Einstein's two postulates

A new starting point

Einstein's 1905 special theory of relativity starts not with a complicated mechanism, but with two simple postulates. These postulates replace the idea of an aether with a new structure for space and time.

The theory is called special because it applies to inertial frames: reference frames moving at constant velocity relative to one another, with no acceleration or gravity included.

First postulate: principle of relativity

Einstein's first postulate states that the laws of physics are the same in all inertial reference frames.

This extends Galilean relativity beyond mechanics to all laws of physics, including electromagnetism. There is no experiment performed entirely inside an inertial laboratory that can reveal the laboratory's absolute uniform motion.

This does not mean observers always measure the same values for every quantity. They may disagree about time intervals, lengths, energies, and fields. The postulate says the laws connecting those quantities have the same form.

Second postulate: constant light speed

Einstein's second postulate states that light in vacuum travels at the same speed $c$ for all inertial observers, regardless of the motion of the source or observer.

This is radically different from Galilean velocity addition. If a spaceship moving at speed $v$ turns on a forward-facing flashlight, both the astronaut and a stationary observer measure the light speed as

$capprox3.00 imes10^8 m/s$

not $c+v$.

Why the postulates are surprising

Classically, if one observer measures an object moving at speed $u$ and another observer moves at speed $v$, the second observer expects speed $u-v$. If light always has speed $c$, then ordinary transformations cannot be exact.

Something else must change. Einstein's conclusion was that measurements of time and space are frame-dependent. Observers in relative motion do not agree on time intervals, lengths, or simultaneity.

Operational meaning

Special relativity emphasizes how measurements are actually made. To measure the time of an event, an observer uses a clock at the event location. To compare times at different places, the observer must synchronize clocks.

Einstein synchronization uses light signals and assumes light travels at speed $c$ in both directions. This connects the definition of time coordinates to the second postulate.

Invariant laws, relative measurements

The postulates do not say everything is subjective. Instead, they identify what is invariant. The speed of light is invariant. The laws of physics are invariant. Later, the spacetime interval will also be invariant:

$Delta s^2=-c^2Delta t^2+Delta x^2+Delta y^2+Delta z^2$

Different observers may disagree on the separate pieces, but agree on the interval.

Low-speed agreement

Special relativity must reproduce classical physics when speeds are much smaller than light speed. This happens because relativistic effects are controlled by the Lorentz factor

gamma=rac{1}{sqrt{1-v^2/c^2}}

When $vll c$, then $gammaapprox1$, and classical results are recovered.

The big idea

Einstein's two postulates say that all inertial observers use the same physical laws and measure the same vacuum light speed. These principles force a new relationship between space and time. Instead of adding light speeds classically, nature preserves $c$ by making time intervals, lengths, and simultaneity depend on the observer.