Final answer:
The law of conservation of momentum is modified by special relativity to include a relativistic factor that accounts for speeds approaching the speed of light. The correct answer is d) Momentum is conserved, with relativistic corrections, meaning momentum is still conserved in relativistic physics but with a modified formula.
Step-by-step explanation:
How Modern Relativity Affects the Law of Conservation of Momentum
The law of conservation of momentum states that the total momentum of a closed system is conserved. In the realm of classical physics, this is represented by π = mv, where π is momentum, m is mass, and v is velocity. However, modern relativity introduces a modification when speeds approach that of light, known as relativistic speeds. According to special relativity, the correct formula for relativistic momentum is p = γmv, where γ (gamma) is the Lorentz factor, γ = 1/√(1 - v²/c²), and c is the speed of light in a vacuum.
Thus, the modification required by relativity is:
- d) Momentum is conserved, with relativistic corrections.
These relativistic corrections ensure that conservation of momentum holds true even at high velocities. When velocity is much less than the speed of light, γ approaches 1, and the classical definition of momentum is approximately correct. But as v approaches c, γ increases significantly, altering the momentum of objects significantly. Thus, the principle of conservation of momentum holds in all inertial frames, as required by the first postulate of relativity, but the expression of momentum must be modified to take into account the speed of the moving object relative to the speed of light.