# Time slowing down due to speed relative to the observer

1. Jul 10, 2013

### grantcallaway

Hi all,

Please forgive my simplistic understanding on this, as I am a novice with an interest in Science, but I have the following question:

I've been reading a book on Einstein, and here's the stuff I get:
Speed is relative since there is nothing to "fix" a grid to which we know to be absolutely at rest. The speed of light is constant relative to anything, no matter how fast it is going, and this causes time to slow down at higher speeds relative to the observer. But my book only seems to explain this as related to only one observer (a light clock made by shining a lazer across a train carriage, and comparing the distance the light travels according to the peson inside the carriage as opposed to the distance light travels relative to an observer standing on a platform).

So supposing I am the observer, and Tracy flies off into space at near the speed of light for say 50 years relative to me (which would be say 25 years relative to her). Assume we were both 30 when she left. When she returns, I would now be 80, but she would only be 55, right?

But then what happens from HER perspective? To her, I am the one moving, so in the time she ages 25 years, I would appear to have aged 12.5 years? So to me, I'm 80 and she's 55, but to her, she's 55 and I'm 42?

Alternatively, if we are certain that Tracy is the one actually moving, then surely speed becomes absolute?
Anyway - was wondering if you could shed some light? (Pardon the pun)

2. Jul 10, 2013

### Staff: Mentor

This is the classic "twin paradox" with many good explanations here and on the web.

The two most important points to keep in mind:
1) The situation is not symmetrical because Tracy experienced acceleration at the turnaround and you didn't. Thus, it's not necessarily illogical that your experiences are different - there really is a physical difference between what happened to the two of you.
2) Although velocity is relative, acceleration is not - there's a definition of acceleration" which is absolute. Imagine that you and tracy are both sealed in windowless rooms, unable to see out. There's no way that you will be able to detect constant motion - but you can detect acceleration (for example, by attaching a weight to the six walls with six springs, then observing the motion of the weight relative to you).

3. Jul 10, 2013

### nitsuj

We could know she is the one moving (label a "home" frame), we could know the symmetries involved, yet we/they could not get any evidence any physical proof that shows both are "younger" or "older" simultaneously. The spacetime separation between them "allows" for such an "odd" situation of each seeing the other as aging slower, however causally is of no consequence. We see this as relativity of simultaneity, and is only odd where time/length are though of as "fixed".

4. Jul 10, 2013

### ghwellsjr

Yes, but we can still define speed to be relative to any arbitrary grid as long as the grid is not changing speed. We call this grid an Inertial Reference Frame (IRF).

We want to be clear that the speed of light with a value of c is also defined to be relative to any IRF gird, not relative to anything, but anything that is itself inertial and for which we can establish a grid. Also, when we say that time slows down at higher speeds, we mean time for any clock or object or observer that is traveling at any speed according to our chosen IRF grid will be ticking slower the faster it travels.

So in the IRF grid in which the platform is stationary, time for the train, the light clock, and the person inside the carriage is ticking slower than the time for the IRF grid.

And in the IRF grid in which the train and its contents are stationary, time for the platform and the observer standing on the platform is ticking slower than the time for this IRF grid.

Right, because in the IRF grid in which you are stationary, Tracy is always flying at near the speed of light so time for her ticks at one-half of the rate of the IRF grid whereas for you it ticks at the same rate as the IRF grid.

No, because she does not remain stationary in an IRF grid. She is stationary in an IRF grid for half her trip and you are the one who is traveling with time ticking at one-half her rate but when she turns around, she must travel even faster than you in order to catch up to you and so her clock ticks even more slowly than yours during the return half of her trip.

Speed isn't absolute but changing speed is and that's what Tracy did and you didn't. That's why there is a difference in how the two of you age.

Last edited: Jul 10, 2013
5. Jul 10, 2013

### grantcallaway

Thanks for taking the time to respond guys. I understand what you are saying regarding "not staying stationery within an IRF grid" due to the turn-around and acceleration, but this assumes that the IRF grid is (in this instance) the earth.

But supposing there was a second earth revolving around the sun in an opposite direction to us, such that both earths pass by within high-five distance twice a year. Relative to earth1, earth2 is moving, so people on earth2 would age slower than those on earth1. But relative to earth2, earth1 is moving, and people on earth1 should be aging slower.

So Tracy and I are born on opposite earths and high five each other at birth. When I turn 100, is Tracy going to be older or younger than me (assuming also that the revolutions around the sun are closer to speed of light :P)

Surely in this case we are both experiencing EXACTLY the same forces, yet we are moving relative to one another?

6. Jul 10, 2013

### ghwellsjr

Although the earth is not inertial as it is constantly accelerating by changing direction, we could approximate the earth to be at rest in an IRF grid when Tracy is traveling at near light speed for many years.

This would not be a good approximation since neither earth is traveling very fast compared to the other one. You would have to say that both earths are traveling at the same speed in the solar system IRF grid and so people on both earths would not see any difference in the relative aging of the people on the other earth.

Even if you want the earths to move at near light speed, since the scenario is symmetrical, you would both age the same in the solar system IRF grid.

Last edited: Jul 10, 2013