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Mathematics for Physics

168 Frame

A coordinate system for measuring events that is used to assign positions and times to physical occurrences.

The coordinate-grid definition of a frame. A reference frame is a grid of meter sticks and synchronized clocks. Synchronized clocks are clocks set so that they read the same time at one common instant. This principle is used to assign unique space and time coordinates to an event.

The shared-frame rule. A reference frame is shared by every experimenter at rest relative to the same origin. At rest is the condition of zero velocity relative to that origin. This principle is used to let a team of observers record one consistent set of positions and velocities.

The frame dependence of intervals. Time intervals and spatial distances between events depend on the reference frame of the observer. A time interval is the elapsed time between two events as read by clocks in that frame. This principle is used to account for time dilation and length contraction.

The frame independence of events. The occurrence itself does not depend on the coordinate labels a frame assigns. This principle is used to look for invariants such as the spacetime interval that every inertial observer agrees on.

Note: Also called a reference frame. Also called a frame of reference.

168.1 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. — reference frame as a coordinate system for event measurements.
  3. Susskind, L., & Friedman, A. Special Relativity and Classical Field Theory. Basic Books, 2017. — events independent of coordinate labels.