Consider the standard relativity configuration. Let a spherical light wave be emitted from the coincident coordinate origins at *t*=0 and *t′*=0. For the rest frame, the spherical wave front is given by

*x*² + *y*² + *z*² = *c*²*t*².

For the frame moving at velocity *v* parallel to the *x*-axis, two-way light must be considered. In Newtonian mechanics, the light wave front going out is given by

(*x′* + *vt′*)² + *y′*² + *z′*² = (*c* + *v*)²*t′*²,

which expanded equals

*x′*² + 2*x′t′* + *vt′*² + *y′*² + *z′*² = (*c*² + 2*cv* + *v*²)*t′*².

In Newtonian mechanics, the returning light wave front is given by

(*x′* − *vt′*)² + *y′*² + *z′*² = (*c* − *v*)²*t′*²,

which expanded equals

*x′*² − 2*x′t′* + *v²t′*² + *y′*² + *z′*² = (*c*² − 2*cv* + *v*²)*t′*².

Add these two expanded equations and divide by two for their average:

*x′*² + *v²t′*² + *y′*² + *z′*² = (*c*² + *v*²)*t′*²,

which reduces to

*x′*² + *y′*² + *z′*² = *c*²*t′*².

This demonstrates the invariance of a wave front in Newtonian mechanics.