So virtual particles are a function of (t)?
Well... Yes. At least the time that they exist. Larger, more massive particles exist for shorter periods of time, for example.
The very elegant experimental proof of the presence of this "froth" in the vacuum field as Feynman described it was to shoot particles from an accelerator through a vacuum. Occasionally, when the "virtual" particles came into existance and were real for a brief instant, they were collided into by one of the accelerator particles. Since the virtual particles exist for a very short period of time, this collision does not occur often. But it does occur. And once it occurs, one of the particle / anti-particle particles is knocked away by the collision. Energy from the collision has to go back into the vacuum field. But the collision is real and can be observed by a particle detector.