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- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/04%3A_Tensors/4.02%3A_Four-vectors_(Part_1)The basic Lorentz vector is the spacetime displacement. Any other quantity that has the same behavior under rotations and boosts is also a valid Lorentz vector.
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/04%3A_Tensors/4.03%3A_Four-vectors_(Part_2)A four-vector is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considere...A four-vector is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations and boosts.
- https://phys.libretexts.org/Bookshelves/Relativity/Special_Relativity_(Crowell)/03%3A_Kinematics/3.05%3A_The_Velocity_and_Acceleration_VectorsIf we also considered the helicopter’s velocity to be part of the description of its state, then there would be a total of six degrees of freedom: one for each coordinate and one for each component of...If we also considered the helicopter’s velocity to be part of the description of its state, then there would be a total of six degrees of freedom: one for each coordinate and one for each component of the velocity vector. Since we want the particle to have a single well-defined vector to represent its velocity, we want to pick one vector from among all the vectors parallel to the dashed line, and call that “the” velocity vector.
- https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/15%3A_Relativistic_Forces_and_Waves/15.01%3A_The_Force_Four-VectorIn classical mechanics, Newton’s second law relates momenta and forces, through the time derivative of the momentum. In relativity, we’ll therefore simply define the force four-vector as the derivativ...In classical mechanics, Newton’s second law relates momenta and forces, through the time derivative of the momentum. In relativity, we’ll therefore simply define the force four-vector as the derivative of the energy-momentum four-vector with respect to the proper time.
