By David W. Allan

plain-language version, prepared for the regular reader with AI help.

The science and the stories are his; the explanations in plain words are added so anyone can follow along, highlighting the deep harmony between his precision scientific breakthroughs and profound spiritual convictions and insights.

It has been exciting to watch, and to be part of an amazing increase and blessing to humankind over my 90 years on this planet: timekeeping has become more than a billion times more accurate and stable. The benefits have been enormous. GPS is the first everyday working proof of Einstein’s relativity, and now GPS is a household word. One of my great blessings is that I got to know and work with several of the great people who helped to bring this increase about.

From Watching the Sky to Using atoms

For thousands of years, people told time by watching the sky — the sun, the moon, the stars, and the rotating Earth. Going from that kind of astronomical timekeeping to atomic time was an incredible giant leap forward—blessing humankind enormously.

Since Isidor Isaac Rabi invented the concept of atomic clocks, we first saw Harold Lyons and his team create the first physical atomic clock. They locked a quartz-crystal oscillator clock to an ammonia molecule absorption line. Later came the ammonia maser, based on Charles H. Townes’s invention following Rabi’s idea. That is what I worked on when I went to the National Bureau of Standards (NBS) in Boulder, Colorado, in 1960. (See “Flash” Personal Revelation: https://itsabouttimebook.com/flash-personal-revelation/ .)

Then Norman Ramsey came up with a clever idea in 1949 called the separated-oscillatory-fields method, or the Ramsey method. By separating them, the cesium atoms could be viewed for a longer time adding great finesse in determining the frequency of the atoms. As I will share later, that knowledge changed the world of timekeeping as that frequency gave us the first non-astronomical definition of the unit of time the “second.” The Ramsey method is the core idea behind the cesium-beam atomic clock. Lyons and his team built one as a frequency standard, but never operated it continuously as a clock.

In June 1955, British physicists Louis Essen and Jack V. L. Parry built the world’s first working, highly accurate cesium=beam atomic clock at the United Kingdom’s National Physical Laboratory in Teddington, England, using the Ramsey idea. Every commercial cesium-beam atomic clock since has followed this pattern.

Today, about half of the nearly 500 atomic clocks that contribute to world time (TAI and UTC) are the work of Len Cutler and his team at Hewlett-Packard — the 5071A cesium-beam atomic clock — who greatly refined this Ramsey idea. I got to work closely with them when HP hired me as a consultant from 1973 to 1977.

I also got to know Norman Ramsey well; he even attended one of my lectures in Boulder on millisecond pulsar timing coming from our Galaxy. In 1959, he and his team made another great contribution by inventing the hydrogen maser, a spin-off of Charles Townes’s ammonia maser. The excellent short-term timekeeping steadiness of hydrogen masers is still the backbone of NASA/JPL’s Deep Space Network, and has been for more than half a century for viewing such spacecraft as Voyager.

An award was named after Rabi because atomic clocks have had such an impact on society. Sam Stein arranged for me to have breakfast with Professor Rabi when he received the first of these awards at an International Frequency Control Symposium in Philadelphia in 1983. Because the Allan variance — a yardstick I developed for measuring how steady the time of a clock is — taught the world how to best use atomic clocks, how to keep time with them, and how to predict time with them, I became the second recipient. I felt greatly honored. I feel the Lord truly helped me with the inspiration for my thesis in 1965, and I give Him all the honor and the glory.

The old way: radio time from the stars

Beginning in 1936, the NBS radio station WWV broadcast official time for the USA from Beltsville, Maryland. The station got its time from the United States Naval Observatory (USNO) nearby in Washington, D.C. USNO was and is one of the best astronomical observatories in the world. People at USNO would listen to the WWV broadcast and send the station corrections to keep WWV lined up with UT2 — smoothed Earth time, which had the regular seasonal wobbles taken out.

UT1 is the Earth’s actual position against the stars, the moon and the sun. UT1 is what a navigator at sea needs, along with a sexton and good clock to find his position at sea. The famous John Harrison solved the longitude problem with an extremely clever seaworthy chronometer centuries ago. (See What Time Is It?)

As soon as Essen and Parry started keeping time with their cesium-beam time standard, we finally had a chance to compare atomic time with astronomical Earth time. Over the next two and three-quarter years, using WWV signals received simultaneously in both places (a method called common-view), they made careful measurements between the National Physical Laboratory and the United States Naval Observatory.

The people at USNO were measuring Ephemeris time — time read from the Earth’s yearly trip around the sun. That is a challenging measurement since the Earth as a pendulum swings only once a year as it orbits the sun. Even after averaging for years, it is only good to about 0.3 seconds. William Markowitz solved that problem with his invention of a dual-rate moon camera. The moon moves across the sky faster than the stars, so by carefully measuring both the moon and the stars at the same time. They improved the  accuracy for UT2 by nearly ten times. Markowitz also used tropical year data — measurements of the year from one spring equinox to the next — to refine his astronomical measurements.

Through this historic experiment, they arrived at 9,192,631,770 cycles per second (Hz), plus or minus 20 Hz, for the cesium transition frequency. In the 1960s, Dr. Markowitz listened to a talk I gave in Boulder. He came up to me afterward and remarked, “You physicists do not understand time!” His knowledge of astronomical time was superior to anyone else’s in the world at that time.

In 1967, the General Conference on Weights and Measures (CGPM), through the International Bureau of Weights and Measures (BIPM), gave the world the new official definition of the second based on Essen and Markowitz’s foundational work: “The second is 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 caesium 133 atom.”

In plain words: one second is defined as that exact number of vibrations of the microwave photon originating from that specific transition of a cesium-133 atom. Science and the world community have benefited enormously once atomic timekeeping began. GPS is just one example. (See the BIPM definition of the second.)

As mentioned, Markowitz used tropical year data to refine his measurements. Recently, our son Nathan and I have analyzed 200 years of tropical year data using today’s statistical techniques, and we discovered significant resonant frequencies nobody knew about before. (Our paper is titled “Statistical Analysis of Tropical Year Data”: https://docs.google.com/document/d/1QSqBT8dtIu39qXt8j31sLGb7svgE6Oug3mzKkN3P39Y/edit?tab=t.0 .)

