Conservation laws have been the foundation of classical physics for centuries, providing essential insights into the behavior of physical systems. However, with the advent of modern physics, particularly quantum mechanics and special relativity, our understanding of these fundamental laws has evolved.

One of the key connections between conservation laws and modern physics lies in the principle of energy-mass equivalence, as described by Einstein's famous equation, E = mc². This equation demonstrates that energy and mass are fundamentally interrelated, and that mass can be converted into energy and vice versa. This concept revolutionized our understanding of conservation of mass and energy, extending conservation laws to encompass even more diverse phenomena.

Another fascinating aspect of modern physics is the breakdown of classical concepts such as definite particles and determined paths. In the realm of quantum mechanics, uncertainty principles challenge the strict conservation of certain quantities like momentum and energy. While energy and momentum conservation hold over relatively long timescales, they can fluctuate on microscopic timescales within certain bounds, owing to Heisenberg's uncertainty principle. This realization deepens our understanding of conservation laws and highlights the intricate interplay between fundamental principles and the fundamental uncertainties of the quantum world.

In the realm of special relativity, conservation of momentum and energy take on new forms. The concept of relativistic mass introduces the idea that an object's mass is not constant but increases with its velocity. This phenomenon, along with the famous equation E = mc², shows how energy and mass are interconnected at high velocities. Additionally, the principle of conservation of angular momentum extends to relativistic scenarios, where the spin of particles becomes important. These developments emphasize the need for expanding our understanding of conservation laws to accommodate the unique properties of the relativistic domain.

While conservation laws remain crucial in modern physics, it is important to recognize their limitations and modifications within advanced theories. The intricate interplay between quantum mechanics, special relativity, and conservation laws continue to be an area of active research and exploration. Scientists are continually refining their understanding of these fundamental principles, with the ultimate aim of developing a unified theory that encompasses all aspects of the physical world.