Which-Path Double Slit

Valid geometry and path-marking inputs show the theory immediately, without generating hits. Physics, marking, target count or seed edits stop playback and reset the trial. Start collects a finite sample; +1/+100 add batches, Pause/Resume preserve the exact sequence. Reset discards hits and redraws the same setup. Starting a completed trial repeats it from its seed. Options contains window, target count, seed, the unmarked reference and setup sketch. The reference changes only the drawing and is omitted when identical to the current curve. Reduced motion generates the chosen sample immediately; hiding the page or navigating stops playback. Only exact raw input texts and marking/reference choices are stored, including blank, invalid, comma, leading-zero and inactive marking drafts. Legacy numeric settings migrate. Profiles, hits, counts, RNG state and playback are not saved; reloading opens a fresh trial.

All geometry is physical: wavelength nm, slit separation/width µm, screen distance m, screen window mm. Ideal equal slits, scalar paraxial Fraunhofer model. With envelope A(y)=sinc²[πay/(λL)] the unnormalized probability is A(y)[1+V cos(2πdy/(λL))]. V is the ideal local interference contrast before finite bins and envelope variation. Approximate fringe spacing is λL/d. No marker means D=0,V=1. Orthogonal pure path-marker states give D=1,V=0: an incoherent sum with the single-slit envelope retained.

For partial marking this model chooses pure marker states |m₁⟩=|0⟩ and |m₂⟩=V|0⟩+D|1⟩, equal path weights and real nonnegative overlap V=√(1−D²). Tracing out the unread marker gives the displayed density. D is optimal prior path distinguishability, not a count of people observing or a simulated detector click. The ideal equality D²+V²=1 is a model assumption; mixed states or additional decoherence generally give an inequality. No conditional eraser/postselection or physical particle trajectory is simulated.

160 detector bins integrate intensities. Coherent and incoherent terms are combined before normalizing over the finite window; averaging separately normalized PDFs would give the wrong partial-marker result. Every hit is conditional on detection within that window, not an absolute source rate or collection efficiency. The dashed unmarked comparison has its own window normalization. Histogram gold counts and blue N_so_far×bin_probability use exactly the same bins as the CDF sampler. Vertical dot displacement is decorative, not a second quantum dimension.

Mulberry32 seed and one draw per hit make samples independent of pause and batch size. No misleading max/min visibility is estimated from noisy sparse counts. Narrow patterns display bin averages with a resolution warning; reduce the window to resolve fringes. Fresnel and edge-phase indicators warn when the paraxial far-field approximation is questionable; they are practical indicators, not error bounds. No Fresnel propagation, recoil, mixed marker dynamics or exact large-angle optics. In warned cases the results illustrate only the specified approximation.

OpenStax: Double-Slit Diffraction · Schwindt, Kwiat, Englert: Quantitative wave-particle duality