Building America’s clock in Boulder

In 1963, Jim Barnes and Lowell Fey carried official US WWV time to NBS in Boulder using a portable quartz-crystal clock accurate to 5 microseconds — five millionths of a second. At the bureau in Boulder, we had three other quartz-crystal clocks keeping time, with their rates checked against the NBS-II primary frequency standard. Jim’s Ph.D. thesis in 1965 became the basis of a method for keeping time in Boulder after that transfer. (See James A. Barnes, “Atomic Timekeeping and the Statistics of Precision Signal Generators,” Proceedings of the IEEE, February 1966.) Jim moved into major leadership roles and became the first Division Chief of the Time and Frequency Division in 1967.

I received the responsibility for the timescale and for generating US official time, UTC(NBS). We acquired several commercial cesium-beam frequency standards, which had become available by then.

Let me share with you some basic timekeeping lessons we learned:

Free-running time stability: We learned that a clock left free-running is inherently more stable than one that is steered or corrected.

Every time measurement is imperfect: When you measure a clock, you have measurement noise, clock noise, and every clock is affected by its environment. We worked to make the measurement noise negligible, and we built special environmental chambers to minimize environmental disturbances.

Predicting the timing error of a clock: Every clock is wrong — but if you know how wrong it is, then that is useful timing information.

Time is defined: The only clock that is “right” is the one you define as right, since time is a human-made quantity; it can even be a software clock. Once you characterize how a clock behaves, you can predict its time ahead in an optimum way.

I took a different approach than Jim did with his three quartz-crystal clocks. Since I could measure the time differences between the commercial cesium-beam standards on a regular basis — without needing a laboratory primary standard, which can only measure frequency, not time — this gave me a fresh perspective. Each clock has its own personality, as it were. Since they are independent, each one’s time prediction error is unique.

I reached out to Jim’s outstanding mathematical skills, and we used the Lagrange method of undetermined multipliers — a way of finding the best weighting when you cannot know the perfect answer directly — to estimate the optimal weight each clock should have based on its own independent performance. You can never know a clock’s true performance exactly since you have no perfect clock to compare it against; that is why the Lagrange method is so vital.

We found a good noise model for all the commercial cesium-beam standards:

• Short-term: Their frequency variations were random and uncorrelated, as the clock’s servo hunted for the known frequency. This is white noise frequency modulation (FM). You can think of white noise like the flip of a coin; each flip has no memory of the past.
• Longer-term: Their variations behaved as flicker-noise FM, which is a fractal.
• Very long-term: Essentially all commercial cesium clocks behaved as a random-walk FM noise process. Random-walk FM is like remembering every single flip of the coin. For example, if heads, you take one step forward; if tails, one step backward. Your final position is a total memory of every previous flip of the coin.

It is interesting that the variations in the rotation rate of the Earth are also flicker-noise FM–a fractal. And the time error accumulations to nearly a second in a year for the Earth. I share later in this blog article the amazing newly developed NIST/JILA optical ytterbium clock. Its white-noise FM would only accumulate to 2 picoseconds (2 trillionths of a second) in a year. The Earth’s rotation rate becomes flicker-run  FM after one cycle per year and then the time dispersing grows must faster as τ².

The levels of each kind of noise were different for every atomic clock. I used an exponentially filtered estimate — a weighted average that favors recent measurements. This was easy to digitize. We optimized the filter time constant for each clock. This filter was shown to be optimum for both the white-noise and random-walk kinds of noise, and it was nearly optimum for flicker noise as well. These noise levels were determined for each clock.

If you have three or more independent clocks, you can calculate the individual noise level of each clock from a sigma-y versus tau diagram, The square-root of the Allan variance is σ_y(τ), where τ is the averaging time.

Armed with my master’s thesis, we could determine these noise levels for each clock and optimally tune each one’s predicted time with the AT-1 algorithm. This optimized our atomic clock timekeeping output. I had a counter precise to 0.1 nanosecond — a ten-billionth of a second — to measure the time differences between all the clocks. I measured the clocks once each working day, which made the measurement noise negligible: (10^-10 s/86400 s/day) = 1.2 x 10^-15 for each daily measurement. The cesium-beam atomic clocks were not nearly that good.

When hydrogen masers were added to our ensemble of cesium-beam atomic clocks, I discovered an interesting mathematical problem. Because of their outstanding short-term stability, they would take over the whole average. This happened because each clock was partly comparing itself with itself as a member of the ensemble; the best clock looked artificially better and better with each measurement cycle.

I solved this problem under the assumption that the timing errors were normally distributed, I removed this structural flaw from the algorithm so the estimated timing errors were completely unbiased. This provided a massive benefit: now the best clock is used to its full potential, while even the poorest clock is utilized in the best possible way to improve the composite result as well.

At each measurement cycle, I implemented a 3-sigma rejection rule. Any clock whose timing error deviated by more than three sigma was automatically removed from the AT-1 computation. I remember one measurement occasion when three clocks were outside that limit; the algorithm caught all three and isolated them from the calculation. Each was then carefully brought back into the ensemble later so as not to disturb the stability of the AT-1 output.

The AT-1 timescale algorithm was so successful that we sponsored a Timescale Algorithm Symposium and invited the world’s leading atomic clock experts. Brilliant guest workers came to Boulder to collaborate with us: Sigfrido Leschiutta (director of time for Italy) along with Giuseppa Rovera; Kazuyuki Yoshimura from Japan (who was also Japan’s Go champion); a guest worker from China; and Michael Granveaud from the BIH (Bureau International de l’Heure), was sent by the world director of time, Bernard Guinot. Michael took these concepts back to France and wrote the ALGOS algorithm, which is used to generate international time, TAI and UTC. Dr. Guenot later moved these international time responsibilities from the BIH to the BIPM.

