Motion vs Rest: How Does Relativistic Time Differ?

[ag048744]

There are two separate clocks, each set in a plane and on the ground. Assuming inertial reference frames, how can this be?
Perspective of the observer in motion:
The observer in motion on the plane will have recorded some time duration. Since the the world outside the plane is moving at a velocity relative to the plane, time on the ground would have slowed down.

Perspective of the observer on the ground:
The observer at rest would have seen the clock inside the plane slowing down since it moving relative to the ground.

Observer vs observer
When the two observers do meet again, what will they have to say about each other's observations? Would they have measured the same relativistic effects? Would the pilot say that the ground observer's clock had slowed down, or would the ground observer say that the pilot's clock had slowed down?

 

[PeroK]

There are two separate clocks, each set in a plane and on the ground. Assuming inertial reference frames, how can this be?
Perspective of the observer in motion:
The observer in motion on the plane will have recorded some time duration. Since the the world outside the plane is moving at a velocity relative to the plane, time on the ground would have slowed down.

Perspective of the observer on the ground:
The observer at rest would have seen the clock inside the plane slowing down since it moving relative to the ground.

Observer vs observer
When the two observers do meet again, what will they have to say about each other's observations? Would they have measured the same relativistic effects? Would the pilot say that the ground observer's clock had slowed down, or would the ground observer say that the pilot's clock had slowed down?

It's a good question, but thinking about planes makes it difficult, because there's also the rotation of the Earth to take into account. Imagine a plane flying West as fast as the Earth was spinning, then that plane would effectively be at rest, while the clock on the ground would be orbiting the centre of the Earth.

There is a famous experiment that put atomic clocks on commercial aircraft and measured exactly what happened to the clocks relative to the clocks on the ground:

https://en.wikipedia.org/wiki/Hafele–Keating_experiment

 

[ag048744]

Oh I see. Let's just assume that the ground is infinitely flat and the plane and the ground are inertial frames of reference. no mass, no gravity and just a centripetal acceleration for when the plane starts to return to the ground observer. What would the observers have to say, when they compare measurements?

 

[PeroK]

Oh I see. Let's just assume that the ground is infinitely flat and the plane and the ground are inertial frames of reference. no mass, no gravity and just a centripetal acceleration for when the plane starts to return to the ground observer. What would the observers have to say, when they compare measurements?

Take it a step further: space ships in space far from Earth. One sets off on a circular trip and returns to the starting point. The other remains "at rest". The one doing the circular trip will find its clock shows less elapsed time upon its return.

 

[ag048744]

What if the spacecraft turned around as minimally as possible, to the point that non inertial effects are negligible?

 

[PeroK]

What if the spacecraft turned around as minimally as possible, to the point that non inertial effects are negligible?

There is no mimimum. If the spacecraft did a short, slow circular manoeuvre, the difference in the clocks would be negligible. In order to see any measurable difference you would need significant speed and/or time/distance travelled.

In the Hafele-Keating it was less than 300 nanoseconds difference over about 50 hours commercial flying.

 

[ag048744]

Hmm I guess there is no way to say as nature does not allow it. The space time diagrams would have lost symmetry while undergoing a noninertial acceleration. It is a similar situation with the twin paradox.
Thank you for your assistance, PeroK. This curious thought has always come up when I study relativity.