Tag Archives: Atomic Clock

What Time Is It?

Ironically, the times the world community has responded to the question, “What time is it?” have changed dramatically over time. Knowing what time it is, has been driven mainly by technological needs and advancements. We will see enormous religious implications to what time it is! We read, “…there should be time no longer (Rev. 10:6).”

Traditionally, time has been kept astronomically. Ironically, the invention of atomic clocks has driven the advancement astronomically! In my lifetime, timekeeping accuracy has moved forward an amazing billion-fold. Historically, the agrarian world cared more about the seasons than about what time it was.

First Atomic Clock

Harold Lyon’s ammonia MASER was the first atomic clock (1949). I went to work at the National Bureau of Standards (NBS) in Boulder, Colorado, in 1960. The physics of the ammonia maser is fascinating, and NBS had one I got to work on. After the invention of the maser, Charles Townes went on to invent the LASER (Light Amplification by Stimulated Emission of Radiation). Can you imagine how many LASER scanners there are across the world, considering there is one at every store’s checkout stand? These most useful devices come from the physics of timekeeping!

Pendulum Clock

Galileo used his heartbeat to measure the period of a swinging chandelier in the cathedral in Pizza, Italy. There is a baptism by immersion font in that same cathedral. (We have been there). From those heartbeat measurements, Galileo deduced some interesting laws of physics—preceding Newton. The pendulum clock was invented by Christiaan Huygens in 1656. It became the world’s standard timekeeper, used in homes and offices for 270 years.

Timekeeping World Changed

The timekeeping world changed dramatically in 1735 with John Harrison’s invention of a marine chronometer. (See Dava Sobel’s LONGITUDE). With Harrison’s chronometer, mariners could determine accurate longitude, which was essential for accurate sea navigation, as the Earth spins under the heavens.

This chronometer gave significant superiority to the English Navy. In 1833, the famous Greenwich Observatory time ball was installed. Thus, the ships at port in London could see to synchronize their chronometers before they went out to sea!

The National Bureau of Standards (NBS) in Washington D.C. started broadcasting the time in 1919 from radio station WWV. They used a precision pendulum chronometer and got the correct time from the nearby United States Naval Observatory (USNO). Then, Quartz clocks were invented in the 1930s with significantly superior timekeeping ability. These were the main timekeepers until the invention of atomic clocks.

Idea of the Atomic Clock

In the 1940s, Nobel Prize winner, Isador Isaac Rabi is credited with the idea of an atomic clock. One can think of the oscillating frequency of a photon coming from an atomic transition in an atom or molecule. We add up the oscillations of these photons and make an atomic clock.

The time and frequency Rabi award was named after him. In 1983, he was the first recipient. I was privileged to have breakfast with him on the day of the award ceremony in Philadelphia. I was greatly honored to be the second recipient a year later.

Atomic Time Generated

If you are going to replace the spinning and orbiting Earth as a clock, then that clock needs to never stop. Keeping atomic clocks running continuously is no small matter. Continuous atomic time was first generated by Louis Essen and Jack Parry at the National Physical Laboratory in Teddington, England. So, in June 1955 atomic timekeeping had its birth in the world at NPL using a transition in cesium. The cesium transition was much more accurate than Lyons’ ammonia maser. Lyons went on to build the world’s first cesium-beam frequency standard, NBS-1, in 1952, but he never turned it into a clock.

 Move To Boulder, Colorado

In 1954, the National Bureau of Standards (NBS) was moved to new laboratories in Boulder, Colorado. You can see Roger Beehler working with NBS-1 in this link: https://www.nist.gov/pml/time-and-frequency-division/time-services/brief-history-atomic-clocks-nist. You can see all the rest of the NBS/NIST cesium-beam standards up to NIST-7. In contrast to astronomical phenomena, atomic frequency standards have gotten ten times better about every seven years.

The square root of the Allan variance can be written in a form that gives an estimate of how stable and accurate an atomic frequency standard can be: σ y (τ) = Δν/(ν Signal to Noise). The fractional frequency is defined as y = (v(t) – vo)/vo, vo is the nominal frequency of the transition of interest. If ν(t) is exactly on frequency, then y(t) is zero. But that rarely happens. The atomic transition line width is denoted by Δν. The Signal/Noise improves as Nτ, where N is the number of atoms or molecules interrogated per second, and τ is the time over which y(t) is averaged.

