Thought experiment: The twin paradox, observed from far away

[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.

 

[Dale]

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.

 

[ironirc]

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

 

[Dale]

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.

 

[PeroK]

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.

 

[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.

 

[PeroK]

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.

 

[ironirc]

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.

 

[ironirc]

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!

 

[vanhees71]

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"?

 

[PeterDonis]

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.

 

[Ibix]

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.

 

[vanhees71]

I agree! The notion of reference frames in GR is a pretty subtle subject. A very nice book about this in the context of cosmology is

E. Mitsou, Jaiyul Yoo, Tetrad formalism for exact cosmological measurements, Springer (2020)

A review paper is here:

https://www.academia.edu/download/69643810/s106377960601003520210914-12830-16x70nd.pdf