The perennial teaching of the Catholic Church on the change of the bread and wine into the Body and Blood of Christ during the Mass (transubstantiation) is that, after the consecration, the substance of the bread and wine have truly been replaced by the substance of the Body of Christ - His Body, Blood, Soul and Divinity. The change is full and complete; no part of bread or wine remains after the change has been effected. This is contrary to the doctrine of consubstantiation affirmed by the Lollards and later by Luther, whereby the substance of the body and blood of Christ are present alongside the substance of the bread and wine, which remain present.
Thus, the dual presence of the substance of bread and wine alongside the substance of Christ's Body and Blood is not affirmed by the Church. In fact, it has been explicitly condemned at several regional Roman synods (1050, 1059, 1078, 1079, all relating to the heresy of Berengarius), and condemned by three ecumenical councils (Lateran IV, Constance, which condemned the proposition that "the substance of the material bread and in like manner the substance of the material wine remain in the Sacrament of the altar", and Trent). Consubstantiation is thus a soundly condemned teaching.
Yet, it seems that consubstantiation must be at least momentarily true of the Holy Eucharist if we affirm that there is truly a change from one substance to another in the Eucharistic species. The change, however quick, happens in a succession of time. At one moment Christ's Body is not present, and at another it is. There must, therefore, be between these two moments a midway point, since time can be infinitely subdivided into smaller and smaller units, and things that seem instantaneous to us (light flooding a room when a switch is turned, a lightning bolt, the blink of an eye) are actually actions that happen by succession and have a beginning, middle and terminal point.
Since this is the case, some posit a moment when Christ's Body is becoming present but is not yet fully present. During this moment, however brief, Christ's Body and the substance of the bread coexist together while the process of transubstantiation is occurring. Thus, we would go first from Bread and Wine to a momentary instant of consubstantiation during the change, resolved finally by transubstantiation when the change is complete.
It is easy to see the logic of this argument. It is also easy to see that it is problematic given the Church's condemnations of consubstantiation in any degree. What, then, is the solution? We hold that the change of transubstantation happens at the words of consecration; but if we can pinpoint a moment in time when the change occurs, that moment can be theoretically slowed down and we can posit a midpoint when the change is in the process of occurring and both substances are simultaneously present. How can we answer this argument?
The classical answer to this difficulty is the one provided by St. Thomas - that the act of transubstantiation is truly instantaneous in the fullest sense of the word and thus admits of no gradation or succession. St. Thomas is a bit speculative in his answer here (STh III, Q. 75 art. 7) and begins by surveying various theories as to whether or not time can in fact be subdivided infinitely, as the argument above would presuppose. Although mentioning the theories of St. Albert and St. Bonaventure that time cannot be infinitely subdivided, Thomas disagrees with them on the specifics of why this is the case. He goes on to conclude all time is ultimately predicated on the movement of heavenly bodies, and as movement itself happens in succession, a subdivision of time into smaller and smaller instants is feasible.
This would at the outset seem to weaken St. Thomas' argument about true, instantaneous change, but in fact it does not, for Thomas explains that there is another type of movement that is not predicated upon the movement of the heavens, nor measured by it - this is the movement of pure, spiritual substances, i.e., the angels, who move from one location to another instantaneously at the speed of thought. Only purely physical objects are subject to physical time, but supernatural agents can truly effect instantaneous movement.
Instantaneous movement or change is possible for three reasons, according to St. Thomas. The first two are somewhat obscure and (it must be admitted) bound up with the imperfect scientific knowledge of the day (St. Thomas speaks of light illumining something instantaneously when we know that it actually moves at 186,282 miles per second). For the Eucharistic transformation to be truly instantaneous, it must happen quicker than 186,282 miles per second - infinitely quicker.
St. Thomas' third explanation for instantaneous change is of most import to this discussion, in which he states that the power to effect change is relative to the power of the agent who can instantly disposes matter to form. God's infinite power to effect transubstantiation makes instantaneous change truly possible.
But when does this change really occur? Following western tradition, St. Thomas pinpoints the completion of the words of consecration as the point at which Christ's Body and Blood become present, but he is careful to deny that we can know exactly at which moment the substance of the Bread and Wine disappear:
"And therefore it must be said that this change, as stated above, is wrought by Christ's words which are spoken by the priest, so that the last instant of pronouncing the words is the first instant in which Christ's body is in the sacrament; and that the substance of the bread is there during the whole preceding time. Of this time no instant is to be taken as proximately preceding the last one, because time is not made up of successive instants, as is proved in Phys. vi. And therefore a first instant can be assigned in which Christ's body is present; but a last instant cannot be assigned in which the substance of bread is there, but a last time can be assigned. And the same holds good in natural changes, as is evident from the Philosopher" [Phys. viii] ((STh III, Q. 75 art. 7).
St. Thomas essentially sees these acts (the presence of the Bread and Wine followed by the appearance of Christ's Body and Blood) not as a single chain of events on one line of causation but rather as two distinct chains of events - not like a single line, but like two lines, one above the other. The first line (the endurance of the substance of the Bread and Wine) ends at the same place the second line begins, but since they are two distinct events it makes no sense to speak of time elapsing between them.
Even so, St. Thomas is guarded in his language and, though he posits the substance of the Bread and Wine disappearing at the same moment as the words of consecration are completed, he points out that we know more about how the substance of Christ appears than how the substance of Bread vanishes, and hence is hesitant to say specifically at what moment this occurs.
Bottom line: The change of the bread and wine into the Body and Blood of Christ is truly instantaneous and takes up no succession of moments - hence, there is never a time when the two substances coexist in a consubstantial manner. Thus transubstantiation happens "outside time" in the conventional sense; as it is a supernatural change effected by an infinitely powerful supernatural agent, its movement from potency to act is not subject to subdivision.
This is why we cannot pinpoint exactly at what moment this all occurs; Thomas centers in on the completion of the words of consecration, but remember, we are talking about an event that occurs much faster than the speed of light, so pointing to specific moments in time is ultimately meaningless. For St. Thomas, and for us, it is sufficient to know that by the time the words of consecration have been said, the change has been effected.