What does it mean, Albert Einstein asked in 1905, to say that a train arrives someplace — in Paris, say — at 7 o’clock?
It should be noted that last week, 30 June, 2019, is the 114th anniversary of Einstein’s publication of “On the Electrodynamics of Moving Bodies“, his Special Theory of Relativity.
What is time or, more familiarly, what time is it? There are those who believe that time doesn’t really exist, that it is a human construct, an invention to mark or measure the continuous stream of reality, of events that happen as one flows seamlessly into the next, that the grandfather clock in your living room that counts down the hours, minutes and seconds is simply an instrument to measure this stream, that time is an illusion. Consider the following thought experiment: by the time you read the following period: “.”, that act of reading will forever be in the past as will every future act of reading until you read every character and line in this article. This is referred to as the “ever present now”, that everything we do, the instant we do it, is forever in the past. All we have then, is the instantaneous present; the past is gone into history, the future hasn’t occurred yet. A basic look at Einstein’s Special Theory of Relativity may provide some clues to this elusive enigma we call time.
Newton regarded time as immutable, absolute and unchanging, independent of the state of an object’s motion, hence the term “Newton’s Clockwork Universe”, that we could predict with perfect accuracy and absolute certainty the outcome of every situation since time was unchanging. To Newton, the motions of the planets and all objects perfectly obeyed his Three Laws of Motion, still pillars of classical dynamics and required study for all physics majors.
Albert Einstein was fascinated with the concept of time and that fascination would play a major role in the development of his Special Theory of Relativity, one of four papers published during his Annus Mirabilis (Miracle Year) of 1905. Entitled “On the Electrodynamics of Moving Bodies“, the Special Theory of Relativity proposed a revolutionary new approach to the concept of time, that it wasn’t fixed and immutable as suggested by Newton’s Clockwork Universe. Following graduation from the Zurich Federal Polytechnic Institute in 1900, he took a job as Technical Expert, Third Class in the Swiss patent office, a position that provided a modest salary and also the flexibility to continue his research and study. This unique situation allowed him to finish and publish Special Relativity along with the other three papers and thus, his 1905 Miracle Year would be realized! It would be another ten years, not until 1915, that his complete theory of gravity, General Relativity, would be published.
While evaluating patents in the Bern patent office and often looking out his window at the clock tower, Einstein openly mused about what would happen or what would be observed if one could ride on a beam of light. The answer to this question will be clear at the conclusion of this article. Consider his famous thought experiment and the paradox suggested by it, also known as “The Relativity of Simultaneity“. An observer stands on a platform and watches a speeding train pass through the station while lightning strikes simultaneously at point A, at the aft of the train and at point B, at the train’s fore (front). To the stationary observer on the platform, the light from both lightning events arrive at the same time, that is, they are simultaneous. Can the same be said of an observer on the train, located at the train’s midpoint as it passes the observer standing in the train station, the train traveling with velocity v, from left to right? This is the paradox, the paradox alluded to with the question posed as the heading of this article.
Before we continue this discussion, we must recall another brilliant individual and his contribution. In 1865, just four decades prior to Einstein’s publication of the Special Theory of Relativity in 1905, the Scottish physicist James Clerk Maxwell published “A Dynamical Theory of the Electromagnetic Field” (page 498 of his paper, pg 49 of this pdf), wherein he described light and all electromagnetic radiation (Infrared, Radio, X-rays, UV, etc), as the propagation of an electromagnetic wave whose speed is 299,792,458 meters/second and is invariant with respect to location and motion of source; that is, the speed of light is the same for all objects, in all directions, both “stationary” and in motion. This breakthrough was a watershed moment in the history of science, a discovery that is on par with Einstein’s Special or General Theories of Relativity. With it, was the elimination of the universal Aether, the medium then thought to be pervasive throughout space and necessary if the classical understanding of a wave as the propagation of energy through a medium was to be adopted for EM radiation. Maxwell’s theory was subsequently born out in 1887 with the Michelson-Morley experiment, correctly concluding, within experimental error and the tolerances available for that period, that Maxwell’s proposition that the speed of light (c) is universally invariant.
So, are the lightning strikes simultaneous or not? Well, that depends on where you are, or so it would seem! The individual standing on the railway station observes them to be so; to the observer on the train, event B occurs first and event A occurs later. Given the nature of the speed of light, that its speed is invariant to location, motion and direction of motion, how can both assertions, at the same time, be true? Either Maxwell was incorrect and the speed of light is not universally invariant or something was wrong with the model, quite a vexing paradox until the immutability of time is called into question. As it turns out, the paradox is resolved if time changes depending on your frame of reference, your location, motion and direction of motion; that is, time is different for the stationary observer on the platform and the observer riding on the train! As it turns out, time slows down as you accelerate faster and faster and will stop if, as envisioned by Einstein, you could ride on a beam of light! Not only does time slow down but your physical length shortens and your mass increases by the same measure as time slows down. At 99.99% the speed of light, time has slowed down by a factor of 71, your mass has increased and length shortened by this same amount!
It should be pointed out that Special Relativity pertains only to non-accelerated or “inertial” frames of reference. It took another ten years for Einstein to develop a fully general theory that pertained to all frames of reference and thus, he published General Relativity in 1915. In the intervening century since then, there have been literally hundreds of tests and practical applications of both theories, all confirming the veracity of each.
It also should be pointed out that the term “Clock” should be considered in the broadest possible terms where anything that is cyclical and rhythmic in nature, anything that depends on or measures time, such as a beating heart or the oscillations of Cesium atom, could be considered a “Clock” and would thus behave according to the principle of Time Dilation as described above.
In 1911, Einstein is quoted as follows when discussing the Twin Paradox, where one twin remains on Earth and the other travels to the stars at relativistic speeds only to return to the earth much younger than the sibling that remained behind:
If we placed a living organism in a box … one could arrange that the organism, after any arbitrary lengthy flight, could be returned to its original spot in a scarcely altered condition, while corresponding organisms which had remained in their original positions had already long since given way to new generations. For the moving organism, the lengthy time of the journey was a mere instant, provided the motion took place with approximately the speed of light.
So the answer to the question, what time is it, really depends on where you are and if you have a Swiss watch (or maybe you should just ask the patent clerk looking out the window)!
Imagination is more important than knowledge
An index of all articles in this blog can be found here.