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Our Place in the Universe

Relativistic time dilation

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on γ = 1/√(1 − v²/c²) and its values at rest, 0.60c and 0.80c, time dilation and dilated intervals, why it goes unnoticed, muon lifetimes as evidence, γ growing without limit near c, the speed at which γ is 2.0, why massive objects cannot reach c, satellite navigation, and the symmetry between observers.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

Why is time dilation unnoticed in ordinary life? Find the dilated 1.00 s at 0.60c and 2.2 μs at 0.99c, and explain muon evidence.

Key term

What is the expression for the relativistic factor γ?

Key term

How is a time interval measured in the laboratory related to the interval measured in the moving frame?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is the expression for the relativistic factor γ?

    Model answer

    The factor is γ = 1/√(1 − v²/c²).

  2. 2

    What is meant by time dilation?

    Model answer

    A clock moving relative to an observer is measured by that observer to run slow compared with an identical clock at rest beside them.

  3. 3

    How is a time interval measured in the laboratory related to the interval measured in the moving frame?

    Model answer

    The laboratory interval is γ times the interval measured in the frame in which the two events happen at the same place.

  4. 4

    Calculate γ for an object moving at 0.60c.

    Model answer

    γ = 1/√(1 − 0.36) = 1/0.80 = 1.25.

  5. 5

    Calculate γ for an object moving at 0.80c.

    Model answer

    γ = 1/√(1 − 0.64) = 1/0.60 = 1.7.

  6. 6

    What is the value of γ for an object at rest, and what does it mean?

    Model answer

    It is 1, which means there is no time dilation at all.

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