One can see from this equation, that as the transition frequency line width, Δν, improves the stability and accuracy potentially improve. The longer the atoms or molecules can be interrogated, the smaller is  Δν. In a cesium-beam atomic clock, the atoms can only be observed for a few milliseconds. When the cesium fountain was invented, the observation time went up to nearly a second, and the accuracies and frequency stabilities achieved improved greatly as well.

One can also clearly see from this equation that the higher the atomic transition frequency the better can be the accuracy and frequency stability. The cesium transition is a microwave frequency. By going to optical and ultraviolet frequencies great advances have been achieved in accuracy and frequency stability. These frequencies are about 100,000 times higher than the cesium microwave transition. In my career time, atomic clock accuracies have improved from 10^-10 to 10^-18; that is a hundred-million-fold improvement.

GPS is One Example

AMAZING. Many Nobel Prize winners have contributed to these incredible advancements in timing technology. Technology has benefited enormously as well. GPS is one great example. The current best atomic clocks are 10,000 times better than are needed for GPS. GPS timing works at the nanosecond level–that is a billionth of a second. That is the time it takes light to travel 30 cm (about a foot per nanosecond).

Official Atomic Time in USA

Since 9 October 1957 NBS in Boulder, CO has maintained an atomic time scale, (NBS-A). The primary cesium-beam frequency standard moved to Boulder in 1954, but time was broadcast from WWV in Beltsville, Maryland. WWV then had a precision quartz-crystal clock and was still getting its time from USNO.

A Millionth of a Second

On 24 April 1963, Jim Barnes and Lowell Fey carried a portable quartz-crystal-oscillator clock from Boulder to Beltsville, Maryland, and back with a precision of 5 µs (A microsecond is a millionth of a second). Then, timekeeping commenced in Boulder using an ensemble of precision quartz-crystal oscillators. Their portable clock trip took NBS-A time to Boulder, and the primary frequency standard was just across the hall. This gave an accuracy for NBS-A to ten significant digits. This was ten times better than the Earth as a clock.

Generating Official Time for the U.S.

Jim Barnes then wrote the first atomic-clock time-scale algorithm program to use the calibrations from the cesium-beam atomic frequency standard across the hall. He then used the calibrated quartz-clock ensemble to carry time forward until the next calibration. When Jim became the Section Chief, I was given the responsibility for generating official time for the United States. I did that for most of my 32 years we lived in Boulder, Colorado.

Algorithm, AT-1 Still Ticking

I believe the Lord gave me the algorithm, AT-1, in 1968, for generating official time for the USA. Then we had an ensemble of eight atomic clocks and the US primary frequency standard to work with. The AT-1 algorithm optimally combines the readings taken from an atomic clock ensemble. The computed output of that algorithm is designed to be better than the best clock in the ensemble. Significant improvements have been made to AT1 by my outstanding colleagues and friends over the years. New and different kinds of clocks have been added with their own challenges and improved performance differences.

With those improvements, as far as I know, AT-1 is “still ticking” today. In 2018, I received the IEEE $10,000 Keithley Award, “For leadership in time determination and precise timing instruments.” I thank the Lord for His help in this work. It has been most insightful and enjoyable.

A Two-Part Device

For human-kind of timing, we can think of a clock as a two-part device. First, a clock has a periodic event device that oscillates at a steady frequency. Second, it has a counter to count those oscillations. For example, most wristwatches and clocks today use a quartz-crystal tuning fork as the oscillator or periodic event device. It oscillates at 32,768 Hz (cycles per second). A 2^15 binary divider is then used to generate one-second intervals, which are then counted to give you a display of hours, minutes, and seconds for your clock or wristwatch.

When measured precisely, we know that every clock is oscillating at the wrong rate and its time is in error. The only clock that is right is the one we define to be right. For the USA, it is UTC(NIST). For the world, it is UTC (Universal Time Coordinated.) Official world time used to be Greenwich Mean Time (GMT). The name was changed from GMT to UTC in 1972, with the introduction of “leap-seconds” as needed to chase the earth’s fluctuations in time.

