Jim lives for a minute. Then he activates the time-and-space machine in his backpack, and travels to position one minute back and one meter back. Then the story repeats, giving Jim a lifespan of 80 internal years, all contained within a single minute of external time.
We could shorten that minute of external time to a second, or to any non-zero length of time, by making him jump back in time even faster.
Bold Hypothesis: We could shorten it to zero.
This works most easily if Jim is made out of ghostly matter that can overlap itself (nothing absurd about this: two photons can be in the same place at the same time), and as we shorten the time interval, we shorten the spatial distance of the jump.
The Bold Hypothesis basically says that just as one can have a time-travel machine, one can have a time-non-travel machine that keeps one in the same place in external time for all one's life.
Given the possibility of time travel, and the possibility of discrete time, it's not hard to argue for the Bold Hypothesis. Suppose at each instant of time, Jim can set the time-machine to determine where he will be in the next internal instant. Then why couldn't he set it so that in the next internal instant he will be at the same external instant as he is now.
Given the Bold Hypothesis, Jim would have a lifespan of 80 internal years, all in one moment.
All this suggests that when thinking about time, we should be careful with moving from our subjective experience of time and change--which Jim would have in his all-at-one-moment life--to claims about what external time is like.
2 comments:
Why should we suppose that Jim experiences anything when the time interval is zero?
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