pcalau12i

The double-slit experiment doesn't even require quantum mechanics. It can be explained classically and intuitively.

It is helpful to think of a simpler case, the Mach-Zehnder interferometer, since it demonstrates the same effect but where where space is discretized to just two possible paths the particle can take and end up in, and so the path/position is typically described with just with a single qubit of information: |0⟩ and |1⟩.

You can explain this entirely classical if you stop thinking of photons really as independent objects but just specific values propagating in a field, what are sometimes called modes. If you go to measure a photon and your measuring device registers a |1⟩, this is often interpreted as having detected the photon, but if it measures a |0⟩, this is often interpreted as not detecting a photon, but if the photons are just modes in a field, then |0⟩ does not mean you registered nothing, it means that you indeed measured the field but the field just so happens to have a value of |0⟩ at that location.

Since fields are all-permeating, then describing two possible positions with |0⟩ and |1⟩ is misleading because there would be two modes in both possible positions, and each independently could have a value of |0⟩ or |1⟩, so it would be more accurate to describe the setup with two qubits worth of information, |00⟩, |01⟩, |10⟩, and |11⟩, which would represent a photon being on neither path, one path, the other path, or both paths (which indeed is physically possible in the real-world experiment).

When systems are described with |0⟩ or |1⟩, that is to say, 1 qubit worth of information, that doesn't mean they contain 1 bit of information. They actually contain as much as 3 as there are other bit values on orthogonal axes. You then find that the physical interaction between your measuring device and the mode perturbs one of the values on the orthogonal axis as information is propagating through the system, and this alters the outcome of the experiment.

You can interpret the double-slit experiment in the exact same way, but the math gets a bit more hairy because it deals with continuous position, but the ultimate concept is the same.

A measurement is a kind of physical interaction, and all physical interactions have to be specified by an operator, and not all operators are physically valid. Quantum theory simply doesn't allow you to construct a physically valid operator whereby one system could interact with another to record its properties in a non-perturbing fashion. Any operator you construct to record one of its properties without perturbing it must necessarily perturb its other properties. Specifically, it perturbs any other property within the same noncommuting group.

When the modes propagate from the two slits, your measurement of its position disturbs its momentum, and this random perturbation causes the momenta of the modes that were in phase with each other to longer be in phase. You can imagine two random strings which you don't know what they are but you know they're correlated with each other, so whatever is the values of the first one, whatever they are, they'd be correlated with the second. But then you randomly perturb one of them to randomly distribute its variables, and now they're no longer correlated, and so when they come together and interact, they interact with each other differently.

There's a paper on this here and also a lecture on this here. You don't have to go beyond the visualization or even mathematics of classical fields to understand the double-slit experiment.

Why interpret it as either? The double-slit experiment can be given an entirely classical explanation. Such extravagances are not necessary. As the old saying goes "extraordinary claims require extraordinary evidence." We should not be considering non-classical explanations unless they are genuinely necessary, and the only become necessary in contextual cases, which the double-slit experiment is certainly not such a case.

My impression from the literature is that superdeterminism is not the position of rejecting an asymmetrical arrow of time. In fact, it tries to build a model that can explain violations of Bell inequalities completely from the initial conditions evolved forwards in time exclusively.

Let's imagine you draw a coin from box A and it's random, and you draw coins from box B and it's random, but you find a peculiar feature where if you switch from A to B, the first coin you draw from B is always the last you drew from A, and then it goes back to being random. You repeat this many times and it always seems to hold. How is that possible if they're independent of each other?

Technically, no matter how many coins you draw, the probability of it occurring just by random chance is never zero. It might get really really low, but it's not zero. A very specific initial configuration of the coins could reproduce that.

Superdeterminism is just the idea that there are certain laws of physics that restrict the initial configurations of particles at the very beginning of the universe, the Big Bang, to guarantee their evolution would always maintain certain correlations that allow them to violate Bell inequalities. The laws don't continue to apply moment-by-moment, they just apply once when the universe "decides" its initial conditions, by restricting certain possible configurations.

It's not really an interpretation because it requires you to posit these laws and restrictions, and so it really becomes a new theory since you have to introduce new postulates, but such a theory would in principle then allow you to evolve the system forwards from its initial conditions in time to explain every experimental outcome.

