Marking the Passage of Time: The Elusive Nature of the Concept

Nature presents us with few mysteries more tantalizing than the concept of “time.” Youngsters, today, might not think the subject worthy of much rumination: After all, one’s personal iPhone can conveniently provide the exact time at any location on our planet.


Human beings have long struggled with two fundamental questions regarding time:

  1. What are the fundamental units in nature used to express time? More simply, what constitutes one second of time? How is one second determined?
  2. How can we “accurately” measure time using the units chosen to express it?

The simple answers for those so inclined might be: We measure time in units of seconds, minutes, hours, and days, etc., and we have designed carefully constructed and calibrated clocks to measure time! That was easy, wasn’t it?

The bad news: Dealing with the concept of time is not quite that simple.
The good news: The fascinating surprises and insights gained from taking a closer, yet still cursory, look at “time” are well worth the effort to do so. To do the subject justice requires far more than a simple blog post – scholarly books, in fact – but my intent, here, is to illustrate how fascinating the concept of time truly is.

Webster’s dictionary defines time as “a period or interval…the period between two events or during which ‘something’ exists, happens, or acts.”

For us humans the rising and setting of the sun – the cycle of day and night is a “something” that happens, repeats itself, and profoundly effects our existence. It is that very cycle which formed our first concept of time. The time required for the earth to make one full revolution on its axis is but one of many repeating natural phenomena, and it was, from the beginning of man’s existence, uniquely qualified to serve as the arbitrary definition of time measurement. Other repeatable natural phenomena could have anchored our definition of time: For instance, the almost constant period of the earth’s rotation around the sun (our year) or certain electron- jump vibrations at the atomic level could have been chosen except that such technology was unknown and unthinkable to ancient man. In fact, today’s universally accepted time standard utilizes a second defined by the extraordinarily stable and repeatable electron jumps within Cesium 133 atoms – the so-called atomic clock which has replaced the daily rotation of the earth as the prime determinant of the second.

Why use atomic clocks instead of the earth’s rotation period to define the second? Because the earth’s rotational period varies from month to month due to the shape of our planet’s orbit around the sun. Its period also changes over many centuries as the earth’s axis “precesses” (a slowly rotating change of direction) relative to the starry firmament, all around. By contrast, atomic clocks are extremely regular in their behavior.

Timekeepers on My Desk: From Drizzling Sand to Atomic Clocks!

I have on my desk two time-keepers which illustrate the startling improvement in time-keeping over the centuries. One is the venerable hour-glass: Tip it over and the sand takes roughly thirty minutes (in mine) to drizzle from top chamber to bottom. The other timekeeper is one of the first radio-controlled clocks readily available – the German-built Junghans Mega which I purchased in 1999. It features an analog display (clock-hands, not digital display) based on a very accurate internal quartz electronic heartbeat: The oscillations of its tiny quartz-crystal resonator. Even the quartz oscillator may stray from absolute accuracy by as much as 0.3 seconds per day in contrast to the incredible regularity of the cesium atomic clocks which now define the international second as 9,192,631,770 atomic “vibrations” of cesium 133 atoms – an incredibly stable natural phenomena. The Junghans Mega uses its internal radio capability to automatically tune in every evening at 11 pm to the atomic clocks operating in Fort Collins, Colorado. Precise time-sync signals broadcast from there are utilized to “reset” the Mega to the precise time each evening at eleven.

I love this beautifully rendered German clock which operates all year on one tiny AA battery and requires almost nothing from the operator in return for continuously accurate time and date information. Change the battery once each year and its hands will spin to 12:00 and sit there until the next radio query to Colorado. At that point, the hands will spin to the exact second of time for your world time zone, and off it goes….so beautiful!

Is Having Accurate Time So Important?
You Bet Your Life…and Many Did!

Yes, keeping accurate time is far more important than not arriving late for your doctor’s appointment! The fleets of navies and the world of seagoing commerce require accurate time…on so many different levels. In 1714, the British Admiralty offered the then-huge sum of 20,000 pounds to anyone who could concoct a practical way to measure longitude at sea. That so-called Longitude Act was inspired by a great national tragedy involving the Royal Navy. On October 22, 1707, a fleet of ships was returning home after a sojourn at sea. Despite intense fog, the flagship’s navigators assured Admiral Sir Cloudisley Shovell that the fleet was well clear of the treacherous Scilly Islands, some twenty miles off the southwest coast of England. Such was not the case, however, and the admiral’s flagship, Association, struck the shoals first, quickly sinking followed by three other vessels. Two thousand lives were lost in the churning waters that day. Of those who went down, only two managed to wash ashore alive. One was Sir Cloudesley Shovell. As an interesting aside, the story has it that a woman combing the beach happened across the barely alive admiral, noticed the huge emerald ring on his finger, and promptly lifted it, finishing him off in the process. She confessed the deed some thirty years later, offering the ring as proof.

