00:01
Hi, so this question is actually quite interesting because it makes us think about special relativity in the context of the earth.
00:09
So we know that the earth, which i will try to sketch here as a sphere, is rotating around its axis, which goes through the north and the south pole, and it's rotating with a period of 24 hours.
00:23
Now, if we have a person that sits somewhere in the space, in space, and this person, sits in an inertial reference frame, so it's not moving.
00:36
This person observes two different clocks, one which sits at the north pole, so you have a clock here, and another clock which sits on the equator.
00:47
So let's place it somewhere over here like that.
00:50
And the question is, which one of these two clocks is observed to run slower by this external observer who sits in an inertial reference frame in space.
01:04
So first of all, if we think about the velocity of these two different clocks with respect to the stationary observer, of course that the clock sitting at the equator will have a velocity, let's call it ve from the equator, which is larger, much larger than the velocity of the clock sitting at the pole.
01:30
Actually, if the clock sits exactly at the north pole, it won't have any velocity, right? so the clock sitting at the north pole will simply be stationary with respect to the external observer, and the clock sitting on the equator will have a large velocity because the earth is rotating and the clock sits at a distance away from the center of rotation from the rotation axis.
01:59
Actually, this is given by the radius of the earth.
02:02
So this means that the clock sitting at the equator is actually moving, while the clock sitting at the north pole is stationary.
02:11
So we know from special relativity that time is dilated proportional to a constant called gamma...