As a side note, you can trivially explain violations of Bell inequalities in local realist terms without even introducing anything new to quantum theory just by abandoning the assumption of time-asymmetry. This is called the Two-State Vector Formalism and it's been well-established in the literature for decades. If A causes B and B causes C, in the time-reverse, C causes B and B causes A. if you treat both as physically real, then B would have enough constraints placed upon it by A and C taken together (by evolving the wave function from both ends to where they meet at B) to violate Bell inequalities.

That's already pretty much a feature built-in to quantum theory and allows you to interpret it in local realist terms if you'd like, but it requires you to accept that the microscopic world is genuinely indifferent to the arrow-of-time and the time-forwards and the time-reversed evolution of a system are both physically real.

However, this time-symmetric view is not superdeterminism. Superdeterminism is time-asymmetric just like most every other viewpoint (Copenhagen, MWI, pilot wave, objective collapse, etc). Causality goes in one temporal direction and not the other. The time-symmetric interpretation is its own thing and is mathematically equivalent to quantum mechanics so it is an actual interpretation and not another theory.

The problem with pilot wave is it's non-local, and so it contradicts with special relativity and cannot be made directly compatible with the predictions of quantum field theory. The only way to make it compatible would be to throw out special relativity and rewrite a whole new theory of spacetime with a preferred foliation built in that could reproduce the same predictions as special relativity, and so you end up basically having to rewrite all of physics from the ground-up.

I also disagree that it's intuitive. It's intuitive when we're talking about the trajectories of particles, but all its intuition disappears when we talk about any other property at all, like spin. You don't even get a visualization of what's going on at all when dealing with quantum circuits. Since my focus is largely on quantum computing, I tend to find pilot wave theory very unhelpful.

Personally, I find the most intuitive interpretation a modification of the Two-State Vector Formalism where you replace the two state vectors with two vectors of expectation values. This gives you a very unambiguous and concrete picture of what's going on. Due to the uncertainty principle, you always start with limited information on the system, you build out a list of expectation values assigned to each observable, and then take into account how those will swap around as the system evolves (for example, if you know X=+1 but don't know Y, and an interaction has the effect of swapping X with Y, then now you know Y=+1 and don't know X).

This alone is sufficient to reproduce all of quantum mechanics, but it still doesn't explain violations of Bell inequalities. You explain that by just introducing a second vector of expectation values to describe the final state of the system and evolve it backwards in time. This applies sufficient constraints on the system to explain violations of Bell inequalities in local realist terms, without having to introduce anything to the theory and with a mostly classical picture.

Quantum mechanics becomes massively simpler to interpret once you recognize that the wave function is just a compressed list of expectation values for the observables of a system. An expectation value is like a weighted probability. They can be negative because the measured values can be negative, such as for qubits, the measured values can be either +1 or -1, and if you weight by -1 then it can become negative. For example, an expectation value of -0.5 means there is a 25% chance of +1 and a 75% of -1.

If I know for certain that X=+1 but I have no idea what Y is, and the physical system interacts with something that we know will have the effect of swapping its X and Y components around, then this would also swap my uncertainty around so now I would know that Y=+1 without knowing what X is. Hence, if you don't know the complete initial conditions of a system, you can represent it with a list of all of possible observables and assign each one an expectation value related to your certainty of measuring that value, and then compute how that certainty is shifted around as the system evolves.

The wave function then just becomes a compressed form of this. For qubits, the expectation value vector grows at a rate of 4^N where N is the number of qubits, but the uncertainty principle limits the total bits of information you can have at a single time to 2^N, so the vector is usually mostly empty (a lot of zeros). This allows you to mathematically compress it down to a wave function that also grows by 2^N, making it the most concise way to represent this.

But the notation often confuses people, they think it means particles are in two places at once, that qubits are 0 and 1 at the same time, that there is some "collapse" that happens when you make a measurement, and they frequently ask what the imaginary components mean. But all this confusion just stems from notation. Any wave function can be expanded into a real-valued list of expectation values and you can evolve that through the system rather than the wave function and compute the same results, and then the confusion of what it represents disappears.

