Hydrogen (H2) exists in two forms having different physical properties. They are known as ortho hydrogen and para hydrogen. The two forms coexist in a mixture. Para hydrogen is more stable than ortho hydrogen. The two forms interconvert very slowly, but the stable ratio of para to ortho hydrogen in a mixture depends upon temperature, the proportion of ortho hydrogen increasing with temperature.
The physical properties of the two forms of hydrogen cannot be explained by treating hydrogen as an absolute object (thinking on the principle of balance), but can be explained using quantum theory by treating it as a relational object: an object defined by drawing a distinction between two sides.
Hydrogen (H2) contains two protons. Quantum theory treats the two protons as being in a relationship. Each proton has a property known as spin. The spin of each proton can be either “up” (↑) or “down” (↓). Together the two protons are in a relationship called a spin system.
Thinking on the principle of a balance, this would be expected to produce four possible spin states: (↑↓), (↑↑), (↓↑) and (↓↓). However, thinking on the principle of relational symmetry, there are two possible spin states, one in which the spins are aligned (symmetric) and one in which they are opposed (antisymmetric).
Thinking on the principle of balance further leads to the expectation that the symmetric state maps to (↑↑) and (↓↓) and antisymmetric to (↑↓) and (↓↑). This mapping would result in the ratio of symmetric to antisymmetric being 1:1. It is actually 3:1. The symmetric state is called the triplet state and the antisymmetric state is called the singlet state.
Although the two forms of hydrogen are relational objects, quantum theory has been constructed on the principle of balance, in equations, presumably because no relational mathematics was available.
The conventional explanation for 3:1 ratio is constructed on the principle of balance. Thus the conventional explanation is that the antisymmetric (singlet) state is (↑↓) + (↓↑) and the symmetric (triplet) state is (↓↓), (↑↓) – (↓↑) and (↑↑).
Thinking on the principle of chiralkine offers an alternative perspective that is simpler to understand and does not require the use of equations.
Chiralkine treats all objects (hence both spinor particles and molecules) relationally. It is constituted in Order 4.
The four spin states of hydrogen (↑↓), (↑↑), (↓↑) and (↓↓) can fundamentally be ordered as a triplet (symmetric) or a singlet (antisymmetric). To see this, map “Up” (↑) and “Down” (↓) to “Same” and “Distinct” and allow these labels to oscillate interchangeably, controlled by the logic gates XOR and XNOR, which represent mutually exclusive ways of drawing distinctions.
Each possible combination of proton spins (↑↓), (↑↑), (↓↑) and (↓↓) can be represented using binary logic inputs like 01, 00, 10, and 11. These are exactly the inputs used in logic gates like XOR and XNOR, which form the basis of digital computation. The logic gates for XOR and XNOR both have the four input pairings. There are only six different ways of ordering four different objects. These constitute three mirror pairs (a triplet). The XOR and XNOR logic gates are mirror symmetric, so interpenetrate to define a six membered cycle. This interpenetration removes one of the four degrees of freedom. It is why there are six logic gates: XOR, XNOR, OR, AND, NAND and NOR. 1 and 0 lose their absolute meanings true and false or same and different in this relational system, just like the two individual protons lose their absolute spins in hydrogen.
The singlet state does not map to any of the six logic gates. Each symbol is simply NOT the other. The singlet state corresponds to a recursive sequence of NOT gates: A NOT gate inverts its input: if the input is True, the output is False, and vice versa. This recursive sequence forms a simple oscillation, where each NOT operation alternates the state generated by its predecessor. Together, the NOT gates define rows for XOR and XNOR, placed one over the other, but braided so that the columns also oscillate between XOR and XNOR: hence in three rows 010 appears in two columns (XNOR) and so does 101 (XOR). This sequence generates a simple oscillation, containing no triplets.
Conclusion
Chiralkine provides a new perspective for understanding quantum spin states. By treating spin as a relational distinction rather than an absolute quantity, chiralkine offers a symmetrical, logic-driven view that naturally explains the 3:1 distribution without invoking equations. The two forms of hydrogen and the two protons together constitute a relational system in which each object is defined relationally by drawing a distinction.