Predicted vs. Observed Fringe Shift

Source

Collection: Wiki SR simulations (v1) — SuperSTEM special-relativity engine build.
Concept: The Michelson–Morley experiment: the aether-wind hypothesis predicts a fringe shift ΔN(θ) = A·cos(2θ) as the interferometer rotates, but the observed shift is a null result (≈ 0), well below the predicted amplitude.
Serves: Confronting a clean theoretical prediction with the actual data: the predicted shift grows with v² and L and shrinks with λ, yet the observation stays flat — the anomaly that special relativity resolved.
Inquiry: If a real aether wind streamed past Earth, how would the fringes move as you rotate the apparatus — and how does that compare with what Michelson & Morley actually measured?
Misconception: That the predicted (aether-wind) curve is what one should see, presuming the aether exists — rather than the hypothesis being tested and rejected by the null result.

Pedagogy principles applied

ID	Principle	How it shows up here
H1	Misconception is structural, not a text card	The "aether wind is detected / full shift" and "opposite-direction shift" errors are wrong prediction choices; the rebuttal appears only if the student picks one.
D6/D7	Guided inquiry reveals in stages	Five step-cards run predict → observe the rotation → compare fringe panels → verify the null result → resolve; the plot's observed curve and data only enter once predicted.
A2	Fewest objects	Opens with the dial, two fringe panels and one ΔN-vs-θ plot — every element is read by a step.
C	Every number earns its place	Predicted amplitude A, ΔN(θ) and the observed shift are each read or compared; L, v and λ drive the prediction the student is testing.
Physics honesty	Time-animation is a real rotation, not a swept velocity	Play rotates the apparatus orientation θ (a genuine physical rotation); the assumed aether-wind speed v is a static slider, never auto-swept.

Speed

Predicted ΔN(θ) Observed (null ≈ 0) Representative 1887 data current θ

Classical prediction (aether wind)

Actual observation

Guided Inquiry

1 · Predict the observed shift

If a real aether wind streams past Earth at speed v, you can compute exactly how far the fringes should move as you rotate the apparatus (the orange curve). Before revealing the actual 1887 data, what will the observed fringes do?

2 · Rotate the apparatus

Press ▶ in the top bar (or drag the dial) to rotate the interferometer through the orientation angle θ. Watch the predicted amplitude A in the sidebar — it grows with v² and L and shrinks with λ. Set the assumed wind speed and arm length to make the prediction as large as you like.

3 · Compare the two fringe patterns

The two panels show the interference fringes at the detector. In the predicted panel the bright/dark bands slide across as you rotate; in the observed panel they stay put. Overlay the representative 1887 data on the plot to see how flat the real measurement is.

4 · What did the observation do?

Across a full rotation, how did the observed shift compare with the aether-wind prediction?

5 · A null result with no classical fix

The aether-wind hypothesis predicts a shift scaling with β² = (v/c)²; the long folded arms make even a 0.4-fringe prediction measurable. Michelson & Morley saw < 0.01. This null result had no classical explanation and pointed toward special relativity. Turn on ∑ Formal for the algebra, or hit Finish to explore freely.

Controls

▾

L = 11.0 m

1 m20 m

v = 30 km/s

060 km/s

1887 data

Readouts

▾

Orientation θ0°

Predicted amplitude A—

Predicted shift ΔN(θ)—

Observed shift—

The time to traverse the arm parallel to the wind differs from the perpendicular arm. Rotating 90° swaps the two arms, so the path difference changes and the fringes shift.

Path-difference change (90° swing)

Fringe shift (full 90° swing)

Shift vs. orientation θ

Amplitude A

With β = v/c ≪ 1 the shift scales with β² — tiny, but the long folded arms make even a 0.4-fringe prediction measurable. Michelson & Morley saw < 0.01.