When you write it out in this expanded form, it's also clear why the uncertainty principle exists in the first place. A measurement is a kind of physical interaction between a record-keeping system and the recorded system, and it should result in information from the recorded system being copied onto the record-keeping system. Physical interactions are described by an operator, and quantum theory has certain restrictions on what qualifies as a physically valid operator: it has to be time-reversible, preserve handedness, be completely positive, etc, and these restrictions prevent you from constructing an operator that can copy a value of an observable from one system onto another in a way that doesn't perturb its other observables.

Most things in quantum theory that are considered "weird" are just misunderstandings, some of which can even be reproduced classically. Things like double-slit, Mach–Zehnder interferometer, the Elitzur–Vaidman "paradox," the Wigner's friend "paradox," the Schrodinger's cat "paradox," the Deutsch algorithm, quantum encryption and key distribution, quantum superdense coding, etc, can all be explained entirely classically just by clearing up some confusion about the notation.

This narrows it down to only a small number of things that genuinely raise an eyebrow, those being cases that exhibit what is sometimes called quantum contextuality, such as violations of Bell inequalities. It inherently requires a non-classical explanation for this, but I don't think that also means it can't be something understandable.

The simplest explanation I have found in the literature is that of time-symmetry. It is a requirement in quantum mechanics that every operator is time-symmetric, and that famously leads to the problem of establishing an arrow of time in quantum theory. Rather than taking it to be a problem, we can instead presume that there is a good reason nature demands all its microscopic operators are time-symmetric: because the arrow of time is a macroscopic phenomena, not a microscopic one.

If you have a set of interactions between microscopic particles where A causes B and B causes C, if I played the video in the reverse, it is mathematically just as valid to say that C causes B and B causes A. Most people then introduce an additional postulate that says "even though it is mathematically valid, it's not physically valid, we should only take the evolution of the system in a single direction of time seriously." You can't derive that postulate from quantum theory, you just have to take it on faith.

If we drop that postulate and take the local evolution of the system seriously in both its time-forwards evolution and its time-reversed evolution, then you can explain violations of Bell inequalities without having to add anything to the theory at all, and interpret it completely in intuitive local realist terms. You do this using the Two-State Vector Formalism where all you do is compute the evolution of the wave function (or expectation values) from both ends until they meet at an intermediate point, and that gives you enough constraints to deterministically derive a weak value at that point. The weak value is a physical variable that evolves locally and deterministically with the system and contains sufficient information to generate its expectation values when needed.

You still can't always assign a definite value, but these expectation values are epistemic, there is no contradiction with there being a definite value as the weak value contains all the information needed for the correct expectation values, and therefore the correct probability distribution, locally within the particle.

In terms of computation, it's very simple, because for the time-reverse evolution you just treat the final state as the initial state and then apply the operators in reverse with their time-symmetric equivalents (Hermitian transpose) and then the weak value equation looks exactly like the expectation value equation except rather than having the same wave function on both ends of the observable, you have the reverse-evolved wave function on one end of the observable and the forwards-evolved wave function on the other. (You can also plug the expectation value vectors on both ends and it works as well.)

Nothing about this is hard to visualize because you just imagine playing a moving forwards and also playing it in the reverse, and in both directions you get a local causal chain of interactions between the particles. If A causes B and B causes C in the time-forwards movie, playing the movie in reverse you will see C cause B which then causes A. That means B is both caused by A and C, and thus is influenced by both through a local chain of interactions.

There is nothing "special" going on in the backwards evolution, the laws of physics are symmetrical so, visually, it is not distinguishable from its forwards evolution, so you visualize it the exact same way, so you can pretty much still maintain a largely classical picture in your head, just with the caveat that you have to consider both directions in order to place enough constraints on the system to explain the observed results. All the "paradoxes" suddenly evaporate away because you can just compute how the system locally evolves in any "weird" situation and look at exactly what is going on.

That is enough to explain QM in local realist terms, doesn't require any modifications to the theory, and has been well-established in the literature for decades, is easy to visualize, but people often seem to favor explanations that are impossible to visualize, like treating the wave function as a literal object despite the wave function being, at times, even infinite-dimensional for continuous observables, or even believing we all live in an infinite-dimensional multiverse. And then they all complain it's impossible to visualize and so confusing and "no one understands quantum mechanics"... I don't understand why people seem to prefer to think about things in a way that they themselves admit just leads to endless confusion.

