No, the Casimir force cannot be fully explained without considering quantum mechanics. The Casimir force is a physical phenomenon that arises due to quantum fluctuations of the electromagnetic field.
According to classical electromagnetism, the energy of the vacuum (empty space) should be zero. However, in quantum mechanics, the vacuum is not completely empty but is instead filled with virtual particles and their associated quantum fluctuations. These fluctuations lead to a fluctuating electromagnetic field even in the absence of any real particles.
When two conducting plates are placed in close proximity to each other, these quantum fluctuations are modified. The presence of the plates imposes boundary conditions on the electromagnetic field, which alters the allowed fluctuations between the plates compared to those outside the plates. As a result, there is a net imbalance in the fluctuating electromagnetic field, leading to a measurable force between the plates. This force is known as the Casimir force.
Quantum field theory, which combines quantum mechanics with special relativity, is used to quantitatively calculate the Casimir force. It involves summing up the contributions of all possible virtual particle modes that can exist between the plates.
Therefore, to understand and calculate the Casimir force accurately, both quantum mechanics and the principles of relativistic quantum field theory are essential. Ignoring these theories would lead to an incomplete or inaccurate description of the phenomenon.