Definition of a Pseudovector
A pseudovector, also known as an axial vector, is a quantity in physics and mathematics that transforms like a vector under proper rotations (like turning around an axis) but gains an additional sign flip under improper rotations (like reflections or inversion through the origin). This behavior distinguishes it from a true vector, which remains unchanged by reflections except for its components.
Key Characteristics and Differences
Unlike true vectors (polar vectors) such as displacement or velocity, pseudovectors describe quantities related to rotation or orientation. Their components transform like a vector, but their direction is defined relative to the orientation of the coordinate system. When the coordinate system undergoes a reflection, a true vector's components simply change sign if they point in the direction of reflection, while a pseudovector's components change sign *regardless* of their direction.
Practical Examples of Pseudovectors
Common examples of pseudovectors include angular velocity, torque, angular momentum, magnetic field, and the curl of a vector field. For instance, if you apply a torque to an object and then view it in a mirror, the torque appears to be applied in the opposite direction in the mirror image, illustrating its pseudovector nature.
Importance in Physics and Engineering
Understanding pseudovectors is crucial in fields like classical mechanics, electromagnetism, and quantum mechanics, where rotational quantities and symmetries play a significant role. Distinguishing between polar vectors and axial vectors is essential for correctly formulating physical laws and interpreting experimental results, especially when dealing with phenomena involving handedness or parity.