1. Jul 30, 2010

### MrHayman2

I have a question regarding the following explanation I have been given as below:

If an astronaut were to travel at or near light speed to another star, there would be a difference in the time elapsed on Earth versues the time elapsed as perceived by the astronaut. The end result being that maybe 1 year would have passed for the astronaut, whereas 10 years have passed on Earth, when he got back.

What I am confused about is the reference frames. If the Earth is viewed as the stationary reference frame, then they see the astronaut zooming away at light speed. If the astronaut is taken as the stationary reference frame, then he sees the Earth zooming away at light speed. When the astronaut returns, it is just the opposite. So why the difference in perceived time between the two reference frames? I do not get it? Wouldn't it just balance out?

2. Jul 30, 2010

### bcrowell

Staff Emeritus

If you search this site, or the general internet, for "twin paradox," you'll find vast amounts of discussion of this. The short answer is that the two frames are not equivalent. The astronaut's frame is an accelerating one, while the Earth's is an inertial frame of reference.

Empirically, the 1972 Hafele-Keating experiment verified directly, using atomic clocks, that the twin "paradox" is indeed what actually happens.

3. Jul 30, 2010

### MrHayman2

Ok if the ship is an accelerating one and the earth is an inertial reference frame. Then does not relativity say that the converse is true. The ship can be considered as the inertial reference frame, in which case the Earth would appear to be accelerating?

I have read over many posts and could not find one that explained this for me. Maybe I missed it??

4. Jul 30, 2010

### Fredrik

Staff Emeritus

Relativity says that this is not the case. The mathematics of the theory tells us which curves in spacetime are to be considered "straight lines", and the term "inertial frame" is defined so that the time axis of an inertial frame always coincides with one of those "straight lines". The astronaut twin in the twin "paradox" scenario isn't moving along such a straight line.

There's also an easy way to distinguish between motion along such a curve and other kinds of motion by experiment: Just use an accelerometer. If it reads zero, you're doing inertial motion. (Acceleration is defined as a measure of the deviation from geodesic motion).

5. Jul 30, 2010

### Staff: Mentor

(At least you tried to look, so that's OK.)

6. Jul 30, 2010

### MrHayman2

Ok, so let me see if I get this. You seem to be saying there is a difference between the two astronauts. Space is curved for one, and straight for the other. If either astronaut had an accelerometer, they could both have zero readings. Why could the astronauts reference frame be taken as the straight one, in which he sees the earth follow the curved path?

If the atomic clock on the planes is considered to be the fixed one, then they observe the one on Earth to have changed, and theirs is the correct one. Whats the difference?

I still do not get it. What if there were two planets and we consider one fixed and one to be moving at near C. If they could only see each other, how do they know which is the one moving and which one is not? Could not either planet be looked at as the inertial frame coinciding with one of those "straight lines, as you say.

You seem to be saying there is something intrinsicly different between the moving one and the stationary one, so that the people on the moving planet, could in fact experimentaly determine they were moving( even without seeing the other planet )??

7. Jul 30, 2010

### MrHayman2

Ok I read the post thank you. I see now the paradox applies specifically to the case of one body is accelerating relative to another body. This acceleration is measureable by the observers in the accelerating reference frame.

If the two frames are just travelling away from each other at constant velocity, then there is no difference.

So then the accelerating inertial and the gravitational reference frames are not equivalent?

8. Jul 30, 2010

### bcrowell

Staff Emeritus

No, one will see a zero reading and one will see a nonzero reading.

One sees a nonzero accelerometer reading and one doesn't.

They can't determine whether they're moving. They can determine whether they're accelerating.

9. Jul 30, 2010

### MrHayman2

The astronaut would only get a non-zero reading if he was using an accelerometer set to the Earth. If he tried to re-callibrate an onboard accelerometer to show his acceleration relative to the Earth, which was initally at some unknown value, he would be unable to do this. Unless he already had another preset acceleromoter, to show him this value.

So acceleration is measured with regard to an absolute reference, whereas constant velocity is relative? If two planets set accelerometers to zero. If one started accelerating he would see this on his acclerometer. He needs no reference to the other planet to observe his acceleration, as it is relative to the Universe.

10. Jul 30, 2010

### MrHayman2

Say the astronaut resets the onboard accelerometer to zero, once they are inflight. He then asks his co-pilot to set the accelerometer to show their acceleration relative to the Earth. Without knowing this value in advance, he has no way to do this directly. He has no way to detect his acceleration, if he cannot look outside, and has an accelerometer which must first be zeroed from some unkown value.

Correct?

So it is something to do with wether the accelerometer is zeroed before or after the accleration begins?

11. Jul 30, 2010

### JesseM

An accelerometer isn't set to any external object, it just measures the local G-forces (in terms of inertial frames, the 'proper acceleration' it measures at any given moment is the same as the coordinate acceleration in the inertial frame where the accelerating object has a velocity of zero at that exact moment). Imagine a ball floating at the center of a room in space (with no air in the room, so the ball is surrounded by vacuum)--as long as the room and the ball both have the same constant velocity, the ball will stay at the center. But if some force accelerates the room, then as long as the ball isn't touching a wall there's no way for the room to exert a force on the ball to make it accelerate too, so the room will accelerate while the ball continues to move inertially, meaning eventually one of the walls of the room will hit the ball. So, an observer in the room can tell if he's accelerating in an absolute sense by placing a ball at the center, initially at rest relative to the walls, and seeing if it stays at the center or crashes into a wall. By similar logic, if the ball was connected to one of the walls by a spring, then as long as the room was moving inertially the spring would stay relaxed, but if the room was accelerating parallel to the axis of the spring the spring would get compressed or stretched until it reached an equilibrium where the spring force on the ball was accelerating it at the same rate the room was accelerating. So, provided the acceleration stays constant for long enough that the spring has time to reach such an equilibrium, the ball-on-a-spring would constitute a simple type of accelerometer, with the length of the spring telling you the rate at which the room was accelerating parallel to it.
Acceleration is absolute in the sense that you can measure it without reference to any external markers, and inertial frames can be defined as frames where an accelerometer at constant position in that frame would always read zero, which means that any object whose accelerometer reads non-zero will have a changing speed in every inertial frame. However, if by "measured with regard to an absolute reference" you mean that acceleration picks out a single preferred frame that's not correct, all inertial frames are still equally valid and they all agree whether something is accelerating or not.
Yes, that's right.
Well, see above, it's not clear what you mean by this since there is no single frame that can be described as the frame of "the Universe".

Last edited: Jul 30, 2010
12. Aug 2, 2010

### MrHayman2

Ok, now I cannot grasp how acceleration can be measured without reference to any external markers. If it is a measurable quantity, which is the same for all reference frames, in that all other reference frames see the acceleration as the same value. Does not relativity say, this measurement must to be made relative to something else? Can I not say that acceleration of a reference frame is relative to all external reference frames. If an accelerating reference frame is relative to all frames external to the one undergoing acceleration, is this not the same as an accelerating frame being relative to everything else, which is the Universe?

13. Aug 2, 2010