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*proper time.*

In

*Modern Physics*, by Serway, proper time is defined as the time interval between two events as measured by an observer that sees both events occur at the same point in space. Additionally, the book mentions that

**proper time will always be the shortest measurement of time for two given events.**

I am having some difficulty understanding this last statement. Suppose that an observer, David, leaves Earth in a spaceship headed for the moon. John, a second observer, is left behind on Earth. In this particular example, if we are interested in calculating the time, as experienced by both observers, that it takes the spaceship to reach the moon, David would measure proper time (and therefore the shortest amount of time for the trip). This makes perfect sense when looking at the trip from John's frame of reference. John will see David's clock run slower and agree that David measures a shorter interval of time than his own. However, from David's point of view it will be John's clock that runs slower. David will claim that John measured a shorter amount of time for the trip than he did.

Then, what is the meaning of the statement:

**proper time will always be the shortest measurement of time for two given events**? That seems only to be true from John's frame of reference. Why should we only consider his point of view? What am I missing?