J. Rogers, SE Ohio
Abstract
The 2019 redefinition of the SI unit system is presented as a triumph of modern metrology — grounding all units in fixed numerical values of fundamental physical constants. This paper argues that the redefinition, while technically sophisticated, operationally preserves and conceals a far older and more fundamental choice: the Babylonian second. Tracing the historical and operational dependency chain from the current SI system back through the meter and kilogram to the second, and from the second back to the Babylonian sexagesimal division of the astronomical day, we show that the physical constants h, c, and G embed this ancient convention as a hidden axiom. The constants are not features of the territory. They are conversion factors between measurement axes, all of which are ultimately anchored to a time unit that no civilization has ever questioned because it was already universal before the concept of a unit system existed. The fish does not know it is in water.
1. The Question Physics Forbids
Ask a physicist what a kilogram really is and you will receive one of two answers. The first is operational: it is the mass of the International Prototype Kilogram, or since 2019, it is the mass defined by fixing the numerical value of the Planck constant h to exactly 6.62607015 × 10⁻³⁴ kg m² s⁻¹. The second is dismissive: it is the SI base unit of mass, and asking what it really is mistakes a definition for a fact about nature.
Both answers are deflections. The operational answer relocates the question — now you must ask what a meter is, what a second is, what the Planck constant is, and whether any of those answers are less circular than the first. The dismissive answer mistakes the framework's refusal to answer for an absence of question.
This paper takes the question seriously. What is a kilogram really? What is a meter? What is a second? And what happens to the physical constants — h, c, G, k_B — when you follow the dependency chain all the way back to its origin?
The answer is not found in modern metrology. It is found in Babylon.
2. The Second: The Invisible Axiom
2.1 Origin
The second is the oldest surviving unit of measurement still in active scientific use. Its origin is the Babylonian sexagesimal system, developed approximately four thousand years ago. The Babylonians divided the astronomical day into 24 hours — itself inherited from Egyptian timekeeping. Each hour was divided into 60 minutes. Each minute into 60 seconds. The result: 86,400 seconds per day.
The choice of 24 and 60 is entirely arbitrary. Twenty-four was chosen for rough compatibility with the number of observable star groups crossing the sky at night. Sixty was chosen because it is highly composite — divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 — making fractional arithmetic convenient in a pre-decimal world. These are reasons of administrative and astronomical convenience. They are not features of the universe.
2.2 Transmission
The Babylonian system passed to Greek astronomy, then to Islamic scholarship, then to medieval European timekeeping, then to the scientific revolution. At every stage the second was inherited, not chosen. Newton did not choose the second. He inherited it. Maxwell did not choose the second. He inherited it. Planck did not choose the second. He inherited it, and it became embedded in h.
No civilization has ever replaced the second with a genuinely different time unit for scientific purposes. The French Revolution attempted a decimal time system — 10-hour days, 100-minute hours, 100-second minutes — but it lasted less than two years before being abandoned. The second survived. It has now been the universal scientific time unit for so long that it no longer appears to be a choice. It appears to be a fact.
2.3 The 1967 Redefinition
In 1967, the General Conference on Weights and Measures redefined the second atomically: one second is 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of caesium-133. This is presented as a move away from the astronomical second toward a more fundamental definition.
It is not. The number 9,192,631,770 was chosen specifically to match the pre-existing astronomical second as closely as possible. The atomic definition is a high-precision realization of the Babylonian second, not a replacement for it. The arbitrariness of the original choice was preserved and laundered through atomic physics.
3. The Meter: Built on the Second
3.1 The Pendulum Origin
The meter was proposed in 1791 by the French Academy of Sciences as a universal and rational unit of length. Two proposals competed. The first was one ten-millionth of the distance from the equator to the North Pole along the Paris meridian. The second was the length of a pendulum that beats exactly once per second — the seconds pendulum, approximately 0.994 meters at sea level.
