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Astronomers are predicting that they will combine in 2020. Thus creating a red nova that will be visible to the naked eye here on earth. The stars are about 1,800 light years from earth.

My question is; if we do indeed see this red nova here on earth in a few years, doesn't that mean that it already happened? Like about 1,800 years ago?

And, if that is true, is there no other way for us to know if this has already happened other than observing the light produced by the red nova?

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Yes, that is exactly what it means. The merger took place in the past and the light will reach us in 2020.

Since light is as fast as anything can travel, then that is the first information we will have about the merger. An exception might be if there were a detectable gravitational wave or neutrino signal that emerges first (but I doubt it). Since these emissions would be produced early in the merger process, also travel at the speed of light (almost, for neutrinos) and because matter is almost transparent to them, then such signals could arrive minutes or hours prior to the visible light. An example of this "multi-messenger" astronomy was seen for Supernova 1987A, where neutrinos were detected some hours before the visible signal.

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