|The facts of the matter|
|May the mass times acceleration be with you|
|Let's get physical!|
|Atoms trying to understand atoms|
Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object." On a more fundamental level, mass is equivalent to inertia, which is the resistance of an object to change velocity when acted upon by a force. When measured at the surface of the Earth, "weight" is the colloquial term for mass (though weight is a force calculated as mass times acceleration due to gravity. The Imperial unit for mass is not the pound, but the slug). In free fall, an object has no weight, but it retains its mass and inertia.
Mass is a central concept in classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic kinematics. In the theory of relativity, the quantity invariant mass, which is close to the classical idea of mass, does not vary between single observers in different reference frames.
Until May 2019, mass was the only basic SI unit defined using a physical artifact. Now, though, it's defined in terms of the speed of light, the Planck constant, and the second (defined in terms of a particular microwave frequency given off by cesium-133). This is important because the basic SI units, let alone the derived ones, are not independent.
As a particularly good example of a definition of mass, the following is borrowed from Landau and Lifshitz. Their Mechanics is the first volume in a series covering most of physics, so the innocent reader might expect a cuddly welcome, but as the first section is titled "Generalised co-ordinates", the reader gets the sinking feeling that he's doomed. Section 5 is called "The Lagrangian for a free particle", and there we meet mass for the first time in this guise:
L is, in this case, a simplified version of a Lagrangian encountered in the equation before, and mass has not been mentioned. A few lines later, m is called mass, just to have a name for it. Then we have "The additive property of the Lagrangian shows that for a system of particles which do not interact we have:"
Luckily, this definition of mass is meaningful if we take the additive property into account, but the reader is probably left wishing for a definition based on a metal prototype.
- Landau and Lifshitz, Mechanics, Pergamon Press 1997.