1. Feb 14, 2015

### willm78

Something sparked my interest yesterday, so I started watching videos and reading about relativity. (This seems to happen every year or so.) I get hung up on the same thing every time!

Many discussions I've seen use the example of an astronaut that takes a trip into space for 10 years or so and then comes back to see that his twin has aged significantly more than he has. If velocity is relative to each observer (correct me if I'm wrong), why do these examples always treat the people on earth as being stationary? To the astronaut, wouldn't it seem as though his twin on earth was the one who had been traveling at a high velocity over the course of the previous 10 years, and thus be the one that has aged slower?

2. Feb 14, 2015

### Staff: Mentor

Hi willm78, welcome to PF!

Velocity is relative to a reference frame. The reference frame of the astronaut is non inertial, so the time dilation formula doesn't apply.

3. Feb 14, 2015

### willm78

Ahh ok, so it has something to do with the fact that the astronaut experience some significant acceleration over the period of his travel?

Still not sure how this affects his frame of reference though.

4. Feb 14, 2015

### Cruz Martinez

Well, you can always distinguish which twin is accelerating, even though their motion is relative. So you can always know which one aged more, the situation is not symetrical. Also, you could consider either one to be at rest, that doesnt matter.

In more adequate terms their paths through spacetime have different proper times.

Last edited: Feb 14, 2015
5. Feb 14, 2015

### Staff: Mentor

Yes, exactly.

It means that the laws of physics don't work normally in the astronaut's frame. Consider Newton's second law, the astronaut experiences a force but does not accelerate. That isn't normal. Similarly with time dilation: the normal formulas don't work in the astronaut's frame.

6. Feb 14, 2015

### willm78

But to the twin on earth, doesn't the effect of gravity make it seem as though he's constantly accelerating? While the astronaut, once he reaches cruising speed and assuming he is traveling in a straight line, does not feel he's moving?

Maybe I'm confusing the local effects of gravity on earth with some global laws of physics?

7. Feb 14, 2015

### wabbit

No, seems a very good point to me: the twin on earth is indeed accelerated and this has the same qualitative effects as for the astronaut. It's just that the effect on earth is quite small because earth gravity is only 1g. You could get rid of it by having the earth-based twin stay in the ISS the whole time instead, but of course that wouldn't significantly change how fast he ages.

8. Feb 14, 2015

### Cruz Martinez

I'm not sure but it sounds as if the traditional formulation of the twin paradox was meant to have a simple mental picture? therefore the twin staying at earth.
I guess that sticks more than having the whole situation out in empty space. Just a thought.
The remark about the twin on earth having non-zero proper acceleration is correct of course.

9. Feb 14, 2015

### Staff: Mentor

Typically the twins scenario has no gravity. Often it even just says "home" rather than "earth" just to avoid implying any gravity.

If you really want to include gravity then you need to use General Relativity.

Last edited: Feb 14, 2015
10. Feb 14, 2015

### Cruz Martinez

Willm, in case you know enough relativity, you could check in Schutz, the section called "The twin paradox dissected" for further clarification. It's on page 25 in the second edition.

11. Feb 14, 2015

### willm78

thanks Cruz, I'll check that out.

Side note, I just read that an inertial observer, in the context of GR, means no force is acting upon him except gravity. Am I interpreting this correctly in that GR differentiates gravity from acceleration?

12. Feb 14, 2015

### Staff: Mentor

We've all been there, and your brain won't really explode... it just feels that way. :)

Seriously, kidding aside, the twin paradox in which two twins start at the same place, move along different paths for a while, then rejoin and compare their ages is surprisingly difficult. There's a really good FAQ here, and you should read it.

But before you take on the twin paradox, you might be better off working through the simpler problem of two astronauts moving relative to one other - constant speed, no acceleration, no turning around, no gravity, no separation and reunion. How is it possible that both see the other as being time-dilated? How can A be slower than B and also B be slower than A? Get clear on this and you'll be able to take on the twin paradox without fear of cerebral detonation.

13. Feb 14, 2015

### willm78

Nugatory thanks for pointing me to the FAQ. I've started to read it, and already I can see it's going to answer my questions. Can you provide a reference link for the other example?

14. Feb 14, 2015

### Staff: Mentor

The word "acceleration" is ambiguous. Sometime it means coordinate acceleration, which is a change in the speed, relative to some other object, of the accelerating object. Other times it means proper acceleration, which is what an accelerometer attached to the object registers.

In general relativity, "acceleration" without any qualifying adjective usually means proper acceleration. However the acceleration of an object freely falling in a gravitational field is coordinate acceleration - the falling object is accelerating relative to an observer on the surface of the earth, but an accelerometer attached to the object will say that no force is acting on the object until its free fall is interrupted by hitting the ground.

15. Feb 14, 2015

### Staff: Mentor

By "your other question" do you mean why the stay-at-home twin doesn't find himself younger because he's subject to the Earth's gravity?

The stay-at-home twin does end up younger than a hypothetical third (should we calling this the "triplet paradox" ) twin who starts out the same age but spends the entire time floating in free fall in empty space far away from any massive object.

It just so happens that you if grovel through the math, you will find that for reasonable earth-like gravitational fields this effect is small compared with the effect of the travelling twin's journey. Thus, despite the gravitational time dilation, the earth-bound twin ends up less aged than than thevtravelling twin.

16. Feb 15, 2015

### A.T.

Gravity doesn't cause proper acceleration (a falling accellerometer measures zero), just coordinate acceleration (change in velocity in non-inertial frames of reference). That's why in GR local gravity is interpreted as a coordinate effect. Check the video below for a comparison of the two models of gravity.

Last edited: Feb 15, 2015