What Is Length Contraction?

John Markley
John Markley
Scientist with beakers
Scientist with beakers

Length contraction refers to a phenomenon in which an object is perceived as shorter along the dimension of its motion by an observer when the object is in motion relative to that observer. It is also called Lorentz contraction or Lorentz–Fitzgerald contraction, after physicists Hendrik Lorentz and George Fitzgerald. The faster an object is moving 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 are likely to encounter in daily life, but in objects moving at an appreciable fraction of the speed of light it becomes more noticeable.

The phenomenon of length contraction is a consequence of special relativity. According to the theory of relativity, the speed of light in a vacuum (approximately 300,000 kilometers, or 186,000 miles, per second), or c, is always constant for all observers. Counterintuitively, this remains the case for light emitted from a source that is moving from the perspective of an observer.

Suppose an object is launched in the direction of travel from a spaceship moving at 5 kilometers per second (KPS) relative to the Earth, propelling it away from the ship 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 on the ship is turned on, 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 velocity of the ship.

The result is that the precise moment at which the ship's light reaches a given location will vary for different observers depending on their velocity relative to the spaceship. Consequently, they will disagree as to what other events were occurring at that same moment. This is called the relativity of simultaneity.

How this relates to an object's detected length is commonly explained in the following thought experiment. Imagine a row of synchronized clocks, where each clock can measure when the left and and right end of a moving object is passing in front of it. After an object moves 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 one clock at the same instant the left end reaches the second clock.

Two observers sharing a frame of reference will agree on the length. As the measurement is based on which events occur simultaneously, however, observers in motion relative to each other will not agree on the length. The greater an observer's speed 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 grow at higher speeds. An object moving 0.05c (5 percent of the speed of light), about 14,990 kilometers (9,314 miles) per second, will appear to be very slightly shortened to a stationary observer — about 99.87 percent of its length at rest if it is oriented parallel to the line of its movement. The length seen by the observer contracts to 97.79 percent of its length at rest at 0.2c, 91.65 percent at 0.4c, and 71.41 percent at 0.7c. At 0.9c the object's detected length is reduced to 43.58 percent, and at 0.999c it contracts to only 4.47 percent. Closer to c contraction grows even more extreme, though the length never contracts to zero.

If there is an observer traveling with the object, this observer does not perceive the object as contracting because, from his or her perspective, the relative velocity of the object is zero. In that observer's reference frame, the object is stationary while the rest of the universe is in motion relative to the observer, and so from that observer's perspective it is the rest of the universe that contracts.

The change in the measured length 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 noticeable length contraction is moving at a significant percentage of the speed of its own light. At such speeds, photons emitted from different parts of the object at the same time will reach the observer at appreciably different times, distorting the object's visual appearance. Thus, an object moving toward an observer at a high speed would be distorted so that it would actually appear longer to visual inspection despite length contraction. An object moving away from the observer would look shorter due to the same time lag effect, on top of the actual length contraction, and an object going past the observer would seem to be askew or rotated.

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Discussion Comments


@Blikissot - This isn't as hard as you might think. It might be explained in a confusing way but if it were shown to you it might make more sense. Sometimes these theories are better drawn than spoken about.


This sounds even more confusing than the already complex Theory of Relativity. but I think I can grasp the concept a little. I guess using computer modeling there would be a way to prove this as opposed to the methods used in the early days of science and physics.

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