Well, sure. As exchemist pointed out, this description doesn't make much sense. Putting aside for the moment the very real issues with energy in physical systems exchemist has already pointed out, I'm not sure what it means to speak of the "infinitesimal end of the quantum vacuum's vibrations."
It is true that our understanding of the vacuum state(s) in its various incarnations in relativistic physics is still a matter of some debate. Operationally, when one wishes to construct a quantum theory that obeys the relevant transformations demanded by any relativistic theory, one immediately runs into several issues. To some extent, these issues are "resolved" in modern physics using a combination of different phenomenological, mathematical, metaphysical, operational, and empirical approaches (EFTs alone combine not only different interpretations of the phenomenology of HEP physics but also the meaning(s) underlying the regularization and renormalization required for finite results in relativistic QFT).
But "infinitesimal" and "quantum" have some degree of inherent contradictions embedded in them. Infinitesimals are usually referenced with respect to the continuum, understanding continuity here in the sense of the usual topology of e.g., the real number line (in contrast, one can define infinitesimals in terms of the epsilon-delta approach to limits and so forth from elementary calculus, but this definition can be defined for the rational numbers without embedding them in the reals; the result is a mess in which most of the very basic theorems of calculus vanish because the rationals are not (Cauchy) complete).
Putting aside also the discreteness inherent in many aspects of quantum theory vs. the continuity implied by infinitesimals, we run immediately into another problem.
The vacuum state in quantum theory is typically the result of the transition from the domain of quantum mechanics to that of relativistic quantum theory and in particular (relativistic) quantum field theory. For various reasons, in this approach one no longer treats space (or spatial coordinates via position) using the methods from non-relativistic quantum mechanics (NRQM). This is because relativity demands some degree of equal treatment for spatial coordinates and time, whereas in NRQM time is generally a parameter and space an operator.
The way in which this equal footing for space and time is achieved is by demoting the position operator and treating what would have been or were operators in NRQM as the "particles" or physical systems acting on the vacuum. So, returning to the discussion of electrons, in the NRQM described by Dr. Bryan the (information about) the electron is encapsulated in the corresponding wavefunction and one obtains information about e.g., its spatial coordinates via the position operator, whereas in quantum field theory the "electron" is itself an operator that itself acts on the vacuum state |0>.
In none of this do we get something like "the quantum vacuum's vibrations, and the forms it takes such as spherical clouds" in any sensical manner. Raising and lowering operators are not really akin to "vibrations" in any intuitive sense one may have unless one has studied harmonic oscillator in classical and quantum theory.
I disagree. In fact, it is in our limited understanding of the vacuums state and of quantum field theory more generally (beyond operational understanding) that we run into obstacles here. If we can't really understand the manner in which to interpret what should have been basic, fundamental physical properties that instead must become running constants in some renormalization scheme in order to yield finite results, we can hardly look here to understand how to combine this knowledge gap with another we are trying to fill.
More importantly, we should instead take the results of quantum theory and the evolution/history of our understanding of it as a guide here, and note how far we pushed the limits of classical physics and its corresponding classical atomism, reductionism, and theoretical structure when we banished from any possible role the very mechanisms that enable physics to begin with. For Newton and contemporaries, as well as for many of those who came later but were instrumental in contributing to modern physics (e.g., Maupertuis, Euler, etc.) the external picture painted by a dynamical cosmos evolving from initial conditions was literally a God's eye view. We could understand the universe (or, more importantly, God) by seeking out those laws which the Creator imbued his creation with. To do so, each experiment (realized or in thought) corresponded to a kind of miniuniverse in which we imagined a perfectly isolated combination of system+environment so as to exclude our roles as observers as well as render negligible any possible other external influences.
Quantum theory, whatever else it has done, forced us to realize that this idealization cannot be fundamental, nor can it be extrapolated universally. We have long since dispensed with the need to invoke a creator or any similar Cause underlying the "laws" of modern physics. But we can no longer seriously consider how we have excluded ourselves from the structure of physical theories while extrapolating the governing equations, laws, dynamics, etc., in these theories to hold universally.