The committee chose the meridian definition. But the seconds pendulum proposal, which lost, makes the dependency explicit: the meter was nearly defined directly as a function of the second. The gravitational constant G and the length of a seconds pendulum are related by:
L = g / π²
where L is the pendulum length and g is gravitational acceleration. A meter defined this way would have been a unit of length derived from a unit of time and a measurement of local gravitational geometry.
The meridian definition won, but the result is nearly identical numerically. The meter and the seconds pendulum are within 0.6% of each other. The choice of the meridian did not escape the second — it merely hid the dependency.
3.2 The 1983 Redefinition
In 1983, the meter was redefined explicitly in terms of the second: one meter is the distance traveled by light in vacuum in exactly 1/299,792,458 of a second. This definition fixes the speed of light c to exactly 299,792,458 m s⁻¹.
The dependency is now completely explicit and fully operational. The meter is defined as a fraction of a second times the speed of light. There is no independent meter. There is only the second, a fixed number, and light.
The meter is the second in disguise.
4. The Kilogram: Built on the Meter and Second
4.1 The Original Definition
The kilogram was originally defined in 1795 as the mass of one cubic decimeter of water at its temperature of maximum density (approximately 4°C). One cubic decimeter is one liter. The kilogram is therefore a unit of mass derived from a unit of volume derived from a unit of length derived — through the near-miss of the seconds pendulum — from a unit of time.
The chain is: second → meter → cubic meter → kilogram.
This was explicit in the original design of the metric system. The units were intended to be rationally interconnected, with length and mass both derived from a common foundation. That foundation, in operational practice, was always the second.
4.2 The Kibble Balance and the 2019 Redefinition
The 2019 SI redefinition fixed the numerical values of seven defining constants, including the Planck constant h, the speed of light c, and the elementary charge e. The kilogram is now defined by fixing h to exactly 6.62607015 × 10⁻³⁴ kg m² s⁻¹.
The primary instrument for realizing this definition is the Kibble balance (formerly watt balance), which relates mechanical power to electrical power through quantum electrical standards. The Kibble balance measures h in SI units. The 2019 redefinition then inverts this: it fixes h and uses the Kibble balance to realize the kilogram.
Examine the units of h:
[h] = kg m² s⁻¹
The kilogram appears in the units of h. The definition of the kilogram by fixing h is therefore circular in the following precise sense: h was measured in units that include the kilogram, and the kilogram is now defined by fixing h. The snake eats its tail.
But look more carefully at the units:
[h] = kg m² s⁻¹ = kg · (m² / s)
The meter is defined as c / (299,792,458 s⁻¹), so m² = c² s² / (299,792,458)². Therefore:
[h] = kg · c² s² / (299,792,458)² / s = kg · c² s / (299,792,458)²
Every unit in h resolves to kilograms and seconds. And the meter resolves to seconds. So the full unit dependency of h is kg and s — kilogram and second. Fix h and c together, and the kilogram is entirely determined by the second plus two fixed numbers.
Operationally, the 2019 redefinition defines the kilogram in terms of the second. The constants h and c are the conversion factors that make the accounting explicit.
The kilogram is the second in disguise, twice removed.
5. The Constants as Babylonian Artifacts
5.1 What the Constants Are
If the meter is the second in disguise, and the kilogram is the second in disguise twice removed, then the physical constants — which are defined as numerical relationships between kg, m, and s — are ratios between different disguises of the same underlying time unit.
Consider the three fundamental constants explicitly in terms of the Planck unit standards m_P, l_P, t_P:
c = l_P / t_P
h = m_P l_P² / t_P
G = l_P³ / (t_P² m_P)
Each constant is a monomial in three Planck unit standards. The Planck unit standards are themselves defined from the SI units. And the SI units — kilogram and meter — both resolve operationally to the second.
This means h, c, and G are ultimately ratios of powers of the second, combined with numerical values chosen to bridge between the independently-defined SI axes. Their specific numerical values — 6.626 × 10⁻³⁴, 2.998 × 10⁸, 6.674 × 10⁻¹¹ — depend on the Babylonian choice of 86,400 seconds per day.