The inability of seafarers to navigate safely by determining their exact location at sea was of great concern to sea powers like England who had a great investment in both their fleet of fighting ships and their commerce shipping. A ship’s latitude could be quite accurately determined on clear days by “shooting” the height of the sun above the horizon using a sextant, but its longitude position was only an educated guess. The solution to the problem of determining longitude-at-sea materialized in the form of an extremely accurate timepiece carried aboard ship and commonly known ever since as a “chronometer.” Using such a steady, accurate time-keeper, longitude could be calculated.

For the details, I recommend Dava Sobel’s book titled “Longitude.” The later, well-illustrated version is the one to read. In her book, the author relates the wonderfully improbable story of an English country carpenter who parlayed his initial efforts building large wooden clocks into developing the world’s first chronometer timepiece accurate enough to solve the “longitude problem.” After frustrating decades of dedicated effort pursuing both the technical challenge and the still-to-be-claimed prize money, John Harrison was finally able to collect the 20,000 pound admiralty award.

Why Mention Cuckoo Clocks? Enter Galileo and Huygens

Although the traditional cuckoo clock from the Black Forest of Germany does not quite qualify as a maritime chronometer, its pendulum principle plays an historical role in the overall story of time and time-keeping. With a cuckoo clock or any pendulum clock, the ticking rate is dependent only on the effective length of the pendulum, and not its weight or construction. If a cuckoo clock runs too fast, one must lower the typical wood-carved leaf cluster on the pendulum shaft to increase the pendulum period and slow the clock-rate.

No less illustrious a name than Galileo Galilei was the first to propose the possibilities of the pendulum clock in the early 1600’s. Indeed, Galileo was the first to understand pendulum motion and, with an assistant late in life, produced a sketch of a possible pendulum clock. A few decades later, in 1658, the great French scientist, Christian Huygens, wrote his milestone book of science and mathematics, Horologium Oscillatorium, in which he presented a detailed mathematical treatment of pendulum motion-physics. By 1673, Huygens had constructed the first pendulum clock following the principles set forth in his book.


In 1669, a very notable scientific paper appeared in the seminal English journal of science, The Philosophical Transactions of the Royal Society. That paper was the first English translation of a treatise originally published by Christian Huygens in 1665. In his paper, Huygens presents “Instructions concerning the use of pendulum-watches for finding the longitude at sea, together with a journal of a method for such watches.” The paper outlines a timekeeping method using the “equation of time” (which quantifies the monthly variations of the earth’s rotational period) and capitalizes on the potential accuracy of his proposed pendulum timekeeper. The year 1669 in which Huygens’ paper on finding the longitude-at-sea appeared in The Philosophical Transactions preceded by thirty-eight years the disastrous navigational tragedy of the British fleet and Sir Cloudesley Shovell in 1707.

As mentioned earlier, John Harrison was the first to design and construct marine chronometers having the accuracy necessary to determine the longitude-at-sea. After many years of utilizing large balanced pendulums in his bulky designs, Harrison’s ultimate success came decades later in the form of a large “watch” design which utilized the oscillating balance-wheel mechanism, so familiar today, rather than the pendulum principle. Harrison’s chronometer taxed his considerable ingenuity and perseverance to the max. The device had to keep accurate time at sea – under the worst conditions imaginable ranging from temperature and humidity extremes to the rolling/heaving motion of a ship at sea

The Longitude Act of 1714 specified that less than two minutes of deviation from true time is required over a six-week sea voyage to permit a longitude determination to within one-half degree of true longitude (35 miles at the equator). Lost time, revenue, and human lives were the price to be paid for excessive timekeeper inaccuracies.

