Special Relativity

Time Dilation, Length Contraction & the Light Cone

Light Clock — Rest vs Moving

Photon (always travels at c)Rest frame — proper timeLab frame — dilated time

Key Parameters

Postulate

c is invariant

Speed of light

299,792 km/s

v / c (sim)

0.866

γ (sim)

2.00

Lorentz form

γ = 1/√(1−β²)

At v = 0.99c

γ ≈ 7.09

The Two Postulates

1. The laws of physics take the same form in every inertial (non-accelerating) frame. There is no privileged stationary observer.

2. The speed of light in vacuum is the same for every observer, regardless of how the source or observer is moving. This single rule forces space and time to mix.

In the simulation, the photon traces the same c in both frames — but the moving clock's photon must travel a longer diagonal. Each tick takes longer, so its clock runs slow.

Consequences

Moving clocks run slow by a factor of γ

Moving rulers contract along the direction of motion

Simultaneity is frame-dependent — order of distant events can flip

Mass and energy are interchangeable: E² = (mc²)² + (pc)²

Nothing carrying information can exceed c

The light cone divides spacetime into past, future, and elsewhere

Where We See It

Atmospheric muons

γ ≈ 30

Cosmic-ray muons created ~15 km up have a half-life of just 1.5 μs at rest — far too short to reach the surface. Yet detectors find them in abundance. From our frame their clocks run slow; from theirs the atmosphere is contracted. Either way, they make it.

Particle accelerators

γ ≈ 7500

Protons at the LHC are pushed to 0.999999991 c. Their internal clocks tick about 7,500× slower than ours, and short-lived particles produced in collisions live long enough to leave measurable tracks before decaying.

Hafele–Keating experiment

Direct test, 1971

In 1971, atomic clocks flown around the world on commercial jets returned tens of nanoseconds out of sync with ground-based clocks — exactly as special and general relativity predict for the combined motional and gravitational effects.

Frame Shift Drive (lore)

ED narrative

ED's FSD sidesteps relativistic time dilation by warping spacetime around the ship rather than accelerating through it — the hull never approaches c locally. Without this trick, supercruise across a system would leave the commander decades out of step with the bubble.