A Note on What This Is
This document is part of a course called “Quantum Mechanics Through Triangles.”
What this is:
- A relational perspective on physics
- An attempt to build deep intuition
- A way to connect ideas for non-physicists
- One coherent stance, followed to its conclusions
What this is NOT:
- The One True Church of All Known Things
- A claim that other views are wrong
- A replacement for rigorous physics training
- A claim of completeness or finality
Taking any framework as absolute truth is an idiot’s view of things. The universe does not care about our frameworks. We use frameworks because they help us think. When they stop helping, we discard them.
This framework helps us. We use it. That is all.
Part I: Symmetry
What is symmetry?
Symmetry means: you can do something, and things look the same.
- Rotate a circle: it looks the same.
- Translate a pattern: it looks the same.
- Swap two identical particles: the physics is the same.
The triangle and symmetry
The equilateral triangle has 6 symmetries:
- 3 rotations (0°, 120°, 240°)
- 3 reflections (through each vertex)
This is the group D₃, the simplest non-trivial symmetry group that is not just rotations.
A
/|\
/ | \
/ | \
B---+---C
Rotate 120°: A→B→C→A
Reflect through A: B↔C
Why symmetry matters
Noether’s theorem: Every continuous symmetry implies a conserved quantity.
| Symmetry | Conservation Law |
|---|---|
| Time translation | Energy |
| Space translation | Momentum |
| Rotation | Angular momentum |
| Phase rotation | Charge |
Symmetry is not decoration. It is the source of conservation laws.
Broken symmetry
The laws may be symmetric, but the state may not be.
A pencil balanced on its tip has rotational symmetry. When it falls, symmetry breaks — it falls in ONE direction.
The universe’s laws are symmetric. The universe’s state is not. This is why there is structure, not uniform soup.
The relational view of symmetry
Symmetry is about what distinctions matter.
If rotating the system leaves physics unchanged, then absolute orientation does not matter — only relative orientation.
If translating the system leaves physics unchanged, then absolute position does not matter — only relative position.
Symmetry tells us what is relational and what is not.
Part II: Superposition
What is superposition?
A quantum system can be in multiple states “at once.”
|ψ⟩ = α|0⟩ + β|1⟩
The system is not in state |0⟩. It is not in state |1⟩. It is in a superposition of both.
The naive mistake
The naive view: “The particle is really in one state, we just don’t know which.”
This is wrong. Bell’s theorem proves it. If the particle had a definite state we didn’t know, certain correlations would be impossible. Those correlations are observed.
The relational view
Superposition is relative.
To YOU, the particle may be in superposition. To another system that has interacted with it, it may not be.
There is no absolute fact about whether a system is in superposition. It depends on who is asking — on what relations exist.
The triangle of superposition
Observer
●
/|\
/ | \
/ | \
/ | \
●────┴────●
State A State B
The observer is in superposition of
"having seen A" and "having seen B"
relative to a third system.
Superposition is not a property of the particle alone. It is a property of the relation between particle and observer.
Measurement and collapse
When you measure, superposition “collapses” to one outcome.
Relational view: Nothing collapses globally. A correlation is established between you and the system. To you, the system now has a definite state. To a third party who hasn’t interacted with either, you and the system are in superposition together.
Part III: Entanglement
What is entanglement?
Two systems are entangled when their combined state cannot be written as a product of individual states.
|ψ⟩ = (1/√2)(|00⟩ + |11⟩) NOT equal to |a⟩ ⊗ |b⟩ for any |a⟩, |b⟩
Measure one, and you instantly know something about the other — regardless of distance.
The naive mistake
“Faster-than-light communication!”
No. You cannot send a message this way. The correlations are there, but you cannot control what outcome you get. When you measure, you get a random result. The correlation only becomes apparent when you compare notes — which requires ordinary communication.
The relational view
Entanglement is shared relation without individual properties.
The two particles do not have individual states. They have a joint state. They are one system, not two.
●───────────● Particle A Particle B The line IS the entanglement. The particles ARE the relation.
Distance is irrelevant because there is no “signal” traveling. The relation exists; it is not created by measurement.
The triangle of entanglement
Observer
●
/|\
/ | \
/ | \
/ | \
●────┴────●
Particle A Particle B
The three form ONE entangled system.
The observer's measurement affects
what relations exist.
