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Ngl I kinda hate quantum physics. "So these balls are spinning except they're 0 dimensional waves and not spinning and also there's color charge and also there's like 20 fundamental particles but half of them decay immediately, and half of the other half can stack in the same quantum state and the others can't, also everything is waves now and all the electrons are the same because fuck you."
[From an engineer not specialized in electrical or computing or nuclear]
Quantum physics is alright. It's just a lot of fancy linear algebra and spinors. I have a lot of problems with the culture surrounding it though.
Like, it seems like scientists want quantum mechanics to feel magical. For example, "quantum wave collapse" is a "collapse" only in some interpretations of quantum mechanics. There was one article by 真理zhenli that talked about this mystification of physics.
Tldr: quantum mechanics is the "shut up and calculate" of physics and a grand theory of everything ain't gonna happen in this century.
Edit: Found the articles: Physicalism was a Mistake; Let us Return to Materialism and A Critique of Idealist Interpretations of Quantum Theory
David Bohm (who was a Communist in his early years) developed a materialistic quantum theory called the de Broglie-Bohm Mechanics or Pilot Wave Theory. It makes much more sense (and the calculations are the same) than the idealistic Copenhagen interpretation IMO.
That's the name.
I'm really partial to Max Planck (especially him making the case that virtually nothing can exist in a vacuum and we can see that that is indeed the case with space, for example)
I mean, he was a fascist, afaik, but eh, I'm going to separate some of his achievements in this case, it's not like he did something useless like make a short story bemoaning "miscegenation" or whatever (looking at you, H.P. Lovecraft)
Context: I still remember reading that particular story where everybody just interbreeds or whatever and it literally makes them into apes or whatever and just... laughing at it all after having finished it bwahahahahah
(especially having grown up as "mixed" individual or whatever we call ourselves)
I wrote the linked articles and am finalizing a math-heavy technical book (when it goes live it will be under ISBN 978-1-291-55573-8) that critiques the doctrine of "value indefiniteness." Value indefiniteness claims systems lack definite properties until measurement causes "collapse," but it suffers from significant philosophical and mathematical flaws and is where all the supposed "weirdness" of quantum mechanics stems from.
If particles "collapse" at measurement, then they do something unique in their dynamics at measurement, rendering "measurement" a fundamental part of the theory. The physicist John Bell argued that treating measurement as fundamental requires a rigorous physical definition that textbooks fail to provide, leaving it ontologically incomplete as a theory of nature. The Soviet physicist Dmitry Blokhintsev showed that collapse introduces non-linear mathematics that produces different statistical predictions than standard quantum theory, making perfect mathematical reconciliation impossible.
Physicists call these issues the "measurement problem," but this term is misleading because "problem" implies it is something to be solved, but the issue is unsolvable. It represents a contradiction between two incompatible premises, meaning one must be wrong. In my view, value indefiniteness is the incorrect premise. My book demonstrates via polar decomposition that the statistical evolution of quantum information is already mathematically equivalent to a stochastic process where bits have definite values at every moment. This transformation reproduces Born rule statistics without proposing a new model, as it is literally mathematically equivalent. It is the same theory just represented under a simple mathematical transformation.
The ultimate difference between quantum and classical statistical dynamics lies in how distributions evolve. Classical statistics computes future states using only current distributions and interaction descriptions. Quantum statistics requires computing a function that additionally takes all past states back to the circuit's beginning as input. The Harvard physicist Jacob Barandes first identified this property as "non-Markovianity" in his 2025 paper "The Stochastic-Quantum Correspondence." Indeed, the majority of my book's pages is dedicated to demonstrating how quantum theory, as written, decomposes mathematically into something that is both purely statistical (no quantum state or phases; they all disappear, leaving you just statistics and operators) where the statistical laws are non-Markovian.
I then analyze major relevant papers including the PBR theorem, Bell’s theorem, the GHZ experiment, the Frauchiger-Renner paradox, and the double-slit experiment to show, mathematically, how this stochastic process explains them without presupposing value indefiniteness.