Well, first, that is not something that actually happens in the real world but is a misunderstanding. Particles diffract like a wave from a slit due to the uncertainty principle, because their position is confined to the narrow slit so their momentum must probabilistically spread out. If you have two slits where they have a probability of entering one slit or the other, then you will have two probabilistic diffraction trajectories propagating from each slit which will overlap with each other.

Measuring the slit the photon passes through does not make it behave like a particle. Its probabilistic trajectory still diffracts out of both slits, and you will still get a smeared out diffraction pattern like a wave. The diagrams that show two neat clean separated blobs has never been observed in real life and is just a myth. The only difference that occurs between whether or not you're making a measurement is whether or not the two diffraction trajectories interfere with one another or not, and that interference gives you the black bands.

This is an interference-based experiment. Interference-based phenomena can all be given entirely classical explanations without even resorting to anything nonclassical. The paper "Why interference phenomena do not capture the essence of quantum theory" is a good discussion on this. There is also a presentation on it here.

Basically, you (1) treat particles as values that propagate in a field. Not waves that propagate through a field, just values in a field like any classical field theory. Classical fields are indeed something that can take multiple paths simultaneously. (2) We assume that the particles really do have well-defined values for all of their observables at once, even if the uncertainty principle disallows us from knowing them all simultaneously. We can mathematically prove from that assumption that it would impossible to construct a measuring device that simply passively measures a system, it will always perturb the values it is not measuring in an unpredictable way.

A classical field has values everywhere. That's basically what a field is, you assign a value, in this case a vector, to every point in space and time. The vector holds the properties of the particles. For example, the X, Y, and Z observable would be stored in a vector [X, Y, Z] with a vector value at any point. What the measuring device measures is |0> or |1>, where we interpret the former to meaning no photon is there and we interpret the latter to mean a photon is there. But if you know anything about quantum information science, you know that |0> just means Z=+1 and |1> just means Z=-1. Hence, if you measure |0>, it doesn't tell you anything about the X and Y values, which we would assume are also there if particles are excitations in a field as given by assumption #1 because the field exists everywhere, and in fact, from our other assumption #2, your measurement of its Z value to be |0> must perturb those X and Y values.

It would be the field that propagates information through both slits and the presence of the measurement device perturbs the observables you do not measure, causing them to become out of phase with one another so they that they do not interfere when the field values overlap.

Interestingly, this requires no modification to quantum mechanics. If a system is physically redundant, we can often ignore parts of it in the mathematics to simplify our calculations, but if we do so, then the mathematics don't directly reflect the physical character of the system because parts of it are ignored. All we have to do is assume that for these kinds of photon-based and interference-based experiments that we are making a mathematical simplification due to redundancies and then can mathematically expand the description where it is more clearly obvious what is going on, and doing so is mathematically equivalent as it leads to the same predictions and, if you simplify it, it would lead to the same traditional way of describing the experiment.

It's sort of like if you have 4, you can expand it into 2+2. It means the same thing, but 4 and 2+2 have physically different meaning, because 2+2 suggests two separate things coming together, whereas 4 suggests only 1 thing. Expanding the double-slit experiment is a bit complicated because position is continuous, but it's trivial to demonstrate it for something like the Mach-Zehnder interferometer. You just map |0> to |01> and |1> to |10>, and then all the paradoxes with that, including the "bomb tester" paradox, disappear.

Quantum mechanics is not complicated. It just appears complicated because everyone chooses to interpret it in a way that is inherently contradictory. One of the fundamental postulates of quantum mechanics is that it is time-symmetric, called unitarity, but almost everyone for some reason assumes it is time-asymmetric. This contradiction leads them to have to compartmentalize this contradiction in their head, which then leads to a bunch of a contradictory conclusions, and then they invent a bunch of nonsense to try and make sense of those contradictions, like collapsing wave functions, a multiverse, cats that are both dead and alive simultaneously, particles in two places at once, nonlocality, etc. But that's all entirely unnecessary if you just consistently interpret the theory as time-symmetric. This has been shown in the literature for decades, called the Two-State Vector Formalism, yet it's almost entirely ignored in the popular discourse for some reason.