A Momentous Day for Timekeeping

Friday the 13th of October, 1967, was a momentous day for timekeeping. The world community shifted from astronomical timekeeping to atomic clocks for keeping time. Atomic clocks have been shown to be much more accurate than any astronomical phenomena. And as mentioned before, atomic clocks have improved by a factor of ten about every seven years. This is like Moore’s law. Today, accuracies of 0.1 picoseconds per day are realized. This is ten thousand times better than is needed for the atomic clocks in GPS. A picosecond is a million-millionth of a second.

A New Definition of The Second

On that day in 1967 the world received a new definition of the second. It is defined as, “9 192 631 770 periods of the ground-state hyperfine transitions of cesium-133.” The previous definition was the Ephemeris second, which is defined by the Earth’s motion around the sun, as well as lunar motion. It is better than a second for timekeeping purposes. The above oscillation frequency for cesium was arrived at by the Paris Observatory, the Greenwich Observatory, and the United States Naval Observatory. The astronomers involved were Bernard Guenot, Humphrey Smith, and William Markowitz, respectively.

I was privileged to know all three of these gentlemen. The 9 192 631 770 periods agreed with the Ephemeris second, as these three gentlemen determined. The cesium definition remains today. With the high accuracies that have now been achieved in atomic clocks, a new definition is a major topic among the scientists involved.

What is Time?

“What Time is it?” is a very different question than, “What is Time?” The most important “time” is God’s TIME. Yet, most don’t have a clue what God’s TIME is. I explain God’s TIME in my two books: It’s About Time and Time & Eternity, The End-Times & Beyond Revealed,” as best I can. Here, I have discussed “time” as generated by humans. In my books, I discuss its relationship to God’s calendars and His TIME. I also discuss what the Apostle John means, “time no longer (Rev. 10:6).” The concept of God’s “One Eternal Round” is profound as well. This is a fun trip through understanding what time is and what time isn’t. Perhaps for more fun for the academics across the world than for my Christian compatriots. But, knowing where we are in God’s TIME should be very important to my academic friends as well.

Time is Metaphysical

It is important to know that time cannot be extracted from the Universe; it is metaphysical. It is an idea in our minds. My dear friend, emeritus professor of philosophy, Chauncey C. Riddle, has the best definition of time that I have seen. He shares, “Time seems to be the possibility of change.” This was particularly interesting to me, because in my master’s thesis, the metric developed optimally measures the change, in a variance sense, in the timekeeping rate of atomic clocks. The world knows it as the “Allan variance.”

As I Google the “Allan variance,” today I got 3,550,000 results, and the usefulness continues to grow. I believe the Lord inspired me in this as well. In 2016, the IEEE/UFFC celebrated the 50th Anniversary of the publication of my thesis. They published a special issue with 16 different papers highlighting different uses of the Allan variance.

At the conference, they gave me the highest IEEE/UFFC award with the citation, “For seminal work to the UFFF community regarding time determination, time prediction, time dissemination and timekeeping through contributions to atomic frequency standards, space-based navigation, time and frequency stability analysis, time-scale algorithms, and timekeeping devices.”

Time Is Not Time

So, time, as we use it and define it, is not time, but a time interval. Scientists assume time runs uniformly throughout the Universe—including Einstein’s relativistic considerations. We contracted with Professor Neil Ashby to do the relativity equations needed for GPS. We are good friends and have written several papers together. Scientists share nothing of time-warp events, which have been documented. We know from our UFT experiments that time and space are mortal limitations. The scientist’s assumption above is incorrect.

God’s Physics

In God’s physics, we learned of a fifth dimension outside the four relativistic dimensions of time and space. We call it the Eternity Domain. This is where God and His angels do their work in the Kingdom of Heaven. Under God’s direction, the Kingdom of Heaven is perfectly organized. That is why the Lord asks us to pray, “Thy Kingdom come, thy will be done on earth as it is in heaven.” Sincere prayer takes us into the “Eternity Domain” where we may learn the TRUTHS of GOD and help bring heaven on earth!

Where Are We in God’s Time?

A significant portion of both of my books deals with where we are in God’s TIME. Please go there to learn what I have learned about God’s TIME. Knowing God’s TIME and preparing for eternity is the most important thing we can do and help others to do. Most of my energies are spent in this direction. I ask the question of the Lord, “What is Thy will to best help me to serve today?”

