Suppose we hear -- through communications at the speed of light -- distant aliens discussing, perhaps announcing, that they plan to do an experiment which might destroy the universe. They provide enough information for us evaluate their proposed experiment, and we conclude that it is a plausible experiment to them do. They also say that they lack the computational resources to simulate what would happen (which is one of the reasons why they are going to do it). However, we have the computational resources to simulate it, do so, and yup: the universe is gonna end when they run their experiment.
We're powerless to stop them, because we have been listening to their communication through a long time delay caused by interstellar distance: there, the lever has already been pulled, and the unstoppable destruction of universe has already begun. The wavefront of the universe's destruction proceeds towards us at the speed of light. Slightly ahead of the wavefront is more communication about the preparation and construction of the experiment, which we continue to listen in on, a countdown to doom.
Of course, as science fiction, inevitable existential doom is a nice plot generator: need to accomplish X before the universe ends.
It's not too unrealistic a scenario: they might have special natural or astronomical resources that allow performing an experiment never before done in the history of the universe. They might lack natural resources like silicon so lack the ability to build supercomputers like ours for simulation. The upside potential of the experiment, if it doesn't destroy the universe, might be great. They might reason that the downside potential, the universe being destroyed, isn't that bad, like the sound of a tree falling with no one to hear it: they won't be around to suffer in the universe's destruction, so they don't care.
We should of course send our computational simulation results back to them in hopes that they receive our frantic big "no" message before they pull the lever. (Maybe also some solved NP problems to prove we do have the compute power; solutions of NP can be checked quickly.) But distances and the rate their experimental preparations are going could make it clear the message won't get to them in time.
The famous physical scenario of the destruction of the universe proceeding as a bubble expanding at the speed of light goes as follows: Our universe is actually a false vacuum, and something (in our case, the alien experiment) triggers vacuum decay to the lower-energy true vacuum. A bubble of true vacuum expands from the site of the experiment destroying everything as it grows. Typical descriptions of such a scary scenario assuage our fears by saying the bubble expands at the speed of light, so we won't know it's coming and won't feel a thing in the fraction of the second it takes to be destroyed: even pain travels slower than the speed of light. But with alien communications about the planning of it also traveling at the speed of light, it is possible to know it's coming.
Less excitingly, it might not be intelligent life but a rare natural phenomenon that will trigger the destruction of universe in this way, and the natural phenomenon is preceded by precursor events which we observe and can then predict the subsequent timeline to doom.
Knowing a wavefront of destruction is approaching us at lightspeed, suppose we take off in spaceships traveling at near-lightspeed ahead of it, seeking to stay ahead of the wavefront as long as possible. But traveling fast causes time dilation. Does a spaceship inhabitant experience more or less time before being overtaken than someone who stayed at home? This should be easy to calculate.
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