Photons, Wavepackets, and Wavefunctions: 3 Wavefunctions: The Formal Description of Potential

In the previous post, we saw that photons are instances and wavepackets are structured potential. Now we step to the final position in the cline of instantiation: the wavefunction.

The wavefunction is the formal mathematical representation of the wavepacket. It is not itself a physical wave. Instead, it encodes the relational structure that governs where and how photons may appear.

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1. Wavefunction vs wavepacket

Concept	Relational Ontology	Stratum
Photon	An actualised event	Instance
Wavepacket	Structured potential for photon instances	Physical potential
Wavefunction	Formal description of the potential	Mathematical representation

• The wavefunction encodes all the information contained in the wavepacket, but in mathematical language.

• It is the map of potential, not the territory itself.

For example:

• The wavefunction may assign a complex amplitude to each point in space.

• That amplitude represents the strength and relational configuration of potential instances at that point.

• Interference arises naturally from the superposition of potentials, not from photons physically splitting.

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2. Amplitudes as gradients of potential

Amplitudes are relational quantities:

• They measure how strongly the system is configured toward actualising a particular event.

• High amplitude → high potential density → more likely to actualise in that region.

• Low amplitude → weakly configured potential → less likely to actualise.

Relationally:

Amplitudes are gradients of potential across the instance space.

This viewpoint removes the mystery of “probability waves” — the wavefunction is simply a formalisation of potential distribution.

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3. The Born rule as relational invariant

The Born Rule is no longer an ad hoc postulate. From the relational perspective:

1. The wavefunction encodes potential amplitudes (gradients of potential).

2. A relational cut actualises one instance (a photon).

3. The squared amplitude is the invariant measure of potential density preserved across the cut.

Thus:

$$P=\mathrm{\mid }\psi {\mathrm{\mid }}^2$$

• Not mysterious; not a collapse of a physical wave.

• Simply the statistical shadow of how potential becomes instance.

Repeated measurements reveal this distribution — the footprint of the underlying structured potential.

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4. Superposition and interference

Superposition encodes relational structure:

• Two overlapping subpotentials can interfere: their amplitudes add (taking phase into account).

• The resulting pattern shows where relational potential is enhanced or diminished.

• When a photon is actualised, the relational cut picks one event from this interference-shaped field of potential.

From this perspective, “interference of a single photon with itself” is just shorthand for the relational potential guiding instance actualisation.

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5. Summary: the triangle complete

Entity	Stratum	Ontological Role
Photon	Instance	Actual event produced by a relational cut
Wavepacket	Physical potential	Structured potential for instances
Wavefunction	Formal description	Mathematical encoding of potential gradients

Key takeaways:

• Photons are instances; wavepackets are potential; wavefunctions describe that potential.

• The Born rule is a natural relational invariant, not a postulate.

• Interference and superposition are features of relational structure, not physical splitting of photons.