The Lord never directs every step in our lives. Given the incredibly important gift of free choice, which is part of our intelligence, He wants us to think for ourselves. TO THINK! That sounds exciting. We grow emotionally, physically, mentally, and spiritually in that Divinely designed process of using our agency to use our time and talents to serve.

THINK – LEARN – SERVE – LOVE!!!

“Seek learning even by study and also by faith (D&C 109:7).” To think and learn the TRUTHS of God that we may better love (Matt. 22:36-40) and serve (Mosiah 2:17). My personal joke is to learn faster than I forget! THINK and LEARN and SERVE and LOVE!!! Therein is the greatest joy in time and eternity. Wise men sought for and found the Savior of the World anciently. Wise humans today are doing the same.

One who thinks comes to Christ in humility. There he/she enjoys the fruits of faith, repentance, and receiving of His mercy and grace. He/she receives the greatest of joy in this life and a fullness of joy in the life to come. It’s about time and eternity! I REJOICE in all the Lord has taught me about time and eternity. But, I am still a babe in the woods. This I know, He is the Way, the TRUTH, and the LIGHT, and the life (John 14:6).

David W. Allan

Photo:  CC Wikimedia

 

Time And Eternity – End Times Revealed

David W AllanI am pleased to have finished my new book, Time & Eternity –  End-Times & Beyond Revealed. I have just sent a draft off to my son-in-law, Kevn Lambson, to format. He did a super job with my first book, It’s About Time, which was the forerunner to this blog site,  Its AboutTimeBook.com  Kevn may help me with the audio version as well. He has a great voice. We are hoping to have both ready this fall.

The contents of the book are how to best prepare for the Lord’s Coming. It is a book of hope and gives insights into God’s infinite love for each of His Children, as manifest in His perfect plan of happiness. Below is a  draft of the information that will be on the back cover of the new book, which will be written by my publisher, Boyd Tuttle.

Draft  of the BACK COVER

David W. Allan, the praying physicist, does his science with the help of the Lord, and what he has accomplished with the Lord’s help is amazing. In his meek and humble demeanor, he gives credit to the Lord for what has come forth from his hands, and he feels enormously blessed as well to have enjoyed—even now in his 86th year of orbiting the sun—the association of outstanding colleagues, who have contributed to his work and still seek his counsel.

He learned with his master’s thesis at the University of Colorado to trust in the Lord, which gave birth to the Allan variance. His message to us is, “We may not know the future, but the Lord does. To do His will makes all the difference.” If you Google “Allan variance” you will get about forty-five million hits.  And, the “Allan Variance” usefulness is still growing.

He has over 130,000 visits to his book’s website: www.ItsAboutTimeBook.com, from over a hundred nations, and it is ever increasing. Over a thousand people have based their research and Ph.D. theses on his work.

Allan has given lectures across the world, and his master’s thesis is the most cited publication to ever come out of the Department of Commerce, where he worked for thirty-two years, and his career has a long list of other exciting inventions, which he credits to the Lord. The variances he and his colleagues have developed allow one to see and characterize the different spectral-noise colors in nature that were not appreciated before.

Historically, time was determined astronomically. But then the length of the “second” was redefined in 1967 from astronomical to atomic. In 1968, Allan wrote the algorithm, AT-1, to optimally combine the readings of an ensemble of atomic clocks to generate official time for the USA, and with improvements by colleagues, AT-1 is still “ticking” today.

The “Allan variance” was used to characterize the atomic clocks to make GPS as accurate as it is. Time accuracy has improved a billionfold in Allan’s lifetime, and his contributions are significant. The output of his AT-1 algorithm is always better than the best clock in the atomic clocks contributing to the ensemble and optimally combines all their time readings.

In 2011 the international telecom community gave him the “Time Lord” award in Edinburgh, Scotland. In 2015, the International Navigation community asked him to write and give a paper, as well as chair a panel in St. Petersburg, Russia, because of the importance of the Modified Allan variance for navigation.

In 2016 the IEEE/UFFC gave him their highest award with the citation, “For [his] seminal [work]…” In 2018, the IEEE, which has the largest scientific papers archive in the world, made an oral history of his life: https://ethw.org/Oral History: David_W._Allan. In 2021, they made him an IEEE Fellow.

