Special relativity--flying clcoks east to west. (1 Viewer)

[Roobs]

heres a question that's got me screwed:

"a plane sets out to fly around the world, carrying an accurate atomic clock. when it returns home will it have gained or lost time. explain"

my reaction is to say that the clock on the plane will be in relative motion to the earth no matter which direction it flies, and should thus lose time. apparently not.

according to the textbook, a clock on fling west to east speeds up relative to the distant stars, and will thus run slower to a clock on earth, hence it wil lose time

a clock fling east to west however, against the roation of the earth, will slow down relative to the distant stars, and thus a clock on earth will run slower, so the plane clock will gain time.


this is where i get confused-- arent all (effectivley) intertial frames of reference equivilant, so why invoke the concept of "relative to the distant stars"

 

[zeropoint]

Hi Roobs,

heres a question that's got me screwed:

"a plane sets out to fly around the world, carrying an accurate atomic clock. when it returns home will it have gained or lost time. explain"

my reaction is to say that the clock on the plane will be in relative motion to the earth no matter which direction it flies, and should thus lose time. apparently not.

Your answer is correct but I suspect your reasoning is not sound.

The earth's surface is rotating, so it is a non-inertial frame of reference.

We can't immediately conclude anything about time-dilation due to relative motion without referring to an appropriate inertial frame.

according to the textbook, a clock on fling west to east speeds up relative to the distant stars, and will thus run slower to a clock on earth, hence it wil lose time

a clock fling east to west however, against the roation of the earth, will slow down relative to the distant stars, and thus a clock on earth will run slower, so the plane clock will gain time.


this is where i get confused-- arent all (effectivley) intertial frames of reference equivilant, so why invoke the concept of "relative to the distant stars"

I don't like the textbook's example of the ``distant stars'', I think that it's more instructive to use the Earth's centre of mass frame, which can be considered as an approximately inertial frame ignorning the slight acceleration due to the Earth's orbital motion about the sun.

Relative to the Earth's centre of mass, the surface ``orbits'' eastward at around 300 m/s. If you combine this with the radius of the Earth you can calculate the centripetal acceleration mv^2/r.

An aircraft which sets off to the East will acquire a speed equal to that of the surface of the Earth plus whatever speed the engines will provide in still air, call that v. Conversely, the plane travelling in the westward direction will have a speed relative to the Earth's centre of mass of 300 m/s - v (very few planes travel in excess of 300 m/s).

It should be clear now that, in order of decreasing acceleration, we have

The east-bound aircraft
The earth's surface
The west-bound aircraft

which explains why the west-bound aircraft gains more time than the others.

 

[Roobs]

just clarifying:

because the surface of the earth is not actually a true interial frame, reference to another ACTUAL inertial frame must be made to make conclusions about special relativity?

thanks

 

[zeropoint]

As far as HSC is concerned, yes.