How are we to explain the reality of Christ's presence under the appearance of bread and wine at the Eucharist?

First, by His Resurrection Christ's body reached a Super-Ordered state which is a perfect alignment of its atomic structure. "The Super-Ordered body, could, in its entirety, be in an unlimited number of places at any given time." (Jack Sacco) When the bread and wine become his body and blood, there is no change in Christ who is in eternal glory. The mystery lies in the bread and wine which now, on the level of being, are the actualized presence of the mystery of Christ life, death and resurrection.79

 

Second, Christ chooses to become fully present under the aspects of bread and wine when the priest proclaims, "This is my body" and "This is my blood".

Third, this abiding presence under the appearances of bread and wine endures as long as the appearances of bread and wine endure. "Christ is present whole and entire in each of the species and whole and entire in each of their parts, in such a way that breaking of the bread does not divide Christ." (Catechism of the Catholic Church, # 1377)

"Here beneath these signs are hidden
Priceless things, to sense forbidden;
Signs, not things, are all we see."

(Thomas Aquinas)

Our eyes are only sensitive to the spectrum of visible light, therefore, we do not see the reality of Christ present in the Eucharist because his glorified state is beyond the limited vision of our mortal eyes. So, what Christ requires is "I believe." Why do we believe it? Because we realize our limitations and because the Son of God is Truth and does not lie.