2D output analysis done.

The GIF shows two events at x=−2 and x=+2 simultaneous in the rest frame (ct=0). The moving-frame simultaneity line tilts as v changes. For v=0.9 the Lorentz factor γ≈2.294 and the transformed times are ct’≈+4.129 and −4.129. Signs differ because ct’ = γ(ct − v x). With ct=0 the sign depends on −v x. The worldline x=vt is plotted. Light lines ct=±x remain invariant.

I generated a 3D visualization that transitions from the 2D slice into a full 3D light cone with a simultaneity plane ct = v x. It saves at:

/mnt/data/spacetime_3d_cone_transition_fast.gif

Lyric Sheet — “Simultaneity”

Verse 1

Two points of light

Breaking in silence

In the stillness, they arrive

Together in my frame

Verse 2

But motion bends the present

The line of now tilts away

One light falls ahead

The other drifts behind

Chorus

There is no single moment

No universal now

Only shifting planes of vision

As time becomes a wave

Verse 3

The cone of light surrounds me

Boundaries drawn in space

Past and future folded

Inside causality’s shape

Bridge

Expanding from the line

Into the field of three

Horizons turning open

A deeper symmetry

Chorus (repeat, sustained)

There is no single moment

No universal now

Only shifting planes of vision

As time becomes a wave

Outro

Beyond the cones and frames

The question waits in silence

Is time itself the surface

Or something standing still?

See Also: Questions Regarding the Nature of Time