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Theme A — Space, Time and Motion

A.5.7 Time Dilation — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 59 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

A.5.7 Time Dilation — IB PHYSICS HL notes: State and use the time dilation equation and derive it from a light clock.To an observer moving relative to a clock near c, the clock ticks slower.A rocket clock reading 15:00 may be read as 14:45 by an Earth observer.The effect is symme…

  • The effect is symmetric
  • A memory aid
  • The derivation only uses speed
  • The speed of light is c for both observers
  • Relativistic speed
  • Proper time

Part 1 of 6Time dilation

To an observer moving relative to a clock near c, the clock ticks slower.
A rocket clock reading 15:00 may be read as 14:45 by an Earth observer.
The effect is symmetric
  • The effect is symmetric each observer measures the other's clock as slower.
A memory aid
  • A memory aid moving clocks run slower, where "moving" depends on the frame.

Part 2 of 6Time dilation equation

Δt
γΔt0
  • Δt is the time measured by an observer moving relative to the clock (s).
  • Δt0 is the proper time interval, measured where the events occur at the same position (s).
  • γ = 1/√(1 − v2/c2).
Since γ is greater than 1, Δt is greater than Δt0.
The equation is on the data sheet.

Part 3 of 6Light clock derivation

1
A light clock has two mirrors a distance L apart — at rest the time for a round trip is Δt0 = 2L/c.
2
For an observer who sees the clock move at speed v, the light follows a longer path 2D.
3
D2 = L2 + (vΔt/2)2, with D = cΔt/2.
4
Solving gives Δt = 2L/(c√(1 − v2/c2)) = γΔt0.
1The derivation only uses speed
The derivation only uses speed distance/time and Pythagoras.
2
It is not required in the exam but shows where γ comes from.

Part 4 of 6Why time slows

1The speed of light is c for both observers
  • The speed of light is c for both observers by the second postulate.
2
The light does not speed up or slow down to hit the mirrors at the same rate.
3
Therefore time itself must stretch.
4
The time interval is measured at the same position in the clock's own frame.

Part 5 of 6Using time dilation

Using time dilation
Identify the proper time — the time on a clock present at both events.
Calculate γ from v.
Δt = γΔt0 to find the time seen by the other observer.
A spacecraft at 0.7c on a journey of 14.2 ly measured from Earth.
  • Earth observer14.2/0.7 = 20.3 years.
  • Traveller (proper time)20.3/γ = 14.5 years.
Check
  • Check the stationary observer always measures the longer time.

Part 6 of 6More from the specification

More from the specification
Time dilation in muon reference frames
  • Time dilation in muon reference frames unstable relativistic muons live longer when observed from Earth reference frames due to special relativistic time dilation.
Length
  • Resistance is directly proportional to the length of a wire.
Gradient
  • Slope of a graph line.
Reference frame
  • Coordinate system used by an observer.
Length contraction
  • Shortening of lengths measured along the direction of relative motion.
Proper length
  • Length measured in the rest frame of the object.
Constant velocity
  • Zero acceleration.
Space-time interval
  • Invariant quantity (cΔt)2 − (Δx)2.
Relativistic speed
  • Relativistic speed a speed close to the speed of light, where Galilean velocity addition no longer gives correct results.

Key terms

TermMeaning
Time dilationMoving clocks measured as running slower.
Proper timeTime interval measured in the frame where both events occur at the same place.
Lorentz factorγ = 1/√(1 − v2/c2.
Light clockTwo mirrors with light bouncing between them to measure time.
Dilated timeTime interval measured in a frame moving relative to the events.
Relativistic speedSpeed close to c.

Avoid these mistakes

1
Using the proper time as Δt instead of Δt0.
2
Dividing by γ to find the longer time.
3
Thinking only the moving clock runs slow — the effect is symmetrical.
4
Forgetting that proper time is measured where both events happen at the same place.
5
Taking light to speed up between mirrors instead of time dilating.

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