3.12.3.2 - Einstein's Theory of Special Relativity
Special relativity describes measurements made in inertial frames. Its two postulates give all these frames the same physical laws and the same vacuum light speed, even when they disagree about an object's velocity.
Describing events in a frame
A frame of reference is a system of positions and clocks used to describe where and when events occur. An event is something occurring at a particular position and time, such as a lamp emitting a pulse or a particle reaching a detector.
A cup on a steadily moving train is at rest relative to the train but moving relative to the platform. Neither description is incomplete once its frame is specified. Position, displacement and velocity require a reference frame; saying only “the cup moves” omits part of the measurement.
The same caution applies to time measurements at separated positions. A frame can use a set of clocks at rest at different locations, synchronised in that frame. “The Earth-frame journey time” can mean the difference between departure and arrival readings on two such clocks, rather than the elapsed time on one clock that accompanies the traveller. This distinction will matter for time dilation.
Recognising an inertial frame
An inertial frame is one in which a body with no resultant force remains at rest or moves at constant velocity: Newton's first law holds without introducing fictitious forces. Inertial frames move at constant velocity relative to one another and do not rotate relative to one another.
A non-rotating spacecraft coasting far from appreciable gravitational effects approximates an inertial frame. A frame fixed in an accelerating rocket does not. A free object that continues on its unforced path can appear to accelerate relative to the rocket, revealing the frame's acceleration internally.
Constant speed alone is insufficient. A car turning a corner changes direction and hence velocity, so it accelerates. A rotating laboratory is also non-inertial. Earth laboratories are often good approximations over limited distances and times; Earth's rotation means the approximation is not exact.
The phrase “moving at constant velocity” needs a reference: the frame must move uniformly relative to an inertial frame. A chair fixed to an accelerating rocket is at rest relative to the rocket but is not thereby inertial.
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