With the Resurrection, Christ's body took on multidimensional aspects. He appeared to the apostles walking on water, passing through closed door while still insisting that his body was real. In the image at left we see Christ appearing to Mary Magdalene after the Resurrection. She thought he was the gardener until Jesus called her by name "Mary", then she recognized him and called him "teacher". In all these appearances, the disciples experienced his real presence and yet a discontinuity. His body had properties now beyond the demensions of time and space.
Actually, Christ's death-Resurrection-Second Coming are one event. Even though he appeared to the Apostles, Christ as He is in himself was already in heaven with the Father. Yet, He had a unique way of realizing his presence to apostles in such a way that he could say to them, "Look at my hands and my feet, that it is I myself. Touch me and see, because a ghost does not have flesh and bones as you can see I have." (Lk 24:39)
Another mode of Christ's presence is in the Eucharist through which He becomes present in many churches. If Christ in himself is only in one place, heaven, how can he be in many other places? "[The] multiplication of his body as such is not multiplied since numerically the body remains one and the same. The multiplication is of the body's relation to space, that is, its presence." (Dr. Ludwig Ott, Fundamentals of Dogma, Herder Book Co., 1955, p, 390) We may compare this presence with television. The broadcaster is really only in the studio. His technological presence is virtual, it is a presence only in image and words. Christ's presence in the Eucharist, on the other hand is, real. Christ is really and truly present in the Eucharist as He is before the Father in heaven as a divine person embodied in a human nature. This is a mystery we cannot fully understand.
Martin Luther himself, although he separated himself from the Church, held on to the belief in the real presence of Christ in many places as he stated: "For I do not want to deny in any way that Gods power is able to make a body be simultaneously in many places, even in a corporeal and circumscribed manner. For who wants to try to prove that God is unable to do that? Who has seen the limits of his power?" (Wispedia Electronic Encyclopedia: Martin Luther)