This post is a continuation of the previous post "What We Didn't Know About Time Travel Could Surprise Us."
It is commonly believed that if we went back in time, history would repeat itself exactly as before if we started with the same initial conditions. It is also commonly believed that chance is a function of our ignorance. If we knew everything that goes into a coin toss, we could predict the outcome 100% of the time. Today we put these beliefs to a rigorous test.
For illustrative purposes, and to keep our first test simple, let's cut our 3D universe down to 2D. Imagine a pencil balanced on its tip. It can fall either right or left. A hand grabs the eraser end and tilts the pencil to the right at some unknown angle that's less than 90 degrees. Which way will it fall? Notice we are not completely informed. We don't know the exact angle of the tilt. Any estimate we make can be way off; yet, we can predict the outcome with 100% accuracy.
The pencil will always fall to the right. This demonstration shows that our ability to make 100% accurate predictions is not dependent on perfect knowledge. There are many things we don't know, like the tilt's angle, but our ignorance does not deter us. More importantly, it does not create a chance environment. Thus the so-called correlation between ignorance and chance breaks down here.
Since it is possible to be ignorant and make 100% accurate predictions, is it also possible to know all there is to know and be uncertain about an outcome?
Imagine a simple universe that contains a particle called B. As time (t) passes, B can move either right or left. Which way will it move? We don't know--so B's movements seem random to us. If we knew what causes B to move right or left, we could predict B's moves and the randomness would disappear, right?
We get all the scientists together and give them a big fat grant. Their mission (if they choose to except it) is to find the initial condition(s) that cause B to move as it does. They discover particle A. When particle A moves right, B moves right. When particle A moves left, B moves left. Perfect! We simply watch A to see how it moves, then we can predict how B moves.
The randomness is gone ... or is it? What causes A to move right or left? Well, nothing. "A" is the "initial condition." Nothing causes it. Nothing precedes it--or it would not be initial. So when A moves, it is completely random.
The above example demonstrates that you can have complete knowledge; i.e., know the initial condition(s) and still have randomness. But suppose the initial condition A moved left the first time history unfolded. We go back in time and A moves left again. Will history unfold the same way?
Let's see. If A has gone left, then B will move left. So far, so good. But which way will B move next? We can't look at A; it has done its job of initiating the universe's evolution. B moves on its own--either right or left. We don't know which direction now that A is out of the picture. So we can't predict with certainty that history will repeat itself because it doesn't have to--even when we know the initial condition with absolute certainty!
Since we no longer can predict B's movements, does that mean we are ignorant? Not if our thought-experiment universe consists only of A, B, time, space, and the rule that particles can go right or left. If that's all there is to know then we know it all--except what B will do next.
We don't know what B will do next because chance is not a function of ignorance in this case--it is a function of more than one option. If, for example, B could only move left, we could be as ignorant as a retarded cockroach and still predict B's movements with 100% precision. On the other hand, we could be geniuses with access to supercomputers and have no clue what B will do next if B can move in a gazillion number of ways (or exist in a gazillion number of varied states).
Finally, history need not repeat itself even if the initial conditions are the same as before and we have perfect knowledge of them.
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