I've also built a simulator you can find below, where you can construct any arbitrary quantum circuit, up to 32 qubits, and it will simulate it as a stochastic process where the bits have definite values at each moment and evolve through stochastic hops. If you change from "single" mode to "shot" mode, it will run the program many times over, forming statistics of the final bits state, and the statistics always match the Born rule, not just at the end but at every time interval.
https://qansel.foleosoft.com/
If you can explain quantum mechanics so simply in this way, why do people treat it as so complicated?
My argument in the book is because this explanation does not actually give you a unique ontology, because when you do take into account the various previously mentioned papers (like Kochen-Specker and GHZ), you find that there are not inconsistencies but ambiguities in the ontology without answering 3 different questions, but the mathematical structure of quantum theory makes it physically impossible, by experiment, to discover the answers to those 3 questions.
Rather, it only constrains to a possible class of answers to those 3 questions. Any choice within that class produces a physically plausible ontology, but they are all empirically indistinguishable from each other.
Another user down below in the replies mentions Bohmian mechanics. Bohmian mechanics is a model within that class. Indeed, Bohm's derivation of Bohmian mechanics begins with a polar decomposition on the quantum state, the same kind of mathematical transformation that my book relies on. It then makes specific choices to the answers to those questions which are motivated by different arguments outside of what is directly empirically verifiable.
For example, one of the questions you have to answer is which basis should be privileged as the "ontic basis," even though all bases are mathematically symmetrical; this is referred to as quantum contextuality and is established by the Kochen-Specker theorem. Bohmian mechanics chooses the position basis, because "position" is the most defining characteristic of a particle, as they are geometric points in space, and a point is most fundamentally defined by its position. In principle, however, you could choose a different basis, like the momentum basis, and build an alternative ontological model which is mathematically equivalent in that it makes all the same empirical predictions, and is also ontologically consistent.
Bohmian mechanics is just one ontological model in a landscape of possible ontological models. It was, again, the physicist Dmitry Blokhintsev who pointed out that we can't actually empirically figure out the correct model due the "finiteness of interaction" as he called it (the inherent limitations in measurement precision given by Planck's constant) preventing us from actually probing answers to those questions.
Physicists don't like not knowing something. If it's knowable, they want to do an experiment to know it. If no experiment can reveal it, many, starting with Bohr and Heisenberg, started to insist that maybe we should stop believing there is anything to be known at all. If there simply is no underlying ontology, then there is nothing to be known to begin with, and thus we can be assured we know everything that there is to know.
This leads into the doctrine of "value indefiniteness": there simply is no ontology underlying the quantum state, and is the basis of the famous Copenhagen interpretation. The particle just has no position at all until you look, the bits in a quantum computer have no values at all until you look.
However, as I argue in the book, you cannot actually make this point of view compatible with realism, because it either is logically incoherent, or it is coherent, but provably deviates from the mathematical predictions of quantum theory. If we are realists who also believe quantum theory, as written, is correct, then "value indefiniteness" must be wrong.
We thus must just accept that the mathematics of the theory does simply leave the underlying ontology underdetermined, and to actually fully specify the ontology, we must either choose a convention (fully aware it is a convention, not necessarily the "correct" ontology but useful for a given experiment), or we must make arguments that go beyond what can be empirically demonstrated: not all answers to those 3 questions are equally reasonable, some are rather absurd and arbitrary, while some you can justify by other means.
There is simply no a priori reason to believe that the laws of physics are structured in such a way to allow humans in their tiny insignificant laboratories on this tiny pale blue dot to discover everything there is to know about the ontology of nature. It is quite easy to imagine the laws of physics being structured in such a way that simply disallows unambiguous answers to certain questions of ontology, and that is ultimately what I am to demonstrate in that book (and the article you cite is just a brief summary of the idea, which I tried to present without mathematics for the Laymen), that the structure of quantum theory fundamentally leaves 3 very important questions, needed to fully specify the ontology, not ruled out but underdetermined, so you can only restrict them to a class of possible answers rather than a singular answer.
You then must either go beyond the pure mathematics / empirical observations themselves to restrict those 3 questions further down to a specific answer, or you must just accept that we can't fully know the ontology and treat the ontology as something conventional. To be conventional does not mean to deny there is an underlying ontology or to resort to subjectivism; it is to choose an ontological model that is convenient given the context of your experimental setup, but with the acknowledgement that it is just a convenient choice, and thus you make no claims to certainty that it is the "true" ontological model, although it is a plausible one.
