Einstein's search for a continuum theory, often referred to as his quest for a unified field theory or theory of everything, was motivated by his dissatisfaction with the probabilistic nature of quantum mechanics and his belief in the existence of a unified framework that would encompass both gravity and electromagnetism.
Einstein's general theory of relativity successfully describes gravity as the curvature of spacetime, but it treats spacetime as a smooth continuum. On the other hand, quantum mechanics, which describes the behavior of particles and their interactions, introduces discrete quantities and the concept of quantized fields.
While Einstein's intuition leaned towards a continuous spacetime, it is important to note that the concept of quantum fields does not necessarily contradict his ideas. In fact, the prevailing view in modern theoretical physics is that particles are excitations of quantum fields.
Quantum field theory (QFT), which combines quantum mechanics and special relativity, treats particles as quantized excitations of underlying fields that permeate all of spacetime. These fields are described by mathematical equations, and particles are interpreted as localized disturbances or excitations of these fields.
In this sense, the idea of particles arising from quantum fields can be seen as a type of continuous field that exhibits quantized behavior. Rather than considering particles as discrete entities separate from the underlying field, QFT provides a framework where particles are emergent phenomena resulting from interactions and excitations of the fields.
Therefore, while Einstein's pursuit of a continuum theory was focused on unifying gravity and electromagnetism, the modern understanding of quantum field theory accommodates both the concept of a continuous underlying field and the existence of particles as excitations within that field. It is important to note, however, that a complete theory that unifies all fundamental forces, including gravity, within a consistent quantum framework is still an active area of research and remains an open question in theoretical physics.