It is known that, while electromagnetic waves can propagate in vacuum as they do not need a medium, mechanical waves (e.g. sound waves) cannot.
However, vacuum has vacuum fluctuations, where (virtual) particles/antiparticles are constantly created and annihilated. Why these cannot save as a medium for the propagation of mechanical waves?
Virtual particles are not real in the sense that they are physically inexistent without having real particles in their immediate surrounding. These are mathematical entities that pop in and out which allow calculations to be made (for example used in Feynman diagrams for accounting transfer of momentum etc). Virtual particles are really not like classical particles.
Sound can be seen as an oscillation in pressure, stress, particle displacement, particle velocity, etc., propagated in a medium with internal forces (e.g., elastic or viscous), or the superposition of such propagated oscillation. A mechanical wave is an oscillation of matter and therefore transfers energy through a medium. A mechanical wave needs an initial energy input. The wave travels through the medium until all its energy is transferred/dissipated. In contrast, electromagnetic waves require no medium, but can still travel through one.
As long as you don't have real particles to facilitate energy transfer, the probability of sound/mechanical wave transmission is nothing more than zero.
According to Wikipedia, a wave is the disturbance of a field.
A field must have a value for each point in space-time.
E.g. A water wave disturbs a body of water which is a field. This is because the displacement of water molecules is defined at each point.
E.g. A sound wave disturbs air pressure which is a field. This is because air pressure is defined at each point.
For a wave to travel through a vacuum, it must have a field to propagate through. Electromagnetic waves are said to disturb the electromagnetic field.
Vacuum fluctuations, as you describe them, cannot serve as this because they are inherently random and so are not defined at every point - hence cannot act as a field.
I agree that it is even dubious with EM waves. One way to explain it though with light is to take the corpuscular (particle) view. In which case, an energy packet can travel through a vacuum without a medium for it to travel through - just like how you could throw a rock into space and it wouldn't care that it's not moving through anything.
If you are interested, this is a very amazing explanation of EM waves: https://www.youtube.com/watch?v=FjHJ7FmV0M4.
