pcalau12i

That’s not true. If you read Schrodinger’s original paper “The Present Situation in Quantum Mechanics” he’s pretty clear that he was attempting to show how ridiculous it is to treat a superposition of states as if a particle is actually smeared out in multiple locations at once, because you could use that particle as the basis of a chain reaction that would eventually affect a macroscopic object, and then you would have to say the macroscopic object is smeared out in multiple places at once. The argument was a reductio ad absurdum for treating microscopic objects as if they are smeared out in multiple places at once. Its fundamental point was simply not a commentary on macroscopic objects but microscopic objects.

You don’t need the wave function to do quantum mechanics, it’s just a mathematical convenience, and so Schrodinger had insisted it shouldn’t be interpreted as a literal physical object as if particles are actually spreading out as waves. In his book “Science and Humanism” he says that the reason he invented the wave formalism is because he didn’t like Heisenberg’s formalism which, even though it made all the right predictions, it didn’t give intermediate states for particles, so it is as if they just hop around from interaction to interaction probabilistically, and the wave formalism was meant to “fill in the gaps” between the interactions.

However, in that book he also says that he believes this project was a failure because all the wave formalism does is move the gap between interactions to a gap between the evolution of the quantum state and observation, which made even less sense, and so he changed his mind and argued that we should abandon the notion of filling in the gaps between interactions, and the illusion of continuous transitions between states is only a macroscopically emergent feature.

I think it’s boring honestly. It’s a bit strange how like, the overwhelming majority of people either avoid interpreting quantum theory at all (“shut up and calculate”) or use it specifically as a springboard to justify either sci-fi nonsense (multiverses) or even straight-up mystical nonsense (consciousness induced collapse). Meanwhile, every time there is a supposed “paradox” or “no-go theorem” showing you can’t have a relatively simple explanation for something, someone in the literature publishes a paper showing it’s false, and then only the paper showing how “weird” QM is gets media attention. I always find myself on the most extreme fringe of the fringe of thinking both that (1) we should try to interpret QM, and (2) we should be extremely conservative about our interpretation so we don’t give up classical intuitions unless we absolutely have to. That seems to be considered an extremist fringe position these days.

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.