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What is the definition of scalars (in physics)?
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A scalar (in physics) is a quantity that is completely specified by a single number (with units) — i.e., it has magnitude but no direction. Equivalently:
- Mathematically a scalar is a rank‑0 tensor: it is unchanged by coordinate rotations (and more generally by whatever symmetry group is being considered).
- In relativity one often uses the term Lorentz scalar for a quantity invariant under Lorentz transformations (e.g. the invariant interval, rest mass).
Examples: temperature, mass (rest mass or invariant mass), electric charge, energy, density, pressure. Non‑examples: velocity and force (they have direction and are vectors). Note: some scalars depend on reference frame (e.g. kinetic energy or speed are scalars in that they have no direction but are not Lorentz/Galilean invariant), and there are pseudoscalars (quantities that behave like scalars under rotations but change sign under parity/reflection).
- Mathematically a scalar is a rank‑0 tensor: it is unchanged by coordinate rotations (and more generally by whatever symmetry group is being considered).
- In relativity one often uses the term Lorentz scalar for a quantity invariant under Lorentz transformations (e.g. the invariant interval, rest mass).
Examples: temperature, mass (rest mass or invariant mass), electric charge, energy, density, pressure. Non‑examples: velocity and force (they have direction and are vectors). Note: some scalars depend on reference frame (e.g. kinetic energy or speed are scalars in that they have no direction but are not Lorentz/Galilean invariant), and there are pseudoscalars (quantities that behave like scalars under rotations but change sign under parity/reflection).
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