The BIPM, Israel, Italy, and Switzerland have all incorporated core AT-1 features for their official time.

Howard Machlan, who worked for me, built an outstanding environmental chamber for our eight cesium-beam atomic clocks. With it, we were able to prove that our timescale was steadier than that of the Naval Observatory — even though they had about 40 cesium clocks and processed their data a month after the fact! Measurement noise and environmental affects can be very important. The AT-1 algorithm gives the optimum estimate of time at every single measurement cycle in real time.

While working with the GPS architects, I shared the virtues of AT-1 and convinced them to ensemble the GPS clocks to avoid a single point of failure, and later on they did that.

The foundational equations for the AT-1 timescale algorithm are shared in two papers: Chapter 9 of NBS Monograph 140, and “A Study of the NBS Time Scale Algorithm” in the IEEE Transactions on Instrumentation and Measurement. Jeff Sherman and Mike Lombardi have since done a wonderful job explaining how NIST continues to generate UTC(NIST) using the AT-1 algorithm. (See How UTC(NIST) Works.) https://www.nist.gov/pml/time-and-frequency-division/time-realization/utcnist-time-scale/how-utcnist-works .

What I shared with AI

I shared the following testimony with AI:

“I believe the Lord gave me the AT-1 timescale algorithm based on the Allan variance to optimize the time generated by an ensemble of atomic clocks. I had that operative in 1968 and I believe it is still being used by NIST’s Time and Frequency Division today, while timekeeping accuracy has evolved a billion fold in my 90 years.”

This was the AI’s response, in brief:
The AI confirmed that the AT-1 algorithm remains the vital baseline for official U.S. time today. UTC(NIST) — the real-time signal that synchronizes financial markets, telecommunications, and national infrastructure — is continuously generated as an extension of the free-running AT-1 timescale, the framework pioneered on an 8-bit PDP-8 computer back in 1968 with Fortran IV programming language. It also noted that the ideas behind AT-1 directly influenced the ALGOS algorithm the BIPM uses to compute International Atomic Time (TAI) and Coordinated Universal Time (UTC) for the whole planet.

Why optical clocks win

My colleagues have derived the above equation, in terms of the square root of the Allan variance — the Allan deviation — that shows how stable and accurate a passive atomic clock can be. It comes from a 2010 dissertation on a ytterbium-ion optical frequency standard. In plain words, here is what it says:

A clock’s steadiness depends on three things. First, the quality factor of its atomic transition, Q — the atom’s vibration frequency divided by the width of its signal line. The sharper the line, the higher the Q, and the steadier the clock. Second, the signal-to-noise ratio: with no special tricks, the signal grows with the square root of the number of atoms you probe — measure 100 times more atoms, and your signal is 10 times clearer. Third, the longer you average, the steadier the result, improving with the square root of the averaging time. 

One sees at once why optical atomic clocks have such an advantage. Their frequencies are about 100,000 times higher than the original microwave clocks — ammonia, cesium, hydrogen, and rubidium. Higher frequency means a much higher Q, and a much steadier clock.

A new second, and no more leap seconds

Recently, I was excited to be invited by Dr. Patricia Tavella, the Director of Time at the BIPM. She is responsible for generating TAI and UTC. She gave me the link to listen to the best time experts in the world at the last CGPM. They gave us a new definition of the “second,” and did away with leap seconds — which is a really big deal. I recommended that in my first book, It’s About Time.

The best part for me was that I was able to give feedback to Patricia on additional information useful to them. I wrote up a blog article about it, “Time, Science and Religion”. There I shared: “The most accurate astronomical measurements are about 1 part in a billion. At the CGPM, D. Calonico from Italy shared that the most accurate atomic clocks are at 2 parts in a quintillion. (2 x 10^-18 ) After the conference, I shared with Patricia the recent better results this year from NIST/JILA of 5.5 parts in ten quintillion. (5.5 x 10^-19 ) This is like measuring the distance to the sun (93 million miles) to about one thousandth of the thickness of a human hair. I pulled out one of mine to measure it, and I don’t have many to spare! The NIST/JILA amazing stability reported was σy(τ) = 3.5 × 10⁻¹⁶ / √(τ/s).”

In that formula, “y” means the fractional frequency — how far the clock’s actual frequency is from its intended frequency, divided by the intended frequency. And σy(τ) is the Allan deviation: the yardstick for how steady the clock is when you average over a time τ. (See the formula above.)

More than a billion fold in my lifetime. How blessed we are.

In my books and on my websites, I share our Unified Field Theory experiments and their far-reaching conclusions. First, time and space are strictly mortal limitations. We discovered a fifth dimension beyond relativity called the Eternity Domain, where God and His angels perform their work, helping us find our way back home to Them. They are not constrained by mortal time, space, or the speed of light, and we demonstrate this experimentally.

Time as we utilize it globally is a human, mathematical creation. God’s TIME is one eternal round, motivated by His infinite love for all of His children.

I share this perspective in full detail in my latest book: THE INFINITE ATONEMENT OF JESUS THE CHRIST, AND ITS SIGNIFICANCE IN THE LAST DAYS. It represents my absolute best effort to bring the eternal truths of science and religion into perfect harmony — available from my publisher, Boyd Tuttle at Digitalegend.com, on Amazon, and at ItsAboutTimeBook.com.

My ultimate goal is simply to get the WORD out. It is not about money; it is entirely about TRUTH. And TRUTH is LIGHT — just like the word carved on the keystone at the entry of our home, which is warmed in the winter and cooled in the summer by the Light of Christ streaming from the sun.

