Section 1.1: Special Relativity Explained

Einstein's special relativity emerged from the need to clarify unexpected results in electromagnetism. James Clerk Maxwell established that light travels at an exact speed of 299,792,458 m/s—consistently, without variance. This raises questions: if I'm running at 5 m/s and shine a flashlight, does the light beam move away from me at a speed greater than that of light? And when accounting for Earth's rotation, does light traveling from East to West move slower than from West to East?

The answer is no—Einstein determined that both time and distance are relative. Let's delve deeper.

Consider the formula for speed: speed = distance/time. Keep this in mind as we explore the torch scenario. Imagine you are stationary with a flashlight while I run past you at 5 m/s, also wielding a torch. We must agree on the speed of the light emitted from our torches. How does this work? If time appears to move slower for me and distances seem contracted in my direction, then we can concur on the speed of light from our torches.

From my viewpoint, your time passes more quickly, and distances seem longer. Conversely, from your perspective, my time is slower, and distances are shorter. This makes it seem like the light from both torches travels at the same speed, albeit with differing perceptions.

However, at a relative speed of 5 m/s, these differences are negligible. Yet, at higher speeds, the variations in the flow of time become noticeable.

Since Maxwell showed that light must always travel at precisely 299,792,458 m/s, Einstein concluded that two observers in different frames of reference would disagree on the passage of time and the relative distances in their motion to maintain this speed of light. Thus, special relativity tells us that as speed increases, time moves more slowly.

Section 1.2: Gravitational Time Dilation

In addition to special relativity, Einstein's general relativity introduces another type of time dilation: gravitational time dilation.

Explaining general relativity in its entirety could take a while, so here are the key points.

According to Einstein, gravity is a result of mass distorting the fabric of space-time. The mass of celestial bodies like planets or the Sun creates wells in this fabric. Space-time links distance and time; thus, when gravity bends space-time, it alters both relative distance and the rate at which time passes. Therefore, the deeper one is within a gravitational well, the slower time moves due to this gravitational effect.

With a foundational understanding of Einstein's groundbreaking theories, we can explore some intriguing consequences.

The phrase "young at heart" refers to someone who maintains youthful vitality, but it also applies to Earth itself. At the core of our planet lies a unique crystalline iron structure that does not flow with the mantle's convection currents. Interestingly, the core does not experience gravity in the same way as the surface; it is equally pulled from all directions, rendering it effectively weightless. However, residing at the center of Earth's gravitational well means time moves more slowly there than on the surface.

The difference in time between the core and the surface may seem minor—time passes 0.017 seconds slower in the core each year. While this difference may appear insignificant, over 4.5 billion years, it means the core is approximately 2.5 years younger than the surface.

This age disparity isn't because the core was formed later; rather, it has experienced 2.5 years less time due to its slower passage through time than the surface.

In a similar vein, the Sun itself is younger than Earth. While Earth resides in its own gravitational well, the Sun exists within a far larger one. Thus, time progresses more slowly on the Sun.

When we consider the surfaces of both bodies, we find that for every year on Earth, time on the Sun's surface passes 66.979 seconds slower due to gravitational time dilation. Earth's orbital speed is insufficient to significantly affect time dilation, making gravitational factors the primary influence. Consequently, while the Sun is older than Earth, calculations from the time Earth was formed reveal that the Sun is actually 9,544 years younger.

Such a time difference is substantial! The development of human civilization has unfolded in less time than this. However, unlike Earth's core, the Sun is visible to us. So, the next time you gaze upward, remember you are looking at an entity that has traveled through time and is nearly 10,000 years younger than Earth.