Skip to main content

Mathematics for Physics

202 Simultaneity

The property of two events occurring at the same time, which is relative: events simultaneous in one frame need not be simultaneous in another.

The relativity of simultaneity. Two events at different places that share one time coordinate in one frame have different time coordinates in a relatively moving frame. Simultaneous events are happenings that share the same coordinate time in a given frame. This principle is used to show that there is no universal now spanning all of space.

Operational light-path disagreement. Because the speed of light is the same for every observer, a light flash from the midpoint of a moving car reaches the rear wall before the front wall as seen from the ground. This principle is used to show that observers in relative motion disagree on the synchronization of clocks.

Invariant causal order. If a signal at or below the speed of light can travel from one event to the other, their time order is the same in every inertial frame. Causally related events are events of which one can influence the other. This principle is used to keep an effect from preceding its cause.

Simultaneity of spacelike events. Two events separated by a spacelike interval can be made simultaneous by choosing one inertial frame. A spacelike interval is a four-dimensional separation too large for light to connect the events. This principle is used to find the relative velocity that equalizes those two time coordinates.

202.1 References

  1. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — source for the heading explanation.
  2. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — frame-dependent now; light-path disagreement.
  3. Griffiths, D. J. Introduction to Electrodynamics. Cambridge University Press, 2024. — relativity of simultaneity; causal order; constancy of \(c\).
  4. Shankar, R. Fundamentals of Physics I. Yale University Press, 2019. — clock synchronization; spacelike simultaneity.
  5. Carroll, S. M. Spacetime and Geometry. Cambridge University Press. — no absolute now; invariant causal order; spacelike events.