Answer my time paradox riddle?

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A man boards a plane in New Zealand on June 4th bound for Hawaii. When he arrives in Hawaii, it is June 3rd. Tragically, the man suffers a heart attack and dies while it is still June 3rd. The gravestone chiselers are confused. The man died on June 3rd. However, he saw the daylight of June 4th, the next day. What would you put as the man's date of death? Explain your reasoning.
 
I would put June 4th. Time is just something invented by man to keep things organized, it doesn't naturally occur, the only thing that does naturally occur to help keep the time is the sunrise and sunset. If he was alive for the sunrise of the next day, even if it is in another part of the world, then he was alive during that day, and thusly died on that day - the 4th.
 
Well it was June 3rd where he was when he died. So he died on June 3rd. It matters what day not the most recent time he saw.
 
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