Einstein and Special Relativity: Speeding Clocks that Run Slow

Albert Einstein revolutionized physics in 1905 with his special theory of relativity. Contrary to the assumptions of Isaac Newton, relativity dictates that there is no absolute flow of time in the universe – no master clock, as it were. An experiment will demonstrate what this implies: Two identical cesium 133 atomic clocks (the time-standard which defines the “second”) will run in virtual synchronization when sitting side by side in a lab. We would expect that to be true. If we take one of the two and launch it in an orbital space vehicle which then circles the earth at 18,000 miles per hour, from our vantage point on earth, we would observe that the orbiting clock now runs slightly slower than its identical twin still residing in our lab, here on earth. Indeed, upon returning to earth and the lab after some period of time spent in orbit, the elapsed time registered by the returning clock will be less than that of its twin which stayed put on earth even though its run-rate again matches its stationary twin! In case you are wondering, this experiment has indeed been tried many times. Unerringly, the results of such tests support Einstein’s contention that clocks moving with respect to an observer “at rest” will always run slower (as recorded by the observer) than they would were they not moving relative to the observer. Since the constant speed of light is 186,000 miles per second based on the dictates of relativity, the tiny time dilation which an orbital speed of 18,000 miles per hour would produce could only be observed using such an incredibly stable, high resolution time-source as an atomic clock. If two identical clocks passed each other traveling at one-third the speed of light, the “other” clock would seem to have slowed by 4.6%. At one-tenth the speed of light, the “other” clock slows by only 0.5%. This phenomena of slowing clocks applies to any timekeeper – from atomic clocks to hourglasses. Accordingly, the effect is not related to any construction aspects of timekeepers, only to our limitation “to observe” imposed by the non-infinite, constant speed of light dictated by relativity.

For most practical systems that we deal with, here on earth, relative velocities between systems are peanuts compared to the speed of light and the relativistic effects, although always present, are so small as to be insignificant, usually undetectable. There are important exceptions, however, and one of the most important involves the GPS (Global Positioning System). Another exception involves particle accelerators used by physicists. The GPS system uses earth-orbiting satellites traveling at a tiny fraction of the speed of light relative to the earth’s surface. In a curious demonstration of mathematical déjà vu when recalling the problem of finding the longitude-at-sea, even tiny variations in the timing signals sent between the satellites and earth can cause our position information here on earth to off by many miles. With such precise GPS timing requirements, the relativistic effect of time dilation on orbiting clocks – we are talking tiny fractions of a second! – would be enough to cause position location errors of many miles! For this reason, relativity IS and must be taken into account in order for the GPS system to be of any practical use whatsoever!

Is it not ironic that, as in the longitude-at-sea problem three centuries ago, accurate time plays such a crucial role in today’s satellite-based GPS location systems?

I hope this post has succeeded in my attempt to convey to you, the reader, the wonderful mysteries and importance of that elusive notion that we call time.

Finally, as we have all experienced throughout our lives, time is short and….



Here’s Religion in a Nutshell!

I’ve learned a few things as I have gotten older…and formed some new perspectives and questions along the way! Near the top of my list of questions are the following two:

What do we really know about our creator and our ultimate human fate?
To what extent has organized religion been beneficial or detrimental to man?

Italy and Religion

As for the first question: Perhaps we really know much less about our creator and our purpose, here on earth, than we think we do. Virtually all of our beliefs come from scripture and hear-say in one form or another. How reliable are the scriptures? For many with a strong sense of faith, the scriptures are enough. For the rest of us, especially those of us whose belief system is rooted in the tradition of “the scientific method,” more proof is required. The paucity of solid, consistent evidence supporting religious doctrine is a problem, but where do we go from here? It appears that faith and common sense will remain necessary, if insufficient, co-attributes.

As for the second question: History proves that many of the darkest periods in mankind’s history have been the result of religious ideologies at war. Is that really what God wants? No, that must simply be what man wants. How can the documented periods in our history of religious strife and the byproducts of pestilence, and human suffering possibly be religiously inspired?

Did the cause of mankind and religion benefit from the Church’s persecution of Galileo Galilei because he espoused and slyly disseminated the Copernican belief that the earth moved around the sun rather than vice-versa? Galileo was sentenced by the Inquisition to house-arrest (in his own Florence villa). That occurred in 1632/33 and resulted from the publications of  his book, the Dialogo, or Dialogue Concerning the Two Chief World Systems. In 1992, the Catholic Church finally got around to officially pardoning Galileo for his “heresy” and disregard for the Church’s scripture-based teachings on the matter at hand. Galileo, of course, was correct in his scientific contention, and proof of that was well established soon afterward. The Galileo episode reveals the risks inherent in taking the scriptures too literally and the Church being too adamant. The stakes are high when it comes to using scripture as a reliable guide for human belief and conduct. The Catholic Church is not alone in its authoritarian approach to religious belief despite flimsy supporting evidence …as in Galileo’s case.

