The Roman Catholic Church teaches a view of Christ's presence in the Lord's Supper known as transubstantiation, which holds that Christ is personally and physically present in the bread and wine even though the elements still appear as bread and wine. Roman Catholicism says that in the Mass, the invisible essence of the elements miraculously becomes Christ Himself, body and soul. Lutheranism and the Reformed tradition both disagree with this view.
Lutheranism's view of Christ's presence in the Lord's Supper is often labeled consubstantiation, though most Lutherans dislike that term. In the Lutheran view, Christ is present in, with, and under the elements of the Lord's Supper. Lutheranism does not explain how this happens, but the result is similar to Roman Catholicism in that the physical body of Christ becomes omnipresent. Both traditions hold to a physical presence of Jesus in the sacrament, which requires His physical body to be present in more than one place at the same time.
Roman Catholics and Lutherans hold their respective views based on their shared understanding of the communicatio idiomatum, the communication of properties or attributes of the two natures of Christ. For both traditions, the divine nature of Christ communicates (or shares) divine attributes such as omnipresence to His human nature; thus, Christ's physical body can be in several locations at once.
Reformed theology rejects this view of the communication of attributes as violating historic, orthodox Christology. According to the Council of Chalcedon, the two natures of Christ are inseparably united in the one divine person of the Son of God without confusion, mixture, or change. The divine nature remains truly divine and the human nature remains truly human, each retaining its own attributes. This must be so. If Christ's humanity acquires a divine attribute, Jesus is no longer truly human and cannot represent other human beings before God or atone for their sin.
For Reformed theology, the communicatio idiomatum means the attributes of each of Christ's natures are communicated to the person of Christ. We can predicate what is true of each nature to Christ's person. So, the person of Christ is omnipresent, but not according to His human nature. He is omnipresent according to His divine nature because only deity is omnipresent. Likewise, the person of Christ died on the cross, but Jesus experienced death according to His human nature, for the divine nature is not subject to death and decay.
As we will see, understanding the Lord's Supper rightly demands a correct understanding of Christology. Indeed, we cannot rightly understand any doctrine unless we rightly understand the doctrine of Christ. Let us be careful in our study of theology to know the person and work of Christ. Consider devoting some time in the next few weeks to studying the doctrine of Christ.