Time Travel's 'Grandfather Paradox' Solves Itself at Quantum Level

[Opmmur]

Time Travel's 'Grandfather Paradox' Solves Itself at Quantum Level

A paradox perennially posed to would-be time travelers may resolve itself — but only for a single photon at a time, and only at the quantum level. The "Grandfather Paradox" points out that if time travel were possible and you went back and prevented your grandparents from meeting, you would prevent your own birth and subsequent time travel. It's an insoluble paradox — except, perhaps, at the smallest of scales.

Researchers at the University of Queensland simulated what would happen if a single photon were to be caught in a "closed timelike curve," a theoretical wormhole that returns the photon to an earlier position in space-time. By interacting with itself, it should affect its own future, creating a nano-scale version of the Grandfather Paradox — but the researchers determined that the inherent "fuzziness" of quantum states prevents that from happening. The photon is already in a quantum superposition of combined existence and nonexistence, so unlike the hypothetical grandfather, it doesn't seem to matter whether it follows one path or another. The study, published in Nature Communications, adds to the growing scholarship regarding the poorly understood border between classical and quantum physics.

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[TimeWizardCosmo]

This was posted on /r/physics yesterday and found the following comment interesting:
drzowie comments on Time Travel Simulation Resolves “Grandfather Paradox”

Heh. This is a pretty facile "resolution". On the one hand, the idea of quantum suppression of paradoxes via destructive interference is sort of obvious (e.g. I remember discussing it in a first year graduate quantum mechanics course in 1989) but on the other hand it is a very subtle problem. CTPs give you extra divergences in every single path integral that includes them (i.e. if there is a closed path around the CTP then the integrals over all paths diverge) , and the current work seems to be trying to address that divergence.

Perhaps there is an answer -- after all, divergences can sometimes arise from a mismatch between a theory's approximation of reality, and reality itself. A nice example is the circuit diagram design rules. It's easy to design a circuit with "divergent" characteristics by, say, connecting a positive voltage supply directly to ground; but real circuits don't actually produce infinite current, the model implicit in the circuit diagram simply breaks down. In the case of CTPs, the model implicit in quantum mechanics is the perturbational, Huygens-wavelet-style approach to physics, where physical solutions are considered to be the ones that produce computable, locally stationary values of the action: CTPs can produce systems where there is no locally stationary value of the action. The way it breaks down is documented very nicely by Kip Thorne in his descriptions of how classical mechanics itself ceases to work anywhere near a CTP.

In the case of CTPs, there are reasons to think that the divergence problem is not simply representational or approximate. That's because there's a more subtle problem having to do with computability of physics. It is no great trick to dream up a CTP scenario that is non-computable -- for example, one where the only physical behavior allowed is the solution to an NP-complete problem (edit: and the time to complete is independent of the problem size - thanks, /u/vytah). How would the actual Universe behave? If CTPs turn out to be possible, and behave consistently under this scenario, then physics will turn out be completely non-computable (the opposite of what one might call the "Wolfram hypothesis").

That would shake the edifice of science to its very roots. But the linked article doesn't consider it at all...