Relativistic mechanics
Force

In special relativity, Newton's second law does not hold in the form F = m a, but it does if it is expressed as

where p = γ(v) m v is the momentum as defined above and m is the invariant mass. Thus, the force is given by

Consequently, in some old texts, γ(v) m is referred to as the longitudinal mass, and γ(v) m is referred to as the transverse mass, which is numerically the same as the relativistic mass. See mass in special relativity.

If one inverts this to calculate acceleration from force, one gets

The force described in this section is the classical 3-D force which is not a four-vector. This 3-D force is the appropriate concept of force since it is the force which obeys Newton's third law of motion. It should not be confused with the so-called four-force which is merely the 3-D force in the comoving frame of the object transformed as if it were a four-vector. However, the density of 3-D force (linear momentum transferred per unit four-volume) is a four-vector (density of weight +1) when combined with the negative of the density of power transferred.
oulipo:avoid_letter[t]