Does Taking a Step Forward Affect Age Difference in Time Dilation?

[Seinfeld]

I just started learning about relativity and time dilation last night. It's extremely interesting, and I have a quick question.

Suppose two people (Steve and John) and standing side by side. Steve is *exactly* 1 year older than John. If either one of them takes a step forward, and the other remains stationary, has the gap between their ages changed?

 

[Crosson]

Suppose two people (Steve and John) and standing side by side. Steve is *exactly* 1 year older than John. If either one of them takes a step forward, and the other remains stationary, has the gap between their ages changed?

No. Their "age" is defined as the amount of time since their birth, as recorded on their birth certificates. The way you determine this is by finding the number of days, hours, and minutes between the current date and time from the date and time recorded on the birth certificate. Steve and John would probably find out the time from their cellphone, or a website that reports an atomic clock time. After doing these calculations Steve would find that he was still *exactly* one year older than John.

 

[JesseM]

No. Their "age" is defined as the amount of time since their birth, as recorded on their birth certificates. The way you determine this is by finding the number of days, hours, and minutes between the current date and time from the date and time recorded on the birth certificate. Steve and John would probably find out the time from their cellphone, or a website that reports an atomic clock time. After doing these calculations Steve would find that he was still *exactly* one year older than John.

This seems like semantics, but in the twin paradox it's generally assumed that "age" would be the amount of time elapsed since birth on a clock which was carried along by the person (the amount of proper time on their worldline). Certainly it would be kind of weird to say two twins are the "same age" if one has only lived a subjective time of 30 years and has the body of a 30-year-old, while the other has lived a subjective time of 80 years and has the body of an 80-year-old.

Anyway, the physical answer to the question is that if both people had been carrying ridiculously precise clocks (I suspect they'd have to be many times more precise than modern atomic clocks) with them since birth, and before taking the step Steve's clock was precisely 1 year ahead of John's, than after taking the step Steve's clock will be very slightly less than 1 year ahead of John's by some extremely tiny amount.