Editing Special relativity (section)

=== Length contraction ===
{{See also|Lorentz contraction}}
The dimensions (e.g., length) of an object as measured by one observer may be smaller than the results of measurements of the same object made by another observer (e.g., the [[ladder paradox]] involves a long ladder traveling near the speed of light and being contained within a smaller garage).

Similarly, suppose a [[measuring rod]] is at rest and aligned along the ''x''-axis in the unprimed system ''S''. In this system, the length of this rod is written as Δ''x''. To measure the length of this rod in the system {{prime|''S''}}, in which the rod is moving, the distances ''{{prime|x}}'' to the end points of the rod must be measured simultaneously in that system {{prime|''S''}}. In other words, the measurement is characterized by {{nowrap|1=Δ{{prime|''t''}} = 0}}, which can be combined with {{EquationNote|4|Equation&nbsp;4}} to find the relation between the lengths Δ''x'' and Δ{{prime|''x''}}:
: <math>\Delta x' = \frac{\Delta x}{\gamma} </math>{{pad|4}}{{pad|4}}for events satisfying{{pad|4}}<math>\Delta t' = 0 \ .</math>
This shows that the length (Δ{{prime|''x''}}) of the rod as measured in the frame in which it is moving ({{prime|''S''}}), is ''shorter'' than its length (Δ''x'') in its own rest frame (''S'').

Time dilation and length contraction are not merely appearances. Time dilation is explicitly related to our way of measuring ''time intervals'' between events that occur at the same place in a given coordinate system (called "co-local" events). These time intervals (which can be, and are, actually measured experimentally by relevant observers) are ''different'' in another coordinate system moving with respect to the first, unless the events, in addition to being co-local, are also simultaneous. Similarly, length contraction relates to our measured distances between separated but simultaneous events in a given coordinate system of choice. If these events are not co-local, but are separated by distance (space), they will ''not'' occur at the same ''spatial distance'' from each other when seen from another moving coordinate system.