When do quantum mechanics and relativity become more useful than classical physics?

In physical science, classical physics (or Newtonian mechanics) effectively describes the motion of ordinary objects on Earth and celestial bodies moving at speeds much lower than the speed of light. However, quantum mechanics and relativity become necessary when physical conditions exceed the limits of classical approximations.1

When Relativity Is Required

Relativistic mechanics must be used when:
* High Velocities: The relative velocities of bodies approach the speed of light.2
* High Energies: Kinetic energies are comparable to the rest mass energy ($m{c}^2$) of the body.2
* Cosmic Scales: Dealing with the structure of the universe, energy sources of stars, or supernova explosions.23
* Precision Timing: Systems like the Global Positioning System require corrections for time dilation.2

When Quantum Mechanics Is Required

Quantum mechanics is essential when:
* Subatomic Scales: Describing the behavior of matter and electromagnetic radiation at atomic and subatomic levels.41
* Discrete Energy States: Phenomena involve quantized energy levels, such as atomic transitions or the structure of atoms and molecules.4
* Microstructures: The sizes and separations of bodies are comparable to or smaller than their Compton wavelengths, where classical determinism is replaced by intrinsic uncertainty.24