If the Babylonians had divided the day into 100,000 equal parts and called each part a second, h, c, and G would have different numerical values. The physics would be identical. The dimensionless ratios — X — would be unchanged. Only the numbers attached to the constants would differ, because those numbers encode the Babylonian convention.
5.2 The Laundering Process
The process by which a Babylonian astronomical convention becomes a fundamental constant of nature has three stages.
First, the convention is inherited so universally and for so long that it ceases to appear as a choice. The second is not chosen by any physicist. It is simply the unit of time. It has been the unit of time for every scientist, in every tradition, for recorded history. It does not feel conventional. It feels like furniture.
Second, the framework accepts the inherited units as primitives — as axioms. In the same way that Euclidean geometry accepts points and lines as primitive and forbids the question "what is a point really?", the SI framework accepts the second, meter, and kilogram as primitive. To ask "what is a second really?" inside the framework is a malformed question. The framework has no mechanism to answer it because it bottoms out there by construction.
Third, the constants are defined as relationships between the axiomatic units. Since the units cannot be questioned, the constants inherit axiomatic status. They become brute facts. They are measured to extraordinary precision, named, given symbols, and treated as features of the territory. The 2019 redefinition elevated them further — they are now definitional, fixed exactly by international agreement. This looks like progress toward fundamentality. It is the opposite. It is the convention being welded shut.
5.3 The Circularity Made Explicit
The 2019 redefinition defines the kilogram by fixing h. The Kibble balance realizes this definition by measuring electrical and mechanical quantities in SI units. The SI units of h include kg m² s⁻¹. The meter is defined by fixing c in m s⁻¹.
Unwind the chain:
kg → defined by fixing h [kg m² s⁻¹]
m → defined by fixing c [m s⁻¹]
s → defined by counting caesium transitions to match the Babylonian second
Every definition points to the second. The second points to Babylon. Babylon points to the astronomical day and the administrative convenience of base-60 arithmetic.
This is not a flaw in the 2019 redefinition. It is the honest structure of any unit system: all chains of definition must terminate somewhere, and that somewhere is always a convention. The flaw is in presenting the chain as if it terminates in something other than a convention — in fundamental constants, in nature itself.
The constants do not terminate the chain. They are links in it.
6. X: What Remains When the Convention Is Removed
6.1 The Dimensionless Ratio
When the arbitrary unit scaling is removed — when the SI quantities are divided by their corresponding Planck unit standards — what remains is a pure dimensionless number. Call it X.
X is the geometric ratio of a physical state to the whole. It is what the measurement was always computing, beneath the layer of unit convention. The equivalence chain makes this explicit:
E/E_P = f·t_P = m/m_P = T/T_P = l_P/λ = p/p_P = ... = X
Every physical quantity, expressed as a ratio to its Planck unit standard, gives the same dimensionless X. The different entries in the chain — energy, frequency, mass, temperature, wavelength, momentum — are not different physical quantities. They are the same geometric relationship expressed through different measurement axes, each axis carrying its own arbitrary unit scaling.
The Planck unit standards are not a special scale. They are the SI unit definitions restated in natural language — the combination of unit standards that, when divided into the SI quantity, cancels the arbitrary scaling exactly. Not approximately, not in some limit, but exactly by definition. That is what they are.
6.2 X Has No Seconds
X has no units. It has no seconds. It has nothing to do with Babylon.
X is the geometry of a physical configuration relative to the total geometric structure of the universe. The universe is the only non-arbitrary reference. Everything else — the second, the meter, the kilogram, the Planck units, the constants — is part of the measurement ritual. It is the map. X is what the map was always trying to describe.
The physical constants h, c, and G encode the Babylonian second. X does not. Change the second — choose a different astronomical convention, a different division of the day — and h, c, G all change their numerical values. X does not change. X is invariant to unit scaling by construction, because it is the ratio that remains after all unit scaling is removed.
This is the sense in which X is the real physical quantity and the constants are not. The constants are specific to a particular unit convention rooted in a particular astronomical history. X is not.
