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Tuesday, September 13, 2016

What We Didn't Know About Time Travel Could Surprise Us

According to Hollywood and even some scientists, going back in time means seeing history repeat itself. We worry that if we interfere with the past, the future might unfold differently, unexpectedly and even disastrously.

Imagine Hitler winning World War II or your parents never getting together, so you are never born--all because you spit on the sidewalk in the year 1933, which set off a chain of events that changed the future.

What I described above is rather nonsensical if we take entropy into account (s=change in entropy; k=Boltzmann's constant; ln is the natural log; omega=number of ways particles can arrange themselves):

If our most common belief about time travel is correct, then entropy would have to shut down, so history could repeat itself exactly as before. But then we might ask, why should history repeat itself exactly as before (assuming we don't interfere)?

To satisfy our curiosity, what would happen if entropy remains intact during our time-travel excursion? Imagine a universe with one particle in it. It can go either right or left as it passes through time. The probability (p) is 0.5 for each move just like a coin toss:

The particle makes three moves, following a path that is one out of eight possible paths. The path it takes is outlined in red:

The red path represents its history. The entropy starts with a single possibility and evolves into eight possible paths.

Now let's find a wormhole and travel back in time to the particle's starting point and watch its history unfold again:

Oh wow! History failed to repeat itself. We didn't interfere. We were good. We watched from afar ensconced in our time-travel VW bug. Relax, it's not our fault. Entropy was just doing its job. There was only a one-in-eight chance history would repeat itself and a seven-out-of-eight chance it would not. I mentioned earlier that we didn't interfere, but we did go back in time and that in itself is a kind of interference that could possibly alter history.

OK, so maybe going through a wormhole is not the best way to go back in time. Sometimes going back in time is described as a movie going in reverse. If we flip a cosmic projector switch and make the particle go back in time, it should follow the red path back to its starting point:

Oh no! What happened? The particle didn't behave like a backward-running film. It took a different path back. And why not? It can go left or right at any node along the path. To get the equivalent of a backward-running flick, the particle's probability distribution would have to exit the theater.

Backward time travel, as we imagine it, requires an entropy of zero: one path the particle can take and not the usual eight. If we treat the particle's present as a single starting point, the change in entropy would evolve as follows:

Just for fun, let's assume the particle's probabilities of going left or right stay intact when time is reversed. Its past would most likely be different than expected. The past it remembers is only one of eight possible paths to its present time.

Now apply what we've learned to your past. Imagine the implications! You go back in time, but you see a different past than you remember. You think to yourself, "This is not my life!" Your past self looks different, like a brother or sister--because you may not be the same person or sex! A different sperm cell beat all the others to your mother's egg. Your parents still gave you the same name (assuming your sex is the same) but you're watching the life of a different person who took your place because you just had to try out that bloody time machine!

Since your past is messed up anyway, you might as well interfere with it, i.e., take advantage. You read in a history book that the racehorse, Fools-errand, won the Kentucky Derby, so you decide to place a bet, but don't place that bet--it's a fool's errand.

For more on this topic, click here or here or here.

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