Gavroy said:hey,
I heard about improper Lorentz transformations, but I did not really understand what they are. I just know that their determinant is -1, but what does this physically mean?
Can somebody explain this to me?
An improper Lorentz transformation is a transformation that involves both a rotation and a boost, which affects both the spatial coordinates and the time coordinate. It is often used in special relativity to describe the transformation of spacetime coordinates between two reference frames that are moving relative to each other.
A proper Lorentz transformation only involves a boost, which affects only the spatial coordinates and leaves the time coordinate unchanged. An improper Lorentz transformation, on the other hand, involves both a boost and a rotation, which affects both the spatial and time coordinates.
An improper Lorentz transformation can be expressed using a 4x4 matrix, known as the Lorentz transformation matrix, which combines the effects of a rotation matrix and a boost matrix. The specific form of the matrix depends on the specific reference frames involved in the transformation.
Improper Lorentz transformations are commonly used in special relativity to describe the transformation of coordinates between two reference frames that are moving relative to each other. They are also used in particle physics, where the momentum and energy of particles are affected by these transformations.
While improper Lorentz transformations are useful in certain situations, they are not applicable in all scenarios. For example, they cannot be used in general relativity, where spacetime is described as curved rather than flat. Additionally, improper Lorentz transformations do not preserve the causal structure of spacetime, which can lead to inconsistencies in certain physical theories.