Difference Between Time Dilation and Length Contraction

Time Dilation vs Length Contraction

Length contraction and time dilation are two important effects of the theory of relativity. These effects are extremely valuable in describing some of the most complicated phenomena encountered. This article will try to explain what length contraction and time dilation are, and the difference between them.

What is Length Contraction?

Length contraction is a concept discussed under the theory of relativity. This can be explained using the special theory of relativity for ease of understanding. To understand the length contraction and time dilation students must have background knowledge in the special theory of relativity. The special theory of relativity only deals with the inertial frames. Although we cannot even remotely understand the special theory of relativity in a few lines of explanation, there are some useful concepts that can be helpful in describing the length contraction and time dilation. The fundamental of special relativity is that, no objects that are moving in inertial frames can have relative velocities greater than the speed of light. The term γ, which is equal to the square root of 1/ (1-V²/C²), tends to infinity when V tends to C, and tends to 1 when V is extremely small compared to C. This is a very significant term in special relativity. The length contraction arises from the Lorentz transformation equations. The proper length of an object is the length measured in a frame, which is still with respect to the object. The improper length is the length, which is measured from a frame, which the object is moving with a relative velocity of V. In the special theory of relativity, the improper length is always smaller than or equal to the proper length. The relationship between these two is given by improper length = proper length /γ. When the relative velocity is negligible compared to the speed of light, γ tends to 1 and the proper and the improper lengths become the same.

What is Time Dilation?

The proper time is defined as the time measured by an observer who is not moving relative to the event. The improper time is the time measured by an observer who is moving with relative velocity V from or to the event. Using the Lorentz transformation equations, it can be shown that the time measured in the event frame is always smaller than or equal to the time measured by the moving frame. Thereby, the proper time is smaller than or equal to the improper time. The relationship between the proper time and the improper time is given by improper time interval = γ * proper time interval. Since γ tends to 1 when the velocity is negligible with respect to C, the relationship turns to the classical relationship.