Time dilation and length contraction
See also: Twin paradox In physics, the twin paradox is a thought experiment in special relativity, in which a twin who makes a journey into space in a high-speed rocket will return home to find he has aged less than his identical twin who stayed on Earth. This result appears puzzling on this basis: the laws of physics should exhibit symmetry. Each twin sees the otherWriting the Lorentz transformation and its inverse in terms of coordinate differences we get
and
Suppose we have a clock A clock is an instrument used for indicating and maintaining the time and passage thereof. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell". For horologists and other specialists the term clock continues to mean exclusively a device with a striking mechanism for announcing intervals of time at rest in the unprimed system S. Two consecutive ticks of this clock are then characterized by Δx = 0. If we want to know the relation between the times between these ticks as measured in both systems, we can use the first equation and find:
- for events satisfying
This shows that the time Δt' between the two ticks as seen in the 'moving' frame S' is larger than the time Δt between these ticks as measured in the rest frame of the clock. This phenomenon is called time dilation Time dilation is a phenomenon described by the theory of relativity. It can be illustrated by supposing that two observers are in motion relative to each other, and/or differently situated with regard to nearby gravitational masses. They each carry a clock of identically similar construction and function. Then, the point of view of each observer.
Similarly, suppose we have a measuring rod at rest in the unprimed system. In this system, the length of this rod is written as Δx. If we want to find the length of this rod as measured in the 'moving' system S', we must make sure to measure the distances x' to the end points of the rod simultaneously in the primed frame S'. In other words, the measurement is characterized by Δt' = 0, which we can combine with the fourth equation to find the relation between the lengths Δx and Δx':
- for events satisfying
This shows that the length Δx' of the rod as measured in the 'moving' frame S' is shorter than the length Δx in its own rest frame. This phenomenon is called length contraction Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer. This contraction is usually only noticeable, however, at a substantial fraction of the speed of light; and the contraction is only in the direction or Lorentz contraction.
These effects are not merely appearances; they are explicitly related to our way of measuring time intervals between events which occur at the same place in a given coordinate system (called "co-local" events). These time intervals will be different in another coordinate system moving with respect to the first, unless the events are also simultaneous. Similarly, these effects also relate 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. However, the space-time interval (see spacetime#space-time interval In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions. According to certain Euclidean space perceptions, the universe has three) will be the same for all observers. The underlying reality remains the same. Only our perspective changes.
<<Table of Contents Special relativity (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies" | Next>> | Show All>>