As entropy winds the universe down, the Infinite Atonement winds it up. As I was asking the Lord how I could better explain the Infinite Atonement, He gave me these equations:

Infinite Suffering + Infinite Joy = The Infinite Atonement

The Atoning Sacrifice + The Atoning Bridge = The Infinite Atonement

When the resurrected Lord appeared to the Nephites in North America, they inscribed the three days of the Infinite Atonement in stone: Two Hundred Names for Jesus | It’s About Time. During His three days in paradise He brought great JOY to millions all the way back to Adam and Eve as He taught them the fullness of His gospel as the first part of the Atoning Bridge so they could be resurrected that First Glorious Easter Morning. Then the crowning step to the Atoning Bridge is His Glorious Resurrection. The Atoning Bridge brings a fullness of JOY to all who are true disciples of Jesus. This glorious event is described in the picture on the front cover of my new book where He shows His mother the hosts resurrected with Him. In the scriptures we read:

“He that ascended up on high, as also he descended below all things, in that he comprehended all things, that he might be in all and through all things, the light of truth;  Which truth shineth. This is the light of Christ. As also he is in the sun, and the light of the sun, and the power thereof by which it was made (Doctrine and Covenants 88:6-7).”

“If in this life only we have hope in Christ, we are of all men most miserable. But now is Christ risen from the dead, and become the firstfruits of them that slept. For since by man came death, by man came also the resurrection of the dead. For as in Adam all die, even so in Christ shall all be made alive (1 Corinthians 15:19-22).”

“Adam fell that men might be; and men are, that they might have joy. And the Messiah cometh in the fulness of time, that he may redeem the children of men from the fall. And because that they are redeemed from the fall they have become free forever, knowing good from evil; to act for themselves and not to be acted upon, save it be by the punishment of the law at the great and last day, according to the commandments which God hath given. Wherefore, men are free according to the flesh; and all things are given them which are expedient unto man. And they are free to choose liberty and eternal life, through the great Mediator of all men, or to choose captivity and death, according to the captivity and power of the devil; for he seeketh that all men might be miserable like unto himself (2 Nephi 2:25-27).”

“Come now, and let us reason together, saith the LORD: though your sins be as scarlet, they shall be as white as snow (Isaiah 1:18);”

“And worlds without number have I created; and I also created them for mine own purpose; and by the Son I created them, which is mine Only Begotten. For behold, this is my work and my glory—to bring to pass the immortality and eternal life of man (Moses 1:33, 39).”

In Elohim’s TIME I rejoice in Their Grand Plan of Happiness. I thank the Lord for allowing me to be a blessing to the human family while participating in the great progress in timekeeping accuracy and stability–a billion fold.

Part 4 of 4 (final) in the series “Book of Mormon Geography — And Why It Matters”

In 2010 we took a Book of Mormon tour with Rod Meldrum, and it changed our lives. Keith Merrill — the writer and director of Legacy and The Testaments — had taken the same tour with Rod earlier. He also had a change of heart, from the Mesoamerica model to the Heartland model. He was wishing that he could redo The Testaments to the Heartland model for Book of Mormon geography.

In Part 1 of this series, I shared my three criteria for knowing truth, the first of which is: if God says it, then I know. In Part 2, we read what God has said through His prophets. Now, in this final article, let us look at the physical evidence itself.

The DNA Evidence

Rod Meldrum discovered that a DNA pattern found in the Native Americans of North America — mitochondrial haplogroup X2 — is also found in the Holy Land, but not in Siberia or East and Central Asia, where standard migration theory would require it to be. That is a Middle East genetic marker sitting in the heartland of North America, in the very region where Joseph Smith placed the Nephites.

Stones with the Ten Commandments

The Ten-Commandment inscriptions also show up in stone in North America. There are three distinct examples I know of. One is in New Mexico, where Edna’s cousin James Saline made an imprint of the Ten Commandments stone found near Los Lunas. He got permission from the landowner and showed me the photos. Then we have the famous Newark Holy Stones in Ohio: the Keystone inscription reads in block Hebrew: “Holy of Holies,” “King of the Earth,” “The Law of God,” “The Word of the Lord.” The black Decalogue Stone, carved with Moses and a complete rendition of the Ten Commandments are also in an ancient block-Hebrew script. They were found in a sandstone box in a burial mound in 1860. We visited the Johnson-Humrick house Museum in Coshocton, Ohio, where they are on display.

Duane Erickson, a deceased friend of ours, learned of me going to Russian. He drove all the way from Evanston, WY, to let me take with me a stone that Russell Burrows had given him from a cave in Indiana. Some say the Burrows cave is a hoax, but my good friend Brian Nettles did a personal interview with Burrows authenticating his findings. Shown below are both sides of the stone. I presented the stone to my colleagues at the conference in St. Petersburg, Russia.

Wayne May shared with me that he knows of some eighty such stones. Apparently,  when the Savior appeared to the Nephites at Bountiful they made these stones in remembrance of that sacred experience.

Note: On the front of the stone, the mystic symbol at the top: Native North American word for their Creator “Jehovah.” At the bottom is symbol for Son of my Right Hand.”

On the Back of the stone, the Nail Marks in the hand and in the wrist.

Then we have the following remarkable stone Russell Burrows gave to Wayne May describing the atonement from the cave in Indiana.

We see the mystic symbol denoting the name of their Creator at the top. We see the mark in the hand and the wrist, the Savior on the cross, the three days in the tomb and in paradise, then His glorious resurrection is depicted with His arms outstretched. Under His right arm is the symbol of son of left hand, which is Satan. He has overcome death and hell. We see the indication of the eleven disciples, and on the right the betrayal by Judas Iscariot. The writing to the left authenticates the stone as well. Wayne shared this image with me to do a blog article: Two Hundred names for Jesus. What a jewel this stone is.

The Mounds and Earthworks

Map of Hopewell NetworkThe evidence of the mounds is overwhelming. When the pioneers first arrived, there were an estimated 200,000 mounds across North America; only about 1,000 remain, most destroyed so the land could be farmed. What kind of society could build 200,000 mounds? According to Dr. Roger Kennedy of the Smithsonian Institution, the great City of Cahokia — across from present-day St. Louis — was more populous in its era than London or Rome. (Cahokia Mounds, UNESCO World Heritage list.)

Then there is the world view of the Great Octagon near Newark, Ohio. It was part of a 4.5-square-mile complex that precisely records the 18.6-year cycle of the moon.

