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 serve both places $$A$$ and $$B$$ at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.

I am very pleased with this suggestion, but for all that I cannot regard the matter as quite settled, because I feel constrained to raise the following objection: “Your definition would certainly be right, if I only knew that the light by means of which the observer at $$M$$ perceives the lightning flashes travels along the length $$A \longrightarrow M$$ with the same velocity as along the length $$B \longrightarrow M$$. But an examination of this supposition would only be possible if we already had at our disposal the means of measuring time. It would thus appear as though we were moving here in a logical circle.”

After further consideration you cast a somewhat disdainful glance at me—and rightly so—and you declare: “I maintain my previous definition nevertheless, because in reality it assumes absolutely nothing about light. There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled. That my definition satisfies this demand is indisputable. That light requires the same time to traverse the path $$A \longrightarrow M$$ as for the path $$B \longrightarrow M$$ is in reality neither a supposition nor a hypothesis about the physical nature of light,