In quantum field theory, virtual particles, including virtual photons, are not considered as "real" particles in the same sense as observable particles. Virtual particles exist as intermediate states in calculations and are used as a mathematical tool to describe interactions between particles.
In Feynman diagrams, virtual particles, such as virtual photons, are depicted as internal lines connecting the interacting particles. They are associated with the exchange of momentum, energy, and other properties between the interacting particles. However, virtual particles do not satisfy the usual on-shell conditions of observable particles, meaning they do not obey the classical energy-momentum relation (E^2 = m^2c^4 + p^2c^2). They are off-shell and have a transient existence during the interaction process.
The Casimir effect, on the other hand, is a real physical phenomenon that arises due to quantum fluctuations of fields in the vacuum. In this effect, two conducting plates in close proximity experience an attractive force. The Casimir effect is often explained in terms of virtual photons mediating the force between the plates.
The virtual photons involved in the Casimir effect are conceptually similar to those in Feynman diagrams. They are virtual particles that arise from the quantum fluctuations of the electromagnetic field in the vacuum. However, there is a distinction in how they are treated. In Feynman diagrams, virtual particles are used as calculational tools and do not have a direct physical interpretation. In the Casimir effect, the presence of the plates modifies the boundary conditions for the quantum electromagnetic field, leading to measurable effects such as the attractive force. In this case, the virtual photons involved can be considered as "real" in the sense that they contribute to observable physical phenomena.
In summary, virtual particles, including virtual photons, are primarily mathematical tools used in quantum field theory calculations. They do not correspond to observable particles. However, in the Casimir effect, the influence of virtual photons on the behavior of the electromagnetic field leads to observable physical effects, making them "real" in that context. The virtual photons in the Casimir effect and those in Feynman diagrams share conceptual similarities but differ in their interpretation and the physical phenomena they are associated with.