What will time dilation look like from multiple reference frames? [duplicate]

Suppose there are 2 observers each with a watch, both show exactly the same time.

Suppose observer A stands on earth (which may be considered an inertial frame of reference) and observer B sits in a spaceship with speed as much as 100,000,000 m/s. When both will later meet on earth again, if the proper time was 100 s, then putting the values in the time dilation equation, the new time will be 106 s i.e. a difference of 6 seconds in the watches.

For observer A, the watch of observer B is the event and it should be showing 100 seconds while his own watch shows 106 seconds has passed. But for observer B, the watch of observer A is the event and he should see that it is the watch of observer A which is showing 100 seconds while his own watch shows 106 seconds.

Following the time dilation principle both observers should see that it is the other's watch which is showing the effect of time dilation and is 6 seconds behind (because the time for the event had slowed down or dilated). But isn't this practically impossible that each one observes a different time in their own and the other's watch? What will happen in actuality?

• It is difficult to read (and moreso digest) a question without paragraphs or some kind of formatting to break it up in a sensible way. Also grammar. – Myridium Jul 31 '17 at 20:17
• "Both show exactly the same time." According to whom? – WillO Jul 31 '17 at 20:27
• "...time dilation principle..." : What is the exact meaning of this principle, if any ??? – Frobenius Jul 31 '17 at 22:39
• This is the best example ever of "unclear what you're asking". – WillO Aug 1 '17 at 1:42
• Also, while I'm sure the formatting did not help any, this really isn't a bad question to ask and doesn't really deserve the downvotes it has attracted. – Kyle Kanos Aug 1 '17 at 14:55