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FiftyTwo comments on Open thread, 16-22 June 2014 - Less Wrong
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I have invented a wormhole with ends separated by ten seconds in time. Unfortunately the power requirements scale exponentially with size so its not practical for anything larger than photons, but it does mean I can send information back in time. How would you exploit this?
Attempt Harry's trick to solve NP problems.
Pre-empt other people's jokes.
High frequency stock trading.
What happens if mutliple agents have this ability? Does the impact of future knowledge cancel out or do we get some sort of weird hyper fast feedback loops?
See Primer (2004 film).
Can you chain these wormholes and send information 10 + 10 + 10 + ... seconds back in time?
Have a program use its own output as input, effectively letting you run programs for infinite amounts of time, which depending on how time travel is resolved may or may not give you a halting oracle.
Also you can now brute force most of mathematics:
one way to do this is using first order logic which is expressive enough to state most problems. First order logic is semi-decidable which means that there are algorithms which will eventually return a proof for correct statements. Since your computer will take at most ten seconds to do this, you will have a proof after ten seconds or know that the statement was incorrect if your computer remains silent.
To expand on this: Moravec's classic "Time Travel and Computing".
What practical benefits or effects on the world do I get out of my new infinite computing power and mathematical proofs? Presumably i can now decrypt all non-quantum encryption, and do various high cost simulations very fast.
It helps with simulation of quantum mechanics, but I don't think that it helps with most classical simulations.
As Eugine mentions, there is a concrete way to use time travel to solve NP problems, those where you can recognize the answer if you have it. In fact, it is possible, under one formalization, to use it to solve a class of problems called PSPACE, which just means problems that you could solve with unlimited time, but limited memory, the obvious guess when NoSuchPlace says "infinite time." But look up the method Eugine mentioned - it isn't obvious how to extend it.
I don't know any applications of PSPACE problems, because they are impractical, but NP problems come up all the time and there is a big industry of solving examples on the edge of practicality. People often do this by converting them to SAT, the universal NP problem and then apply "SAT solvers"; so googling something like "sat solver applications" gives various suggestions, such as microchip design. Of course, if you really could solve SAT problems, you'd use much larger examples that people don't even bother with today. And if you could really solve PSPACE problems, you'd try even more exotic things.
It won't give you a halting oracle without an infinite computer. The best it can do is effectively give you 2^n computing time, where n is the number of bits in memory.
Set up a website where people can send messages to themselves in the past in multiples of ten seconds, for a cost. Program it to automatically increase the cost as you start running out of bandwidth. Let other people figure out what to do with it.
There are a few experiments that you should try to see what you could do. For example, it seems like a good idea to have it send a message about a car accident far enough back to prevent it. But if you get the message that your car will crash, you'd have to not drive and send the message to prevent a time paradox, which means that you might get the message even if the car didn't crash. You could experiment by using things like coin flips to determine car crashes. My guess is that if you send a very specific signal in the case of something bad, then you're very unlikely to get that signal unless it would happen. Otherwise, every signal would be self-consistent, and thus equally likely.
Given that you obviously broke both General Relativity and Quantum Field Theory (see Hawking's Chronology Protection Conjecture) on a macroscopic scale, I recommend using an array of those as a source of free unlimited energy. Please disregard the small side effect of vacuum decay leading to the Universe destruction bubble expanding at the speed of light.
Would you mind elaborating? The Wikipedia article on the CPC seems to indicate that our best approximations to quantum gravity basically throw up their hands, and I've never found Hawking's original CPC to be anything more than, well, conjecture.
General relativity without quantum stuff admits closed timelike curves, but does not allow exploiting them due to the uniqueness of the metric. Quantum field theory on a CTC background very likely diverges in the way Hawking described. Actual quantum gravity might offer some hope, but in the weak field limit it is likely to match existing models, so the wormhole in question is very unlikely to be in this regime.
Attempts to form self perpetuating reactions have all spontaneously failed. Unsure why as equipment appears unaltered, suspect some sort of anthropic force at work.