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Why does increased time dilation imply decreased precision? If we can precisely measure the energy deployed, can't we also precisely estimate time dilation and account for it?

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Now you've got two problems.

Yes, but it's a well-defined problem with known solution. As complexity goes, it's not exactly the n-body problem in an exact numerical simulation.

do you mean that literally? overcoming laws of physics is a bit more difficult than calculating the n-body problem, to be honest.

edit: to make this clear, the solution to the n-body problem is known. its just not analytical.

This isn't a matter of "overcoming the laws of physics"... what's being conjectured in the article may or may not be a physical reality.

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