SCENE: The library at Chateau Steelypips. DADDY is typing on the computer, while THE PIP plays on the floor. Enter STEELYKID.
STEELYKID: I'm already four years old.
DADDY: Yes, yes you are.
THE PIP: Thbbbbbbbpppt!
STEELYKID: How old is The Pip?
DADDY: Eleven months. Not quite one year.
STEELYKID: When The Pip is four, how old will I be?
DADDY: You'll be seven.
STEELYKID: And when he's seven, how old will I be?
DADDY: You'll be ten.
THE PIP: (pulls himself to a standing position) GA BA DA BA Phbbbbt! (falls down)
STEELYKID: Daddy, how old are you?
DADDY: I'm forty-one.
STEELYKID: And when I'm forty-one, how old will the Pip be?
DADDY: Well, there's really no way to say, honey. You see, that's thirty-seven years in the future, and thirty-seven years is a long time. It's conceivable, barely, that somebody might invent a cheap way to get into space by that time, and possibly even some amazing star drive that would allow you to accelerate to speeds close to the speed of light.
STEELYKID: I like space. I want to go to space!
DADDY: Right, so if somebody did invent a way to make space travel practical, I'm sure you would go. And at that point, it becomes really difficult to even say what your age is.
DADDY: You see, the theory of relativity tells us that time is not a separate thing in its own right, but merely another aspect of four-dimensional spacetime. We experience a universe not of three dimensions of space and a single universal time, but four dimensions of spacetime. And those dimensions are interrelated-- what one observer sees as two events happening at the same time in two different places, a different observer may see as happening at different times in the same place.
THE PIP: AH YA YA YA (bangs on trash can)
DADDY: So, space and time are different aspects of the same thing, but they're not exactly the same. When you want to calculate the distance between two points in spacetime, you add together the distances in space along the three different dimensions, using the Pythagorean theorem, but you subtract the distance along the time dimension. This means that for any two events, in order to keep the same spacetime interval between those events, a moving observer who sees an increase in the time separation between them must also see an increase in the spatial separation.
DADDY: This allows a really elegant understanding of the nature and perception of time. In the four-dimensional spacetime view, we are always moving through spacetime at a constant speed c, the speed of light. Even when we're not moving in space, we're moving through time at a rate of one second per second into the future. When you put everything in terms of spacetime, that's equivalent to moving at the speed of light, which is where Einstein's famous $latex E=mc^2 $ comes from-- it's the energy of an object that's stationary in space due to its motion through time.
THE PIP: (climbs up step into living room) Ahhh bffffft. (climbs back down step, flopping headfirst onto the rug) Ba ba da ba phhpppt.
DADDY: But the really cool thing about this spacetime picture is the way that motion affects things. Because distance in spacetime is the difference between distance in time and distance in space, if you increase the speed at which you move through space, you must also increase the speed at which you move through time, to keep a constant spacetime speed of c. But a faster speed through time means that you see a smaller amount of time pass between any two events than somebody with a slower speed through space.
DADDY: This means that the amount of time you see pass between two events depends on how fast you're moving. If you get in a spaceship and fly off at speeds approaching the speed of light, but The Pip remains on Earth, what you see as five years passing might appear to him as eight. In which case, he would think he was the same age as you when you return. Or even older, depending on the speed. If you both got on space ships at different speeds, he could even end up thinking that he had become even younger relative to you.
DADDY: So, when you're forty-one according to your clock, The Pip might be forty-three, or thirty-six, or, really, any age at all. In fact, in a world with relativistic transportation, it becomes tricky to assign any meaning to the concept of age. Is your age based on the elapsed time on Earth? The time elapsed in the rest frame of your birth? The time experienced along your own worldline? If the latter, how do you keep track? If one of the former, how do you avoid absurdities like infants who are legally permitted to vote, or elderly people who can't get into an R-rated movie? The implications for law and policy alone are staggering, to say nothing of human relationships.
DADDY: And that's without even getting into questions of general relativity and gravitation. If one of you were to use a fast spaceship to visit the region near a black hole, the question of age gets even more complicated. Some exotic constructions in general relativity might even allow you to travel backwards in time, confusing matters even more, and opening all sorts of movie plot possibilities.
DADDY: So, honey, it's just impossible for me to say how old The Pip will be when you're forty-one. I'm not sure it's even a well-defined question in a relativistic universe.
THE PIP: (pulls self up on trash can, totters one step and grabs Daddy's leg) DA DA DA GA BA!!!!
STEELYKID: Daddy, when I'm forty-one, how old will The Pip be?
DADDY: (sighs) Thirty-eight, honey. He'll be thirty-eight.
STEELYKID: I love you, Daddy.
DADDY: And I love you too, honey.
THE PIP: Phhhbbbbbbbbttt!!!
(Note to RSS readers: if you want to see the cute SteelyKid picture that is the featured image for this post, you need to click through to the full post.)
Chad Orzel wrote (September 27, 2012):
> [...] DADDY: So, when you’re forty-one according to your clock [...]
> Is your age based on the [...] time experienced along your own worldline? If [so], how do you keep track? [...]
That's a great question
(on which to hang even "How to Teach Relativity to Your Incidental ScienceBlog Reader", IMHO).
But how do you first get around the inevitable infantile (sophomoric?) replies like
"According to my clock.", or
"That's what my clock was supposed to keep track of, from the outset, wasn't it?"