To deny the underlying ontology leads to nonsense and cannot be meaningfully reconciled with realism, at least under the basic requirements I put forward for any sensible realist ontology in the book, one of those requirements being the "no-solipsism" requirement, which is that your model should never produce multiple incompatible mental states for other observers. That is to say, the mental states of other observers must always be invariant.
The famous Frauchiger-Renner paradox, published in the journal Nature under the title "Quantum theory cannot consistently describe the use of itself," demonstrates quite unambiguously that every "value indefinite" interpretation fails this simple criterion. (Again, the mathematics of which I cover in my book in more detail, when the book is released.) If you read the paper, they also point out that Bohmian mechanics (a realist model) does not run into this problem, but requires answering a question which traditional quantum theory leaves underdetermined. My book ultimately generalizes that point.
Outline of notes
Left notes here because I don't know whether I understood everything.
Concepts
Value indefiniteness: systems lack definite properties until measurement causes “collapse”. Suffers from philosophical and mathematical flaws.
Problems with collapse:
pcalau12i's Book
The book:
I didn't know you were here on Lemmygrad. Thanks for the write-up, I really enjoyed it. This is the first time I had to take notes on a comment lol.
I really think that Bohmian mechanics (or something similar) are the way to go to study quantum theory. Not only because of what you've already mentioned, but because it's also an evolution on stochastic processes, which were literally how quantum mechanics started out (I think it was Planck who used statistical mechanics to analyse the empirical results of the black body radiation problem).
Apologies for not having much to add because my whole quantum theory education was composed of youtube videos, reading stuff online and learning some linear algebra. However, I look foward to read your book. Do advertise it here when it's done. Do you know how many pages it is yet?
The digital PDF is about 150 pages, so it's not incredibly long. (Page count may be different for physical version.) It is also written so that one can follow along even if they have no technical background, although it will be harder to do so. The mathematics used are explained, with some GNU Octave code at the end of each chapter just to give you some hands-on with the math. So if you want to learn it in the process of reading it, you can, but someone who already knows the basics of quantum computing could probably skim through the whole first third of the book, with only the latter 100 pages actually assuming you know the mathematics enough to be able to simulate a quantum circuit.
Also, as per your notes, " non-Markovian (ie: non-Stochastic)", non-Markovian does not mean non-stochastic.
Consider that you apply a logic gate to a bit. The outcome effect on the bit will depend upon two things: (1) the definition of the logic gate, given by a truth table, and (2) the present value of the bit. You could thus imagine that the present bit's value at time t is p[t], its future value at time t+1 is p[t+1], and the truth table is given by T[t] describing the interaction or logic gate at time t, and then you could define this transition in terms of:
p[t+1]=f(T[t],p[t])
i.e., some function that takes the truth table and the present state of the bit as an input, and outputs the future / altered state of the bit.
This is the structure of a Markovian transition law. It takes what is effectively a truth table describing the effect of an interaction (represented by a matrix) as an input, as well as the present state of the system, into a function, and the function outputs the altered state of the system.
A non-Markovian law takes a different form.
p[t+1]=f(T[t],p[t],g(...))
If you want to evolve p[t] to p[t+1], you additionally need a second function g(...), which is defined recursively into the past, meaning it expands out into...
g(...)=g(T[t-1],p[t-1],g(T[t-2],p[t-2],g(T[t-3],p[t-3],g(...))
Every layer you expand g(...) goes one time interval back into the past, until it reaches a base case where the expansion stops.
That is to say, if you want to compute how a logic gate stochastically perturbs a bit's value in a quantum circuit, you need a function which takes into account not just the current truth table for the current logic gate (the operator given by U) and the current statistical distribution of the bits (given by |ψ|²), but all previous ones as well, going back to the beginning of the circuit.
Let me give an analogy. Imagine you have a machine which you pass a white ball into and sometimes outputs a red ball or a green ball. You are not sure what determines whether or not it outputs a green or red, so you study the white ball very closely, but no matter how detailed your measurements are, you cannot find anything that distinguishes one white ball from another. They all seem truly identical.
