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Building a Wave (Quest for Entropy #5)

Marijus Masteika

Published Aug 6, 2026• 0 citations
Publisher

Abstract

Quest for Entropy #5: I wanted a probability cloud that spreads into a shape and then stops — and oscillates. I built six worlds to find one. Here is exactly how each of them failed. - Nothing here is a claim about how quantum mechanics works, and no Born rule is derived or attempted. This is what classical probability distributions can and cannot do. - Six systems, one ruler, finite runs. The ordering held at every resolution I tried; the exact numbers are the ruler's.

DOI
10.5281/zenodo.21826121

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Quest for Entropy #5: I wanted a probability cloud that spreads into a shape and then stops — and oscillates. I built six worlds to find one. Here is exactly how each of them failed. - Nothing here is a claim about how quantum mechanics works, and no Born rule is derived or attempted. This is what classical probability distributions can and cannot do. - Six systems, one ruler, finite runs. The ordering held at every resolution I tried; the exact numbers are the ruler's.
Quest for Entropy #2: how a clockwork with no dice fakes quantum mechanics — the machine taken apart, the exam it passed, and the one wall it cannot get past. This is a demonstration, not a discovery about nature. It does not say our universe is a clockwork, does not reinterpret quantum mechanics, and does not dodge Bell's theorem — the hidden machinery is global, not local, exactly because Bell rules out the local kind (we checked). The recipe was found by an optimizer and only later shown to sit at a fixed point of the geometry; the build is engineering, and we say so. The claim is only this: quantum-looking behaviour can come out of a deterministic machine plus a physical measurement — not that this is why our world is quantum. Everything here describes one family of machines at the settings we tested, and where it fails, it fails in public.
How much of quantum mechanics can a machine with no dice fake? This deposit accompanies the article "The Universe with No Dice" (Quest for Entropy #1), which builds a fully deterministic, classical toy universe and shows that a bounded observer inside it counts Born-rule statistics and double-slit interference to within about one percent of the quantum prediction, with the model's exact failure mode published as a falsifiable limit rather than hidden in error bars. Article: https://questforentropy.substack.com/p/the-universe-with-no-dice Code and reproduction instructions: https://github.com/masteris777/quest-for-entropy-the-universe-with-no-dice
Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments.
I suppose one could imagine laws of physics which would dictate that a world be exactly so, and not otherwise, allowing no detail to be varied. But what could dictate that those laws of physics be ‘the’ laws of physics? By considering a spectrum of possible laws, one could again consider a spectrum of possible worlds. In fact the laws of physics of our actual world, as presently understood, have no such dictatorial character. So that even with the laws given, a spectrum of different worlds is possible. There are two kinds of freedom. Although the laws say something about how a given state of the world may develop, they say nothing (or anyway very little) about in what state the world should start. So, to begin with, we have freedom as regards ‘initial conditions’. To go on with, the future that can evolve from a given present is not uniquely determined, according to contemporary orthodoxy. The laws list various possibilities, and attach to them various probabilities. The relation between the set of possibilities and the unique actuality which emerges is quite peculiar in modern ‘quantum theory’ – the contemporary all-embracing basic physical theory. The absence of determinism, the probabilistic nature of the assertions of the theory, is already a little peculiar… at least in the light of pre-twentieth-century ‘classical’ physics. But after all everyday life, if not classical physics, prepares us very well for the idea that not everything is predictable, that chance is important.
Quest for Entropy #6: I tried to build a probability wave and failed. So this time I went looking for one that already exists — a droplet of oil that bounces on a vibrating bath and builds its own wave, one splash at a time. Then I sat it down for a quantum exam. - Not a claim that quantum mechanics works this way, and not a derivation of anything quantum. No Born rule appears here and none is attempted. - The orbital-looking pictures are wave modes of a confined system. The resemblance to atomic orbitals is a shared equation, not shared physics. - Nothing here says pilot-wave theory is right or wrong. Walking droplets are a classical analogue, not evidence about what quantum particles do. - The walker results are cited from published work, not reproduced here — including the double-slit replication failure. - "A record that steers" and "stays versus passes through" are readings of why the walker behaves as it does — directions to explore, not established mechanisms.