"... I predict that scientists might one day adopt a new principle: "NP-complete problems are hard." That is, solving those problems efficiently is impossible on any device that could be built in the real world, whatever the final laws of physics turn out to be. The principle implies that time travel is impossible, because such travel would enable creation of uber-computers that could solve NP-complete problems efficiently. Further, if a proposed theory were shown to permit such computers, that theory could be ruled out. Application of this principle would be analogous to applying the laws of thermodynamics to conclude that perpetual-motion machines are impossible (the laws of thermodynamics forbid them) and to deduce previously unknown features of of physical processes." Scott Aaronson, The Limits of Quantum Computing, Scientific American, March 2008.
Alas, my time machine short stories are limited to the realm of fiction. Dr. Aaronson uses an interesting argument in banishing time machines to fiction. It's postulating that NP-complete problems are hard to solve. What in the world does that mean? NP-Complete refers to a type of problem that is difficult to solve, not only for humans, but for computers too, even quantum computers. An example of an NP-Complete problem is Free Cell. It is easy to verify the game has been solved, all the cards are stacked on the top right. But solving the game is not done easily, it takes many steps for solve a game, especially in written program for a computer. Free Cell is one of more than 3000 known NP-Complete Problems. (I am looking for Web articles that clearly explain NP-Complete, but the best I can do so far is a Wikipedia article that says, "All or part of this article may be confusing or unclear." It goes down hill from there on the other articles I've Googled for a general audience.)
There is a simpler class of problems, call P. These kinds of problems are solved more quickly than NP-Complete, especially as the number of elements (such as cards in Free Cell) grows. There is a conjecture that either:
(a) NP-Complete problems can be reduced to P complexity problems. In other words, there are ways to make NP problems more quickly solvable.
(b) NP-Complete problems cannot be reduced to P complexity problems. In other words, NP problems are hard and cannot be solved more quickly in a computer program.
Aaronson believes the latter. It is a conjecture, based on observation that no proof has come forth for (a) and try as they can, the NP problems are hard for everyone, including MIT professors like Aaronson. If Aaronson is correct, and (b) is one of the foundational laws of the universe, then time machines are impossible, just as perpetual motion machines are impossible because of the laws of thermodynamics. The reason time machines would be impossible is that a time machine would allow us to construct a computer that uses a time-loop, which loops forward into time and then back, to perform the calculation, over and over and over, while in our world outside of the time-loop, the computer would solve the problem in mere moments (even thought the time-machine loop may have iterated for billions of years in processing time). Such an arrangement would violate the hardness law of NP problems.
But thinking of the laws of thermodynamics, wouldn't those laws rule out the spontaneous organization of the universe just prior to the Big Bang? Wouldn't it rule out a perpetual motion universe, or metaverse spawning many multiverses? NP-Completeness and Free Cell games have a correspondence to the impossibility of perpetual motion machines, like the universe and metaverse that spawns it.
Think of that the next time you play Free Cell. Unwittingly, you may be playing a game that points to the face of God.