Now, the Lord has impressed upon him to write another book: TIME AND ETERNITY, THE END-TIMES AND BEYOND REVEALED. This book could be a “game changer” in helping people prepare for the Lord’s coming. His insights and perspectives are clearly inspired and of great worth.

_______________________

David W. Allan

P.S.  My goal is simple, “Help the people of the world know of God’s infinite love and of His perfect plan of happiness in the midst of all our imperfections, and to be of service to you.” I have come to know that the  most important unit in time and eternity is FAMILY. My greatest blessings are to have a wonderful family and to know the Creator of it all. He has taught me how to be a creator and I rejoice in HIs infinite love. I believe one of my most important proofs is validating the scriptures scientifically. And, LDS Living picked up on it as well. Both of my books treat this important topic as well to counter the growing atheism in the world.

A discount price is available for my new book on the book’s preorder page.

There Should Be Time No Longer

Truth is knowledge of things as they are, and as they were, and as they are to come. (D&C 93:24)

It’s About Time to learn the “Truth” about TIME!  I have been called, “Mr. Time.” I am not; but, I know Who is!  Also, being 84 years old this month (25 September 2020), and remembering the wonderful colleagues I have been privileged to work with over the years, I felt impressed to write some interesting insights regarding TIME from both a scientific and religious point of view.  I use the above Biblical phrase to catch our attention to the enormous increase in timekeeping accuracy we have enjoyed over the years in contrast to this scripture, and the benefits have been enormous; GPS is a classic example.  The title may appear contradictory, but you will see at the end, it is not.

Timekeeping accuracy has increased a billion fold in my lifetime.  It has been so exciting to work with and know many of the players in this rapidly advancing field over my sixty years doing time and frequency metrology (the science of measurement).  Many of them are Nobel laureates and their contributions have been enormous.  Many have passed on.

Here I will share some fascinating scientific aspects of time development, and then conclude with what is really most important — the religious truths about TIME.  We have before us the 2020 autumnal equinox (22 September 1331 UTC (7:30 a.m. MDT)), when the spin axis of the earth is exactly at 90 degrees to the line from the center of the earth to the sun.  And the time for that changes every year because the time for an earth  orbit around the sun is out of sync with the spin rate of once per day of the earth with respect to the sun.  Everyone knows the number of days in a year is not a whole number bringing about the leap year phenomena.  Interestingly and in contrast, If you were on the unique planet Mercury, you would see that the Mercury day and year are harmonically synchronized.

Starting With Solar Time

As science came of age following the renaissance, we started out with solar time, where the length of the second was 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day — making the length of the second 1/86400 of an average mean solar day (60 x 60 x 24 = 86400 seconds in a day).  Then astronomers noticed random variations in solar time.  Because of these variations, in 1956, the ephemeris second became the next definition as decided by the International Bureau of Weights and Measures (BIPM): the second was defined as the, “fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.”  A tropical year is the time between one vernal equinox and the next (365.24219 ephemeris days in the year 2000).  Earth time (solar-time) has slowed down about 60 seconds since the year 1900.  Astronomical time accuracy is like +/- 0.0002 of a second of error in a day.  This seems small, but for a system like GPS, this error is enormous where GPS needs about a billionth of a second level of accuracy using atomic clocks to work as it does.

Atomic Clocks

In the 1940s Nobel Laureate, I. I. Rabi, thought of atomic clocks.  I had breakfast with him in 1983 in Philadelphia, PA, when he received the first Frequency Control Symposium Rabi Award named after him.  I felt greatly honored a year later to be the second recipient of the Rabi Award.  Based on Rabi’s concepts the first atomic clock was invented in 1948-49 by Harold Lyons, et. al. at NBS in Washington, D.C., based on an ammonia-molecule microwave resonance, but its accuracy was not significantly better than astronomical time.

However, because of its excellent short-term frequency stability, the first atomic clock I worked on in 1960 was an ammonia maser (microwave amplification by stimulated emission of radiation).  Shimoda, Wang, and Townes wrote a pioneering paper on ammonia masers.  I got to know all three of these gentlemen and great scientists from Japan, China, and the USA, respectively.  Charles Townes went on to invent the LASER (Light Amplification of Stimulated Emission of Radiation).

