You mean define them independently ?

Hi Shubhajit,

I believe that with only ONE SINGLE mass or ONE SINGLE CHARGE it is not possible to find a useful definition of charge or mass. The reason is that charge is defined as the force exerted by a charge on a small test charge (not influencing the field of the charge). With just one charge present in the universe, there is no constructive, i.e. practical experimental way to define a charge. The same measurement procedure applies for defining mass as the force which this mass exerts on a small test mass so small that it does not alter the gravitational field of the mass.

As for mass, it follows from Einstein's general relativity theory what would happen if there was only one single mass in the universe: It would not exhibit any inertia (sometimes called "Mach's principle"). It wouldn't have any weight, because there was no second mass to which its mass could be related. Just one mass defines a space-time the curvature of which defines the gravitational force (there are 10 components of the metric tensor). However, there is NO self-interaction of a mass in its own gravitational field.

To summarize, charge and mass are not defined in an "absolute" manner, but in a "practical" manner and my answer would be that this is - from an absolute point of view - not possible with only one single charge or mass present in the universe. Or put differently: Mass and charge are not inherent quantities of matter, completely independent of the environment, but rather they are quantities of matter which need at least a second reference point for their measurement. The measurement procedure is the definition.