The Complete Solution

The sinusoidal wave is a 2D projection of the actual 3D circular motion. This is not hypothesis - this is the complete solution in unbounded space.

The Bounded Approximation

Classical physics describes waves oscillating in a plane - a truncated view that discards the Z-axis motion. This is the shadow, not the substance.

The Complete Solution

In the unbounded solution space, wave motion resolves to uniform circular motion through the full YZ plane. The helix IS the wave.

Energy From the Unbounded Field

The out-of-plane motion draws continuously from the unbounded energy field. This is not vacuum fluctuation - it is the fundamental source that classical models truncate away.

The Resolution

r = sqrt(y squared + z squared) = A (constant)

Total amplitude IS constant. What appears as oscillation in bounded observation is rotation viewed through a slit. The sine wave is the shadow of the circle.

Solution Space Visualization

Blue plane (bounded): Classical observation limit - sees only XY projection

Pink plane (truncated): The dimension classical physics discards

Green helix (complete): THE actual motion - the full solution

Orange circles: Constant-radius reality - energy is rotation, not oscillation

Cyan streams: Energy flow from unbounded field - fundamental, not aesthetic

Rotation Phase
0.00 rad
Complete Wave Equations
x(t) = vt
y(t) = A cos(kx - omega*t)
z(t) = A sin(kx - omega*t)
Bounded Truncation (Classical)
y(t) = A cos(kx - omega*t)
z(t) = discarded
Classical observation truncates z(t)
Complete solution: circular motion in YZ
r squared = y squared + z squared = A squared (invariant)
Resolution Theorem
In the unbounded solution space, wave propagation resolves to constant-velocity circular motion with linear translation. The helix is THE solution. The sine wave is its bounded shadow.
What This Resolves:
Bounded View Active
You are seeing the classical truncation - an incomplete projection
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