In the spring of 1905, a reticent Einstein boarded a tramcar a few miles away from the Zytglogge Tower — the sumptuous clock tower that dominates Bern — on his way home. Einstein, a mere patent clerk, wrapped up his work as soon as he could to contemplate the truths of the Universe in his free time. It is Einstein’s sheer genius that while we ridicule our fantasies as daydreams, we reverentially refer to his as thought experiments. And one of his thought experiments conjured on that very tram revolutionized modern physics.
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Einstein imagined what would happen if the tramcar were to travel at the speed of light. With the grand clock tower in his sight, Einstein realized that if he were traveling at 186,000 miles per second, the clock’s hands, which already moved so solemnly, would now appear to completely freeze. At the same time, Einstein knew that, back at the clock tower, the hands would be sidling conventionally — time would be running normally. For Einstein, however, time slowed down. He concluded that the faster you move through space, the slower you move through time. How was this possible?
Einstein was heavily influenced by the works of two great physicists. First, there were the laws of motion discovered by his idol, Newton, and second, were the laws of electromagnetism laid down by Maxwell. The two theories, however, were contradictory. Maxwell postulated that the speed of an electromagnetic wave, such as light, is fixed — an exorbitant 186,000 miles per second. He claimed that this was a fundamental fact about the Universe.
Whereas, Newton’s law implied that velocities are always relative. The speed of a car traveling at 40 mph is 40 mph relative to a stationary observer, but only 20 mph relative to a car traveling adjacent to it at 20 mph. Or, 60 mph to the same car whizzing by in the opposite direction. This concept of relative velocity is incompatible with Maxwell’s apparently fundamental fact when applied to the speed of light. This presented Einstein with a grievous dilemma.
The contradiction led Einstein to make a mind-boggling yet also one of the most groundbreaking claims in the history of physics — a collocation of statements that is, of course, not surprising at all. To understand the contradiction and consequently why time slows down, consider another ingenious thought experiment, one of Einstein’s absolute best. Einstein imagined a man on a station platform, on both sides of whom two lightning bolts strike. The man, standing right in the middle of these two points, observes the resulting beams of light from both sides at the same time.
However, things get peculiar when a fellow on a train views this scene while he moves past it at the speed of light. According to the laws of motion, light from the bolt closer to the train will reach the man earlier than the light from the bolt further from the train. The measurement of the speed of light made by both men will differ in their magnitude. But how is this possible when we recall that the speed of light, according to Maxwell, must be constant, regardless of the motion of an observer – a so-called “fundamental” fact of the Universe?
To compensate for this discrepancy, Einstein suggested that time itself slowed down such that the speed of light remained constant! Time for the man on the train passed slower relative to the time for the man on the platform. Einstein called this time dilation.
Gravitational Time Dilation
Einstein called his theory Special Relativity. It was special because it dealt with constant velocities. To reconcile it with the real world, where objects accelerated and decelerated all the time, he needed to investigate the repercussions of his theory when it involved acceleration. This effort to generalize and account for all general phenomenon led him to the discovery of a relationship between time and gravity; he called this new-found theory of gravity “General Relativity”.
Newton believed that the flow of time was like an arrow; it moved unflinchingly in one direction only – forward. Einstein on that tramcar hypothesized that time varied inversely with velocity. And for its malleability, it deserved, like space, its own dimension. In fact, Einstein claimed that the two were one and the same thing, a flexible 4-dimensional fabric on which the events of the Cosmos unfolded. He called it the fabric of space-time. When Einstein published his work, he received the same reaction one would expect when such a phenomenal work is published – incredulity.
According to General Relativity, matter stretches and contracts the fabric of space-time, such that objects aren’t mysteriously pulled towards the center of the Earth, but rather pushed downwards by the warped space above them. Emulating a slope, the curvature of space-time accelerates objects that move downward, although the rate of this acceleration isn’t the same at all points. The force of gravity is stronger towards the surface of Earth, where the curvature is more intense than it is on its fringes.
