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Theme A — Space, Time and Motion

A.5.3 Postulates of Special Relativity — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 55 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

A.5.3 Postulates of Special Relativity — IB PHYSICS HL notes: State Einstein's two postulates and explain why Galilean velocity addition fails near the speed of light.Newton treated space and time as fixed and absolute.The time interval between two events was the same in all fram…

  • Near the speed of light, space and time become relative
  • Nothing can travel faster than c
  • In its own frame an observer is always stationary
  • Two observers always measure c
  • If it differed, you could tell you were moving
  • A runner with a flashlight measures c

Part 1 of 6Limits of Galilean relativity

Limits of Galilean relativity
Newton treated space and time as fixed and absolute.
  • The time interval between two events was the same in all frames.
Near the speed of light, space and time become relative
  • Near the speed of light, space and time become relative lengths and time intervals depend on the frame.
Velocity addition works well for speeds much less than c, but fails near c.

Part 2 of 6Why Galilean addition fails

Why Galilean addition fails
A rocket at 0.7c releasing a probe at 0.5c ahead would give 1.2c for a stationary observer.
Nothing can travel faster than c
  • Nothing can travel faster than c so this is impossible.
A correct law must keep the speed of light the same for all observers.

Part 3 of 6First postulate

1
The laws of physics are the same in all inertial frames of reference.
2In its own frame an observer is always stationary
  • In its own frame an observer is always stationary so they cannot tell if they are moving.
3
An experiment on a moving train gives the same result as on a platform.

Part 4 of 6Second postulate

Second postulate
The speed of light in a vacuum, c, is the same in all inertial frames.
Two observers always measure c
  • Two observers always measure c whether travelling or not.
If it differed, you could tell you were moving
  • If it differed, you could tell you were moving which would contradict the first postulate.
A runner with a flashlight measures c
  • A runner with a flashlight measures c and so does a stationary observer, not c plus the runner's speed.
This holds only for the speed of light, not other speeds.

Part 5 of 6Consequences

1
Time dilation and length contraction follow from the second postulate.
2
Simultaneity becomes relative.
3
The Lorentz transformations replace the Galilean ones.
4Both postulates must be recalled
  • Both postulates must be recalled they underpin the equations of special relativity.
5Moving observers cannot see light slow or speed up
  • Moving observers cannot see light slow or speed up time and space adjust instead.

Part 6 of 6More from the specification

More from the specification
Invariance of light speed and muons
  • Invariance of light speed and muons relativistic muons moving near light speed validate Einsteinian postulates across all inertial reference frames.
Postulates of Special Relativity
  • Einstein's postulates state that the laws of physics are identical in all inertial reference frames,
  • and the speed of light in a vacuum c is invariant, independent of the motion of the emitting object or observer.
Proper Time and Time Dilation
  • Proper time is the time interval measured by an observer in whose reference frame two events occur at the same spatial point;
    • according to an observer on Earth watching a high-speed particle moving relative to them, measured time dilates as Δt = γ·Δt₀.
Length Contraction and Spacetime Invariance
  • The proper length of an object is measured in its rest frame;
    • moving observers measure a contracted distance along the direction of relative motion,
  • while the spacetime interval (Δs)² = (cΔt)² - (Δx)² remains invariant across all inertial frames.
Distance
  • Total length of path travelled, a scalar.
Gradient
  • Slope of a graph line.
Proper length
  • Length measured in the rest frame of the object.
Constant velocity
  • Zero acceleration.
Space-time interval
  • Invariant quantity (cΔt)2 − (Δx)2.

Key terms

TermMeaning
First postulateLaws of physics are identical in all inertial frames.
Second postulateSpeed of light in vacuum is the same in all inertial frames.
Inertial frameNon-accelerating frame of reference.
Absolute timeNewtonian idea of time identical in all frames.
Relativistic speedSpeed close to the speed of light.
Speed of light c3.00 × 108 m s-1 in a vacuum.

Avoid these mistakes

1
Saying the speed of light depends on the observer's motion.
2
Adding light speed to the speed of the source.
3
Stating only one postulate.
4
Applying the second postulate to speeds other than c.
5
Assuming time is absolute when speeds approach c.

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