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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 really 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 as well as its 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 in concept is close to the classical idea of mass, does not vary between single observers in different reference frames.
Mass is the only basic SI-unit defined by means of a physical artifact — the search for an alternative has gone on for a long, long time, but nothing adequate has yet been found. This is quite 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.