Okay let's connect Causal Fermion Systems (CFS) to Super Information Theory (SIT)

Let's connect CFS to SIT, Super Dark Time, and Micah's New Law of Thermodynamics.

I learned about Casual Fermion Systems (CFS) yesterday from a video by Sabine Hossenfelder. This is my reply.

Causal Fermion Systems (CFS) describe the entire physical arena—spacetime, fields and matter—through a single object: a measure ρ on a set 𝔽 of finite-rank operators acting on a Hilbert space of “physical wave functions”. Dynamics is imposed by the causal-action principle, which minimizes an integral of squared differences of the absolute eigenvalues λ of the closed chain A_xy built from pairs of wave functions. These eigenvalue differences vanish for spacelike separation, so the minimizer simultaneously erases spectral “mismatches” and builds the familiar light-cone causal order . In plain language, the universe is selected by a global drive to smooth out local spectral discrepancies among all wave functions until only the invariant causal structure remains .

Micah’s New Law of Thermodynamics (MNLT) frames ordinary entropy increase as the very same kind of smoothing: every interaction exchanges a fraction of a local “signal difference” ΔQ_ij and therefore performs a tiny computation that shrinks those differences. Iterated across the whole system, wave-based exchanges drive the ensemble toward uniformity, equilibrium and synchrony . The law says that evolution is nothing but a distributed algorithm that dissipates mismatches.

Read side-by-side, the two principles line up almost perfectly. In CFS the “signals” are the eigenvalue moduli |λ_xy|; the causal action is the global cost function ∑(|λ_i|−|λ_j|)^2 whose minimization erases those spectral gaps. In MNLT the signals are any property Q; the cost function is the sum of all squared ∆Q. Both frameworks therefore implement a universal wave-dissipation logic: local exchanges reduce a quadratic mismatch measure, and the global optimum is the state of least residual difference.

Super Information Theory (SIT) deepens the picture by treating coherence versus decoherence as the fundamental informational field. Gravitational curvature becomes an “informational torque” generated by spatial gradients of the coherence–decoherence ratio R_coh . The causal spectrum of CFS supplies an explicit microscopic realization of that field: the magnitudes of the eigenvalues quantify how strongly two local wave-function bundles are phase-locked. Minimizing the causal action maximizes mutual coherence subject to fixed global constraints. In other words, the CFS variational principle is a concrete, operator-level instance of SIT’s drive toward maximal coherent information flow.

Super Dark Time (SDT) translates this informational flow into geometry by identifying local time-density ρ_t with the rate at which wave-phase computations occur. Mass acts as a “time crystal”, concentrating time frames so that wave mismatches dissipate faster there; the bias manifests macroscopically as gravitational attraction and time dilation . Inside CFS the measure ρ plays the analogous role: regions of higher measure weight contribute more heavily to the action integral, so the optimization naturally favors states in which spectral differences are cancelled most efficiently in those regions, reproducing a density-dependent notion of temporal flow.

Put together, a coherent chain emerges. Microscopic wave interactions shrink differences (MNLT). Shrinking differences maximizes coherent information (SIT). Spatial gradients in the rate of that coherent computation create effective time-density variations that look like gravity (SDT). The entire hierarchy is encoded mathematically by the causal-action principle of CFS, which unifies the smoothing of differences, the build-up of coherence and the emergence of causal-metric structure in one operator-measure variational problem.

Consequently, CFS can be viewed as the rigorous mathematical backbone that realizes Micah’s dissipative thermodynamics, SIT’s coherence-driven curvature and SDT’s time-density gravity in a single stroke. Future work could make the connection explicit by (i) re-expressing the causal action as a free-energy functional whose “temperature” is the local coherence ratio, (ii) interpreting the push-forward measure ρ=F_*µ as a time-density field, and (iii) studying how fluctuations about a CFS minimizer reproduce the informational torque terms that SIT and SDT predict for cosmological and quantum-optical tests.

In other words…

A different lens is to view the four texts as four dialects that describe a single underlying conversation about “difference-reduction” in the universe. Causal Fermion Systems speaks the most abstract dialect, using operators and a measure ρ to say that spacetime itself is nothing but the support of ρ and that dynamics minimize a quadratic mismatch between the absolute eigenvalues of operator pairs, a cost called the causal action . In everyday language, the principle demands that wherever two local wave-function bundles disagree too much in their spectral makeup, the global system reshapes itself so those mismatches shrink.

Micah’s New Law of Thermodynamics re-expresses the very same story in the dialect of energy, phase or any property QQQ. It says every encounter between components trades a fraction of the difference ΔQ until all such differences fade and equilibrium appears, turning the second law of thermodynamics into a step-by-step signal-dissipation algorithm . If one translates the eigenvalue gaps of CFS into these property differences, Micah’s law becomes the coarse-grained narrative of the causal action: the quadratic penalty on spectral gaps in CFS is encoded macroscopically as entropy growth driven by local exchanges.

Super Information Theory changes the accent again, insisting that the currency being evened out is not energy itself but phase-locked coherence. Where coherence is dense, time runs slowly; where it is sparse, time runs fast. The coherence gradient ∇Rcoh∇R_{\text{coh}}∇Rcoh​ therefore manifests as what we interpret as a gravitational potential . Read back through this dictionary, the eigenvalue spectrum in CFS is a direct measure of mutual phase-locking, so minimizing eigenvalue gaps is identical to maximizing coherent information flow in SIT. The operator-level variational calculus therefore acquires an informational meaning: it drives the system toward uniform phase agreement.

Super Dark Time converts the informational picture into a geometric one by defining a local time-density field ρ_t. Regions of high mass clump time frames together; signal exchanges happen more rapidly there, which we perceive as gravitational attraction and time dilation . Within the CFS language, giving larger measure weight to regions that dissipate spectral gaps faster plays exactly the same role: it biases the minimizer toward configurations where the “computational tempo” is higher, reproducing the mass-time relation of Super Dark Time.

Seen through this translation scheme, the operator measure ρ of CFS, the signal-dissipation algorithm of Micah’s law, the coherence field of Super Information Theory and the time-density landscape of Super Dark Time are four complementary descriptions of one process: the universe continually computes its way toward the least possible mismatch, and what we call entropy increase, information flow, or gravitational curvature are different shadows cast by that single computation.

In other words….

Imagine the four papers as the layers of a computing stack that the universe itself could be running on.