Mass is a fundamental property of physical bodies. It represents the amount of matter in an object and determines its resistance to being accelerated by a force (inertial mass). It also dictates the strength of its mutual gravitational attraction to other bodies (gravitational mass). The equivalence principle of general relativity postulates that these two types of mass are identical.
Historical Context
Before the metric system, mass was measured using chaotic, localized units like pounds, ounces, stones, or grains. These were often based on arbitrary local standards, leading to significant confusion in commerce and science.
The metric system aimed to fix this. Originally, the gram was defined as the absolute weight of a volume of pure water equal to the cube of the hundredth part of a meter (1 cubic centimeter), and at the temperature of melting ice.
Because mass is more practically measured in larger quantities, the standard became the kilogram (1000 grams). From 1889 until 2019, the global standard was the International Prototype of the Kilogram (IPK), affectionately known as "Le Grand K", a cylinder of platinum-iridium alloy securely stored in a vault at the BIPM in Sèvres, France.
The problem with a physical artifact is that it can change. Despite the most careful storage, comparisons over a century showed that the mass of the IPK and its official copies were drifting relative to each other by about 50 micrograms. This instability threatened the foundation of the entire SI system.
The 2019 Redefinition and the Planck Constant
On May 20, 2019, metrology experienced a historic shift. The kilogram's definition was completely severed from "Le Grand K" and instead tethered to a fundamental constant of quantum mechanics: the Planck constant ($h$).
The kilogram is now defined by taking the fixed numerical value of the Planck constant h to be exactly 6.62607015 × 10⁻³⁴ when expressed in the unit J⋅s, which is equal to kg⋅m²⋅s⁻¹, where the meter and the second are defined in terms of the speed of light c and the cesium transition frequency ΔνCs.
The Kibble Balance
How do you measure mass using a quantum constant? The answer is an extraordinarily complex device called a Kibble balance (formerly known as a watt balance).
A traditional balance compares an unknown mass against a known artifact mass. A Kibble balance compares the gravitational force on a mass with the electromagnetic force generated by a coil of wire in a magnetic field.
- Weighing Mode: A current is passed through a coil in a magnetic field to create an upward force exactly equal to the downward gravitational pull on the mass being measured ($mg = IBL$).
- Velocity Mode: The same coil is moved through the same magnetic field at a constant velocity, inducing a voltage ($V = BLv$).
By combining these two measurements, the macroscopic mechanical power ($mgv$) is equated to the electrical power ($VI$). Crucially, the voltage and current are measured using the Josephson effect and the quantum Hall effect, respectively. These quantum phenomena relate voltage and electrical resistance directly to the Planck constant and the elementary charge. Thus, the macroscopic mass is mathematically linked to the fundamental quantum realm.
Mass vs. Weight
While often used interchangeably in daily life, mass and weight are distinct physical quantities. Mass is intrinsic to the object; it is a measure of its inertia. An object has the same mass on Earth, on the Moon, or floating in deep space.
Weight is the force exerted on that mass by gravity ($W = mg$, where $g$ is local acceleration due to gravity). The weight of an object will vary depending on where it is in the universe. Laboratory balances and scales actually measure weight (the force required to support the object), but they are rigorously calibrated against known mass standards so their displays accurately report mass, assuming the local value of gravity is known and compensated for.
Air Buoyancy Correction
When an object is weighed in air, the surrounding air exerts an upward buoyant force on it, just as water does on a submerged object. This principle, derived from Archimedes, dictates that the buoyant force is equal to the weight of the displaced air.
Because mass standards and the objects being weighed often have different densities, they displace different volumes of air. If this difference is not accounted for, the resulting mass measurement will contain an error. High precision mass metrology requires applying an air buoyancy correction. This involves calculating the exact density of the air within the laboratory at the time of the measurement, which requires highly accurate simultaneous measurements of ambient temperature, barometric pressure, and relative humidity, often utilizing the CIPM formula for the density of moist air.
Mass Standard Classifications
Mass standards (weights) are manufactured to specific tolerance classes defined by international and national organizations. The two primary classification systems used globally are established by the International Organization of Legal Metrology (OIML) and the American Society for Testing and Materials (ASTM).
OIML vs. ASTM Classes
The OIML system is widely used internationally and categorizes weights into classes such as E1, E2, F1, F2, M1, M2, and M3, with E1 being the most accurate.
- Class E1: Highest precision, used as primary reference standards for calibrating other weights. Requires vacuum environment handling.
- Class E2: Used for calibrating high precision analytical balances and Class F weights.
- Class F1 & F2: Used for high accuracy industrial scales and calibrating Class M weights.
- Class M1, M2, M3: Used in general commercial and industrial applications.
The ASTM system is prevalent in the United States and uses a numeric classification system from Class 000 (most accurate) to Class 7.
- Class 000 to 0: Extreme precision, typically used in national laboratories and as primary standards.
- Class 1 & 2: Used for calibrating precision balances and as working standards in accredited laboratories.
- Class 3 to 7: Used for moderate accuracy balances and general industrial applications.
Laboratory Realization and Handling
The realization of mass at the highest levels of accuracy demands meticulous laboratory practices to prevent contamination or damage to the standards.
- Handling: Precision weights must never be touched with bare hands. Oils, moisture, and dirt from skin will immediately alter the mass. Weights are handled using specialized forceps (with non-metallic, non-abrasive tips) or clean, lint-free gloves.
- Magnetic Susceptibility: The material of the mass standard and its environment must be carefully considered. Even slight magnetic properties in a weight can interact with the magnetic fields of the balance's electromagnetic force restoration cell or the surrounding environment, causing significant measurement errors. High class weights are manufactured from special non-magnetic stainless steel alloys.
- Cleaning: Weights accumulate microscopic dust and films over time. Cleaning procedures are highly formalized, often involving specialized solvents like ethanol or distilled water, followed by a stabilization period to allow the weight to reach thermal equilibrium and surface moisture to evaporate before calibration.
- Thermal Equilibrium: Before a mass standard can be accurately calibrated, it must be allowed to acclimate to the laboratory's ambient temperature. A temperature difference between the weight and the air inside the balance weighing chamber will create convection currents that cause unstable and erroneous readings.