# Thought experiment: The twin paradox, observed from far away

• B
• ironirc
ironirc
Consider the classic twin paradox scenario involving twins A and B, who start at the same location. Twin B embarks on a journey, traveling 1 light-year away from A at a speed of 0.86c, before returning. Upon reunion, A and B agree that A has aged more than B.

Now, let's introduce an observer located 100 light-years away, positioned perpendicularly to the path between A and B. This observer will witness the events 100 years later due to the speed of light. Given that the distance between the observer and B is initially 100 light-years and B moves only 1 light-year away, the relative velocity between the observer and B remains relatively low. Therefore, I argue that only minimal relativistic effects come into play for the observer.

My conclusion is that from the observer's perspective, there's almost no discernible difference in age between A and B when they reunite. This seems to contradict what A and B experience.

ironirc said:
the relative velocity between the observer and B remains relatively low
The relative velocity between B and the distant observer is still 0.86 c.

vanhees71, FactChecker and Ibix
Dale said:
The relative velocity between B and the distant observer is still 0.86 c.
I applied the pythagoras idea there. sqrt(100^2 + 1^2) = 100.005

ironirc said:
I applied the pythagoras idea there. sqrt(100^2 + 1^2) = 100.005
Velocity is the rate of change of position, not the rate of change of distance.

vanhees71, ironirc and Ibix
ironirc said:
I applied the pythagoras idea there. sqrt(100^2 + 1^2) = 100.005
By your calculations, an object moving in a circle around you would be moving with zero relative velocity. That is not the case.

vanhees71, Dale and Ibix
A general point is that SR texts often use "observer' as a synonym for "global inertial reference frame" without hammering hard enough on the point that "an observer" in this context is a massive network of information gathering devices all through spacetime, not just a bloke with binoculars and a notepad. Then people come away with the notion that where you are located is a part of analysis using an inertial frame. It never is. In fact, one major reason to use reference frames is to study a global view, free of an individual's perspective.

vanhees71, FactChecker, jbriggs444 and 1 other person
More generally, if observers ##O_1## and ##O_2## are at rest with respect to each other, then the measured velocity of an object ##X## is the same for both observers, regardless of their position. This applies in both Newtonian physics and Special Relativity and follows from the definition of velocity as the rate of change of displacement over time. Note that displacement and velocity are vector quantities. Speed is the magnitude of velocity and not rate of change of distance over time.

In general, therefore, the relative velocity and speed of a object do not depend on from where you are observing the object.

topsquark
Ibix said:
A general point is that SR texts often use "observer' as a synonym for "global inertial reference frame" without hammering hard enough on the point that "an observer" in this context is a massive network of information gathering devices all through spacetime, not just a bloke with binoculars and a notepad. Then people come away with the notion that where you are located is a part of analysis using an inertial frame. It never is. In fact, one major reason to use reference frames is to study a global view, free of an individual's perspective.
Thanks, Though I'll need to study this further to comprehend what you're saying.

Dale said:
Velocity is the rate of change of position, not the rate of change of distance.
It took a while to realize. I understand now, that B changes position in the coordinate system of the observer.
Thanks!

FactChecker, Ibix and Dale
Ibix said:
A general point is that SR texts often use "observer' as a synonym for "global inertial reference frame" without hammering hard enough on the point that "an observer" in this context is a massive network of information gathering devices all through spacetime, not just a bloke with binoculars and a notepad. Then people come away with the notion that where you are located is a part of analysis using an inertial frame. It never is. In fact, one major reason to use reference frames is to study a global view, free of an individual's perspective.
Isn't "observer" rather a synonym for local inertial reference frames, i.e., a tetrad along the worldline of the "pointlike observer"?

topsquark
vanhees71 said:
Isn't "observer" rather a synonym for local inertial reference frames, i.e., a tetrad along the worldline of the "pointlike observer"?
It depends on which reference you look at. "Observer" is one of those terms that is used in multiple different, incompatible ways in the literature, unfortunately. Your definition is the most rigorous and the most general (since it works just as well for non-inertial observers and in curved spacetimes where there are no global inertial frames), but not all references are aiming for that.

topsquark
vanhees71 said:
Isn't "observer" rather a synonym for local inertial reference frames, i.e., a tetrad along the worldline of the "pointlike observer"?
I would agree (I think I said something like "an observer is a tetrad while a global inertial frame is a tetrad field" in a recent thread), but I would suspect that the OP has been reading something that says observer and global inertial frame are equivalent. I find the terminology silly, but it's not uncommon. If a book is going to use "observer" to mean global inertial frame then it really ought to stress that it's really talking about a huge network of people (or at least measuring devices) sharing information, in my opinion.

Last edited:
vanhees71, topsquark, jbriggs444 and 2 others
Ibix

• Special and General Relativity
Replies
35
Views
1K
• Special and General Relativity
Replies
20
Views
2K
• Special and General Relativity
Replies
24
Views
2K
• Special and General Relativity
Replies
5
Views
811
• Special and General Relativity
Replies
20
Views
2K
• Special and General Relativity
Replies
36
Views
4K
• Special and General Relativity
Replies
98
Views
3K
• Special and General Relativity
Replies
85
Views
5K
• Special and General Relativity
Replies
115
Views
6K
• Special and General Relativity
Replies
48
Views
3K