c·t = CONST, THAT CLICKS EPISODE 22 ／ Filling the blank Episode 1 left in "what the operations are"
95% of the operational budget goes to components in which nothing happens
The instruction set of
the universe-as-computer
The ML rate is proportional to energy, so the allocation of operations
is exactly the universe's energy budget. Counted, the result is exasperating.
When Episode 1 took the universe's spec sheet, the operation count was left blank inside — the Margolus–Levitin limit counts only transitions to orthogonal states and does not ask what is being done. Today we fill that blank. The ML rate is proportional to energy, so operations are allocated exactly as energy is. Counted, the result is fairly exasperating — 95% of the operational budget goes to components in which nothing happens.
01Operations are allocated as energy is
Since the rate is proportional to \(E\), the allocation of operational resources is exactly the universe's energy budget.
| Component | Energy fraction | Operation rate today |
|---|---|---|
| Dark energy | 68.5% | \(3.27\times10^{103}\) /s |
| Dark matter | 26.5% | \(1.26\times10^{103}\) /s |
| Baryons | 4.9% | \(2.34\times10^{102}\) /s |
| Photons | 0.0054% | \(2.58\times10^{99}\) /s |
| Neutrinos | 0.0038% | \(1.81\times10^{99}\) /s |
02The vacuum has nowhere to transition to
One remark bites here. The \(E\) in the Margolus–Levitin limit is energy measured from the ground state. But the vacuum energy is that ground state.
Conclusion of §02
The vacuum has nowhere to transition to.
So it should not be counted as operations — and with that one remark, 68.5% of the budget disappears.
That leaves 31.5%, of which 84.1% is dark matter. As far as we know, dark matter interacts only gravitationally — there is nothing to change its state.
The thing this episode most wants to say
The universe allocates 95.0% of its operational budget to components in which nothing happens.
Vacuum (68.5%) + dark matter (26.5%) — neither of which changes state.
Figure: the universe's energy = its allocation of operational resources. Raise the strictness of "what counts as an operation" with the slider and the surviving budget collapses in stages — from \(10^{121}\) counting everything, to \(10^{115}\) counting only starlight.
03So what are the baryons doing?
Look inside the surviving 4.9%. The most spectacular thing baryons do is stellar fusion. Estimate the total energy the universe has radiated as starlight since it began.
Hubble volume × cosmic luminosity density
$$3.17\times10^{11}\ \mathrm{Mpc^3}\times2\times10^{8}\ L_\odot/\mathrm{Mpc^3}=2.43\times10^{46}\ \mathrm{W}$$integrate over the age and compare with the total energy
$$\frac{1.06\times10^{64}\ \mathrm{J}}{7.90\times10^{69}\ \mathrm{J}}=1.3\times10^{-6}$$The energy the universe has ever shone as starlight is one millionth of the total. Fusion, the most conspicuous activity in the universe, at that scale.
04The instruction set
| Component | Fraction | What it actually does | An operation? |
|---|---|---|---|
| Vacuum | 68.5% | sits in the ground state; nowhere to go | × |
| Dark matter | 26.5% | gathers gravitationally; does not interact | × |
| Baryons | 4.9% | chemistry, fusion, life | ○ |
| Radiation | 0.009% | free propagation (Episode 11: completely at rest) | △ |
Episode 11 counted that "in this picture the photon gas is completely at rest". The fourth row restates it — radiation propagates without changing state. So calling it an "operation" in the ML sense is doubtful.
05The reveal — the ML limit counts only an upper bound
Episode 1's honest line said "this is a spec sheet, not a benchmark". Today we measured that gap — 95% of the spec is allocated to components with no prospect of being used.
① "The vacuum has nowhere to go, so do not count it" is this document's judgement. It follows the standard reading of ML's \(E\) as energy above the ground state, but whether cosmological vacuum energy counts as that ground state is not obvious — de Sitter space has a horizon temperature and fluctuations. What is solid in §02 is the observation that naively feeding in the total energy is wrong.
② "Dark matter does nothing" reflects current knowledge. It changes if a non-gravitational interaction is found. And gravitational structure formation is a genuine change of state, so "does nothing" applies only in the ML sense.
③ The luminosity density \(2\times10^8\,L_\odot/\mathrm{Mpc^3}\) is indicative, shifting by factors of a few with waveband and redshift dependence. Past star formation was higher, so multiplying by \(t_0\) is crude — read \(10^{-6}\) as an order-of-magnitude claim.
④ The energy fractions are today's values. The operation count \(\Omega=\int(2E/\pi\hbar)dt\) integrates over the past, so an exact breakdown needs \(\int\rho_i V\,dt\) per component (radiation's share is far larger in the radiation era). §04's table is a snapshot of today.