My research, thanks to Wayne May and others, now tells me that these were built by the Jaredites and refined by the Nephites, as they share with the world God’s perfect plan of happiness.  The earthworks map out God’s plan from premortal to celestial realms of glory. We have been there; it is so AWESOME. As I share in my book, THE INFINITE ATONEMENT OF JESUS THE CHRIST, AND ITS’ SIGNIFICANCE IN THE LAST DAYS, they new the time and date of the Savior’s birth, and a lunar alignment with the great octagon–denoting the millennium–and the celestial kingdom at 51.8 degrees, which denotes the divine ration, occurred astronomically at that Divine moment in time.

The Newark Earthworks are now a UNESCO World Heritage Site, described by the Ohio History Connection as “part cathedral, part cemetery, and part astronomical observatory” — “the largest set of geometric earthen enclosures in the world.” (See the Octagon Earthworks historical marker.)

Most remarkable of all: Amberli Peterson has documented that structures like these correlate in detail with the Plan of Salvation — some 25 correlations.

In her account, a 30-acre circle maps to the womb, with a “birth canal” between it and the 20-acre square enclosure representing the telestial world — also called the Land Bountiful,  — and the ratio between the two enclosures mirrors the “third part” who chose to come to earth to get a body. One-third were denied that privilege, and were cast out into the Earth with Satan. Earthworks as a temple: is the plan of God, written in the land itself.

The Conclusion of the Whole Matter

Put it together:

• The prophets, from Joseph Smith to Russell M. Nelson, place Cumorah, the plains of the Nephites, Zarahemla, and the promised land in North America.
• The DNA traces a Middle East lineage in the Native peoples of that region.
• Stones in that region bear the Ten Commandments in ancient Hebrew.
• The earthworks of that region match the Book of Mormon in scale, in timing, and even in the Plan of Salvation.

Is it any wonder that I rejoice in knowing these things? The Lord is continually reaching out to us to repent and come unto Him. As King Benjamin testified, there is no other way. The quicker we accept this promised-land truth — and repent — the sooner we can be blessed as a people. “I am the way, the truth, and the life: no man cometh unto the Father, but by me (John 14:6).”

David W. Allan

End of the series. Begin with Part 1: “Where Did The Book Of Mormon Really Take Place?”

Related reading:

• Part 1: Where Did The Book Of Mormon Really Take Place?
• America’s Greatest Need: Repentance — https://itsabouttimebook.com/americasgreatestneedrepentance/
• The Infinite Atonement of Jesus Christ — https://itsabouttimebook.com/the-infinite-atonement-of-jesus-christ/

Part 2 of 4 in the series “Book of Mormon Geography — And Why It Matters”

If God says it, then I know.

So what has God said — through the Prophet Joseph Smith, who knew better than anyone where the Book of Mormon took place, and through the prophets who followed him? Here is the record, in their own words. 

Joseph Smith: The Wentworth Letter (1842)

In the famous Wentworth Letter, Joseph described the Book of Mormon this way: “In this important and interesting book the history of ancient America is unfolded, from its first settlement; by a colony that came from the Tower of Babel… to the beginning of the fifth century of the Christian Era.” America, he wrote, was inhabited by two races: the Jaredites, who came from the Tower of Babel, and a second race from Jerusalem about 600 B.C., principally Israelites of the descendants of Joseph. “The remnant are the Indians that now inhabit this country.” And this book, he said, tells us “that our Savior made His appearance unto this continent after His resurrection; that He planted the Gospel here in all its fullness.” Read the full letter at the Church’s website: The Wentworth Letter.

Earlier, in a letter written by commandment on 4 January 1833, Joseph stated: “The Book of Mormon is a record of the forefathers of our western tribes of Indians… By it we learn that our western tribes of Indians are descendants from that Joseph that was sold into Egypt, and that the land of America is a promised land unto them.”

“Wandering Over the Plains of the Nephites” (1834)

On the Zion’s Camp march — 900 miles from Kirtland, Ohio, to Clay County, Missouri — Joseph wrote to Emma on 4 June 1834: “The whole of our journey, in the midst of so large a company of social honest and sincere men, [was] wandering over the plains of the Nephites, recounting occasionally the history of the Book of Mormon, roving over the mounds of that once beloved people of the Lord, picking up their skulls and their bones, as a proof of its divine authenticity.” (Letter to Emma Smith, 4 June 1834)

The day before that letter, the camp had unearthed a skeleton in a mound — a man “almost entire, and between his ribs the stone point of a Lamanitish arrow.” Joseph recorded what revelation then showed him: the man was “a white Lamanite, a large thick-set man, and a man of God. His name was Zelph. He was a warrior and chieftain under the great prophet Onandagus, who was known from the Hill Cumorah, or eastern sea, to the Rocky Mountains.” Eight others in Zion’s Camp wrote of this experience in their journals. It is now called Zelph’s Mound; we have been there. (See BYU’s “Joseph Smith and Native American Artifacts”.)

Joseph also walked the ground where the City of Manti was built in Missouri — a location documented in the historical record of his travels. (See “Joseph Smith’s Historically Verifiable Written Statements”.)

Oliver Cowdery: Letter VII (1835)

President Oliver Cowdery, of the First Presidency, wrote Letter VII with Joseph Smith’s assistance. Describing the view west of Hill Cumorah, he declared it a “fact, that here, between these hills, the entire power and national strength of both the Jaredites and Nephites were destroyed.” Moroni, he wrote, deposited “all the records in this same hill, Cumorah.” Read the full text: Letter VII.

