Special Relativity · 02 / 06

Relativity of Simultaneity

Two spatially separated events can share the same time coordinate in one inertial frame and receive different time coordinates in another. Simultaneity is frame-dependent, not universal.

The learner question

Can two events be simultaneous for one observer but not another?

Yes. The disagreement is not caused by signal delay or faulty clocks. It comes from how different inertial frames assign coordinates to the same pair of events.

Lorentz time coordinate
t=γ(tvxc2)t'=\gamma\left(t-\frac{vx}{c^2}\right)

Below we use units with c=1c=1. The platform assigns both events t=0t=0.

Event-coordinate lab

Keep the events fixed. Change only the observer.

γ = 1.250
moving-frame simultaneity line
platform t = 0
rear · platform
front · platform
rear · t′ 0.75
front · t′ -0.75
frame speed
0.60 c
rear event t′
0.75
front event t′
-0.75
Δt′ front−rear
-1.50
Moving-frame speed v0.60 c
Event separation Δx2.00 light-seconds
frame idea
The events do not move

The two flashes are the same physical events in every frame. Only their coordinate labels change.

frame idea
Simultaneous means equal coordinate time

In the platform frame both events have t = 0. In the moving frame their t′ values separate as soon as v is nonzero.

frame idea
The ordering flips with frame direction

Reverse the frame velocity and the event that was earlier becomes later. For spacelike-separated events, no invariant time order exists.

What the slider is showing

A moving frame slices spacetime into “now” differently.

For the platform, the horizontal line through both events is one instant of time. A moving inertial frame uses a tilted simultaneity line. The light cone stays fixed while the frame's space and time axes tilt together.

current verdict
front event occurs earlier in the moving frame

This statement concerns assigned event coordinates, not visual appearance.

Transfer check

Two events are simultaneous in the lab at x = −1 and x = +1. A ship moves in the +x direction. Which event gets the earlier ship-frame time coordinate?

← Frames & Postulates
Next: Spacetime Interval · planned