This is something that I have repeatedly read about, and I just cannot seem to understand it.
For those that don't know, the theory is that if you have two twins, and one gets on a ship and takes a trip at near-the-speed-of-light velocity... when they return to earth, they will have aged less than the other twin that stayed on the planet the whole time.
For purposes of discussion, I prefer the example of two identical watches that are synchronized, and one takes a similar journey as the twin mentioned above. According to the theory, when the two watches are brought back together, one should be chronologically behind the other.
Here's my problem... why is either watch affected by it's velocity? If we're talking about mechanical watches, wouldn't the gears that drive the motion of the watch continue to function appropriately regardless of where they're going or how fast they are getting there?
Furthermore, if we provide a specific frame of reference... let's say 1 earth-year... for the journey of our near-light-speed ship, wouldn't one year have passed for both watches? And therefore, shouldn't both watches reflect the same date and time when they are brough back together?
They're not. They are simply ticking as normal - but they are being taken on different length paths through space-time. The one that takes the shorter path naturally ticks less, and hence appears younger when the two watches get back together and are compared. The length of a path through space-time equals the time experienced along that path. But space-time is strange - the *longest* (space-time) distance between two points is a straight line!!
Pick two points in space-time: say P1 is Time's Square 00:00:00 1st Jan 2000; and P2 is Time's Square 00:00:00 1st Jul 2008. So sitting still in Time's square in order to get from P1 to P2 is the LONGEST space-time path between these points. Any other path will be shorter! Repeatedly flying back and forth from JFK to Sydney to get from P1 to P2 will be slightly shorter than staying still, so your watch (and your heart) will tick slightly less on this journey - although almost immeasurably less. Travelling out to Alpha Centauri and back at just under the speed of light will just about get you from P1 to P2 and that path will be much much shorter than sitting still, and so your watch will tick considerably less seconds on this path - perhaps only a few days' worth!! So a watch left to sit still between P1 and P2 will tick away 8.5 years, and your watch on your space-trip may only tick away one week!
The twins conundrum didn't originate with Jester4kicks, so I doubt he knows the answer. My own guess is that there's a certain ironic appeal in contriving a situation where twins are no longer the same age.
When I promoted the thread I was hoping that another question would get answered in passing. If it is the path through space/time that governs how much time ticks by, and if from the point of view of twin A the other twin B traveled a few light years out and back, while from the point of view of twin B it was twin A who traveled a few light years out and back, then how come the twins are no longer the same age when they're again together.
Why wouldn't both the watch on Earth and the the one on the spaceship have indicated the same time had passed - namely 1 year? I believe, however, that the watch on the spaceship, having been calibrated here on Earth, will not show accurate time on the spaceship travelling at near the speed of light.
The basic answer is that the twin that went in the rocket has to accelerate to turn around and head back to Earth. Even though velocity is relative, acceleration is absolute. That is everybody will agree which twin is accelerating and which one isn't. This acceleration introduces an absolutely agreed upon difference in their paths through spacetime which is responsible for one being younger than the other when they are reunited.
How does flying back and forth make the space-time path shorter?
Because the journey is not a striaght line through space-time, but is weaving about. Just like in everyday life: a wavy path between two points must be LONGER than the straight line; in the topsy turvy geometry of space-time, a wavy path must be SHORTER than the straight line.
The GPS's atomic clock is affected by this also right?
I want to try something and get CD to check if it makes sense.
You wouldn't ask this question if we said that no clocks are "affected" by this. They all tick along keeping perfectly good time within their frame of reference.
However, relativity theory has to transform between the different frames of reference and that produces different numerical values for a "tick" as you transform space and time variables. Neither clock (on earth or in the GPS satellites) are changed. But the calculations to compare them to one another (in whichever reference frame you pick) changes the numbers attached.