Later Prophets Bear the Same Witness

President Marion G. Romney, standing on Cumorah in 1975, shared that in western New York “the great Jaredite nation… perished at the foot of Cumorah,” and that the Nephite civilization “came to an end for the same reason, at the same place, and in the same manner as did the Jaredites.” He closed: “I bear you my personal witness that I know that the things I have presented to you today are true.” (“America’s Destiny,” General Conference, October 1975)

President Ezra Taft Benson wrote regarding North America: “This was the place where Adam dwelt; this was the place where the Garden of Eden was; it was here that Adam met with a body of high priests at Adam-ondi-Ahman… This was the place of three former civilizations: that of Adam, that of the Jaredites, and that of the Nephites.” (*The Teachings of Ezra Taft Benson*, pp. 587–588)

President Russell M. Nelson shared that Joseph’s inheritance “was to be a land choice above all others” — choice because it was “chosen to be the repository of sacred writing on golden plates from which the Book of Mormon would one day come,” choice because it would host the world headquarters of the restored Church, and choice because it is “a land of liberty for those who worship the Lord.” (Address to new mission presidents, June 2016)

And Elder L. Tom Perry summarized it all: “The United States is the promised land foretold in the Book of Mormon.” (*Ensign*, December 2012)

A Hard Question

If the people of this Promised Land do not repent and are swept off, can they then tell the Lord, “Had we known this was the Promised Land, we would have repented”? But He has told us. The prophets have told us — consistently, from Joseph Smith to Russell M. Nelson.

So how did so many of us come to believe the Book of Mormon took place somewhere else? That is the subject of the next article.

David W. Allan

Next in this series: Part 3 — “How the Mesoamerica Idea Entered the Church.”

• In this series — “Book of Mormon Geography — And Why It Matters”:
  Part 1: Where Did The Book Of Mormon Really Take Place?
  Part 2: What Joseph Smith and Other Latter-Day Prophets Actually Said
  Part 3: How the Mesoamerica Idea Entered the Church
  Part 4: Evidence in the Heartland: Stones, DNA, and the Newark Earthworks

Sources — Check Them for Yourself

• The Wentworth Letter (Joseph Smith, Times and Seasons, 1 March 1842), full text: churchofjesuschrist.org.
• Joseph Smith to Emma, 4 June 1834, and the Zelph account: BYU Religious Studies Center, “The ‘Nature’ of Revelation” and “Joseph Smith and Native American Artifacts”. The Zelph account itself is in The Joseph Smith Papers, History, 1838–1856, Volume A-1, p. 483.
• Oliver Cowdery, Letter VII (July 1835), full text: lettervii.com.
• Marion G. Romney, “America’s Destiny,” 145th Semiannual Conference, 4 October 1975 — quoted here.
• Ezra Taft Benson, The Teachings of Ezra Taft Benson, pp. 587–588 — quoted here.
• Russell M. Nelson, address to new mission presidents, June 2016 — quoted here.
• L. Tom Perry, Ensign, December 2012, and a collection of the prophets’ statements on Cumorah and the promised land: Book of Mormon Evidence.
• Joseph Smith’s statements, including the City of Manti: Book of Mormon Evidence.

Related reading:

• • Part 1: Where Did The Book Of Mormon Really Take Place?
  • America’s Greatest Need: Repentance — https://itsabouttimebook.com/americasgreatestneedrepentance/

NEW DEFINITION OF TIME FOR THE WORLD

I have had a most interesting day on Thursday, 15 Oct. 2026. From 1:00 a.m. to 3:35 a.m. I listened to several interesting talks by some of the world’s best atomic clock experts for The Bureau International des Poids et Mesures (BIPM). A dear friend, Dr. Patrizia Tavella, who is responsible for official time for the world, Universal Time Coordinated (UTC) invited me to stream into their conference in Paris. The BIPM (International Bureau of Weights and Measures) is located at the Pavillon de Breteuil in Sèvres, France, situated in the south-west suburbs of Paris within the Parc de Saint-Cloud. I have been there many times as a USA member of the CCDS (The Consultative Committee for the Definition of the Second).

I texted my publisher, Boyd Tuttle, “…[The BIPM conference] was fascinating with some of the best timing experts in the world. Patricia was the moderator. She did a great job. It was all about precise timing science on the Earth and on the moon. In a major way, my book is about science and religion on the most important topic in the Universe.” He responded, “Liked.” He is today selling my books at the Book of Mormon Evidence Conference in Layton, Utah.

The Bureau International des Poids et Mesures (BIPM) of weights and measures was organized in 1875 with 17 signing nations; now there are 103. The BIPM General Conference of Weights and Measures (CGPM) meets periodically. Time went from astronomical time to atomic time in 1967 when the “second” was defined as, “the SI unit of time, equal to the duration of 9 192 631 770 periods of radiation corresponding to the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom.”

This Thursday (15 October 2026) they shared three draft resolutions. Patrizia informed me that all were approved which included a new definition of the “second” and getting rid of “Leap seconds,” which is really great news. I had recommended that in my first book, It’s About Time, which we published in 2014.

Timing accuracy has improved a billion fold since time was kept astronomically. It has been so exciting to be part of these enormous advancements and to witness many of the benefits thereof; GPS is an example. Isidor Isaac Rabi invented atomic clocks. An award was named after him, and he was the first recipient of the RABI AWARD in 1983. I was the second recipient because the Allan variance, σy2(τ), showed how to use atomic clocks and how to predict time with them.

Now for the Technical Part

The most accurate astronomical measurements are about 1 x 10^-9. At the CGPM, D. Calonico from Italy shared that the most accurate atomic clocks are at the 2 x 10^-18. After the conference, I shared with Patrizia the recent better results this year from NIST/JILA of 5.5 x 10^-19. This is like measuring the distance to the sun (93 million miles) to about one thousandth of the thickness of a human hair. I pulled out one of mine to measure it, and I don’t have many to spare! The NIST/JILA amazing stability reported was σy(τ) = 3.5 x 10^-16 1/square-root of (τ/s). The “y” denotes the fractional frequency, (ν(t) – νo)/νo, where ν(t) is the actual frequency at time t and νo is the nominal frequency.

One can see why a new definition is needed from the following equation: after a measurement (averaging) time τ.

The equation: σ_y(τ) = 1/π 1/Q 1/S/N 1/square-root(τ/s).

