In fact it clear from the statement that it (the rod) is movingDaveC426913 said:
It is safe to assume that the observer is at rest relative to the spaceship, but we are not told the velocity of the spaceship (and observer) relative to the rod.Skyxplorer said:
Length contraction is a phenomenon predicted by Einstein's theory of special relativity, where an object moving relative to an observer will measure shorter in the direction of motion compared to its proper length (the length measured in its rest frame). This effect becomes significant at speeds approaching the speed of light.
When a rod moves at a high velocity inside a spaceship, observers inside the spaceship will measure the rod's length as its proper length. However, an observer outside the spaceship will measure the rod to be contracted along the direction of its motion due to length contraction. The contracted length can be calculated using the Lorentz factor.
The Lorentz factor, denoted as γ (gamma), is calculated using the formula γ = 1 / √(1 - v²/c²), where v is the velocity of the moving object and c is the speed of light. In length contraction, the contracted length L observed by an external observer is given by L = L₀ / γ, where L₀ is the proper length of the rod.
Length contraction is a physical effect that arises from the nature of space and time as described by special relativity. It is not merely an observational artifact; it indicates that measurements of length depend on the relative motion between the observer and the object being measured.
Length contraction is not noticeable in everyday situations because the speeds involved are much lower than the speed of light. However, it becomes significant in high-speed scenarios, such as particles moving close to the speed of light in accelerators, where experimental evidence supports the predictions of special relativity.