This blog post examines how quantum mechanics and classical physics, despite having different frameworks, exhibit identical solutions under specific extreme conditions, thereby converging into a single physics.
Physics underwent a major transformation in the 20th century. The emergence of special relativity and quantum mechanics, in particular, brought about revolutionary changes. Yet, when viewed from the perspective of how scientific progress occurs, these two examples reveal distinct characteristics.
The special theory of relativity, published in 1905, not only altered fundamental concepts of physics like time and space but also necessitated rewriting many of the formulas appearing in physics. This includes the addition rule for velocities, long accepted as a valid formula for relative motion. This law explains the common-sense observation that a train traveling at 150 km/h sees another train on the tracks moving in the opposite direction at 150 km/h appear to be fleeing at 300 km/h. However, according to the special theory of relativity, this addition law is not accurate.
This does not mean classical physics was completely negated by the new theory. Even from the perspective of special relativity, the equations of classical physics provide sufficiently accurate descriptions and predictions for most situations. For instance, if the train mentioned earlier were traveling at 150,000 km/s, a clear discrepancy would arise between the new theory and classical physics calculations. However, even at speeds exceeding the speed of sound, around 1,500 km/h, the results of both calculations provide sufficiently good approximations. While the special theory of relativity fully encompasses the explanatory power of classical physics, classical physics remains valid within the restricted domain of the special theory’s applicability—namely, the condition that ‘the speed is not particularly high.’ Viewed this way, we can confidently assert that the special theory of relativity achieved progress in physics by encompassing classical physics while expanding the realm of explanation and prediction.
What, then, is the case with quantum mechanics? In 1910, physicists sought to explain the dynamic states of electrons belonging to atoms, but classical physics proved incapable of such an explanation. Ultimately, physicists constructed the framework of quantum mechanics based on premises incompatible with classical physics, thereby finally providing an accurate and consistent explanation for the problematic phenomena. While the motion of free electrons unconstrained by atoms can be explained by classical physics, quantum mechanics is necessary to describe electrons within atoms. When an electron inside an atom gains sufficient energy, it becomes a free electron. This resembles the electron breaking free and crossing over from the domain of quantum mechanics into that of classical physics.
The problem is that quantum mechanics’ equations fail to effectively explain phenomena that classical physics has successfully described. This raises the question of whether quantum mechanics’ emergence truly signifies progress in physics. Phenomena like billiard ball collisions, which quantum mechanics alone cannot explain, still reside firmly within classical physics’ domain. Chaos theory, which developed from 1980 onward, reveals another facet of the relationship between the two theories. Chaos theory examines how two initial states that are very slightly different evolve over time. However, in quantum mechanics, there are cases where the meaning of the concept ‘two initial states that are very slightly different’ cannot be clearly defined. This implies that chaos theory can only hold within the territory of classical physics.
However, quantum mechanics and classical physics are curiously connected. If we assume the extreme conditions corresponding to an electron just released from an atom, remarkably, the equations of quantum mechanics take a form consistent with those derived by classical physics. This indicates that the two theories, each explaining distinct domains of phenomena, meet at the boundary between these domains under extreme conditions, forming a smooth connection. Through this connection, classical physics and quantum mechanics establish themselves as complementary parts constituting physics.
Had classical physics been discarded and vanished, or had classical physics and quantum mechanics failed to connect seamlessly into one, the evaluation of 20th-century physics’ progress would have been a matter of debate. However, when we consider the entirety of physics as we know it today, it becomes clear that the emergence of quantum mechanics itself resulted in progress for physics. Thanks to classical physics, special relativity, and quantum mechanics, we have gained a ‘diverse yet interconnected physics’ for a ‘diverse yet interconnected world’.
