The paradox of unsourced information

Ted Chiang

In a previous post in this blog I discussed the paradoxes that would take place if time travel were possible. One of them was this:

• The existence of objects without a cause, illustrated by the science fiction story Find the sculptor by Sam Mimes, which can be summarized thus: on his first trip, the inventor of the time machine jumps 100 years into the future, where he finds a statue that has been erected in his honor. He takes the statue, travels with it 100 years into the past (i.e., to the starting point of his journey), and places it in the same place where he found it, where it will remain for 100 years without anyone touching it. But who made the statue? Nobody. It is an object without a cause, that only exists during those hundred years.

As I explained in another post, this form of time travel violates the principle of energy conservation. The object existing during a time loop appears abruptly when the traveler locates it in the past, and disappears abruptly a hundred years later, when the traveler takes it back in time. The total energy of the universe undergoes a sudden increase at the beginning of the loop, while at the end of the loop it suddenly returns to its normal value. This violation of the most important principle of physics is a very powerful argument to conclude that time travel is impossible.

In his science fiction short story, The Merchant and the Alchemist's Gate, science fiction writer Ted Chiang offers a version of this paradox that, instead of being applied to objects, is applied to information. Let us look at the argument:

• A small merchant from Islamic Egypt travels 20 years into the future and meets himself, who has meanwhile become a very rich man. His older self advises him to go back in time and dig in a deserted place. He does so, and finds a hidden treasure, thanks to which he becomes rich. He goes back to the future and asks his other self: How did you know that the treasure was there? And his older self answers: Because I remembered having found it there. But where did the information about the treasure come from initially? From nowhere. So the old merchant adds: I have no explanation except that it was the will of Allah, and what other explanation is there for anything?

Stephen Hawking

The paradox of unsourced information is not as destructive as the paradox of the object without a cause, because it does not violate the principle of conservation of energy, but it does violate the principle of conservation of information, less well known, but perhaps as important as the other. This principle was questioned by Stephen Hawking in relation to the no-hair theorem of black holes, which I discussed in another post, although towards the end of his life he turned to the opposite position and asserted that the quantum information contained in an object it is not lost: it is neither created nor destroyed.

In one of the first posts in this blog I offered a proof that time travel and free will are incompatible. Hence, since we are aware that free will exists, we should conclude that time travel is impossible. In another story (What's expected of us) Ted Chiang plays with the opposite conclusion: that, since time travel is possible (his story takes this for granted), free will does not exist. If this were true, materialists would surely use it as a scientific proof of their philosophy, even though science cannot prove that only matter exists.

However, I would not say that this is what Ted Chiang really thinks, for in his science fiction stories he often starts from outragingly strange starting points as if they were real and deduces the consequences from those premises. This does not mean that Chiang believes that such things are possible; it is just a game that the author plays with himself and with the reader.

In any case, the number of different paradoxes that could take place if time travel to the past were possible grows continually. With each new paradox, the probability that time travel be feasible decreases. Perhaps, after all, the A theory of time is correct: the past does not exist, and therefore traveling to it would be impossible.

The same post in Spanish

Thematic Thread about Time: Previous Next

Manuel Alfonseca