Twin Paradox

Well, according to the twins paradox, Mary is suppose to age slower than John because shes moving near C relative to John. But if relative to Mary John is travelling near c and relative to Mary John's clock ticks slower as you previously stated, isn't John suppose to age slower than Mary? So in the end, who does age slower???
- Anonymous

So long as they continue in fixed relative motion, there's no objective way to say. Say at time t=0 they started at the same age and the same place. Later on, each wants to see how much the other has aged. They get a picture of the other sent to them. The picture looks young, but they have to make some allowance for the time it took to send the picture, since it was taken a while ago. After making that allowance, each concludes that the other was still not aging as fast as they themselves were. However, each says that the other did not make a big enough allowance, since according to them the relative speed of the light and the other observer was less than c. they each have a consistent account, equally good.

In order to make a comparison that everyone will have to agree on, we have to get John and Mary back to the same place at the same time. Then we can take a picture and everyone in any frame can look and see who aged more. That means that one or both of John and Mary have to change their motion, i.e. accelerate. Say that it's John who fires his rocket engines and accelerates back toward Mary. He no longer is using a non-accelerating frame, so our old rules describing how things look from his point of view don't apply. Mary's frame is ok. She says John isn't aging fast enough, so she must be right. We conclude that John's acceleration back toward Mary must make him see her as aging faster. We can get quantitative about this, figuring out how things look from accelerating frames.

If we then add one more principle, that one can't distinguish between the effects of gravity and acceleration, then we have the ingredients for General Relativity.

Mike W.

(published on 05/08/2011)

My understanding is that the faster an object travels the slower time passes for that object. The example has always been the spaceship leaving earth and returning 20 years later with occupents that have only aged 2 years. Given that space is infinite and a void how do you know what is traveling fast and what is traveling slow. It seems that speed is the rate of relative different motion between two objects (car and road). What is the stationary point of relevence in space against which motion is measured?
- doug schenk (age 58)
n myrtle beach, sc, usq

Doug- you've put your finger on exactly the right question to help get further into understanding relativity. That's unusual, since people often say things like "time slows down when you move fast" without realizing that such statements are gibberish if you're also saying that velocities only have relative meaning. So this is a great question. I'll try to answer in the framework of Special Relativity, with just a few remarks at the end about more general coordinates.

Actually, some very closely related questions have come in and been answered, so I'm marking this as a follow-up to group them. Follow up again if  the last answer isn't quite enough. It should at least get you started.

Mike W.

(published on 03/13/2011)

Let's assume there are three clocks. Clock A continues as is, Clocks B and C instantly accelerate to close to the speed of light in opposite directions. After 24 hours on Clock A, what will clock A perceive clock C and B to read? What will clock C perceive clocks A,B and C to read? After the 24 hours on clock A both clocks B and C turn around and over another 24 hours on clock A return to the original point and stop. What will each of the clocks read now?
- doug schenk (age 58)
n. myrtle beach, sc, usa

After 24 hrs on clock A , A says that B and C read a lot less than 24 hours. 
It's a little trickier to answer what B and C say at the moment A says 24 hrs have elapsed, since these guys don't agree on what events are simultaneous. In other words, the phrase "at the moment" turns out not to have a shared meaning for different observers. So I'll move on to the next question.


When they all come back together, the clocks on B and C don't read nearly 48 hours, unlike clock A. The explanation is partly given above.

Mike W.

(published on 05/10/2011)