Recent polls have shown that many Catholics do not really believe that the Eucharist is the true body and blood of Jesus.
This is not so surprising given the poor catechesis and instruction given by the church in our times. According to this doctrine, during the consecration at Mass, the substance of the bread and wine is changed into the substance of the Body and Blood of Christ, while the accidents (physical appearances) of bread and wine remain.
The word “substance” used in the explanation of what occurs has different meanings in scholastic philosophy and modern physics, and few Catholics are students of Scholastic philosophy. Unlike its philosophical meaning meaning , in physics a substance is totally defined by its observable properties or accidents. To someone not aware of these differences the catechism definition sounds like gibberish.
My own approach to trying to grasp the meaning of this mystery is to contemplate the mathematical nature of physical reality. When as a young student of complex numbers I had a teacher who was fascinated by a subsection of that subject called conformal mapping. Using binomial transformations of coordinates from one space to another we could change the shapes of any patterns to something quite different in the transformed space. Circles could become squares or triangles and vice versa in the other space. Some of these transformations, like the Schwarz-Christoffel transform, preserve the character of other equations such as electrical potential in both spaces, and are two dimensional tensors. In my ignorance I wondered what was the real shape of the fields since they looked different in each space, while being the solutions to the exact same equation. Of course all the shapes and fields are real even though you might call them different names depending on which space you were referring to, but their essence as solutions to the same equation was identical.
Dirac a father of quantum physics claimed it was useless to think of an electron in any way but as a solution to mathematical equations. But mathematics itself is not physical. That is I cannot buy or describe a pound ,or meter or an hour, of mathematics or logic or theorems. The latter terms are spiritual things like intelligence, love, justice etc.
So reality is not just determined by material dimensions of space force and time but has spiritual dimensions. And if we knew how to quantify them all (good luck with that) we might be able to construct a tensor that would enable some understanding of the real presence of Christs body in the Eucharist. My understanding of the words of consecration are a short hand symbol for invoking activation of such a tensor by God.