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Time Dilation: Moving Clocks Tick Differently

Manual: General · Subject: Physics

Discover that motion changes how time is measured.

Time Is Not Universal

The Core Idea

If two observers move relative to each other, they do not always measure the same amount of time between the same events. A moving clock is observed to tick more slowly than a clock at rest, from the perspective of the other observer.

Time Dilation Formula

The relation is Δt=γΔτ\Delta t = \gamma \Delta \tau where Δτ\Delta \tau is the proper time measured by the clock itself and γ=11−v2/c2\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}. When vv is small compared with cc, γ\gamma is close to 11.

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Interpretation

As speed vv gets closer to cc, the factor γ\gamma grows, so time dilation becomes more dramatic.

How to Read the Formula

  1. 1

    Identify the proper time Δτ\Delta \tau on the moving clock.

  2. 2

    Find the relative speed vv.

  3. 3

    Compute γ=11−v2/c2\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}.

  4. 4

    Multiply to get Δt=γΔτ\Delta t = \gamma \Delta \tau.

What does time dilation mean?

What symbol is commonly used for the time dilation factor?

When the speed vv is very small compared with cc, what is γ\gamma approximately?

Why This Feels Strange

Time dilation sounds impossible at first because our everyday experience is too slow to notice it. But at speeds near cc, the effect is real and measurable.