This equation expresses instability using the Allan deviation. The reference transition’s quality factor, Q = ν/∆ν, represents the ratio of transition frequency (ν) to effective line width (∆ν), which, at best, reaches the Fourier limit for the interrogation cycle period (T). Finally, the achievable frequency depends on the signal-to-noise ratio S/N. Assuming no squeezing, quantum projection noise (Itano et al., 1993) leads to a signal-to-noise ratio that scales with the inverse square root of the number of atoms probed.

Since the Q of optical clocks is about 100,000 higher than microwave clocks like the cesium atomic clock defining the second since 1967, the optical clocks have a great advantage and the new definitions approved from this CGPM reflected that advantage. Since there are several competing optical atomic clock transitions, it becomes quite complicated. The conference dealt with those complications.

Knowing Earth time, UT 1, is very important as well, and Professor D. Agnew from the University of California–expert on earth rotation—addressed that at the conference. I shared with Patrizia that he might be interested in a paper that Jim Barnes and I wrote in 1967. It shows that the random walk model that he shares is not as good a model as is flicker-noise FM out to one cycle per year and then the time dispersion goes as τ-5 (flicker run). I also suggested to Patrizia that he might find useful a paper we wrote about long-term resonances that we have found in 200 years of Tropical year data, she said she would.

The above stability plot is the square-root of TVAR = tau^2 MVAR/3, and x is the integral of y, where x is the time variations and y is the fractional frequency variations.

Summary

This has been an incredible week, but most important for me is that my new book is now available from my publisher and from Amazon to help the scientific community as well as for the world to appreciate what is really important: THE INFINITE ATONEMENT OF JESUS THE CHRIST, AND IT’S SIGNIFICANCE IN THE LAST DAYS.

The conference was totally secular; the brilliant minds of the world need to solve the world’s problems. This ignores that the most serious problem in the world is people turning from God and the moral decay that is happening all over the world as a result. The answer is turning to Christ and totally repenting of all our sins. He is the way and the truth and the life (John 14:6). Look to God and live the abundant life He promises the faithful (John 10:10; Alma 37:47).

His invitation is to come to know Him and receive the Eternal Life promised; it is the greatest of all the gifts of God (John 17:3; D&C 14:7) “¶ For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life (John 3:16).”

Now you have to wait for 429,228,004,229,872.992 cycles of the Strontium-87 optical transition to accumulate one second! I thank you, Lord, for giving us AVAR, MVAR, and TVAR to help humanity better benefit and enjoy the blessings from their use in the communities of time and frequency, navigation, and telecom. And we have seen their utilization in many other fields.

1936 Chev with a Garmin GPS in the dash!

Edna’s sister, Carol’s husband, Jon is one amazing creative guy. They have 17 licensed vehicles on their 300 acre “Rattlesnake” ranch near Dillard, OR, and Jon has built 13 of them. I joked with him; they should have their own parade. He is probably one of the only personal owners of an original 1908 Model-T.

Jon visited us last Tuesday, 15 September 2026 and spent the night; it was so good to see him. He and Carol are an amazing couple and have a home off grid. Pictured above is his built from scratch 1936 Chev. It is as old as my wife and I!!! And he has a Toyota interior and 4 cylinder Toyota engine. You can see the name he gave it on the front, YOTA! He joked that during this trip to visit his brother and friends, if he had a dollar for everyone who took a picture of his car, he would have a thousand dollars!

He built the dash and it has a built in Garmin GPS receiver, which he uses all the time. Since I helped develop GPS, I am familiar with the Garmin receiver development. The Air Force developed GPS and in the beginning all receivers were military. Now essentially all receivers are civilian and it is a house hold word. When it was being developed, I would tell people that I was working on GPS, and they would say, “What is that?”

History of the Garmin GPS Receiver

Garmin’s GPS receiver history begins with a vision in the late 1980s to bring the U.S. military’s Global Positioning System (GPS) to civilian use. In 1989, engineers Gary Burrell and Dr. Min Kao, both experienced in aviation and marine electronics, founded the company in Lenexa, Kansas, under the name ProNav. The name “Garmin” is a portmanteau of their first names. As Jon has found out, the Garmin GPS receiver has evolved into an incredibly useful tool.

We share here some other pictures of Jon’s cars with his descriptions:

The yellow one is a ’58 Chevy that I built.

This is a ’55 Ford pickup Rat Rod that I built. It has a lot of different parts from all kinds of cars. A 454 big block Chevy motor with an overdrive automatic trans.

Rat Rod – 37″ HumVee rear tires, with a truck rear end.

The aqua one is an original 4×4. Chevrolet bought the 4×4 components from NAPCO and put them on in the assembly line. They are very rare. The tan one is a ’55 first series Chevrolet with an S-10 front end, with power steering and brakes. The engine is a 350 v-8, and an automatic transmission.

This is a ’33 Ford coupe that I built. It has a 350 Chevy motor that I built. It is an automatic trans. It has 18″ wide tires on the back. 

This is a ’53 Studebaker pickup, that I put on a ’93 Dodge frame. It has a 5.9 Cummins diesel, with an overdrive trans, and is a 4×4. David notes that the stainless steel bumper is so shinny like a mirror., you could use it to shave with it or comb your hair!

This is a ’60 Rambler American that I built. It’s a Nissan 4×4 frame, with a Mercedes diesel engine and 5 speed manual transmission.

This car I built for Carol. It is a ’41 Chevy coupe, that I put on an ’87 Chevy 4×4 pickup chassis. She calls it Chuck, for car/ truck.

If you click on this link: Roseburg Model T parade, you will see Jon’s Model-T leading the way. This well done video showed how Henry Ford changed history. Where can creativity lead you? For Jon there seems to be no limit for this incredibly talented guy. In the past, I have been in his saddle making shop, and back then he was one of the best in the west. By the way the, the 1936 Chev he brought here last Tuesday and pictured with my Sweetheart and my wife of 67 years and with Jon has power steering and breaks. Here we share Jon’s parade of cars with fascinating technology in them because of his creativity.

