Aging Earth
Why does the Earth's rotation make some of us age faster?
As soon as you flick the switch, light immediately floods your room. No matter how hard you squint, you can't catch its' movement across the room from its source. It's just too fast. That's what this website's name, Speed Limit C, alludes to. "c" is the universe's speed limit, approximated at 300,000,000 meters per second. However, c merely defines the fastest speed that's possible in the universe. Most objects are limited by a speed much lower than c because of their mass. The greater the mass of an object, the lower its speed limit is. On the other hand, light is made of massless photons, giving it the ability to travel at the universal speed limit or what most of us know as the speed of light: c.
A vast number of experiments have confirmed that light in a vacuum will always travel at c. It is possible for light to travel slower when it's going through another medium, causing refraction -- why a spoon looks crooked in a glass of water. But, for today, let's assume light is in a vacuum and always travels at c. However, this fact brings up some interesting possibilities.
Imagine this scenario. There is a man in a train that travels very quickly, at a speed of c/2. In the train, he faces a mirror 2 meters away from him while holding a flashlight towards it. From inside the train, this is a straightforward scenario. The man holds the flashlight to the mirror, it travels at c, hits the mirror, and returns to the man with a total distance traveled of 4 meters (Figure 1 - top view from inside train).
Figure 1
Figure 2
However, things aren't always so simple. Say we continue with this scenario, except a woman stands outside the train and watches it zoom past her. If she, on the ground, was able to see what was going on in the train, things would no longer make sense. Since the car is moving, everything inside the car (light, man, mirror) also moves during the experiment. From the time when the man turns on the flashlight to the time when the light bounces back and reaches him, both he and the mirror have moved in the direction of the car's velocity. Therefore, from the woman's perspective, the light must have traveled diagonally to catch up with the man, which would have a distance of more than 4 meters (Figure 2 - top view of train moving to the right).
Now we're faced with some issues. The woman saw the light move in a longer distance than the man did. We also know that light moves at the same speed, c, for both of them. Knowing that speed is defined by the equation v=d/t (speed = distance/time), we can make a conclusion: Since both the man and the woman saw the same speed of light while the man saw observed a shorter distance traveled, time must have been shorter for the man. Just like this, many thought experiments corroborate the principle of time dilation: the faster you move through space, the slower time will pass for you.
Figure 3
Now we come back to our original question of why the Earth's rotation (Figure 3) makes some of us age faster. First, think of a spinning ceiling fan. Imagine a bug sitting on the farthest edge of the fan piece will move around in large circles. However, another bug that sits on the middle of the fan, through the axis of rotation, does not move at all. Similarly, the rotation of the Earth constantly moves people at the equator at a speed of approximately 460 meters every second. On the other hand, those at the poles of the earth don't have any added speed from rotation. Since those at the equator are moving faster than those at the poles, time dilation makes time move slower for the people at the equator. Consequently, people at the Earth's poles will age faster than if they were at the equator.
However, don't worry too much if you aren't exactly on the equator. An equation called the Lorentz Transformation (Figure 4) can help us calculate the time dilation associated with reference frames of different velocities. What we find is that the change in the time between the reference frame of the equator and poles is so small that we can't actually notice it.
Moreover, the people at the poles don't actually live shorter lives. Instead of their time being cut short, it's better described as being squeezed into a smaller time period. For them, everything will feel complete and normal, regardless of whether they live. People are only perceived to age "faster" when another person observes them from a greater velocity.
Figure 4