Time Dilation Explained: Why Planes Lose Time

[morgan?]

in a discussion of spacetime, i was given this example of time dilation:

you have two perfectly synchronized clocks. one goes on an airplane while the other stays on the ground. the one in the plane flies around the world. when it lands, the clock on the plane is behind the clock on the ground.

why does this happen?

 

[smallphi]

GR postulates that a clock measures the integrated spacetime interval along its world line. The two clocks follow different world lines between the same two events (plane leaves and plane lands). The integrated spacetime interval (for clocks also known as proper time) doesn't have to be the same for different worldlines.

Analogously, if you draw two points on a sheet of paper and two different curves connecting them, their lengths (the analogue of the integrated spacetime interval in GR) don't have to be the same.

Evaluating the effect and which clock shows bigger time requires GR. SR is incapable of taking into account the fact that due to Earth's gravity, clocks at different height run at different rate. There is a discussion of the effect in James Hartle's introductory GR textbook (chapter 6.6 Newtonian gravity in spacetime terms) and a problem where you have to prove the formula shown there.

 

[Ich]

Even if you neglect GR, it is not true that the plane's clock will always be behind the ground clock. It depends on the direction of flight (westward or eastward) and the speed of the plane.
Do you already know how to calculate time dilatation and want to understand that specific problem? Otherwise I would suggest that you first consider non-rotating scenarios.

 

[Mk]

Even if you neglect GR, it is not true that the plane's clock will always be behind the ground clock. It depends on the direction of flight (westward or eastward) and the speed of the plane.

How does that make a difference?

 

[pervect]

How does that make a difference?

It makes a difference because the Earth is rotating. While an earth-centered frame isn't quite inertial because of gravity, it's close, assuming you don't have great changes in height.

In this almost-inertial frame, a plane sitting on the ground has a considerable east-west velocity due to the rotation of the Earth.

 

[Pippo]

taking as a ref point a star the two planes have different speed, the one going west and the one going est.