The Lorentz transformation is a mathematical formula used in the theory of special relativity to describe how measurements of space and time vary between different frames of reference that are moving at constant velocities relative to each other.
Length contraction is a phenomenon predicted by the Lorentz transformation, where objects appear shorter in the direction of motion when measured by an observer in a different frame of reference. This effect is only noticeable at high velocities relative to the speed of light.
No, length contraction cannot be proven definitively as it is a theoretical concept based on the assumptions and equations of the Lorentz transformation. However, there is strong empirical evidence, such as the results of particle accelerator experiments, that support the predictions of length contraction.
The Lorentz transformation also predicts time dilation, where time appears to pass slower for objects moving at high velocities relative to an observer. This means that time is not absolute and can vary depending on the frame of reference of the observer.
The Lorentz transformation is a well-established and tested theory, but it may not apply in extreme scenarios such as near black holes or in the very early universe. However, for most everyday situations, the Lorentz transformation accurately describes the relationship between space and time in the theory of special relativity.