But that wasn't the thing I was even talking about when I said the game is not accurate. In real life, if you "take a picture" of an electron's location while it is buzzing around the nucleus unpredictably, it doesn't stay in that last position as long as you continue looking at the "picture". It will continue buzzing around the nucleus unpredictability and your "picture" is just its location in an instantaneous moment. Also, the unpredictable movement of particles is not nonlocal, they cannot suddenly hop from one side of the solar system to the other. You can only find them in places that they would have had enough time to reach.

Why is adding an additional unprovable postulate to quantum mechanics (the universal wave function) and believing we live in an invisible infinite-dimensional infinitely branching multiverse more reasonable than just accepting that quantum mechanics is a time-symmetric theory?

I don't think AI safety is such a big problem that it means we gotta stop building AI or we'll destroy the world or something, but I do agree there should be things like regulations, oversight, some specialized people to make sure AI is being developed in a safe way just to help mitigate problems that could possibly come up. There is a mentality that AI will never be as smart as humans so any time people suggest some sort of policies for AI safety that it's unreasonable because it's overhyping how good AI is and it won't get to a point of being dangerous for a long time. But if we have this mentality indefinitely then eventually when it does become dangerous we'd have no roadblocks and it might actually become a problem. I do think completely unregulated AI developed without any oversight or guardrails could in the future lead to bad consequences, but I also don't think that is something that can't be mitigated with oversight. I don't believe for example like an AGI will somehow "break free" and take over the world if it is ever developed. If it is "freed" in a way that starts doing harm, it would be because someone allowed that.

don't mind me i have autism

Many worlds theories are rather strange.

If you take quantum theory at face value without trying to modifying it in any way, then you unequivocally run into the conclusion that ψ is contextual, that is to say, what ψ you assign to a system depends upon your measurement context, your "perspective" so to speak.

This is where the "Wigner's friend paradox" arises. It's not really a "paradox" as it really just shows ψ is contextual. If Wigner and his friend place a particle in a superposition of states, his friend says he will measure it, and then Wigner steps out of the room for a moment when he is measuring it, from the friend's perspective he would reduce ψ to an eigenstate, whereas in Wigner's perspective ψ would instead remain in a superposition of states but one entangled with the measuring device.

This isn't really a contradiction because in density matrix form Wigner can apply a perspective transformation and confirm that his friend would indeed perceive an eigenstate with certain probabilities for which one they would perceive given by the Born rule, but it does illustrate the contextual nature of quantum theory.

If you just stop there, you inevitably fall into relational quantum mechanics. Relational quantum mechanics just accepts the contextual nature of ψ and tries to make sense of it within the mathematics itself. Most other "interpretations" really aren't even interpretations but sort of try to run away from the conclusion, such as significantly modifying the mathematics and even statistical predictions in order to introduce objective collapse or hidden variables in order to either get rid of a contextual ψ or get rid of ψ as something fundamental altogether.

Many Worlds is still technically along these lines because it does add new mathematics explicitly for the purpose of avoiding the conclusion of irreducible contextuality, although it is the most subtle modification and still reproduces the same statistical predictions. If we go back to the Wigner's friend scenario, Wigner's friend reduced ψ relative to his own context, but Wigner, who was isolated from the friend and the particle, did not reduce ψ by instead described them as entangled.

So, any time you measure something, you can imagine introducing a third-party that isn't physically interacting with you or the system, and from that third party's perspective you would be in an entangled superposition of states. But what about the physical status of the third party themselves? You could introduce a fourth party that would see the system and the third party in an entangled superposition of states. But what about the fourth party? You could introduce a fifth party.... so on and so forth.

You have an infinite regress until, at some how (somehow), you end up with Ψ, which is a sort of "view from nowhere," a perspective that contains every physical object, is isolated from all those physical objects, and is itself not a physical object, so it can contain everything. So from the perspective of this big Ψ, everything always remains in a superposition of states forever, and all the little ψ are only contextual because they are like perspectival slices within Ψ.

