While it is nothing but a thought experiment in the realm of science fiction, it also has very real-world implications. That we shall consider in my next post....



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