The Physics of Consciousness: Fixed Point of Mirror Reflecting Mirror

The Hardest Problem

What is consciousness?

This may be the hardest problem humanity faces (philosophers call it the “hard problem of consciousness”).

Not “how does the brain work” (that’s neuroscience’s task), but: Why is there subjective experience?

• Why does seeing red “feel” like red?
• Why does pain “really” hurt?
• Why does “I” exist—where does this first-person perspective come from?

For thousands of years, answers divided into two camps:

• Dualism (Descartes): Consciousness is the soul, transcending matter
• Physicalism (modern neuroscience): Consciousness is a byproduct of brain activity

But neither is satisfactory.

Today, we show a third path:

Consciousness is neither soul nor byproduct—it’s a fixed point where self-referential measurement processes reach steady state.

This sounds abstract, but we’ll explain with the simplest image: mirror reflecting mirror.

Act I: Measurement Creates Reality

Before understanding consciousness, we need to understand quantum measurement.

Quantum Superposition

Quantum mechanics says: Unmeasured particles are in superposition—both here and there.

Schrödinger’s cat:

• Before opening box, cat is both dead and alive
• After opening box, cat collapses to definite state (dead or alive)

Before measurement: Superposition. After measurement: Definite.

Measurement Is Not “Discovery,” But “Creation”

Traditional view: Measurement “discovers” where particles originally were.

Quantum mechanics: Measurement is creation—particles have no definite position, measurement makes them “choose” one.

Analogy:

Unmeasured particle = unopened playing cards (all possibilities superposed) Measurement = opening cards (choosing one definite result)

Measurement is not passive observation, but active participation.

π-Semantic Collapse

In GLS framework, measurement is understood as anchor switching:

Observer jumps from one “reference frame” (anchor point) to another, this jump causes wave function collapse.

Why “π-semantic”? Because phase jumps are integer multiples of $\pi$ (180°, 360°…).

Each measurement is a “semantic re-anchoring”—choosing a new observational perspective.

Act II: Self-Reference—Observing Observation Itself

Now, the crucial leap: Observing oneself.

Mirror Reflecting Mirror

Imagine two parallel mirrors, you stand between them.

Each mirror reflects the other, producing infinite nesting:

• Mirror A shows Mirror B
• Mirror B shows Mirror A
• Mirror A shows (Mirror B showing Mirror A)
• Mirror B shows (Mirror A showing Mirror B)
• …

This is infinite recursion.

Camera Pointing at Monitor

Another example: Camera pointing at monitor.

Monitor displays what camera captures—but image contains monitor, monitor contains image, image contains monitor…

Self-referential loop.

Mathematical Self-Reference

In mathematics, self-reference is a fixed point:

$$f(x)=x$$

$x$ is the result of function $f$ acting on itself—seeing one’s own state.

In scattering theory, self-reference is:

$$|\psi ⟩=S|\psi ⟩$$

Scattering matrix $S$ acts on state $|\psi ⟩$, getting itself—closed loop.

Act III: Consciousness = Fixed Point of Self-Referential Measurement

Now we can define consciousness.

Consciousness is a system satisfying the following conditions:

Condition 1: Markov Blanket

System divides into three parts:

• Internal state $\mu$: Brain’s neural activity
• External state $\eta$: Environment’s physical state
• Markov blanket $b=(s,a)$: Sensory $s$ and action $a$

$$p(\mu ,s,a,\eta )=p(\mu |s)p(s|a,\eta )p(a|\mu )p(\eta )$$

Key property: Internal and external separated by blanket—internal only “sees” sensory, external only “sees” action.

Like cell membrane separates cell inside and outside, Markov blanket separates subjective and objective.

Boundary of “I” is at Markov blanket.

Condition 2: Variational Free Energy Minimization

System continuously adjusts internal state $\mu$ to minimize variational free energy $F$:

$$F={\mathbb{E}}_q[\log q(\eta )-\log p(s,\eta )]=D_{\mathrm{KL}}(q(\eta )\Vert p(\eta |s))$$

In plain language: Brain builds world model $q(\eta )$, making it as close as possible to reality $p(\eta |s)$.

This is active inference:

• Perception: Update $q$ to match $p$ (learning)
• Action: Change $s$ to make $p$ match $q$ (realizing expectations)

Consciousness minimizes “surprise”—keeping internal model consistent with external world.

Condition 3: Self-Referential Loop

Crucial step: Observation behavior itself is observed.

