Mass measurement is fundamental to a number of scientific disciplines. It’s also a complex subject since different atoms and elementary particles, theoretically with the same amount of matter, have different masses.

Weighing is one of the most common ways to measure mass. People use balances to weigh things all the time. But what does this tell us about mass?

## Definition

It is common to confuse the terms mass and weight. While the former refers to an object’s inertial force due to gravity, the latter describes the amount of matter that an object contains. The more matter an object has, the more it will weigh.

The standard unit for mass is the kilogram. It is one of seven base units of the International System of Units (SI). The SI was defined in a coherent manner through the fashioning of metre and kilogram artefacts and an international body, the Conference générale des poids et mesures or CGPM, to oversee systems of weights and measures based on them.

While the metric system’s other bases (such as the metre) have lost their link with a physical prototype, the kilogram and the SI remain part of the physics world today. Like other metric units, kilograms are measured in multiples and fractions of the kilogram. A kilo is 1,000 grams, for example.

## Units

The kilogram (symbol kg) is the base unit of mass in the International System of Units. It is often simply called a kilo colloquially. It is a common measure used in science, engineering and commerce worldwide.

The SI meter, second, ampere, kelvin, mole and candela are derived from the kilogram. Therefore, any uncertainty in the definition of the kilogram is carried into these derived units.

Scientists around the world argue that the current definition of the kilogram is imprecise and introduces uncertainties into measurements and physical constants that depend on it, such as the Planck constant h. These scientists are calling for a new definition of the kilogram, based on a fixed numerical value of the Planck constant.

Currently, the physical prototype of the kilogram is kept in a lab in Sevres, France in several nested evacuated glass domes. Each country that subscribes to the International Metric Convention receives one of these national prototypes. The primary standard of the kilogram in the United States is a platinum-iridium cylinder kept at NIST.

## Active gravitational mass

Mass is a property of objects that defines, roughly speaking, how much matter they contain. It is one of the central concepts in classical mechanics, and is also the basis for the gravitational force between two objects.

In classical mechanics, inertial mass and gravitational mass (which we typically call weight) are equal. This equivalence is mandated by Newton’s third law.

It’s also a key tenet of general relativity, and is sometimes referred to as the strong equivalence principle. Inertial mass and passive gravitational mass are not the same, and there is no empirical evidence that the equivalence of these two properties exists in practice.

Active gravitational mass is the amount of spacetime curvature induced by an object’s motion, as measured through the transverse and longitudinal velocities it induces in test particles at rest near its path. It is a critical measurement for the study of general relativity and its effects, such as the deflection of light or the orbits of planets around stars.

## Passive gravitational mass

A physical property of an object, passive gravitational mass measures how much the object resists acceleration. This is the opposite of weight, which measures the force exerted on an object by gravity.

In classical physics, it is not clear why passive gravitational mass should be identical to inertial mass. However, Einstein’s general theory of relativity requires that both be the same. This is known as the strong equivalence principle.

Various experiments have been performed to test the equivalence principle. In one experiment, a Teflon cylinder is pulled up and down while a laser beam is passed through it. This produces a time-varying gravitational field that can be measured.

A recent classification of the “kilogram” as a unit of inertial mass, based on atom count methods with matter wave interferometers, is critically analyzed. The underlying process of reasoning that leads to this conclusion unravels some deeper issues. These issues concern the working principles of these instruments as well as the notion of universal free fall.