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Theme A — Space, Time and Motion

A.5.9 Simultaneity in Special Relativity — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 61 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

A.5.9 Simultaneity in Special Relativity — IB PHYSICS HL notes: Explain the relativity of simultaneity using the train and lamp example.Simultaneous means occurring at the same time.The relativity of simultaneity — whether spatially separated events happen at the same time is not…

  • In Galilean relativity simultaneity was absolute
  • Length measurement requires ends at the same time
  • The order of some events can differ between observers
  • Events at the same ct are simultaneous in S
  • Inertial frame
  • Space-time diagram

Part 1 of 6Simultaneous events

1
Simultaneous means occurring at the same time.
2The relativity of simultaneity
  • The relativity of simultaneity whether spatially separated events happen at the same time is not absolute.
3
It depends on the observer's reference frame.
4In Galilean relativity simultaneity was absolute
  • In Galilean relativity simultaneity was absolute in special relativity it is not.

Part 2 of 6Statement of the effect

1
Two events at different points that are simultaneous in one frame are not simultaneous in a frame moving relative to the first.
2
In the second frame the events happen one after another.
3
It follows from the constant speed of light for all observers.
4
The effect is very small at everyday speeds and grows with speed.

Part 3 of 6Train and lamp example

1
Person B is in a train carriage moving right at constant velocity and switches on a lamp above.
2
B sees the light reach the two ends X and Y of the carriage at the same time.
3
Person A on the platform also measures light moving at c in both directions — the second postulate.
4
The carriage moves right — so the left end X moves towards the light and the right end Y moves away.
5
A sees the light reach X before Y.
  • The difference in times is tiny and depends on the speed of the carriage.

Part 4 of 6Consequences

1
Simultaneity in one frame does not carry over to another moving frame.
2
It explains why time dilation and length contraction are consistent.
3Length measurement requires ends at the same time
  • Length measurement requires ends at the same time which differs between frames.
4The order of some events can differ between observers
  • The order of some events can differ between observers but only if they are not causally connected.

Part 5 of 6Using space-time diagrams

1
Simultaneity can be visualised on a space-time diagram.
2Events at the same ct are simultaneous in S
  • Events at the same ct are simultaneous in S events on a line parallel to the x' axis are simultaneous in S'.
3
Observer A sees light reach X before Y in the ct'–x' system, while B sees them at the same time.
4
Simultaneity is not possible for two frames moving relative to each other.

Part 6 of 6More from the specification

1Non-simultaneity of muon decay events
  • Non-simultaneity of muon decay events spacelike separated creation events for relativistic muons occur at different times across relatively moving reference frames.
2Relativity of simultaneity
  • Relativity of simultaneity events occurring simultaneously for an observer on Earth do not occur simultaneously for a moving rocket traveller.
3Spacetime interval invariance
  • Spacetime interval invariance the spacetime interval combining elapsed proper time and spatial distance remains invariant across all inertial reference frames.
4Lorentz coordinate transformation
  • Lorentz coordinate transformation relates spatial distance and time coordinates between stationary and moving reference frames in uniform relative motion.
5Relativity of Simultaneity
  • Two spatially separated events that appear simultaneous to a stationary observer on Earth are not simultaneous to an observer travelling inside a high-speed rocket moving at relativistic velocity.
6Lorentz Transformation and Spacetime Coordinates
  • The Lorentz transformation equations link spacetime coordinates measured in different inertial reference frames using the Lorentz factor gamma = 1 / sqrt(1 - v2/c2, reconciling the invariance of light speed.
7Proper Time and Time Dilation
  • The proper time interval Delta t0 is defined as the time interval between two events measured in an inertial frame where both events occur at the same spatial position;
    • a moving traveller observes dilated time Delta t = gamma * Delta t0.
8Length Contraction Along Direction of Motion
  • An observer measures the proper length L0 of an object when at rest relative to it;
    • an observer in relative motion measures a contracted distance or length L = L0 / gamma along the direction of travel.
9Proper length
  • Length measured in the rest frame of the object.
10Velocity addition
  • U = u' + v.
11Space-time interval
  • Invariant quantity (cΔt)2 − (Δx)2.
12Stationary
  • Not moving.
13Distance
  • Total length of path travelled, a scalar.
14Gradient
  • Slope of a graph line.

Key terms

TermMeaning
SimultaneityOccurring at the same time.
Relativity of simultaneitySimultaneity depends on the observer's frame.
Inertial frameNon-accelerating frame of reference.
EventOccurrence at a particular place and time.
Space-time diagramPlot of ct against x showing events.
Second postulateSpeed of light is the same for all inertial observers.

Avoid these mistakes

1
Assuming simultaneous events in one frame are simultaneous in all frames.
2
Thinking the light travels at different speeds for the two observers.
3
Forgetting that the end moving towards the light is reached first.
4
Applying the effect to events at the same location — the effect is for spatially separated events.
5
Treating the effect as an optical illusion — it is real.

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