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A fringe shift measures a change of relative phase between interfering waves in units of a full fringe spacing. A changing optical path difference $\Delta \ell$ gives a shift $\Delta N=\Delta \ell /\lambda$ for monochromatic light.

An interferometer compares round-trip light travel times along perpendicular arms as its orientation changes. The absence of the classical stationary-aether fringe shift at the expected scale constrains orientation dependence of the round-trip speed of light. The result is consistent with special relativity, but alone does not select it uniquely from every alternative theory.^[ref]

The instrument's stone support and floating mounting allowed the experimenters to change its orientation while limiting mechanical disturbance. The measured quantity was the fringe shift produced as the apparatus rotated, rather than a direct timing of a single light pulse.^[ref]

The Michelson-Morley experiment splits coherent light into two perpendicular arms, reflects the beams and recombines them to observe interference fringes. Rotating the apparatus interchanges each arm's orientation relative to a proposed stationary luminiferous aether. The historical experiment used multiple reflections to increase the effective optical path and a rotatable support to compare orientations.^[ref]

For equal one-way effective arm lengths $\ell$, a classical stationary-aether model givesA right-angle rotation should reverse their difference, producing a fringe shift of approximately $2\ell v^2/(\lambda c^2)$. The observed orientation-dependent shift was much smaller than the stationary-aether prediction. In special relativity, the apparatus rest frame has the same vacuum speed of light along both arms, so no such orientation-dependent shift is expected. The result supports special relativity but does not, by itself, uniquely establish every postulate or exclude every modified aether theory.

For the rocket, take its tail at $x^{\prime }=0$ and nose at $x^{\prime }=L_0$, with coincident frame origins when $t=t^{\prime }=0$. Denote emission, reflection and return by $A,B,C$. In the rocket's inertial frame, their coordinates $(t^{\prime },x^{\prime })$ areThe inverse Lorentz transformation is $x=\Gamma (x^{\prime }+u{t}^{\prime })$, $t=\Gamma (t^{\prime }+u{x}^{\prime }/c^2)$, where $\Gamma =(1-u^2/c^2{)}^{-1/2}$. Thus the same spacetime events, in coordinates $(t,x)$, areThere is no requirement that emission have $t=0$ in this chosen laboratory coordinate system.

The nose-to-tail travel time is $\Delta t_{AB}=\Gamma L_0(1-u/c)/c$. If $L$ is the laboratory length measured at one laboratory time, a left-moving pulse and the right-moving tail close their initial separation at speed $c+u$. ThereforeThis derives length contraction from the pulse's travel. Comparing the positions of the two endpoints at different laboratory times would not measure the rocket's laboratory length.

A Rayleigh interferometer compares optical paths through a sample and a reference. A path-length difference $\Delta \ell$ shifts the interference phase by $2\pi \Delta \ell /\lambda$. In analytical ultracentrifugation, sample and reference sectors produce concentration-dependent fringe shifts, allowing radial concentration scans without requiring the solute to absorb at the probe wavelength.^[ref]