Invariant (physics)
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In mathematics and theoretical physics, an invariant is that which remains unchanged under some transformation. Examples of invariants include the speed of light under a Lorentz transformation and time under a Galilean transformation. Many such transformations represent shifts between different possible observers, and so invariance under the transformation often represents a fundamental conservation law.
Invariants are very important in modern theoretical physics, and many theories are in fact expressed in terms of their symmetries and invariants.
Covariance and contravariance generalize the mathematical properties of invariance in tensor mathematics.
[edit] Examples in Special Relativity
x2 + y2 + z2 − c2t2 = s2
This is an invariant expression, so one can also write the following expression. x'2 + y'2 + z'2 − c2t'2 = s2
Using Lorentz Transformations due to Special Relativity to rewrite x', y', z' and t' in terms of x, y, z, and t one arrives at the original expression.
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French, A.P. (1968). Special Relativity. W. W. Norton & Company. ISBN 0393097935.