I am a cradle Catholic who, as the years have passed, has adopted a modified perspective on a number of issues. As a youngster attending Catholic school and, later, catechism, I grew up with the confusing image of a two-faced God: One who might send you to hell for defying his law, but at the same time, was always there to forgive a true contrition – even for repeat offenses. Happily, the Church, today, projects a much more benevolent God. As an adult, I view some of the harsher aspects of religious doctrine as artifacts of a less enlightened and informed time when the Church, like a good shepherd, felt obligated to forcibly engage and impress its flock of followers who might otherwise have gone astray.

Stanford Chapel Moasic_1

Many years ago, one of the better priests to rotate through our parish was blessed with a fine sense of humor. During his sermon one Sunday in the midst of Lent, Father Nathan related a dream he had experienced in his youth: He was sitting in hell, seated between Adolph Hitler and Attila the Hun. Another of the inmates approached them and asked Hitler, “What are you in here for?” Hitler replied that he had committed unspeakable crimes against the Jewish people. The inmate then addressed Attila the Hun, “What about you?” The burly Hun replied, “I ravaged, pillaged, and raped thousands of my enemy, showing no mercy.” Turning to the youthful Nathan, he asked, “And you?” “ I ate a hot dog on Friday,” the future priest replied. True story about the dream… or not: I am not certain. It could easily have been Father Nathan’s wry way of making a point. He certainly got a hearty response from the congregation!

 In Defense of Organized Religion

As a cradle Catholic, I deeply respect the fine charitable work that emanates from the Church and its many positive influences. This has been the case for centuries and continues today. The Church is divinely inspired, yet it is administered by human beings, and we humans ARE fragile creatures who, despite good intentions, often lose our compass bearings. Religious doctrine reflects man’s propensity to lose his way, to stray from the path of rightousness and honor. I believe that many of her policies and doctrines stem from the Church’s realization that the human flock needs a good shepherd to show the way. We are today, a much more informed and enlightened flock than our ancestors, generations ago, and the Church needs to adjust to that fact in the way she shepherds and in the messages she sends. On the other hand, it strikes me that while technology progress has exploded in recent decades and made the world more accessible to us, basic human nature seems not to have changed a wit since recorded antiquity – blame it on the genes! A good shepherd is still necessary – one bearing an enlightened message.

These days, I gravitate heavily to the idea that one can find salvation in whatever the hereafter by simply living an honest, hardworking, constructive existence while doing no harm to one’s fellow man or the society of man. Put simply, live by the Golden Rule with one additional caveat: Do unto others as you would have them do unto you….AND conduct yourself as to do no harm to the greater good – to the societies of men and women necessary for humanity to both survive and thrive.

Many of the things that religions have banned or declared sinful should be explained by the Church in their more proper, practical context. Sex outside of marriage, for example: Is it to be discouraged because sex is “bad” or simply because church doctrine forbids it? Most mature adults realize that religious policy, in that case, is rooted in the practical reality that children which may be conceived are best nurtured and raised within a dedicated family unit – for their own good and the good of society. If the necessary degree of parental dedication can be demonstrated without the need for official paperwork….so be it, but, given human nature, that may more easily be said than done…and the Church recognizes that fact. The growing numbers of single parent households across this nation signal the recent failure of the Church’s message; as a result, we are beginning to feel the practical ramifications as a society. I wish that messages from the pulpit sounded less authoritarian and more often appealed to the sound, practical aspects of church doctrine.

I am quite convinced that organized religion which becomes too organized, bureaucratic, and intolerant tends to stray beyond the simple, essential message of the Golden Rule and, inevitably, does more harm than good in this world of ours. Along with the Golden Rule as a guide, I would include the admonition to “KNOW what is right, and DO what is right.” That is the obligation of each and every one of us. Perhaps when we, the sheep, have finally learned the twists and turns of the pathway and have learned not to stray from it, the Shepherd can relax.

Falling Feathers and Pennies: Did You Know This?

If you simultaneously release a feather and a penny, side-by-side, which will hit the ground first?  If you say, “The penny, of course,” the science of physics has news for you. That is not always true! Inherently, they reach the ground at the same time. Read on to understand why!

Feather & Penny Falling_1

By the year 1604, Galileo Galilei had deciphered a long-standing mystery of physics: “The law of fall.” Until that time, “natural philosophers,” as scientists were called, had puzzled for centuries over the question: “Precisely how do physical bodies of mass like a feather and a penny fall to earth under the influence of gravity.” It was clear that objects seemed to fall faster the longer they fell – but according to what mathematical principles?

