# Definition of a scalar

1. Jun 2, 2013

### copernicus1

Is there conventional terminology to distinguish between scalars that transform between frames and those that don't? For example, energy is a single-component quantity but it isn't the same in every frame, whereas the length of a vector is also a scalar but is the same in every frame. Do we just call these both scalars, and be precise about what we mean, or are there terms for these different kinds of single-component quantities?

2. Jun 2, 2013

### WannabeNewton

In general, it is understood very easily from context. However there are names ascribed to certain special scalars, as far as physics goes, that distinguishes them based on frame invariance. For example, scalars invariant under Galilean boosts are called Galilean invariant scalars and scalars invariant under Lorentz boosts are called Lorentz invariant scalars or just Lorentz scalars. Thus the Lagrangian density is a Lorentz scalar whereas the time-like component of the 4-momentum, which is the energy as you stated, is not a Lorentz scalar (nor even a Galilean scalar). As purely mathematical mappings however, they are both functions of space-time into the reals so there isn't much distinction in that regard.