Month Of Equations: What Does Length Contraction Really Mean?

Length contraction formula
Length contraction formula

Meaning of the Equation of Length Contraction:

Length of an object in a moving frame is less than the length of that object in its rest frame. In other words, moving objects are shortened.

A consequence of relativity, length contraction is another buzz-topic after time dilation that is interesting to most physics enthusiasts.The Lorentz factor as given in the formula depends upon the relative velocity(v) between the object and the observer and is always greater than 1.The equation for length contraction means that when we measure the length of a moving object as an observer at rest, the length appears to be shorter than the length we may measure while moving with the same speed as that of the object. Let us again take the basic approach to understand this:

Consider a person holding a stick while sitting in a train moving with a speed close to that of light. If we want to measure the length of an object, we place that object against a metre stick and then find the positions of both of its endpoints simultaneously. The person measures the length of the stick using a metre-scale, let’s say it is measured to be ‘L0’. Now, an observer at rest standing outside the moving train also tries to measure the same stick and he finds out the length of this stick say ‘L’. Length contraction would cause the length ‘L’ of the stick to be essentially less than ‘L0’. But the question is how?

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Imagine it this way- the observer standing on the ground noted the position of the front end (A) of the moving stick, but while he moved to the other end of the stick (B) to note its positions w.r.t. A, the stick covered some distance in the forward direction and the rear end B is now ahead of its position that it was when the position of A was measured. This leads to a shorter length of the same stick measured in a moving frame by an observer at rest.

We must also note here that due to relativity if the person in moving train would try to measure the length of a stick held by the observer on the ground, he would also find it contracted as the motion is relative. This is something like when we see fast moving cars in daily life. The faster-moving cars appear somewhat shorter in length as compared to the ones at rest

  • As per the extremely short lifespan of the elementary particles named muons, the muons must not be able to reach the Earth’s surface. However, because of their velocity of motion close to the speed of light, their lifetime passes slowly and hence, they are able to make it to the surface of Earth. Another way around, we may say that due to relative motion, the layers of the atmosphere are thinned (contracted) for the muons and they are able to land on Earth. 
  • Heavy ions are considered to be spherical at rest. But while traveling nearly at the speed of light, they would assume the form of pancakes (flat disks) as predicted by the principle of length contraction. The results obtained from particle collisions can only be explained when the increased nucleon density due to length contraction is taken into account

Another noteworthy point related to this amazing phenomenon is that the contraction only occurs in the direction of motion of the moving object and not perpendicular to it. So. if a person holds a paintbrush in the moving train to mark a line on the nearby walls, doesn’t matter whether the train is moving or at rest, the marking will be at same height as there is no vertical movement of the train.

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