Time dilation affects not only the flow of time but also the physical properties of objects, including their dimensions. When an object is moving relative to an observer or is in a gravitational field, time dilation can cause a contraction in the object's length along its direction of motion. This phenomenon is known as length contraction or Lorentz contraction.
According to special relativity, as an object approaches the speed of light, its length in the direction of motion appears shorter to an observer who is at rest relative to the object. This contraction factor is given by the Lorentz factor:
γ = 1 / √(1 - v²/c²)
where γ is the Lorentz factor, v is the velocity of the object relative to the observer, and c is the speed of light in a vacuum.
As the object's velocity approaches the speed of light (c), the Lorentz factor approaches infinity, resulting in significant length contraction. However, it's important to note that length contraction is only noticeable when objects are moving at relativistic speeds, which are a substantial fraction of the speed of light.
In the case of objects affected by gravity, as described by general relativity, time dilation due to gravitational fields can also cause length contraction. In regions of strong gravitational fields, such as near massive objects like stars or black holes, spacetime is curved, and time dilation occurs. This gravitational time dilation leads to a contraction of lengths in the direction of the gravitational field.
The effect of time dilation on contracting objects is significant at speeds close to the speed of light or in strong gravitational fields. In everyday life, these effects are negligible and not directly observable. However, they have been verified and measured in experiments involving high-speed particles, satellites, and gravitational observations, as mentioned earlier.