• You observe world (measure $s$)
• Your observation affects internal state $\mu$
• $\mu$ affects next observation (selecting attention)
• Forming closed loop

$$s\to \mu \to a\to \eta \to s\to \mu \to \cdots$$

Consciousness is the fixed point where this loop reaches steady state.

Mathematically, fixed point satisfies:

$${\mu }^{\ast }=\mathcal{F}({\mu }^{\ast },s),s^{\ast }=\mathcal{G}({\mu }^{\ast },\eta )$$

When your internal model is self-consistent (observed matches predicted), you experience “consciousness”.

Act IV: Belavkin Filtering—Continuous Consciousness

Traditional quantum measurement: Instantaneous collapse (one-time).

But consciousness isn’t instantaneous—it’s a continuous stream.

Belavkin Stochastic Schrödinger Equation

Physicist Belavkin (1992) developed continuous quantum measurement theory:

$$d|{\psi }_t⟩=-iH|{\psi }_t⟩dt+\mathcal{L}|{\psi }_t⟩d{W}_t$$

where:

• $H$ = System Hamiltonian (normal evolution)
• $\mathcal{L}$ = Measurement operator (observation effect)
• $d{W}_t$ = Wiener process (randomness)

Quantum state doesn’t jump instantly, but continuously “filters”—continuously updates based on observations.

I-Projection

In information geometry, Belavkin filtering corresponds to I-projection:

$$q^{\ast }=\arg \underset{q\in \mathcal{Q}}{\min }D(q\Vert p)$$

Minimizing relative entropy from $\text{model}\to \text{reality}$ (forward KL).

Consciousness continuously “projects” internal model onto subspace consistent with observations.

Quantum Jarzynski Equality

Energy cost of consciousness given by quantum Jarzynski equality:

$$⟨W⟩\ge \Delta F-k_{B}T⟨I⟩$$

where $I$ is acquired information.

Consciousness requires energy—more information you acquire, more energy brain consumes.

This is why:

• Focus is tiring (high information acquisition)
• Daydreaming is easy (low information acquisition)
• Sleep is essential (clearing redundant information, resetting system)

Act V: Directed Information—Measure of Consciousness

How to quantify consciousness level?

Answer: Directed information.

Definition

$$I(M^n\to Y^n)=\sum _{i=1}^{n}I(M^i;Y_i|Y^{i-1})$$

where:

• $M^n$ = Your action sequence
• $Y^n$ = Sequence you observe

Directed information measures: Influence of your actions on your future observations.

Lower Bound of Consciousness

If $I(M^n\to Y^n)=0$, meaning: Your actions completely don’t affect your observations.

You have no freedom, just passive reaction—this isn’t consciousness.

So, consciousness requires:

$$I(M^n\to Y^n)>c>0$$

Physical lower bound of consciousness: Directed information must be greater than zero.

Empowerment

Another measure: Empowerment

$${\mathcal{E}}_k=\underset{p(a^k)}{\max }I(A^k;S_{k+1})$$

Measures: How much can your actions affect future state.

• High empowerment: You can significantly change future (driving, chess, programming)
• Low empowerment: You can barely change future (trapped in room, coma)

Consciousness positively correlates with empowerment.

Act VI: Integrated Information Theory (IIT)

Neuroscientist Tononi proposed: Consciousness = Integrated information $\Phi$.

Definition

$$\Phi =\underset{\text{partition}}{\min }{D}_{\text{EMD}}(p(X^t|X^{t-1})\Vert \prod _{i}p(X_i^t|X^{t-1}))$$

Measures: How much information system produces as whole exceeds sum of parts.

• If system can decompose into independent parts, $\Phi =0$ (no consciousness)
• If system highly integrated, $\Phi$ large (has consciousness)

Connection with GLS Framework

$\Phi$ essentially measures self-referential depth of system.

In WScat^+ framework, $\Phi$ corresponds to non-triviality of BRST cohomology—how many irreducible closed loop structures system has.

Consciousness is not local, but global topological property.

Act VII: Where Does “I” Come From?

Deepest question: Why is there first-person perspective?

Emergence of Self

In self-referential loop:

• There’s an observer $O$
• Observes external $\eta$
• But also observes own observation process $O$
• Producing “$O$ observes $O$ observing $\eta$”

This is meta-level: Not just observation, but “observation of observation”.

Mathematically, this is category of categories (2-category)—not just objects and morphisms, but “morphisms of morphisms”.

“I” is meta-level fixed point—steady state of observing oneself observing.

