When God created the Universe, He created a two-fold order: material and spiritual.
First Vatican Council: “This one true God, by his goodness and almighty power, not with the intention of increasing his happiness, nor indeed of obtaining happiness, but in order to manifest his perfection by the good things which he bestows on what he creates, by an absolutely free plan, together from the beginning of time brought into being from nothing the twofold created order, that is the spiritual and the bodily, the angelic and the earthly, and thereafter the human which is, in a way, common to both since it is composed of spirit and body.” (First Vatican Council, session 3, chapter 1, n. 3; citing Fourth Lateran Council, confession of faith.)
Physical objects are of the material order; so, too, is the human body. Atoms and molecules, light and other forms of energy, are all of the material order. Spiritual things, such as angels, human souls, and the souls of animals, are of the spiritual order. There is nothing else in Creation but the material and the spiritual. God is the only uncreated thing. He is neither material, nor spiritual. It is sometimes said that God is “spirit” in that spiritual things are closer in resemblance to His infinite and unique Divine Nature. However, this is by way of analogy, since God is uncreated.
Accidents and substance are not two separate things, but rather a way of dividing a thing into non-essentials and essentials, into the qualities of a thing and the thing itself. The accidents are any qualities of a thing that, if changed, do not cause the thing itself to become something else; they are non-essential. The substance is not a quality of the thing, but rather whatever is essential to the nature of the thing; it is the thing itself, apart from particular non-essential qualities. If the substance changes, the thing changes into some other type of thing. Accidents cannot exist without substance, since accidents are not the thing itself, but only qualities of the thing. Substance, in created things, does not exist without accidents; for God has ordained that created things have various changeable qualities. Only the Divine Nature is unchanging substance without accidents.
Each order has its accidents and substance. Material things have accidents and substance, and spiritual things have accidents and substance. Thus, the human body is comprised of accidents and substance, and the human soul is comprised of accidents and substance. Human nature is body and soul united as one. Like us, the human nature of Christ is of both orders: the body is material and the soul is spiritual. His body has accidents and substance; His soul has accidents and substance.
Before the consecration of the Eucharist, the bread and wine have the ordinary substance and accidents of any bread or wine. The bread and wine are made of molecules, and these molecules have substance and accidents. In other words, the molecules of bread and wine have qualities, like smell, taste, color, shape, etc., which are the accidents, and these molecules have substance, which are the things themselves. A material object is its molecules. The molecules are not solely accidents, nor solely substance. The division of a thing into accidents and substance means that the molecules are comprised of accidents and substance. This philosophical distinction cannot be separated from the physical object, whether it is bread and wine, or body and blood. The distinction applies to physical things, and also to spiritual things (the human soul, the angelic spirit).
If some foolish person were to claim that the molecules do not change at all in the consecration of the Eucharist, this would imply that molecules are entirely accidents (or that there is no change of substance). If the molecules were entirely accidents, then all the molecules of bread and wine (supposedly the accidents) could be taken away, and what was left would still be bread and wine (the substance) — which is absurd. Instead, the truth is that material objects, like bread and wine, are made of molecules, which themselves have accidents and substance: the accidents of the molecules and the substance of the molecules.
For if the molecules of bread and of wine were entirely accidents, what would the substance be? Would it be some other material thing in addition to the bread and wine? But the bread and wine that are used are ordinary, mere material objects. Would it be something other than material or spiritual? But Creation has two orders, material and spiritual, not three or more. The term substance is a way of describing the essential nature of the bread and of the wine (or of any material or spiritual thing). It is not an entirely separate thing from the physical molecules of bread or of wine.
Therefore, at the consecration of the Eucharist, when the substance of bread changes into the substance of Christ’s body, and the substance of wine changes into the substance of Christ’s blood, the molecules do change. What changes? The substance of the molecules change, and the accidents of the molecules do not.
At the consecration of the Eucharist, two things happen simultaneously:
(1) a change of substance
The substance of the bread changes into the substance of the body of Christ by transubstantiation, and the blood, soul, and Divinity of Christ become present by concomitancy. We could use the word concomitancy more narrowly, applying it only to the blood and the soul, in which case we would say that the Divine Nature becomes present by its hypostatic union with the human nature of Christ. But I prefer to use the term more broadly, as it is simple and clear.
The substance of the wine changes into the substance of the blood of Christ by transubstantiation, and the body, soul, and Divinity of Christ become present by concomitancy.
It is a dogma of the Catholic Faith, and a required belief under pain of heresy, that the substance of the bread changes only into the body of Christ, not into His soul, not into His Divinity, not even into the substance of blood. It is likewise a dogma that the substance of the wine changes only into the blood of Christ, not into His soul, not into His Divinity, not even into the substance of body.
How do substance and accidents relate to Christ’s presence in the Eucharist?
The accidents of the bread remain, while the substance of bread is changed into the substance of Christ’s body. However, these accidents do not exist separately from the substance of Christ’s body; they become the accidents of that substance (of Christ’s body). For accidents cannot exist apart from a substance. Does this imply that the substance of Christ’s body lacks its usual accidents? No, for the accidents of Christ’s body are simply hidden. This is proven by the case of various Eucharistic miracles, in which Christ permits some of the accidents of His body or blood to become visible.
The soul of Christ is present in the Eucharist by concomitancy, not by a change of substance. The soul of Christ retains its usual accidents and substance. The accidents of a soul united to its body include changing thoughts and emotions; these are not substance, since they can change without changing the nature of the thing. And this point about thoughts and emotion also proves that the substance of Christ’s body, blood, and soul continue to have their usual accidents (though hidden). If Christ were present in the Eucharist without accidents, then his human nature would be unable to have thoughts or emotions, which would make it not so different from a dead body. Such a presence could not be accurately called full and real, if that were so.
Instead, Christ is alive and fully present, in His whole person. He is able to function as a whole person, with thoughts and emotions, in a personal and real presence. Christ is present in the Eucharist just as He was present when He walked this earth, with two exceptions. First, His accidents are hidden from our eyes, but not from the eyes of faith. Second, His human nature is glorified, which explains how he can be wholly physically present in every part of the host at the same time.