Entanglement and the triangle
The triangle is the minimal closed structure.
Entanglement is the quantum version: three systems (or two, plus the relation itself) forming a closed relational structure that cannot be decomposed into parts.
Entanglement IS triangular structure at the quantum level.
Part IV: Consciousness
A warning
Consciousness is where physics meets philosophy meets neuroscience meets confusion. We make no strong claims here. We offer a perspective.
The hard problem
Easy problems: How does the brain process information? How do neurons fire? These are hard but tractable.
Hard problem: Why is there subjective experience at all? Why does it feel like something to be you?
The naive mistakes
Mistake 1: “Consciousness is just computation.” But a thermostat computes; is it conscious?
Mistake 2: “Consciousness is quantum.” But quantum effects in warm, wet brains decohere in femtoseconds.
Mistake 3: “Consciousness is separate from physics.” Then how does it affect your brain to make you talk about it?
The relational view
Consciousness may be what observation looks like from the inside.
In the relational view, observation is not passive. It is an interaction that creates correlation. The observer is not outside the system; the observer IS part of the relational structure.
Consciousness is the structure of self-referential observation.
The triangle of consciousness
Self (observer)
●
/|\
/ | \
/ | \
/ | \
●────┴────●
World Experience
(observed) (observation)
The three are ONE structure.
"You" are not inside looking out.
"You" ARE the triangle.
What we do NOT claim
- We do not claim this solves the hard problem.
- We do not claim consciousness is “just” physics.
- We do not claim the triangle explains qualia.
We claim only that the relational view offers a way to THINK about consciousness without falling into naive dualisms or naive reductions.
Self-reference again
Consciousness involves a system modeling itself.
The course describing itself. The observer observing itself. The triangle with one vertex pointing at the whole triangle.
●
/|\
/ | \
●──┼──●
|
↓
(same triangle)
Self-reference is not a bug. It may be the source of consciousness.
Part V: The Unity
These are not four separate topics
- Symmetry tells us what distinctions don’t matter.
- Superposition is having multiple distinctions at once.
- Entanglement is shared distinctions without individual ones.
- Consciousness is being the distinction-maker.
They are all about the structure of observation and distinction.
The triangle unifies
OBSERVER
(consciousness)
●
/|\
/ | \
/ | \
(symmetry) | (entanglement)
/ | \
●────┴──────●
DISTINCTION DISTINCTION
(superposition of both)
The triangle is the minimal structure where:
- An observer exists
- Distinctions are made
- Relations close on themselves
This is why the triangle keeps appearing. It is not a metaphor we impose. It is the shape of observation.
Part VI: For the Non-Physicist
You don’t need equations
The core ideas are simple:
- There is no view from outside. You are part of what you observe.
- Relations are primary. Things are secondary — they are nodes in a web of relations.
- The triangle is minimal. Three points, three relations, closed structure.
- Symmetry, superposition, entanglement, consciousness are aspects of the same thing: the structure of observation.
The equations help but are not required
Physicists use equations because they are precise. But the ideas behind the equations can be grasped without them.
If you understand:
- Things don’t have absolute properties, only relative ones
- A system can be “both” until relation forces “one”
- Two things can share a relation without having individual states
- You are not outside looking in; you are inside looking around
Then you understand the core of quantum mechanics relationally.
Part VII: Honesty
What we know
- Quantum mechanics works. Predictions match experiments to 12 decimal places.
- Symmetry principles are powerful and correct.
- Entanglement is real and verified.
What we don’t know
- Why quantum mechanics is true. (No one knows.)
- What consciousness is. (No one knows.)
- Whether the relational view is “correct” or just useful. (No one knows.)
What we believe
We believe the relational view is productive. It helps us think. It connects ideas. It avoids certain confusions.
We do not believe it is the final truth. There is no final truth we have access to. There is only productive thinking.
Coda
The triangle is:
- The minimal closed structure
- The shape of observation
- The form of distinction
Symmetry, superposition, entanglement, consciousness — these are how the triangle appears in different contexts.
We do not worship the triangle. We use it to see.
When it stops helping, we will use something else.
Until then: three points, three edges, closed loop, zero internal freedom.
The triangle.
This document is part of “Quantum Mechanics Through Triangles.”
Relational. Accessible. Honest about what we know and don’t know.
Not a church. A lens.