If the force of gravity increases as we move downward, a free-falling object falls faster at a point on the surface, say B, than it does at a higher altitude, say A. For the free-falling object, according to Special Relativity, time at B must pass relatively slower than it would pass at A, because the object’s velocity is faster at B.
What is time?
What time is the correct time then? Well, none of them. Einstein postulated that there is no absolute time. Time is relative depending on the system of forces one is subject to, formally known as a frame of reference. Time running in your own frame is known as the proper time. If the laws of motion must be the same for all observers, regardless of their motion, then time must slow down, such that the faster you move, the slower your clock runs relative to another clock. This is what Anne Hathaway referred to in Interstellar when she said to Mathew McConaughey, after landing on a faraway planet: “One hour on this planet is 7 years on Earth.”
Refer again to Einstein’s thought in the tramcar. Is the appearance of the slower clock a constraint of our primitive neurological build up, or does time really slow down? And what does time’s slowing down even mean? The capriciousness of time compels us to ask – what is time itself? This is not just a question that obnoxious philosophy undergrads ask each other at frat parties. The notion of time has perplexed natural philosophers and physicists since antiquity.
The primary function of time is to keep a chronological track of events. However, until the last 400 years, people determined time on the assumption that stars moved around us, rather than the Earth moving around them. Despite the incorrect ground for its inference, “time” still fared well. It worked because days and seasons repeated predictably, and when you have something that repeats predictably, you have a timekeeping mechanism.
Galileo used the recursive nature of such a mechanism to compute motion. Describing motion would be impossible without any reference to time. However, this time was never absolute. Even when Newton formulated the laws of motion, he recruited a notion of time wherein two clocks don’t tick in steps with an absolute, independent time, but rather with each other. Synchronization is the reason we have built such highly sophisticated and accurate atomic clocks.
This notion of time is structured on simultaneity, a simultaneity or a crucial coincidence of two events, such as the arrival of a train and a unique alignment of the hands of a clock just when the train arrives. Einstein’s theory states that these coincidences must be influenced by how one moves. If the two observers on the platform and the train cannot agree on what is simultaneous, they cannot agree on how time itself flows!
To understand the influence of motion on predictability let us consider the simplest timekeeping mechanism. Imagine a timekeeping apparatus comprised of a photon that reflects back and forth between two finitely distanced mirrors. Let’s agree that one second passes each time the photon reflects. Now, hang two such clocks at points A and B above and on the surface of Earth (discussed in the previous section) and let them measure the time right when the free-falling object falls past them. The free-falling object measures the time passing in its own reference frame with a similar clock. What do they measure?
Observing the reflection of a photon between two moving mirrors is analogous to observing a tennis ball bouncing in a moving train. Even though the ball bounces perpendicularly for someone in the train, for a stationary observer outside it, the ball bounces in triangles.
As the apparatus moves forward, the photon, after it is first released, like the ball, appears to travel a longer distance after it is reflected. Our measurement of time has therefore distorted! Furthermore, the faster the apparatus moves, the longer the photon takes to reflect, thereby stretching the duration of a second! This is why the flow of time at point B turns out to be slower than at point A (recall how, due to gravity, the object falls faster at point B than point A). This programmable graphic limns the triangular motion of the photon and consequently the delay in the flow of time brilliantly.
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 nanoseconds. Still, Einstein’s discovery is nothing short of groundbreaking. Gravity really impedes the flow of time, which implies that the more massive the object, the slower time passes in its vicinity.
That being said, the selection of light clocks to prove this seems convenient, given that the entire article talks about the slowing down of light. However, time dilation affects every clock, whether it relies on the simplest of an electromagnetic phenomenon or a complex combination of electromagnetism and Newton’s laws of motion. General Relativity’s universality assures this. In fact, even biological processes, and consequently, time, is dilated. Yes… your head is slightly older than your feet!