Is the following example using a US Banknote a Bootstrap Paradox? In January 2015, the US Govt prints a USD 10 banknote with serial no. #123456. In February 2015, it is issued for circulation and goes to John, a time traveller. John goes back in time to December 2014 and uses USD 10 banknote #123456 to buy some stuff. He then time travels back to February 2015. Are there now 2 same USD 10 banknotes #123456 in circulation? One that is printed and issued by the Govt and one that was taken back in time by John to buy stuff?
closed as off-topic by Ward, user14111, Shevliaskovic, Lobo, Valorum Apr 6 '15 at 8:53
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What you have postulated is not quite the complete bootstrap paradox, but I think think your question itself is pointing out the pitfall of successfully creating the paradox. For a proper Bootstrap paradox, the item is created (say at time 0), obtained by the time traveler (at time +1), taken to the past and left behind by the time traveler (at time -1), then the item remains in normal time span until time +1, where-in the time traveler re-obtains that item that has been taken into the past, and again re-takes that item into the past. The item never continues to exist at any point past time +1. Also, that item never gets re-created at time 0 on the second pass nor on all further passes; its creation is "lost to time".
So in your example for a proper bootstrap, one criteria is that the bill that got taken into the past needs to be the bill that "John" obtains again in Feb 2015 and takes back into the past again. However another criteria will be that bill also needs to NOT be re-minted on the second pass. Somehow the Govt needs to learn that this "counterfeit" bill is in circulation and therefore not mint it. So the scenario grows more complicated and unlikely just to achieve the paradox.
Your question points out one of the inherent logic problems with the bootstrap paradox: it presumes that when the item is progressing from past to present in normal time, somehow the item does not get re-created again on that second cycle. But in your example, why would that USD 10 banknote NOT get re-created by the Govt? (which is what you were trying to point out in your question). It is a fun plot for a novel, but that plot usually has holes, which your question brings out quite nicely.
Wikipedia also notes that another logic problem with successfully creating a bootstrap paradox is that physical aging of the item is going to occur. It is supposed to go forward and back / forward and back over-and-over forever. However real objects will wear out during their span of "normal time" from past to present. So many plots that attempt the bootstrap paradox of a physical item cannot really be sustainable for an infinite number of loops
So this "supposed" time travel paradox actually does not really pan out as a true paradox. But you might be able to elaborate upon a set of circumstances that do address both plot holes. Say your Grandfather has a watch A he bought in 1920. In Jan 2015 your Mother has that old watch refurbished so its now A'. In Feb 2015 she gives it to you, and you time travel back to 1920. You intercept your Grandfather just before he obtains watch A, and give him watch A'. Your Grandfather then passes along watch A' until your Mother has it refurbished in Jan 2015 and it become watch A''. And the loop continues. Now we have filled the two holes: the original watch A gets "lost" (since your Grandfather no longer buys it and presumably it goes to some other owner). And the watches A', A'', A''', etc get refurbished each loop, which deals with the wear-and-tear issue.