Special Relativity · 01 / 06

Frames & Postulates

Special relativity begins with inertial frames and two commitments: the laws of physics take the same form in every inertial frame, and light in vacuum has the same speed c for every inertial observer.

The learner question

What breaks if light refuses to obey ordinary velocity addition?

In Newtonian mechanics, speeds simply add between moving frames. That works well at ordinary speeds. But applying it to light would make different inertial observers measure different light speeds, contradicting the relativistic postulate.

Relativistic velocity addition
u=u+v1+uv/c2u=\frac{u'+v}{1+u'v/c^2}

Below, all velocities are shown as fractions of cc, so the formula uses c=1c=1.

Frame-comparison lab

Launch the same signal from a moving frame.

γ = 1.250
Galilean prediction
Relativistic measurement
source
source
classical light can exceed c
Lorentz velocity addition
frame speed v
0.60 c
signal in ship u′
1.00 c
classical prediction
1.60 c
relativistic result
1.00 c
Frame speed v0.60 c
Signal in moving frame
frame idea
An inertial frame moves without acceleration

Special relativity compares frames in uniform relative motion. No inertial frame is physically privileged as the universal frame at rest.

frame idea
Light speed is invariant

Set the signal to light and move the source frame. Relativistic velocity addition keeps the observed vacuum light speed at exactly c.

frame idea
Space and time must adjust instead

If c is invariant, observers cannot all share Newtonian simultaneity, lengths, and time intervals. Lorentz transformations replace Galilean ones.

Postulate 1

The laws of physics have the same form in all inertial frames. Uniform motion alone cannot reveal a preferred inertial frame.

Postulate 2

Every inertial observer measures the same vacuum light speed c, independent of the source or observer motion.

Transfer check

A spacecraft moves at 0.8c and shines a flashlight forward. What speed does an inertial observer on Earth measure for the light?

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