Gravitational time dilation

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Here is another question
As far as I know, gravity slows time...So it would be true that a person who lives in for example the moon would live less than a person who lives on earth?
Or a person who lives on 25th floor lives longer than a person who lives in basement? Of course the difference would be very very very small.
 

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Here is another question
As far as I know, gravity slows time...So it would be true that a person who lives in for example the moon would live less than a person who lives on earth?
Or a person who lives on 25th floor lives longer than a person who lives in basement? Of course the difference would be very very very small.
Before I answer your question, I have a challenge for you: Define exactly what you mean by "lives longer", and do so without directly or indirectly talking about events happening at the same time (unless they also happen in the same place, in which case you can consider them a single event). Until you can do this, relativity will continue to confuse you.

And to answer the question you're asking: If two identical twins are born on the 25th floor, and one of them goes to live with the family in the basement while the other stays with her natural family on the 25th floor.... The next time they meet, the basement-dweller will have aged slightly less than the 25th-floor twin. This is just another version of the twin paradox, and the explanation is the same: The basement-dweller and the 25th-floor twin have taken different paths through space-time. The earth's gravity has curved spacetime (this is what gravitational time dilation is about) in such a way that the 25th-floor twin's path is longer in time.

The same considerations apply for the earth/moon case, but if we don't start with twins born in one event at the same time and place and meeting later in another single event, it's much harder to define exactly what is meant by "lives longer" or "less aged" - and that's the point of the challenge above.
 

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