Chapter 17: Vlatko Vedral — Information as the Primary Wave
Who is Vlatko Vedral
Professor of Quantum Information Science at Oxford. Author of Decoding Reality and Introduction to Quantum Information Science.
Core thesis: The universe is made of information, and information is quantum. Physics = information processing.
Key Vedral Concepts → Hz Translation
| Vedral Term | Hz/Wave Equivalent |
|---|---|
| "It from bit" + Landauer | Every bit erased costs $k_B T \ln 2$. Erasure = collapsing a Hz mode. Reality = what survives erasure |
| Mutual information = reality | $I(A:B) = S(A) + S(B) - S(AB)$. High $I$ = phase-locking between modes A and B. Reality = phase-coherent regions |
| Entanglement = correlation | Non-separable wave: $\Psi_{AB} \neq \psi_A \psi_B$. Same as Tononi's $\Phi > 0$. Same as Levin's gap junctions |
| Quantum Darwinism | Only information that can be copied into many Hz modes becomes "classical". Pointer states = stable solitons |
| Vacuum = superposition of all bits | Hz vacuum = sum over all $k,\omega$ modes. $|\Omega\rangle = \sum_{k} c_k |k\rangle$. Matter = excited modes |
| Maxwell's demon = biology | Life uses information to reduce entropy locally. In Hz: cells pump specific $k$-modes to fight decoherence |
| Matter = frozen information | $E=mc^2$ → $m = E/c^2 = \hbar\omega/c^2$. Mass = trapped Hz mode. Stable soliton |
Core Equations Translated
1. Landauer Limit = Click Cost
Vedral: Information erasure is physical. Minimum cost per bit:
$$ E_{Landauer} = k_B T \ln 2 $$
Hz: Erasing a bit = forcing a Hz mode from superposition to one eigenstate. Same "click" as Penrose OR. Detector bandwidth $B$ requires $E \geq \hbar B$. For $T=300$K: $k_B T/\hbar \sim 10^{13}$ Hz.
Levin connection: Rewriting bioelectric memory pays $N_{bits} k_B T \ln 2$. 1-head → 2-head planaria ≈ pJ.
2. Mutual Information = Phase-Locking
Von Neumann entropy: $S(\rho) = -\text{Tr}[\rho \ln \rho]$
For systems A,B:
$$ I(A:B) = S(A) + S(B) - S(A,B) $$
Hz: Independent oscillators: $\rho_{AB} = \rho_A \otimes \rho_B$, $I=0$. Phase-locked: $\phi_A = \phi_B + \phi_0$, $I = 2S(A) > 0$.
Tononi: $I$ = $\varphi$. Vedral: universe maximizes $I$. Tononi: consciousness maximizes $\Phi$. Levin: Gap junctions $G_{ij} > 0$ → $I(cell_i : cell_j) > 0$ → tissue "knows" itself.
3. Everything is Quantum Information
Margolus-Levitin bound for system with energy $E$:
$$ E \geq \frac{\pi \hbar}{2 \Delta t} N $$
To exist for time $\Delta t$, need energy. For stable particle: $\Delta t \to \infty$ → locked by interaction → $E = mc^2$.
Hz: Stable particle = Hz soliton with $\omega^2 = k^2c^2 + m^2c^4$. For $k=0$: $\omega = mc^2/\hbar$ → $E=\hbar\omega = mc^2$.
Penrose OR: OR when superposition of solitons costs $E_G$. Vedral: $E_G = k_B T_{grav} I_{geom}$, $T_{grav} = \hbar/g$.
4. Quantum Darwinism = Stable Bioelectric Patterns
Environment copies pointer states:
$$ \rho_S \to \sum_k p_k |\pi_k\rangle\langle\pi_k| \otimes |\mathcal{E}_k\rangle\langle\mathcal{E}_k| $$
$|\pi_k\rangle$ = pointer states. $|\mathcal{E}_k\rangle$ = environment records.
Hz: Extracellular matrix + water = environment. Only measures certain $k$-modes of $V(x,t)$. Levin's bioelectric code = pointer states. Cancer = environment stops copying organ mode.
How Vedral Unifies Part 3
$$ \text{Vedral: } I(A:B) \xrightarrow{G_{ij}>0} \text{Levin: phase-lock} \xrightarrow{\sum I} \text{Tononi: } \Phi \xrightarrow{E_G \sim I^2} \text{Penrose: OR} $$
- Vedral: Reality = network of mutual information. $I > 0$ = things exist for each other.
- Levin: Bioelectricity raises $I$ between cells. Gap junctions = channel for $I$.
- Tononi: $\Phi$ = total $I$ that can't be partitioned. Measures unity.
- Orch-OR: When $I$ between mass distributions → $E_G \propto I^2$ → OR. Picks one reality.
Vedral Predictions for Hz Ontology
- Landauer for morphogenesis: Changing anatomy dissipates $E \geq k_B T \ln 2 \times N_{modes}$. Testable heat spikes.
- Entanglement in tissue: Gap junctions should show quantum discord at 300K. Discord = min quantum mutual info.
- Mass from information: Erasing $10^{23}$ bits → $E = mc^2$. Primordial BH = mass dumps from cosmic info erasure.
- Consciousness = max $I$: Brain maximizes mutual info per Landauer cost. Efficiency $I/E$. Meditation = reduce $E$, keep $I$.
Information Has Mass
Vedral + Landauer + $E=mc^2$:
$$ m_{bit} = \frac{k_B T \ln 2}{c^2} \approx 10^{-38}\,\text{kg} \text{ at 300K} $$
Delete 1 TB → release $10^{-26}$ kg as heat.
Hz implication: Bioelectric code $\tilde{V}(k)$ has mass. 2-headed worm weighs more than 1-headed by $\Delta m = \Delta I \times m_{bit}$. ~$10^6$ bits → $10^{-32}$ kg.
Penrose: $E_G$ in OR = gravitational energy of information differences. OR when info difference ≈ 1 Planck mass.
Next Derivations
- Margolus-Levitin for bioelectric fields: Max compute rate = $2E/(\pi\hbar)$. Does Levin's tissue saturate it?
- Quantum discord in gap junctions: Use Vedral's formulas.
- Landauer cost of Orch-OR: Show it equals Penrose's $E_G$.