6.3 The Planck Jacobians
The transformation from SI units to X is a Jacobian — a precise accounting of the arbitrary scaling inserted at each axis of measurement, so it can be removed cleanly. The Planck unit standards are the Jacobian coefficients.
This transformation is not a change of scale. It is the removal of the fiction that the measurement axes were independent. Energy, frequency, mass, temperature, momentum, and wavelength were calibrated independently, by different experimental and historical traditions, using instruments ultimately anchored to the Babylonian second. The constants h, c, G, and k_B are the mismatch factors between these independently calibrated axes. They are not constants of nature. They are the correction factors required when you measure the same underlying geometry through multiple incompatible unit systems and then try to relate the results.
Apply the Planck Jacobians and the mismatch disappears. All axes collapse to X. The correction factors are no longer needed because the thing being corrected — the independent unit scaling — has been removed.
7. Why This Is Hard to See
The difficulty is not mathematical. The argument in this paper requires only algebra and dimensional analysis. The difficulty is historical and cognitive.
The second has been the universal time unit for longer than the concept of a unit system has existed. It was not chosen by any scientist. It was not questioned by any scientist. It was simply there, as water is simply there for a fish. The habit of measuring time in seconds was installed before there was any concept of a measurement convention to install. It does not feel like a choice because there was never a moment of choosing.
The framework then accepts the second as a primitive — an axiom. This is correct behavior inside the framework. Points are primitive in Euclidean geometry. Asking what a point really is inside Euclidean geometry is a malformed question. The framework cannot answer it because the framework bottoms out at points by construction. In the same way, asking what a second really is inside the SI framework is a malformed question. The training pipeline teaches this correctly: here are the units, here are the constants, here is how to use them. The question of what the units really are does not arise inside the training, and so it does not arise in practice.
The constants then inherit the axiomatic status of the units through a third layer: they are precise, they appear in the laws, they are measured to parts per billion, they were elevated to definitional status in 2019. They look like facts about nature. They look like the place where the chain of definition ends. They do not feel like Babylonian astronomy in mathematical disguise.
Three nested layers of invisibility. The second is invisible because it is ancient. The units are invisible because the framework treats them as primitives. The constants are invisible because they inherit their status from the units. To see through all three simultaneously requires stepping outside the framework entirely — which the framework, by construction, provides no mechanism to do.
8. Conclusion
The 2019 SI redefinition did not ground the unit system in nature. It grounded it in fixed numerical values of physical constants. Those constants are monomials in Planck unit standards. Those Planck unit standards are the SI unit definitions restated in natural language. Those SI unit definitions resolve, operationally and historically, to the second. The second is the Babylonian division of the astronomical day.
The chain is:
h, c, G → Planck unit standards → SI units (kg, m, s) → the second → Babylon
This is not a flaw. Every unit system must terminate in a convention. The flaw is in the claim — implicit in the framing of the 2019 redefinition, explicit in the standard pedagogy — that the constants are fundamental features of the territory rather than links in a chain of human convention.
The question "what is a kilogram really?" is not malformed. It is the question that traces this chain. The answer is: a kilogram is a particular human-chosen ratio of the Babylonian second, expressed through the Planck constant and the speed of light, which are themselves conversion factors between independently-calibrated measurement axes all anchored to the same ancient time convention.
The universe does not have kilograms. The universe does not have seconds. The universe does not have h, c, or G in the sense of intrinsic features of the territory. The universe has X — the dimensionless geometric ratio of each configuration to the whole. That ratio is invariant to every unit convention, every redefinition, and every choice of base-60 versus base-10 time division.
The Planck Jacobians are the ladder that takes you from the Babylonian second to X. Use the ladder. Then throw it away.
What remains is the geometry. It has nothing to do with Babylon.
The author notes that the argument presented here does not invalidate any experimental result, any prediction, or any calculation performed using SI units or physical constants. It concerns only the interpretation of what those constants are — not their operational utility. The map works. The map is not the territory.
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