In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) [1] 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 ...

In the literature of relativity, space-time coordinates and the energy/momentum of a particle are often expressed in four-vector form. They are defined so that the length of a four-vector is invariant under a coordinate transformation. This invariance is associated with physical ideas.

2025年3月5日 · In the Minkowski space of special relativity, a four-vector is a four-element vector that transforms under a Lorentz transformation like the position four-vector. In particular, four-vectors are the vectors in special relativity which transform as

Our basic Lorentz vector is the spacetime displacement \ (dx^i\). Any other quantity that has the same behavior as dx i under rotations and boosts is also a valid Lorentz vector. Consider a particle moving through space, as described in a Lorentz frame.

2018年3月22日 · The mathematical definition of a 4-vector is quite straightforward: it's an element of a 4-dimensional vector space V V which is equipped with a Minkowski metric η η (i.e. a bilinear, real-valued function with a (−, +, +, +) (−, +, +, +) or a (+, −, −, −) (+, −, −, −) signature).

4-vector. The moral of this story is that the above definition of a 4-vector is a nontrivial one because there are two possible ways that a 4-tuplet can transform. It can transform according to the 4-vector definition, as in eq. (12.2). Or, it can transform by simply having each of the Ai transform separately (knowing how the dxi transform ...

The four-vector is introduced that unifies space-time coordinates x, y, z and t into a single entity whose components get mixed up under Lorentz transformations. The length of this four-vector, called the space-time interval, is shown to be invariant (the same for all observers).

Although the use of 4-vectors is not necessary for a full understanding of Special Relativity, they are a most powerful and useful tool for attacking many problems. A 4-vectors is just a 4-tuplet A = (A0, A1, A2, A3) that transforms under a Lorentz Transformation in the same way as (cdt, dx, dy, dz) does. That is:

In relativity, a four-vector is a vector with four components. A general four-vector ~A is denoted by a letter with an arrow on top, and its four com-ponents are defined as. ~A O! (A0;A1;A2;A3) This definition contains an important point.

In three dimensions we define a vector as a quantity with magnitude and direction. Extending this to spacetime, a four-vector is a quantity with magnitude and direction in spacetime. Implicit in this definition is the notion that the vector’s magnitude is a quantity independent of coordinate system or reference frame.