Do heavier objects fall faster than light ones? It would intuitively seem so! Is the instantaneous velocity of a falling object proportional to the distance traversed during fall – or perhaps to the time duration of fall?

By way of clever experimentation and logical deductions, Galileo deduced the law of falling bodies under the influence of gravity:

Every body subject to fall inherently accelerates at a
fixed rate as it falls, irrespective of its weight (mass).

With a fixed, equal rate of acceleration as decreed by the law of fall, motion physics tells us that two bodies released from rest will fall side-by-side all the way down. The law also dictates that objects in free-fall reach instantaneous velocities which are proportional to the time duration of fall from a rest condition. For objects here on earth, a falling object adds slightly less than 32.2 feet per second to its velocity for each additional second of fall.

The wording of “the law of fall” contains two important implications. First, the key word, “inherently,” implies that the falling body is subject only to a constant force of gravitational attraction. Second, the term “fixed” rate tells us that the acceleration is a fixed numerical value for all bodies of mass… in a given gravitational field. The earth’s gravity is essentially constant over all regions of the globe…at its surface. The moon’s gravitational field is also essentially constant at its surface, but its numerical value is just under one-third that of the earth. A specific body of mass will fall faster here, on earth, than it would on the moon.

Note that “mass” denotes the amount of material present in a body, while “weight” denotes the force of gravitational attraction acting on that mass. When you weigh yourself, you are measuring the force of the earth’s gravitational attraction on your mass!  Double the mass of a body, and you double its weight in a given gravitational field!

Everyday observation tells us that a penny always falls faster than a feather. How, then, do we reconcile our observations with the law of fall and the statement in the opening paragraph of this post? The key to the seeming impasse regarding the falling feather and the penny resides in the word, inherently, as used in the statement of the law of fall which assumes only gravity acting on the object. When objects fall, here on earth, there is an additional force acting on them besides the force of gravity as they fall, and that is the retarding force of air resistance!

If our feather and penny experiment is conducted in a tall glass cylinder with all of its air removed, the feather and the penny will fall precisely side-by-side. I witnessed this at the Boston tech museum many years ago.

The weight of the feather is much less than that of the penny, and the increasing force of air resistance generated during the fall becomes a much larger percentage of a feather’s weight (gravitational attraction) than in the case of a penny. This fact negates the equal acceleration during fall imposed by the law of fall. Physics has a name for the condition which is the basis for the law of fall: It is called the equivalence of  the “gravitational mass” and the “inertial mass” of a body (do not worry if this last comment is confusing to you; a further look into motion physics would quickly make its meaning clear).

Galileo was the first “modern” physicist. His ability to recognize and isolate the “secondary effect” of air resistance in the matter of falling bodies enabled him to bypass the confusion that our everyday experiences often injected into the early study of pure physics. Isaac Newton carried Galileo’s insights much further in his own, subsequent work on motion physics. Newton’s three laws of motion, which every beginning physics student studies, along with his theory of universal gravitation explain precisely the behavior of falling bodies that we have just examined.

One parting comment: Albert Einstein made careful note of the law of fall and the fact that the gravitational mass of an object is precisely equivalent to its inertial mass. Again, it is that latter relationship which dictates that all masses inherently fall with a fixed and equal value of accelerated motion in a given gravitational field. Unlike many fine scientists of the time, Einstein reasoned that the equivalence of gravitational and inertial mass was no coincidence of nature – that something very profound for physics was implied. His persistent curiosity in the matter led him to his theories of relativity which, in 1905 and again in1916, revolutionized all of physics as well as our concept of physical reality.

As for Galileo, his formal statement of the law of fall did not occur until the year 1638, four years before his death. Even though he had reached his major conclusions by 1604, it took him that long to firmly claim priority of his findings by publishing his classic book of science, Discourses on Two New Sciences.

SI ExifGalileo_Sustermans_1








The Master and his most important scientific book

For much more information on this and other aspects of motion physics, see my book, The Elusive Notion of Motion: The Genius of Kepler, Galileo, Newton, and Einstein. See also, several other posts on Galileo, Newton, and Einstein by clicking on the “Home” page in the blog header and searching the archives using a keyword such as “science” or by going to the “science” categories in the archives.

 My book and how to order it can be found by clicking on the link below:

 My Motion Physics Book