Length contraction is the phenomenon where an object appears shorter along the dimension of its motion to an observer when it is in motion relative to them. It is a consequence of special relativity, where the speed of light is constant for all observers. The effect increases at higher speeds and is negligible in everyday life. The relativity of simultaneity means that observers moving relative to each other will disagree on the length of an object. The measured length change differs from how the object would appear visually due to the delay effect of photons emitted from different parts of the object.
Length contraction refers to a phenomenon in which an object is perceived to be shorter along the dimension of its motion by an observer when the object is in motion relative to that observer. It is also called the Lorentz contraction or Lorentz-Fitzgerald contraction, after physicists Hendrik Lorentz and George Fitzgerald. The faster an object moves relative to the observer, the more it will contract from the observer’s perspective. This effect is so small as to be negligible at speeds humans may encounter in everyday life, but in objects moving at an appreciable fraction of the speed of light it becomes more apparent.
The phenomenon of length contraction is a consequence of special relativity. According to the theory of relativity, the speed of light in a vacuum (about 300,000 kilometers or 186,000 miles per second), oc, is always constant for all observers. Counterintuitively, this remains the case for light emitted by a moving source from an observer’s perspective.
Suppose an object is thrown in the direction of travel by a spacecraft moving at 5 kilometers per second (KPS) relative to the Earth, propelling it away from the spacecraft at 1 KPS. An observer in the ship will perceive it as moving away at 1 KPS, while an observer on Earth will perceive it moving at 6 KPS. If an external light is turned on the ship, the observer in the ship will detect the light moving away from the ship at c, but the observer on Earth will also perceive the light moving at c, not c plus the speed of the ship.
The result is that the precise moment the ship’s light reaches a given location will vary for different observers depending on their speed relative to the ship. As a result, they won’t agree on what other events were happening at the same time. This is called the relativity of simultaneity.
How this relates to the sensed length of an object is commonly explained in the following thought experiment. Imagine a row of synchronized clocks, where each clock can measure when the left and right ends of a moving object pass in front of it. After an object has moved past the row of clocks, an observer can determine its length by calculating the distance two clocks would have to be from each other for the right end of the object to reach a clock at the same instant as the right end of the clock. left end reaches the second clock.
Two observers who share a frame of reference will agree on the duration. Since the measurement is based on which events occur simultaneously, however, observers moving relative to each other will disagree on the length. The faster an observer travels relative to the clocks, the more their measurements will differ from those of an observer at rest relative to them.
The effect of length contraction increases at higher speeds. An object moving at 0.05c (5 percent of the speed of light), at about 14.990 kilometers (9.314 miles) per second, will appear to be slightly shortened to a stationary observer—about 99.87 percent of its rest length if it is oriented parallel to the line of its movement. The length seen by the observer reduces to 97.79 percent of its rest length at 0.2 c, 91.65 percent at 0.4 c, and 71.41 percent at 0.7 c. At 0.9c the detected length of the object shrinks to 43.58 percent and at 0.999c it shrinks to only 4.47 percent. The contraction closest to c becomes even more extreme, although the length never contracts to zero.
If there is an observer traveling with the object, this observer does not perceive the contracting object because, from his point of view, the object’s relative velocity is zero. In that observer’s frame of reference, the object is stationary while the rest of the universe is in motion relative to the observer, and thus from that observer’s perspective it is the rest of the universe that is contracting.
The measured length change of an object undergoing length contraction differs from how the object would actually appear visually, as seen by the human eye or a camera, because an object moving fast enough to produce significant length contraction will it moves at a significant percentage of the speed of its own light. At these speeds, the photons emitted simultaneously from different parts of the object will reach the observer at significantly different times, distorting the visual aspect of the object. Thus, an object moving toward an observer at high speed would be distorted such that it actually appears longer on visual inspection despite the length contraction. An object moving away from the observer would appear shorter due to the same delay effect, plus effective length contraction, and an object moving past the observer would appear crooked or rotated.
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