What effects? And no, Casimir effect is not the answer since it can be derived without virtual particles. Anyways, this topic has been discussed here many times, and there are even two insight articles about that:We can certainly feel their effects
As discussed in detail in the companion article, virtual particles are defined as (intuitive imagery for) internal lines in a Feynman diagram.
There is considerable confusion about various notions around the concept of particles of subatomic size, and about the notion of a virtual particle.
There is no reason to think that they exist in the first place. Mathematics of QFT are quite straightforward when it comes to virtual particles - they are simply propagators appearing in perturbation series. No perturbation series - no virtual particles.and see no reason to drop this viewpoint
There is no need to if you know and understand what is the very definition of a virtual particle. It's not that this notion existed before QFT and then physicists came to model it mathematically. It came after the mathematics were introduced and it's only a name for some part of it.Can you conduct an experiment to say whether a virtual particle exists or not?