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I am not a mathematician but am troubled by many of the basic mathematical assumptions and their implications for the universe. I always saw time as the succession of physical events, say cogs going round in a clock or planetary revolutions around the sun. You time your egg at 4 minutes assuming the regularity of the watch spring or pendulum. Succession implies an order and therefore time's arrow seems part of the definition.
If this is the case (I am neither physicist nor mathematician), is it conceivable that any two physical events are absolutely simultaneous? If you were observing what might seem like simultaneous events, say a car driving through a red light would it be theoretically possible to distinguish minutely between the time you receive the light data of the car and the light data of the traffic light even though it forms one coherent picture in your apprehension of the event?
Perhaps I read too much Ballardian sci-fi as a young man, but if everything we experience around us can ultimately be broken down into imperceptible discrete "events" then you could view no two events as synchronous. Perhaps I don't understand Einstein's thought experiment of the torch beam in the train, but his platform observer surely sees the light events in the same order as the passenger, or is he saying that the man on the platform can see more intervening events during the passage of the light beam from the torch to the carriage ceiling?