Can you imagine how many billion laser scanners there are now in the world — every grocery store checkout counter, etc.?  And now also, lasers are fundamental building blocks for the most accurate clocks in the world.  The uses of lasers are enormous, laser ranging, and it goes on and on.  It is fun to think that lasers were given birth in time and frequency metrology.

Essen and Perry at the National Physical Laboratory (NPL) in Teddington, England, began atomic-clock timekeeping in June 1955 using a resonance in the cesium-133 atom (not radioactive).  The accuracies increased and in 1967 on Friday the 13th of October that year the second was again re-defined and the definition remains with us to this day:

“the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom” (at a temperature of 0 K)”.

One may ask where that number came from — tying the astronomical measurement of time to that of an atom?

The Role of Standards Laboratories

The National Bureau of Standards (NBS), where I worked, had a standard-time transmission radio station (WWV) in Beltsville, Maryland.  That signal was received at the United States Naval Observatory (USN0) and at NPL in the UK.  Following several years of work, Essen and William Markowitz from the United States Naval Observatory (USNO) determined the relationship between the hyperfine transition frequency of the cesium atom and the ephemeris second.  Using a common-view measurement method based on the received signals from radio station WWV commonly received at NPL and USNO, and gave us 9,192,631,770 Hz (cycles per second) for the cesium frequency with respect to the ephemeris second.

Markowitz, an astronomer in charge of time at the USNO, was an interesting guy.  He told me one time that physicists don’t understand time.  He is right, but neither do astronomers.

The famous Greenwich (zero) meridian-line goes through the Royal Greenwich Observatory.  Later, for timekeeping purposes, RGO moved down to Herstmonceux Castle in southern England.  Humphrey Smith, who was the director of time services there, tells a little bit about that in this audio link.  This is the meridian line used by all navigation systems and for mapping.

Before atomic clocks, quartz-crystal oscillator-clocks were our timekeepers, and every laboratory and observatory had some of these in a very good environment to provide the best frequency stability and hence timekeeping ability.  James A. Barnes as part of his Ph.D thesis had developed the NBS-A time-scale algorithm to calibrate three quartz-crystal clocks using Roger Beehler’s (NBS) primary cesium-beam standard across the hall at the NBS-Boulder, CO, laboratories.  Then Jim and Lowell Fey carried one of those quartz clocks to WWV in 1965 to transfer the time from Beltsville to Boulder to set the time for the NBS-A time-scale algorithm, and to improve the timekeeping for the USA.

Best Atomic Clocks

I was working on my master’s thesis at the same time as Jim.  That fall we invited the makers of the best atomic-clocks to do a comparison at our lab in Boulder.  The two-sample variance, which was named the Allan variance and which came out of my thesis, became the analysis tool to compare all these new and exciting atomic-clock timekeeping devices.

I had used this tool to characterize some unusual time variations in two of the NBS radio stations: WWVL and WWVB, and I prepared a paper on same, which was to be given in Ankara, Turkey.  So in August 1967, I arranged to visit the primary timekeeping centers on my way to Ankara.

James Steele was my kind host at NPL and Humphrey Smith at RGO (Herstmonceux Castle).  I was greatly impressed with their work.  My next visit was with Bernard Guinot, at the Paris Observatory (OP).  We became good friends over the years and had many great discussions regarding time-scale algorithms, clocks, astronomy, and the like.  He was then head of the BIH (Bureau of the hour) and responsible for generating time for the world.

Jim Barnes became Section Chief and turned over the timekeeping responsible to me.  I then had an ensemble of eight commercial atomic clocks, and I wrote the AT-1 algorithm in 1968, to combine their readings in an optimized way using the Allan variance to characterize their varying timekeeping performances.

Dr. Guinot sent Michael Granveaud to Boulder to work with me, and then Michael returned and wrote ALGOS, which still keeps time for the world.  AT-1 is a better algorithm, but ALGOS is more politically correct working with all the nations who contribute across the globe.  With significant improvements by my colleagues, AT-1 is still keeping official time for the USA today.

Guinot was particularly intrigued by the paper that Helmut Hellwig, Dave Glaze, and I gave in Cagliari, Italy, on “An Accuracy Algorithm for an Atomic Time Scale.”   This paper shows how to combine accuracy and stability nicely.  It is highly relevant today with the amazing accuracies and stabilities of optical clocks.  In simple terms, accuracy can be thought of as agreement with some standard, and stability means minimal changes over time.

