I built a small neural network (a GRU) that works similarly to how you and I work. It sees short, noisy snapshots one at a time, has a small internal memory that carries forward, and its only job is to predict the next snapshot. You see a little, you remember a little, you predict. It asks one question: is physical law what any finite observer must build to predict reality?
First I tested whether memory helps equally everywhere. I ran it on real data from 13 instruments: LIGO, EHT, Planck CMB, solar wind, sunspots, and others; same observer, only the data changed. Some domains are readable in one shot, others only make sense if the observer accumulates over time. That variation isn't random, it actually falls along a single axis. EM domains cluster at the low-accumulation end, gravitational waves at the high end. Four different architectures (GRU, LSTM, ViT, Transformer) give the same ordering. Light at one end of the axis, gravity at the other... Suspiciously concise.
The obvious next question: if observation cost has this much structure, is it pointing at something intrinsic? So I put the observer behind six detectors around a gravitational source in simulation, trained only on signal prediction, no physics in the training. The observer recovers the 1/r potential (8/8 seeds, controls dead). In the relativistic case it recovers redshift and delay. After 9 different variations, mass remained hidden in static fields, which turned out to be structural, not a bug. Mass only shows up when something changes in time (a memoryless observer fails completely). Across 30 real black hole mergers, observation cost tracks spectral complexity, not mass.
One curious and unpredicted result: I also tested where accumulation hurts. A periodic signal observed through the same pipeline produces zero persistence (180+ runs) when the observer's windows don't line up with the signal's cycle. Accumulating phase-shifted fragments destroys the coherent structure, meaning the observer is better off not accumulating. You might notice this is structurally identical to wave-particle duality: tracking where each observation came from destroys the interference.
First I tested whether memory helps equally everywhere. I ran it on real data from 13 instruments: LIGO, EHT, Planck CMB, solar wind, sunspots, and others; same observer, only the data changed. Some domains are readable in one shot, others only make sense if the observer accumulates over time. That variation isn't random, it actually falls along a single axis. EM domains cluster at the low-accumulation end, gravitational waves at the high end. Four different architectures (GRU, LSTM, ViT, Transformer) give the same ordering. Light at one end of the axis, gravity at the other... Suspiciously concise.
The obvious next question: if observation cost has this much structure, is it pointing at something intrinsic? So I put the observer behind six detectors around a gravitational source in simulation, trained only on signal prediction, no physics in the training. The observer recovers the 1/r potential (8/8 seeds, controls dead). In the relativistic case it recovers redshift and delay. After 9 different variations, mass remained hidden in static fields, which turned out to be structural, not a bug. Mass only shows up when something changes in time (a memoryless observer fails completely). Across 30 real black hole mergers, observation cost tracks spectral complexity, not mass.
One curious and unpredicted result: I also tested where accumulation hurts. A periodic signal observed through the same pipeline produces zero persistence (180+ runs) when the observer's windows don't line up with the signal's cycle. Accumulating phase-shifted fragments destroys the coherent structure, meaning the observer is better off not accumulating. You might notice this is structurally identical to wave-particle duality: tracking where each observation came from destroys the interference.
Overview with links to each paper: https://www.wvrk.org/works/why-physics-has-laws