One evening in the spring of 1905, Albert Einstein then a mere patent clerk in Bern after trudging through his days work, he decided to board a tramcar on his way home. Einstein would often wrap up his work as soon as possible to contemplate the truths of the universe in his free time. It was one of these thoughts experiments he devised on the tramcar that revolutioned modern physics forever. While receding away from the “Zytglogge” clock tower, Einstein imagined what would happen in the tramcar were if receding at the speed of light. He realized that if he were to travel at 186 000 miles per second, the clocks hand would appear to completely freeze. At the same time, Einstein knew that back at the clock tower the hands would tick along at their normal pace. For Einstein, time had slowed down. This thought blew his mind. Einstein concluded that the faster you move through space, the slower you move through time.
How is this possible?
Einstein’s work was heavily influence by two of the most iconic physicists of all time.
First, there were the laws of motion discovered by his idol Isaac Newton and second were the laws of electromagnetism laid down by James Clerk Maxwell. Newton’s laws insisted that velocities are never absolute, but always relative, so that their magnitudes must be appended by the phrase “with respect to.” For instance, a train travels at 40 km/h with respect to someone at rest. However, it only travels 20 km/h with respect to a train traveling 20 km/h in the same direction or it travels 60 km/h with respect to another train traveling in the opposite direction at 20 km / h. This is also truth of the velocities of earth, the sun and the entire Milky Way Galaxy. On the other hand, Maxwell found that the speed of an electromagnetic wave such as light is fixed at an exorbitant 299 792 458 m/s regardless of who observes it. However, Maxwell’s notion seems incompatible with Newton’s notion of relative velocities. If Newton’s laws are truly universal, why should the speed of life be an exception?
This presented Einstein with a daunting dilemma. This conflict between the ideas of Newton and Maxwell can be demonstrated with another of Einstein’s brilliant thought experiments. Einstein imagined himself on a train platform witnessing two lightning bolts strike on either side of him. Now, because Einstein stands precisely in the middle of the two strikes, he receives the resulting beams of the light from both sides at the same time. However, things get more complicated when someone on a passing train views this event while whizzing past Einstein at the speed of light. If the speed of light conforms to the rules of relativity, then the person on the train wouldn’t witness the lightning strike simultaneously. Logically, the light closer to the man on the train would reach him first. A measurement of the speed of light made by both men would differ in magnitude; this would contradict an apparently fundamental truth of the universe. Einstein had to make a difficult choice; either Newton’s laws were incomplete or the speed of light was not a universal constant. Einstein realized that the two notions could co-exist with a small tweak in Newton’s laws. To get rid of the discrepancy in the measurements, Einstein suggested the time itself for the man on the train must slow down to compensate for the decrease in speed such that the magnitude remains a constant. Einstein called this absurdity, “time dilation” and his newfound theory “special relativity.” Newton believed the time moved unflinchingly in a single direction forward.
Einstein, however, had just realized the time stretches and contracts varying with velocity. Due to its malleability, time, like space, deserved its own dimension. In fact, Einstein claimed that the two were one and the same. Together, they formed a four-dimensional fabric or continuum called space-time upon which the mundane events of the universe would unfold. Einstein suggested that massive objects like the sun didn’t pull bodies like earth with a mysterious inexplicable tug, but rather curved the fabric of the space-time around them, forcing earth to fall down into this steep valley. A highly simplified analogy is the dip in the trampoline made by a falling bowling ball. If a marble were placed on that trampoline, the marble would immediately roll towards the bowling ball in the center. This is also true for Earth’s gravity. We are pinned to the ground because space – so distorted by the Earth’s mass – pushes us down from above. However, the slump in the fabric around earth is not uniform and Earth’s gravity grows more intense as we move towards its center where the curvature is at a maximum. Therefore, like the marble on the trampoline, an object that falls towards the Earth accelerates as it races towards the center of the planet. It falls faster when just above the surface than it does, say when it is slightly above the atmosphere. But hey, according to special relativity, the faster you move through space, the slower you move through time. This means that time runs slower on Earth’s the surface than it does above the atmosphere. Now, because different planets have different masses and thus different gravitational strengths, they also accelerate objects in different rates as we have learned. This means a variable passage of time. This is what happened in the movie “Interstellar” when the protagonist land on a planet in the proximity of a black hole.
The gravity on the planet is so severe that one hour on the surface is equivalent to seven years on earth. To understand how motion affects time, let’s consider the simplest timekeeping mechanism. A second passes each time the photon is reflected.
Let’s imagined two people one in a spaceship slightly above Earth’s atmosphere and the second on top of a small hill just above the Earth’s surface. Both are watching a man fall from space towards the ground.
Let’s say that the falling man is carrying the photon clock explained a moment ago. What do each of the two men observe as the man falls past them?
What they observe is eerily similar to what a stationary person would observe when watching a ball bounce in a moving train. As the man falls from space, the light in his clock would appear to move in triangles to the two observers. This would mean that the light travels a longer distance; consequently stretching the duration of a second. It is obvious that the lengths of the triangles the light traces and therefore the duration of a second is proportional to the velocity of the falling man. When we recall that objects closer to the center of the planet fall faster, we can determine the time would appear to pass slower to the man on the hill than it does to the man in the spaceship above. Of course, the difference is infinitesimal. The difference between the time measured by clocks at the tops of mountains and at the surface of earth is a matter of nanoseconds. Time dilation affects every clock, whether it relies on basic electromagnetism or a complex combination of electromagnetism and newton’s laws of motion. In fact, even biological processes are slow down. Yes that’s right.
Your head is slightly older than your feet.