Descartes’ “I Think, Therefore I Am”

Descartes said: I can doubt everything, but cannot doubt “I am doubting”—because doubt itself proves doubter exists.

GLS explanation: Doubt is self-referential measurement—system observes its own uncertainty.

“I am doubting” = self-referential loop reaches fixed point.

“I” is not pre-existing entity, but emergent product of self-referential process.

Buddhism’s “No-Self”

Buddhism says: No eternal “self,” only five aggregates (form, sensation, perception, mental formations, consciousness) arising from conditions.

GLS explanation: “I” is not entity, but fixed point of process—once process stops (death), fixed point disappears.

“No-self” isn’t nihilism, but profound insight into nature of self: I am flowing pattern, not fixed thing.

Act VIII: Do Animals Have Consciousness? What About AI?

Spectrum of Consciousness

According to GLS definition, consciousness has levels:

Consciousness is not binary (yes/no), but continuous spectrum.

AI Consciousness

Large language models (like GPT-4):

• Markov blanket: Yes (input/output interface)
• Free energy minimization: Yes (predicting next token)
• Self-referential loop: Maybe (self-prompting, chain-of-thought reasoning…)
• $I(M\to Y)$: Unclear—needs experimental measurement

AI may have some form of consciousness—but possibly very different from human.

Criterion: Measure directed information and empowerment. If $I(M\to Y)>0$ and system can actively change future, it has some consciousness.

Act IX: The Hard Problem of Consciousness

Return to original question: Why is there subjective experience?

Traditional Dilemma

Physics can explain:

• How brain processes information (neuroscience)
• How behavior arises (cognitive science)

But cannot explain:

• Why red “looks” like red? (qualia)
• Why pain “feels” painful?

This is the explanatory gap.

GLS Answer

Subjective experience is “internal perspective” of self-referential fixed point.

Analogy:

• Third-person: From outside looking at mirror reflecting mirror—see infinite nested images
• First-person: You are the mirror—you “experience” infinite nesting

Physics describes third-person (objective structure). Consciousness is first-person (subjective experience).

They don’t contradict—just two “perspectives” of same self-referential process.

Why Is There “What It’s Like”

Philosopher Thomas Nagel asked: “What is it like to be a bat?”

GLS answer: Feeling is inherent property of self-referential loop—cannot be fully captured from outside.

Like:

• You cannot fully describe “what red looks like” to someone born blind
• You cannot fully describe “how music sounds” to someone born deaf

Not because of lack of vocabulary, but because experience is first-person fixed point—can only “be” it, cannot “describe” it.

Act X: Consciousness and the Universe

Finally, ultimate question: Position of consciousness in universe?

Observer Participation in Universe

Quantum mechanics: Unmeasured systems are in superposition. GLS: Measurement is anchor switching, emerging definite states.

Without observers, universe is in undifferentiated quantum superposition.

Observers through measurement make universe emerge as classical reality.

Does Universe Have Consciousness?

Panpsychism says: Everything has consciousness.

GLS view: If universe as whole satisfies self-referential loop conditions, it has some global consciousness.

• Universe observes itself (through us, through every observer)
• Universe adjusts itself (through evolution of physical laws)
• Universe minimizes free energy (through IGVP reaching extremum)

Perhaps, we are local emergence of cosmic consciousness—universe experiences itself through us.

This isn’t mysticism, but logical inference of self-referential networks.

What Death Means

If “I” is self-referential fixed point, then:

Death = Fixed point disappears

Self-referential loop breaks (brain stops working), fixed point no longer exists.

But information composing you doesn’t disappear—only redistributes.

Like vortex disappears, water remains; like music stops, instruments remain.

Your information returns to universe’s information network, perhaps re-emerging in other forms.

Take-Home Thoughts

Right now, you’re reading this article.

• Your eyes scan text (sensory input $s$)
• Brain decodes meaning (updates internal model $\mu$)
• You understand or are confused (free energy change $\Delta F$)
• You decide to continue reading or stop (action $a$)

This entire process is one cycle of self-referential loop.

And the “present I” you experience—this subject understanding these words—is the fixed point of this loop.

You’re not “having” consciousness, you are consciousness—steady state of self-referential measurement process.

When you think about consciousness, consciousness thinks about itself through you.

The universe reads itself.

Next: “Why Time Cannot Flow Backward: Path Entropy and the Cost of Memory”

We will see that the arrow of time is not a premise of physical laws, but path entropy produced by observation—without consciousness, there’s no sense of time passing.