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Einstein’s Principle of Relativity

Key idea: Learn Einstein’s two postulates of special relativity and how they force Lorentz transformations, replacing Galilean ideas at high speeds.

  • GCE A-Level H3 Physics 2027
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Learning objectives

  • discuss qualitatively the results of the Michelson–Morley interferometer experiment and its implications on the ether theory (knowledge of the details of the experiment is not required)
  • state the postulates of the special theory of relativity, that in all inertial frames, the laws of physics are the same and the speed of light in free space is the same regardless of the motion of the light source or observer
  • appreciate the failure of Galilean transformation equations when applied to a moving source of light

Einstein’s special theory of relativity starts from two postulates. Together, they explain why Galilean ideas work at low speeds, but break down for light.

In the maintained sequence, treat this as the conceptual checkpoint after Michelson-Morley and before simultaneity/time-mixing derivations.

Two inertial observers in relative motion both measuring the same vacuum light speed c
The source and observers may move relative to one another, but every inertial observer measures the same vacuum light speed, c.

1. Definitions (Must Know)

  • Inertial frame: a frame where Newton’s laws hold in their standard form (no fictitious forces needed).
  • Postulate: a foundational statement accepted as a starting point (then tested by its consequences).
  • Speed of light in vacuum: c ≈ 3.00 × 10⁸ m s⁻¹.

2. Key Ideas (What Earns Marks)

  • Postulate 1 (Principle of Relativity): the laws of physics are the same in all inertial frames.
  • Postulate 2 (Constancy of light speed): in vacuum, light has the same speed c for all inertial observers, independent of the motion of the source or observer.
  • These postulates force you to abandon Galilean velocity addition for light, motivating Lorentz transformations.

Quick comparison:

PostulateWhat you stateWhat it rules out
1. Relativity principleNo preferred inertial frame for physics lawsAbsolute rest frame for laws
2. Invariant cAll inertial observers measure c in vacuumGalilean addition for light (c± u)

3. Detailed Explanations

A. What Postulate 1 really claims

Postulate 1 is not just about mechanics (Galilean relativity). It says all physical laws (including electromagnetism) take the same form in every inertial frame. There is no preferred inertial frame.

B. Why Postulate 2 is a shock to “common sense”

In Galilean relativity, speeds add: you might expect “observer sees c± u”. Postulate 2 says this is not allowed: all inertial observers must measure c for light in vacuum.

This creates a contradiction with Galilean transformation ideas at high speeds, and the resolution is that time and space coordinates must transform differently (Lorentz transformations).

The Michelson–Morley experiment is historically important because it supports the idea that there is no detectable “ether wind” and is consistent with c being universal in inertial frames:

4. Common Mistakes

  • Writing principal instead of principle (it’s the principle of relativity).
  • Saying “speed of light is constant in all frames” without stating “in vacuum” and “in inertial frames”.
  • Mixing “same laws” with “same measurements”: different inertial observers can measure different times/lengths, but the laws connecting them are the same.
  • Treating Galilean velocity addition as valid for light (it is the classical, low-speed limit).

5. Exam Tips

  • If asked to “state the postulates”, write them cleanly as two separate bullet points (as in Section 2).
  • When asked about “no preferred frame”, use a closed-lab phrasing: “no internal experiment in a uniformly moving lab can detect its uniform motion.”
  • Use c ≈ 3.00 × 10⁸ m s⁻¹ (SI units) unless the question specifies otherwise.

6. Worked Examples

Modelled example 1

Galilean prediction vs Einstein postulate (concept)

Core

Problem

A spaceship moves at u relative to Earth and emits light forward. Contrast Galilean velocity addition with Einstein’s second postulate.
Study the worked solution

  1. Apply Galilean addition

    Method

    Earth would predict c + u.

    Reason

    Galilean kinematics adds source-frame velocity to frame velocity.

    Working

    v_Earth = c + u

  2. Apply the postulate

    Method

    Earth measures c in vacuum.

    Reason

    All inertial observers measure the same vacuum light speed, independent of source motion.

    Working

    v_light = c

Guided practice 2

Classify the statement (postulate 1 or 2?)

