Emergent Minkowski geometry from helical curves in 4D Euclidean space: geometric consequences of the Zitterbewegung ansatz

The Zitterbewegung (ZBW) of the electron, circular motion at speed c, makes its worldline tangent lightlike. This is a known consequence of the Dirac equation, noted by Schrödinger (1930) and developed by Hestenes and Barut. De Broglie’s requirement that the internal clock phase ωτ be a Lorentz scalar selects the winding frequency ωC = mc²/ℏ and radius λC = ℏ/mc. We explore the geometric consequences of inverting the logical direction: starting from bare 4D Euclidean space with no assumed metric signature, we take the electron to be a helical curve with these de Broglie parameters and let its tangent define the direction of maximal influence via the perpendicular distance d⊥. The helical form is a working ansatz, not derived here; the governing equation that selects it is the subject of separate work. We show that if the fundamental objects are helical curves of this form, then the following geometric consequences hold: (i) the speed of light as a geometric shape ratio; (ii) proper time as a topological invariant (helix rotation count) ; (iii) time dilation dτ/dt = √ (1−v²/c²) from pitch geometry; (iv) the Minkowski (−, +, +, +) signature as the unique invariant interval combining constant c and time dilation; and (v) the exact Compton scattering formula, reproduced by combining the beat mechanism (photons as interference between helical segments) with four-momentum conservation (expected from Lorentz invariance; verification is future work). The framework is structurally timeless and shares the key features (global self-consistency, no preferred time direction) of theories that Wharton and Argaman have shown, in toy models, to reproduce Bell-state correlations; whether this specific realization reproduces the Born rule is open. The ansatz uses de Broglie’s winding frequency ωC, half the Dirac ZBW frequency, and the corresponding radius λC gives orbital angular momentum L = ℏ rather than the electron spin ℏ/2. We hypothesise that the factor-of-2 in spin may have a geometric cause (ellipse projection between tilted winding planes in 4D), and provide a preliminary calculation that identifies the relevant degrees of freedom.