Chapter 3: Einstein's Postulates
In 1905, Albert Einstein published "On the Electrodynamics of Moving Bodies," introducing special relativity. Instead of saving the aether with complicated mechanisms, Einstein started fresh with two simple postulates. Their consequences would revolutionize our understanding of space, time, and reality itself.
The Two Postulates
First Postulate: Principle of Relativity
The laws of physics are the same in all inertial reference frames.
This is essentially Galileo's principle, extended to include all physics (not just mechanics). No experiment can distinguish between being at rest and moving uniformly.
Second Postulate: Constancy of Light Speed
The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or observer.
This is the revolutionary step! It directly contradicts Galilean velocity addition and eliminates the need for the aether.
Why the Second Postulate is Revolutionary
Consider this thought experiment: You're on a train moving at 0.5c (half the speed of light). You shine a flashlight forward. According to Galilean relativity, someone on the ground should measure the light speed as c + 0.5c = 1.5c.
But Einstein says:
Both you (on the train) and the observer on the ground measure the light traveling at exactly c. Not 1.5c, not 0.5c—exactly c = 299,792,458 m/s.
How is this possible? If the speed is the same but the distances and times are different, then space and time themselves must be different for different observers!
- • Moving clocks run slower (time dilation)
- • Moving rulers are shorter (length contraction)
- • Simultaneity is relative (different observers disagree on "now")
Immediate Consequences
No Absolute Time
Time is not universal. Moving clocks tick slower. Two observers can disagree on whether two events happen simultaneously.
No Absolute Space
Lengths are not absolute. Moving objects contract in their direction of motion. There is no preferred "at rest" frame.
Speed Limit
Nothing can travel faster than light. As objects approach c, they require infinite energy to accelerate further.
Mass-Energy Equivalence
E = mc². Mass is a form of energy. Small amounts of mass contain enormous energy.
The Logical Structure
From just two postulates, all of special relativity follows through pure logic:
The Lorentz factor \( \gamma = 1/\sqrt{1 - v^2/c^2} \) appears everywhere. At low speeds (v ≪ c), γ ≈ 1 and we recover Galilean physics. As v → c, γ → ∞.
Einstein's Genius
Einstein didn't discover the Lorentz transformations—Lorentz did. Einstein's genius was in the interpretation:
Lorentz's View
Length contraction and time dilation are real physical effects caused by motion through the aether. The aether exists but is undetectable due to a conspiracy of compensating effects.
Einstein's View
There is no aether. The transformations reflect the actual structure of spacetime. All inertial frames are equally valid—there is no absolute "truth" about lengths and times.
"Imagination is more important than knowledge." Einstein had the courage to take the mathematics seriously and abandon common-sense notions of absolute space and time.