Three Quarks and the Trinity:
Scientific Models for a Mystery

The Trinity


Last Trinity Sunday our priest talked about trying to understand the Trinity, the fundamental mystery of our Catholic faith.   He solicited analogies from the congregation and then gave his own:  a candle.   A functioning candle comprises the wax, the wick and fire, three separate things but one entity.

Other analogies have been used, for example, the triangle, with the three corners of the triangle representing God the Father, God the Son, and God the Holy Spirit.  (See the featured image.)  And here’s a familiar one, with prepositions: God, the Father, above me; God the Son, beside me; God the Holy Spirit, within me.

All such analogies call to mind the story of the blind sages telling what an elephant is by what they felt of his body.   They do not explain the fundamental mystery of the Trinity, and probably that is as it should be.

Nevertheless, as humans we want to understand, and as a physicist (albeit no longer practicing) my route to understanding often uses scientific terms as the signposts.   However, I do take Sts. Augustine and Anselm to heart in traveling this road:  “Credo ut intelligam,” (I believe in order to understand).   So, take this blind man’s thoughts only as models, like the ball-and-stick representations of molecules, as to what that elephant, the Trinity, might be.


A stumbling block in my conversion process was dealing with the concept of the Holy Trinity.  As a Jew, a cornerstone of my minimal religious faith was the Sh’ma Yisrael, that God was One:

“שְׁמַע יִשְׂרָאֵל יהוה אֱלֹהֵינוּ יהוה אֶחָד – 

Sh’ma Yisra’el YHWH Eloheinu YHWH Eḥad” Hear O Israel, the LORD is our God, the LORD is one. Deut. 6:4-9

To resolve this seeming contradiction I turned to the Patristic fathers. Their notion, stemming from the Greek philosophers, was that God was one substance (ὁμοούσιον, homoousian, same in being, same in essence), but three consubstantial persons (hypostasis).

This explanation  did not enlighten me, so I turned to scientific models for the Trinity.


In an early post, I speculated on whether the superposition principle of quantum mechanics might offer an analog of the Holy Trinity. Here’s the general notion: a state in quantum mechanics can be represented as the superposition of several component states. By superposition we mean that the actual state, like Schrodinger’s cat, is represented as a combination of different states.

Now in quantum mechanics such superposition is removed on measurement (either by collapse or by transfer to an alternate world/alternate mind–see Free Will and God’s Providence, Part IV) to yield the particular component state which the measurement was designed to detect. If we are to carry the analogy further, what would be the analog of a measurement to detect one of the component God-states? What do we seek when we seek God, the Father,  God, the Son, God, the Holy Spirit? Theologians and philosophers will give subtle and complex answers, but I’ll state my own simple-minded view. We seek:

  • God the Father as the author of the Universe, of the laws of nature and mathematics, as Creator of all things, to worship and adore; we seek God in prayer (the “Our Father); we offer up to him the sacrifice of His Son in the Holy Mass.
  • God the Son as our salvation, to help us spread His Word and Message, by speech and deed; we seek the the Son in Intercessions in the Liturgy of the Hours; we take him to ourselves in the Sacrament of Holy Communion; we seek his forgiveness, when in the Sacrament of Reconciliation we ask Him (in the person of a priest) to forgive our sins.
  • God the Holy Spirit to change us, to alter our mind and heart to be better and approach the ideal given in Scripture. we seek the Holy Spirit in the Sacraments of Baptism and Confirmation; we ask His help when faced with moral dilemmas or avoiding sin.

When we seek God in any of these modes, we reach to God as that person of the Trinity, we “decompose” the superposition, we collapse the Trinity to the person that we seek.

I should note that objections to this model have been raised (see comments in the linked post), but I emphasize again that these models are an aid to understanding, not a true explanation.    This model has the properties proposed by the Patristic fathers: God as one entity, one essence, one state;  God as three persons, three components, unlike.


Here’s another scientific Trinitarian model, the resonance structure of the carbonate ion.

In the above picture O atoms connected by a single bond have 6 unbonded electrons around them and the O atom connected by a double bond has 4 unbonded electrons around it. Each O atom has 8 electrons (including bonding electrons) around it (the octet rule).


Resonance structures are used to represent a superposition of Lewis Bond structures, when these individually do not give a correct picture of chemical bonding.  The three oxygen atoms are physically distinct, as in the corners of a triangle, but can no longer be adequately represented by one picture of single and double bonds; they are equivalent, although spatially different.

There are many such examples of resonance structures, with two, three or more different   Lewis structures.  In some the molecules are not symmetric, so the Lewis structures will not be equivalent.   This resonance scheme shows that the theoretical framework of Lewis bond structures does not always give a complete picture of chemical bonding.


And here’s still another scientific Trinitarian model.    A proton is presumed to be stable (i.e. will not decompose spontaneously into other particles) because it is the lowest energy “baryon.”  Moreover, according to the Standard Model for particle physics, a proton is stable—won’t decompose—because it has three quarks, and that number has to be conserved.   A representation of the quark structure of the proton is shown below.

Quark Structure, from Wikimedia Commons

Quarks are characterized as being either “u,” (up) or “d,”  (down) and having “colors” (red, blue, green) as well as “flavors.”  None of these properties correspond to their ordinary meanings.  So the  proton has one “blue” “up”  quark, one “red”  “up” quark, and one “green” “down” quark.  The wavy lines between the quarks represent attractive quark-quark forces.   This type of force is unusual in that it almost vanishes when two quarks are close together, but increases rapidly as the quarks get further apart.   Such behavior means that it is practically impossible to separate the quarks, i.e. decompose a proton by physical means.

Are there are really quarks in a proton?   Stanford Linear Accelerator experiments suggest that protons have an internal structure that corresponds to the proposed quark structure.  Although isolated quarks have not been detected, these postulated particles are fundamental to the accepted “Standard Model” of particle physics.

Is this example apt for the Trinity?   Not so much.   The proton, like God, is a fundamental indivisible entity.  (The case for the proton being indivisible is not as strong, however, as that for God.)   Other than being a trinity, the quarks in a proton do not represent the three persons of the Trinity.  So, it makes a catchy title, but in the end it’s not all that useful.


Here’s the message that I hope this piece conveys:   the Holy Trinity is a mystery.    We can give examples, use models (i.e. employ retroductive reasoning), but these are only aids to understanding;  they are not complete explanations.

And so it is appropriate that the Trinity, the Godhead, remains a mystery.  As my wife has commented, “Aquinas has said ‘God is rational, it’s only our minds that are limited.’ ”



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5 thoughts on “Three Quarks and the Trinity:<br>Scientific Models for a Mystery”

  1. Fr. Khouri, I’ll quote the last paragraph of my article:
    “Here’s the message that I hope this piece conveys: the Holy Trinity is a mystery. We can give examples, use models (i.e. employ retroductive reasoning), but these are only aids to understanding; they are not complete explanations.”

  2. Josephine Harkay

    Since God is a spirit, any comparison with material things is futile. The ancient Israelites had it easy to believe in one God. We Christians experience the same one God in three different ways. But for me the the most puzzling thing is that Jesus, the Second Person of the Blessed Trinity become man, also lives forever in heaven as a man. Are we going to adore the spiritual Godhead and Jesus separately with His human body?

    1. Leave the Holy Trinity alone. Latins must always attempt to explain the inexplicable and in the process dumb down a great mystery as well as showing irreverence for the God who is God and we who are not.

  3. Pingback: FRIDAY EDITION – Big Pulpit

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