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Modern Physics
Modern Physics

Relativity of Simultaneity

Δt′=γ(Δt−vΔxc2)\Delta t' = \gamma\left(\Delta t - \frac{v\Delta x}{c^2}\right)

Events that are simultaneous in one frame may not be simultaneous in another. Two events separated in space will have different time separations in different reference frames.

Variables

Δt'
Time interval in moving frame
Allowed values: greater than 0
s
Δt
Time interval in rest frame
Allowed values: greater than 0
s
Δx
Spatial separation in rest frame
m
γ
Lorentz factor
Allowed values: 1 or more
unitless
v
Relative velocity
m/s
c
Speed of light
Allowed values: greater than 0
m/s

Derivation

Part of the Lorentz transformation for time coordinates.

Your notes

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Constants in this formula

c
Speed of Light in Vacuum
299,792,458. Exact by definition.
m/s

Other modern physics formulas with the same quantities

Where this formula is listed

Common questions

What is the Relativity of Simultaneity formula?

Relativity of Simultaneity is written Δt′ = γ(Δt − vΔx/c²). Events that are simultaneous in one frame may not be simultaneous in another. Two events separated in space will have different time separations in different reference frames. It belongs to Modern Physics, under Special Relativity.

What are the units in Δt′ = γ(Δt − vΔx/c²)?

In SI units, Δt′ is time interval in moving frame, measured in s; Δt is time interval in rest frame, measured in s; Δx is spatial separation in rest frame, measured in m; γ is lorentz factor (dimensionless); v is relative velocity, measured in m/s; c is speed of light, measured in m/s.

How is the Relativity of Simultaneity formula derived?

Part of the Lorentz transformation for time coordinates. The result is Δt′ = γ(Δt − vΔx/c²).