But then, later, you discover that there seems to be a perfect correlation between whether or not the white ball comes from dispenser A or dispenser B as to whether or not the machine will transform it into a red ball or a green ball. The "cause" of the machine outputting a red or green ball seems to have no relevance to the actual details of the white ball itself, but rather, where the white ball came from in the past.
The non-Markovian stochastic laws in quantum theory behave in a similar fashion. The statistical laws don't just care about the current statistical state of the system, but also where it came from, meaning, they also take into account its historical evolution as well. This means the same logic gate can have different behavior if the gates preceding them in quantum circuit are different, or if the bits begin with different initial values.
The logic gates are described by unitary operators which are complex-valued, and so they don't directly tell you the stochastic perturbation each logic gate applies to the bits. Stochastic perturbations are described by a stochastic matrix which are real-valued, positive, and all columns must sum to 1. So, you have to somehow compute what the correct stochastic matrix is from the unitary operators.
It's proved in the academic literature many times over that it's impossible to assign a single real-valued stochastic matrix to each unitary matrix that remains always positive where columns always sum to 1. The only possible way around this is to allow the assignment of different stochastic matrices to the same logic gate under different conditions. That is to say, the behavior of the same logic gate can change if the surrounding context around the logic gate changes.
The simplest example of this is the Hadamard gate in a quantum circuit that starts in a degenerate distribution. If you apply the Hadamard gate once, it behaves like a fair coin flip. If you flip a coin twice, the first time, the outcome is a uniform distribution, and the second time, the outcome is also a uniform distribution. But for the Hadamard gate, it only gives you a uniform distribution if you apply it once. If you construct a quantum circuit consisting of two Hadamard gates, it gives you a degenerate distribution.
There is no stochastic matrix that reproduces this behavior. You have to assign two separate stochastic matrices to the two separate instances of the two Hadamard gates: the first one moves it to a uniform distribution, [0.5 0.5; 0.5 0.5], and the second moves it to a degenerate distribution, either [1 1; 0 0] or [0 0; 1 1] depending upon whether the bit was originally initialized to 0 or 1. The book gives a general formula for computing the correct stochastic matrix for any logic gate, but the formula requires you to take in as input all previous gates and statistical distributions of the bits in the circuit up to that point.
more notes lol
where:
statistical distribution: |ϕ|^2
Right, I think I understood it now. Just to be clear, this is your setup:
The ball itself doesn't matter, its past does. Or in the case of qubits, its current value and its context.
I don't know if this came up when you described the non-Markovian example, but this reminded me of a Turing machine. Like, a Turing machine T can be described by f:Q~i~ → Q~j~, where Q~i~ and Q~j~ are possible states of T. A regular Turing machine acting through time could be described by f:Q[t] → Q[t+1] and with some boundary condition Q[0]. However, in your example, this hypothetical machine X can also "read" its own past. So, X would be described as g:{Q[t], {Q[t-1], Q[t-2], Q[t-3] ... Q[0]} → Q[t+1].
I think I would understand the math of your book, but not a lot about the concepts where it's applied. I hit a limit on my knowledge when you mentioned quantum gates and matrices on your comment. I don't know anything about those. I'm going to read more on that both because of curiosity and because I'm reallyyyyy rusty with my math skills.
Thanks for the write-up. I have a lot of review and studying to do. If you don't mind me asking, do you work mostly on the theory or do you also deal with the practical reality of quantum computing?
Also
Based
I don't know anything about how to actually engineer one if that's what you're asking. I only know how to program them. I have run programs on some of IBM's quantum computers, just as a way to make sure the theory really does produce the results I'd expect in reality.
Okay, now I'm dead-ass interested, ngl
(My favorite work by Lenin is also Materialism and Imperio-criticism, which I regard to be probably his greatest work, especially if you're interested in epistemology)
I haven't read Materialism and I yet. Is it good?
It's Lenin's best work, imho
I adore it
String theory is the worst.
Not to mention the religious or woo woo crap infecting the discipline (multi-verse stuff, you know the drill)