How Accurate can Clocks Be?

One of my colleagues and a dear friend, Dr. Elizabeth Donley (now Chief of the NIST Time and Frequency Division in Boulder, CO), has written an equation, which shows the potential accuracy and stability of atomic clocks in terms of the square-root of the Allan variance.  From it, she shows that the potential accuracy can improve with the frequency of the resonance, with the signal-to-noise, which improves as the square-root of the averaging time used to determine the frequency, and with the line-width of the atomic resonance.  From this equation, one can see why optical clocks now being researched are reaching eighteen-digits of potential accuracy and stability.  Optical atomic clock frequencies are about 100,000 times higher than the cesium microwave frequency.

The accuracies now being achieved are like measuring the distance to the sun (93 million miles) to 0.003 of the width of a human hair.  I pulled out one of mine to measure it, and I don’t have many to spare!  This is like 0.1 picosecond/day.   GPS operates at the billionth of a second accuracy level (nanosecond); a picosecond is a thousand times smaller than a nanosecond!  And the end is not in sight with things improving by about a factor of ten every seven years — Moore’s Law.  It has been a great privilege to know some of the scientists helping make this continued incredible progress.

Variations always occur in nature and in all timekeeping devices.  There is no perfect clock!  With the help of colleagues over the years, we have developed statistical techniques (Allan variance, the Modified Allan variance, and the Time variance) giving a full spectrum of colors of these variations.  All three of these have become IEEE international standards, and are broadly used in time and frequency metrology, in navigation, and in telecom systems.

We have shown that using the classical variance that one learns about in a college statistics class is like taking a black-and-white picture of a rainbow; you get intensity, but no color.  The above three variances give you both intensity and full color for the common power-law spectral variations we see in clocks.  Hewlett Packard asked me to write an application note for them, “The Science of Timekeeping.”  In it is a description of the spectrum of variations in timekeeping devices:

The different slopes denote different colors of time variations.  This application note was published in 1997, and the clocks now are about a thousand times better than the best shown here.  I prepared a tutorial for the IEEE web site on the development of these three variances:   The ordinate on this chart is the square-root of the Allan variance times the prediction or timekeeping interval.  Notice that the variations in the earth’s spin rate are one of the most divergent time-varying slopes of all in the long-term.

A lot of the above information is also contained in my IEEE ORAL HISTORY, which Dr. Donley came to our home and recorded on  5-6 November 2018. I wrote this application note with the help of my good friends, Prof. Neil Ashby, who did the relativity equations for GPS, and with Cliff Hodge, of NPL, who is a space clock expert.

Where Are We Going From Here?

As technology continues to escalate, and morality is declining due to increasing secularism and  materialism.  Where are we going?  I believe we live in the most exciting time in history, but I also believe in the above scripture with exciting promises associated therewith.  Another translation reads, “that no more time should intervene and there should be no more waiting or delay.” (Amplified Bible)  The last five chapters of my book, “It’s About Time”,  deal with this question, and I show the difference between man’s time and God’s time.  The basic premise of the book is that if something is true in science, and something is true in religion, they must agree.  Hence, the subtitle is “Science harmonized with religion.”

“It’s About Time” to know the truth about who we are and where we are in God’s time.

On 25 September 2020 the VIRTUAL EXPO, I will be sharing details on where we are in God’s TIME.

On 26 September 2020 join in national and  international prayer to “heal” our land and forgive our sins.

On 27 September 2020, let us make it a sacred Sabbath drawing our selves and as many as we can closer to God.

We now have proof that America is the “Promise Land” spoken of in the Book of Mormon, and it is critical for the inhabitants there of to serve God or they will be”Sept off.”

The evidence of God’s love is profound for those who have eyes to see and hearts to feel.  He is inviting us to graduate into His millennial paradisaical glory with a new heaven and a new earth — exciting, but the end of worldliness has to come first. when the above scripture and the Amplified version take on great significance.  We are greatly blessed to live at this TIME in history.

Most look to the dark, but let us look to the light; IT IS GLORIOUS.  The ride home to celestial realms of glory will be more spectacular than anything we can imagine.  There we will be ONE with God in fullness of joy.

David W. Allan