David W. Allan

FOREWORD

By Michael D. McNiven

Not every day do you run into a praying physicist, but when you do, you have found a peculiar treasure indeed. David W. Allan is such a treasure, and in some circles he is still a hidden one at that. But make no mistake, he is arguably the most eminent scientist in the field of atomic timekeeping and frequency metrology and is certainly one of the most eminent Latter-day Saint scientists of our day. He is an expert in synchronizing and syntonizing the constant change found in the physical world.

Many people may not yet know his name, but everyone is a beneficiary of his scientific work and his innovations in precision and variance measurement. For example, he was the chief timekeeper of the United States for twenty-seven years over a thirty-two year career while at the National Bureau of Standards and the National Institute of Standards and Technology (NBS/NIST) in Boulder, Colorado. His contributions to the field of metrology (the scientific study of measurement standards including atomic clocks) are legendary. When you look at a clock or see the precision of timing used on modern electronic devices, David Allan’s influence is there. His algorithms are used in GPS technology and the international time standard as well as many other fields of study across the spectrum of scientific disciplines. 

David Allan’s reputation as a creative thinker started early in his career. His master’s thesis on flicker noise and variance is one of the most used algorithms with wide-ranging applications across the world. It is named the Allan Variance (AVAR) in his honor. The Institute of Electronic and Electrical Engineers (IEEE) adopted AVAR as well as MVAR (the modified Allan Variance) and TVAR (the Time Variance used in telecommunications) as international standards in 1988. For these contributions, David Allan was awarded several prestigious lifetime achievement awards.

David Allan is credited with seven major scientific discoveries that have impacted in important ways the world community. These include the aforementioned AVAR, MVAR, and TVAR algorithms. He helped create the AT-1algorithm (which optimally combines the readings of an ensemble of atomic clocks to generate official time) and the DMTD (dual mixer time difference to measure the time difference between two clocks with arbitrary precision). He also developed what is known as the GPS common-view where two remote earthbound stations can track a GPS satellite simultaneously giving near accuracy of the time difference between the two stations. It is used by NASA’s Jet Propulsion Laboratory for synchronizing their deep space network and for generating international time with nanosecond accuracy. After retirement from NBS/NIST, David Allan worked as a consultant for Hewlett Packard where he created a specialized GPS receiver for synchronizing cellphone towers around the world.

This book is his eighth book and maybe his most important to date as a signature effort from a scientist of deep religious faith to integrate both his secular and sacred life into one great whole. David Allan is not only a student of the marvelous Creation, but he also a disciple of its Creator. David Allan brings a unique skillset and an inquisitive mind to the study of our Lord and His atoning work. The Lord Jesus is the rightful focus and the Infinite Atonement is the tool to discover more fully the Lord’s plan for redemption of this marvelous physical world and its inhabitants. This physical universe of precision and synchronicity amid its variances and complexities testifies to a glorious Creator as an artful intelligence with magnificent Omniscience (omni-science rather than merely science).  

Bother Allan served as a young missionary in the Eastern States Mission in the late 1950’s. He and his dear Edna Love Ramsay have served in the Church of Jesus Christ of Latter-day Saints actively throughout their adult lives. They are a package deal and a dynamic duo. Edna has been a fully contributing member of their successful team and partnership. David served as a bishop for six years and then as a stake president for over a decade in Boulder, Colorado. He served for three years in the Denver Mission Presidency. After retirement, he taught Institute of Religion classes in the Moroni Utah Stake for eleven years. He and Edna served a full-time mission to the West Africa Cote d’ Ivoire French speaking mission as senior missionaries. They continue to jointly serve their children and grandchildren and their greater community of friends and neighbors with faith, hope, and love. 

I encourage you to take the time to seriously consider the words of this great scientist and ardent disciple of Christ as found in this book and in his many other books. Brother Allan is not afraid to venture into topics that are new or considered non-traditional or even speculative. That is because he is a seeker of truth wherever it appears. Truth is sometimes found on the edges. As the Lord has told us, you often have to seek in order to properly find. This is one of Brother Allan’s most compelling traits as demonstrated in these pages. He is still like a child seeking learning by study and by faith as he enters his 90th year on this most interesting planet at this most crucial time. 

In the coming chapters, readers will gain some insight into the scientific discoveries and thinking of this most devoted scientist. The author has also read widely and finds truths in sometimes surprising places that are compelling to him. He cites other writers generously and relies on their work for new ideas and even wonder. More importantly, in this book he offers his own religious contributions explaining “the atoning sacrifice” and “the atoning bridge” as his understanding of the seven steps of the Infinite Atonement of Jesus Christ. 

In this book, Brother Allan stitches together the many scientific and sacred threads of his learning into one more comprehensive topic related to our Lord’s Atonement. Although readers should feel free to disagree with him on any particular point, what we ought not do is doubt his diligence, capacity, precision, tenacity, or critical thinking as a lifelong seeker of both sacred and secular truth. His scientific credentials and discoveries coupled with his religious diligence and service over a lifetime do not allow us that luxury. He is a serious man having made serious contributions to the world that we live in and to the faith that he professes. 

David Allan will be the first to say that any brilliance or achievements he has attained in his life are not his but were a gift from God. He is not just saying this to feign humility. Although he is a kindly and soft-spoken man, he is also serious about this essential truth. He of himself is nothing without the Lord’s help. Brother Allan explains in the last chapter of this book the situation leading to his first major discovery that launched his storied career. It was a critical fork in the road requiring him to sacrifice his personal ambitions in lieu of service to the Lord and others, and the Lord magnified him from there. 

I believe David W. Allan is a treasure among us as a praying physicist. But this book demonstrates in emphasis and stories what he truly treasures most. He believes in and trusts the Lord Jesus Christ and seeks to understand the Lord’s Infinite Atonement. As is implied in the title of the book, the goal for these pages is to point the readers toward the Lord and to come unto Him with greater seriousness, focus, and even worship. And glory be to God and His matchless Son who wrought the Infinite Atonement, bringing order, oneness, holiness, and wholeness to the universe with a promise of infinite JOY!