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Theme A — Space, Time and Motion

A.5.6 Space-Time Interval — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 58 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.5.6 Space-Time Interval — IB PHYSICS HL notes: Define the space-time interval, proper time and proper length as invariant quantities.Time and distance change between inertial frames at speeds near c — these frames are not absolute.Some quantities are the same in all inertial fr…

  • Some quantities are the same in all inertial frames
  • Galilean relativity
  • Special relativity
  • Δt and Δx are different in two frames
  • Proper time interval t0
  • Proper time may be measured in the moving frame or the rest frame

Part 1 of 6Invariant quantities

Invariant quantities
Time and distance change between inertial frames at speeds near c
  • Time and distance change between inertial frames at speeds near c these frames are not absolute.
Some quantities are the same in all inertial frames
  • Some quantities are the same in all inertial frames they are invariant.
  • Proper time t0.
  • Proper length L0.
  • Space-time interval Δs.
They follow from Einstein's second postulate.

Part 2 of 6Space-time in Galilean and special relativity

Galilean relativity
  • Galilean relativity space and time are the same in all frames, t = t' and x = x'.
Special relativity
  • Special relativity space and time are connected as four coordinates (x, y, z, t) for an event.
Motion spans both space and time.
The length of the arrow for the space-time interval is the same in all inertial frames.

Part 3 of 6Space-time interval

Space-time interval
(Δs)2
(cΔt)2 − (Δx)2
  • Δt is the time separation, Δx the spatial separation and Δs the interval, in metres.
Δt and Δx are different in two frames
  • Δs is the same.
Used to construct space-time diagrams and to compare events in different frames.

Part 4 of 6Proper time

1Proper time interval t0
Proper time interval t0 the time between two events measured in the frame where both events occur at the same place.
2
It is measured by a single clock present at both events.
3
The time measured from a frame moving relative to the events is longer.
4Proper time may be measured in the moving frame or the rest frame
  • Proper time may be measured in the moving frame or the rest frame it depends on where the events are.

Part 5 of 6Proper length

1Proper length L0
Proper length L0 the length measured in a frame where the object is at rest.
2
A person on a train measuring a book on the train measures L0.
  • An observer on the platform measures a shorter length.
3
If the person on the platform has the book at rest, they measure L0 and the train observer sees it shortened.
4Do not assume proper quantities belong to the stationary frame
  • Do not assume proper quantities belong to the stationary frame they belong to the frame at rest with respect to the object or events.

Part 6 of 6More from the specification

More from the specification
Invariant spacetime interval for relativistic muons
  • Invariant spacetime interval for relativistic muons the spacetime interval separating muon creation and decay events remains invariant between Earth and muon rest frames.
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.
Relativistic speed
  • Relativistic speed a speed close to the speed of light, where Galilean velocity addition no longer gives correct results.

Key terms

TermMeaning
InvariantQuantity with the same value in all inertial frames.
Space-time intervalΔs, with (Δs)2 = (cΔt)2 − (Δx)2.
Proper timeTime between events at the same place in a frame.
Proper lengthLength of an object measured in its rest frame.
EventOccurrence at a point in space and time.
Four-dimensional coordinatesSet (x, y, z, t) describing an event.

Avoid these mistakes

1
Thinking proper time is always measured in the stationary frame.
2
Treating Δt and Δx as invariant — only Δs is.
3
Forgetting the c in (cΔt)2.
4
Measuring proper length with moving rulers.
5
Using Δs2 = (Δx)2 − (cΔt)2 with the wrong sign convention.

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