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This question of Aeviternity will likely be new for many of you. But, to explain it, one must simply remember back to our discussion of the "levels of mutability" back in ST.I.Q9.A2. If time follows upon mutability (as we have assumed throughout this entire question), these different levels of mutability will result in different "levels of time." Above our own experience of constant substantial change and below God's level of complete immutability, there is the "middle" level of the heavenly bodies, angels, and souls of the just who *merely* experience some sort of accidental change without substantial change. The measure of this accidental change is called "aeviternity."
To illustrate, Fr. Garrigou-Lagrange writes in Life Everlasting, "Discontinuous time, then, is opposed to continuous or solar time. It is found in angels and separated souls, as the measure of successive thoughts and affections. One thought lasts for one spiritual instant. The following thought has its own spiritual instant. To illustrate: here on earth a person in ecstasy can remain two solar hours, or many hours, in one sole thought which represents to it one sole spiritual instant. Similarly, history characterizes different centuries, for example, the thirteenth or the seventeenth, by the ideas which predominate in each of these centuries. Thus we speak of the century of St. Louis, of the century of Louis XIV. Hence a spiritual instant, in the lives of angels and separated souls, can last many days, even many years, measured by our solar time, just as a person in ecstasy can remain thirty successive hours absorbed in one single thought."