⑤ "Operations" remains an upper bound on transitions permitted by energy, not meaningful computation (same caveat as Episode 1 ①). All this document did was decompose that bound by component.
Exercises (solvable with this episode's formulas alone)
- Why is the operational budget "exactly the energy budget"?
Show the answer
Because the Margolus–Levitin rate \(2E/\pi\hbar\) is proportional to \(E\). So each component's operation rate is just its energy fraction. - Why should the vacuum not be counted, and how much disappears?
Show the answer
ML's \(E\) is energy above the ground state, and the vacuum energy is that ground state — there is nowhere to transition to. That removes 68.5%, leaving 31.5%. - What fraction is "doing something"?
Show the answer
Baryons 4.9% + radiation 0.009% = 4.91% (15.6% even excluding the vacuum). So 95.0% of the operational budget goes to components in which nothing happens (vacuum + dark matter). - What fraction of the total has been radiated as starlight?
Show the answer
Hubble volume \(3.17\times10^{11}\) Mpc³ × luminosity density \(2\times10^8L_\odot/\mathrm{Mpc^3}\) = \(2.4\times10^{46}\) W; over the age of the universe, \(1.1\times10^{64}\) J, or \(1.3\times10^{-6}\) of the total. Fusion, the most conspicuous activity there is, at one part in a million. - (Harder) How does today revise Episode 1's "0.035 operations per bit"?
Show the answer
95% of those 0.035 go to components in which nothing happens, so effectively \(0.035\times0.049=1.7\times10^{-3}\) — one operation per 580 bits. This is the content of the gap Episode 1 flagged as "a spec sheet, not a benchmark".
Summary — 95% went to components in which nothing happens
We filled the blank Episode 1 left in "what the operations are". The Margolus–Levitin rate \(2E/\pi\hbar\) is proportional to energy, so the allocation of operational resources is exactly the universe's energy budget — dark energy 68.5%, dark matter 26.5%, baryons 4.9%, radiation 0.009%.
Then one remark bit. ML's \(E\) is energy above the ground state, and the vacuum energy is that ground state — nowhere to transition to. That removes 68.5%, and of the remaining 31.5%, 84.1% is dark matter (gravitational interaction only). Only 4.91% can be said to be doing anything.
The universe allocates 95.0% of its operational budget
to components in which nothing happens
We looked inside the surviving 4.9% too — the energy the universe has ever shone as starlight is \(1.3\times10^{-6}\) of the total. Fusion, the most conspicuous activity in the universe, at one part in a million. And Episode 1's "0.035 operations per bit" falls to an effective one per 580 bits.
The reveal was the nature of the ML limit itself — it looks only at energy and does not ask whether a transition occurred. So vacuum and dark matter contribute to the bound. Today we measured the gap Episode 1 flagged with "this is a spec sheet, not a benchmark". 95% of the spec is allocated to components with no prospect of being used.
This document is Episode 22 of "c·t = const, That Clicks", written for physics-minded high-school and university readers. The Margolus–Levitin limit (rate \(2E/\pi\hbar\)) and its measurement of energy above the ground state are standard. The energy fractions \(\Omega_\Lambda=0.685\), \(\Omega_c=0.265\), \(\Omega_b=0.049\), \(\Omega_\gamma=5.4\times10^{-5}\), \(\Omega_\nu=3.8\times10^{-5}\) are standard Planck-era values. The per-component operation rates, "excluding the vacuum leaves 31.5%, of which 84.1% is dark matter", "4.91% is doing something", "95.0% of the operational budget goes to components in which nothing happens", and the \(1.3\times10^{-6}\) fraction radiated as starlight are computed here (kenshou/calc26.py). "The vacuum has nowhere to go, so do not count it" is this document's judgement — it follows the standard reading of ML's \(E\) as energy above the ground state, but whether cosmological vacuum energy is that ground state is not obvious (de Sitter space has a horizon temperature and fluctuations). What is solid in §02 is the observation that naively feeding in the total energy is wrong. "Dark matter does nothing" reflects current knowledge and applies only in the ML sense — gravitational structure formation is a genuine change of state. The luminosity density \(2\times10^8\,L_\odot/\mathrm{Mpc^3}\) is indicative, shifts by factors of a few with waveband and redshift dependence, and past star formation was higher (so \(10^{-6}\) is an order-of-magnitude claim). The energy fractions are today's; an exact breakdown of \(\Omega=\int(2E/\pi\hbar)dt\) needs \(\int\rho_iV\,dt\) per component (radiation's share is far larger in the radiation era). "Operations" remains an upper bound on transitions permitted by energy, not meaningful computation. Linear expansion (\(c\cdot t=\)const, \(R_h=ct\)) is a minority model under examination. The academic standard remains the \(\Lambda\)CDM model including inflation. ── To make a PDF, use your browser's Print dialogue (sliders freeze and answers are hidden in the print version).