You cannot derive Ψ mathematically because there is no way to get from inherently contextual ψ to this preferred nonphysical perspective Ψ, so you cannot know its mathematical properties. There is also no way to define it, because each ψ is an element of Hilbert space and Hilbert space is a constructed space, unlike background spaces like Minkowski space. The latter are defined independently of the objects the contain, whereas the former are defined in terms of the objects they contain. That means for two different physical systems, you will have two different ψ that will be assigned to two different Hilbert spaces. The issue is that you cannot define the Hilbert space that Ψ is part of because it would require knowing everything in the universe.

Hence, Ψ cannot be derived nor defined, so it can only be vaguely postulated, and its mathematical properties also have to be postulated as you cannot derive them from anything. It is just postulated to be this privileged cosmic perspective, a sort of godlike ethereal "view from nowhere," and then it is postulated to have the same mathematical properties as ψ but that all ψ are also postulated to be subsystems of Ψ. You can then write things down like how a partial trace on Ψ can give you information about any perspective of its subsystems, but only because it was defined to have those properties. It is true by definition.

In a RQM perspective it just takes quantum theory at face value without bothering to introduce a Ψ and just accepts that ψ is contextual. Talking about a non-contextual (absolute) ψ makes about as much sense as talking about non-contextual (absolute) velocity, and talking about a privileged perspective in QM makes about as much sense as talking about a privileged perspective in special relativity. For some reason, people are perfectly happy with accepting the contextual nature of special relativity, but they struggle real hard with the contextual nature of quantum theory, and feel the need to modify it, to the point of convincing themselves that there is a multiverse in order to escape it.

The development process of capitalism does not so much as produce “centralisation” (which is ill defined tbh) but socialisation (the conversion of individual labor to group labor), urbanisation and standardisation.

This is just being a pedant. Just about every Marxist author uses the two interchangeably. We are talking about the whole economy coming under a single common enterprise that operates according to a common plan, and the process of centralization/socialization/consolidation/etc is the gradual transition from scattered and isolated enterprises to larger and larger consolidated enterprises, from small producers to big oligopolies to eventually monopolies.

Furthermore, while it is true that socialist society develops out of capitalist society, revolutions are by definition a breaking point in the mode of production which makes the insistence that socialist societies must be highly centralised backwards logic.

Marxism is not about completely destroying the old society and building a new one from the void left behind. Humans do not have the "free will" to build any kind of society they want. Marxists view the on-the-ground organization of production as determined by the forces of production themselves, not through politics or economic policies. When the feudal system was overthrown in French Revolution, it was not as if the French people just decided to then transition from total feudalism to total capitalism. Feudalism at that point basically didn't even exist anymore, the industrial revolution had so drastically changed the conditions on the ground that it basically already capitalism and entirely disconnected from the feudal superstructure.

Marx compared it to how when the firearm was invented, battle tactics had to change, because you could not use the same organizational structure with the invention of new tools. Engels once compared it to Darwinian evolution but for the social sciences, not because of the natural selection part, but the gradual change part. The political system is always implemented to reflect an already-existing way of producing things that arose on the ground of its own accord, but as the forces of production develop, the conditions on the ground very gradually change in subtle ways, and after hundreds of years, they will eventually become incredibly disconnected from the political superstructure, leading to instability.

Marx's argument for socialism is not a moralistic one, it is precisely that centralized production is incompatible with individual ownership, and that the development of the forces of production, very slowly but surely, replaces individual production with centralized production, destroying the foundations of capitalism in the process and developing towards a society that is entirely incompatible with the capitalist superstructure, leading to social and economic instability, with the only way out replacing individual appropriation with socialized appropriation through the expropriation of those enterprises.

The foundations remain the same, the superstructure on top of those foundations change. The idea that the forces of production leads directly to centralization and that post-capitalist society doesn't have to be centralized is straight-up anti-Marxist idealism. You are just not a Marxist, and that's fine, if you are an anarchist just be an anarchist and say you are one and don't try to misrepresent Marxian theory.

We are starting from a dislike of anarchism’s dogma of decentralisation and just working backwards.

Oh wow, all of Marxism is apparently just anarchist hate! Who knew! Marxism debunked! No, it's because Marxists are just like you: they don't believe the development of the past society lays the foundations for the future society, they are not historical materialists, but believe humanity has the free will to build whatever society they want, and so they want to destroy the old society completely rather than sublating it, and build a new society out of the ashes left behind. They dream of taking all the large centralized enterprises and "busting them up" so to speak.