About 4 min

Problem

Classify: (1) no closed experiment detects uniform train motion; (2) all inertial observers measure the same vacuum light speed.

Try this before viewing the solution

Hints

Hint 1: separate laws from light speed
Postulate 1 concerns laws in inertial frames; Postulate 2 specifically concerns c.
View solution step by step

  1. Classify statement 1

    Method

    Postulate 1.

    Reason

    No inertial frame is preferred by the laws of physics.

    Working

    same law form in inertial frames

  2. Classify statement 2

    Method

    Postulate 2.

    Reason

    It directly states invariance of vacuum light speed.

    Working

    c invariant

Common misconception 3

Why Galilean transformations fail (one sentence)

Find and correct the mistake

Learner claim

A learner keeps t' = t and ordinary velocity addition while also claiming every inertial observer measures c. Explain why the two claims are inconsistent.

Try this before viewing the solution

Required replacement

View solution step by step

  1. Follow Galilean consequence

    Method

    Observers would obtain c± u.

    Reason

    Absolute time plus linear coordinate shifts produce ordinary velocity addition.

    Working

    v' = v-u

  2. Identify contradiction

    Method

    The measured light speed would depend on observer motion.

    Reason

    This contradicts Postulate 2.

    Working

    c' ≠ c

  3. Use the correct framework

    Method

    Space and time must transform by Lorentz transformations.

    Reason

    They preserve the invariant speed c.

    Working

    t' ≠ t generally

Examiner practice 4

“Same laws” does not mean “same measurements”

4 marks

Examination question

Two inertial observers assign different time intervals to the same event pair. Explain why this does not contradict Postulate 1. [4 marks]

Try this before viewing the solution

View solution step by step

  1. State the postulate

    1 mark

    Method

    Physical laws have the same form in all inertial frames.

    Reason

    No inertial frame is preferred.

    Working

    law form invariant

  2. Separate coordinates

    1 mark

    Method

    Event coordinates may differ by frame.

    Reason

    Time and position are frame-dependent.

    Working

    (x,t) ≠ (x',t')

  3. Apply to interval

    1 mark

    Method

    Different measured intervals are allowed.

    Reason

    The observers use different coordinate assignments.

    Working

    Δ t ≠ Δ t'

  4. Conclude consistency

    1 mark

    Method

    Both observers can use the same laws and obtain mutually consistent predictions.

    Reason

    Lorentz transformations relate their measurements.

    Working

    same physics, different coordinates

Challenge 5

When do we expect the postulates to apply?

Minimal support

Independent transfer

State the frame class covered directly by the postulates and explain why an accelerating or rotating laboratory is outside that direct setup.

Try this before viewing the solution

Hints

Hint 1: use the no-acceleration criterion
The standard postulates compare frames moving at constant relative velocity.
View solution step by step

  1. Identify the domain

    Method

    The postulates apply directly to inertial frames.

    Reason

    Such frames have constant relative velocity.

    Working

    a_frame = 0

  2. Mark the boundary

    Method

    Accelerating and rotating frames require additional treatment.

    Reason

    They are non-inertial and introduce frame-acceleration effects.

    Working

    a_frame ≠ 0

7. Mind Stretchers

Mind stretcher 1: What has to “give”?Extension

If both postulates are true, which everyday assumptions must fail at high speeds: (i) absolute time, (ii) absolute length, (iii) simple velocity addition? Explain briefly.

Answer

All three classical assumptions fail in their naive forms: time and length become frame-dependent (time dilation and length contraction), and velocity addition must be replaced by the relativistic formula so that c remains invariant.

Mind stretcher 2: Why “in vacuum” mattersExtension

Postulate 2 says the speed of light is c in vacuum for inertial observers. Why do we include “in vacuum” rather than “in any material”?

Answer

In materials, light’s speed depends on the medium (refractive index) and can be different from c. The postulate is about the fundamental invariant speed in vacuum that appears in the spacetime structure (Lorentz transformations).

8. Optional/Enrichment: Where the Postulates Lead Next

The next steps are the consequences you’ll use in H3:

Next in the maintained sequence: Simultaneity.

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H3 Physics
Edition
GCE A-Level H3 Physics 2027