4 March 2025. Why exactly is the quantum world so weird?

[socrattus]

The weirdness of quantum theory is largely self-imposed. The EPR paper demonstrates that if you believe the wave function is a complete description of the physical system, it leads to absurdities. Ever since Bell's theorem, people just accepted that maybe quantum mechanics is absurd, and so they started to adopt viewpoints of nonlocal collapsing wavefunctions, things not having properties until you measure them, or even an ever-branching multiverse.

But Bell's theorem has a bit of major flaw.

Let N denote a specification of all the beables, of some theory, belonging to the overlap of the backward light cones of spacelike separated regions 1 and 2. Let A be a specification of some beables from the remainder of the backward light cone of 1, and B of some beables in the region 2. Then in a locally causal theory {A|A, N, B} = {A|A, N} (2) whenever both probabilities are given by the theory.

Notice how Bell talks about "backwards light cones." How on earth, given the postulates of quantum mechanics alone, can you mathematically derive the "backwardness" of a light cone? Every operator in quantum mechanics is time-symmetric, that's one of its foundational postulates. There is no way within quantum theory to distinguish between one light cone as the "backward" one as opposed to the other. The rest of what Bell wrote is great, just delete the word "backward," then his formulation of causality is consistent with the postulates of quantum theory, but then violations of Bell inequalities don't become an issue nor contradict with local realism in any way. The supposed conflict between local realism and Bell's theorem is mathematically impossible to derive from the postulates of quantum mechanics, and requires you to introduce an additional postulate outside of the theory.

Of course, that's not to say that speaking of the asymmetry of time is meaningless, but it's ultimately a macroscopic feature of the universe, as it requires referencing the past hypothesis to make sense of it, which is a feature of general relativity and can't be derived from the postulates of quantum theory (to our knowledge). It's physically real, but macroscopic. If you zoom in on little particles buzzing around, you can't tell whether or not their buzzing around is going forwards in time or in the reverse. It's a meaningless concept at such a scale.

If you just stick with the mathematics of quantum theory at face value and don't try to introduce extra postulates on top of it, then the supposed weirdness to a significant degree goes away. There is no need to pretend that particles are in multiple places at once until you measure them, the wave function just becomes an epistemic description.

Indeed, one thing most believers in the non-epistemic wave function love to sweep under the rug is that any wave function can be expanded out into a list of expectation values for all of the observables of the system, and you can also expand out all unitary operators to apply directly to the list of expectation values rather than to the wave function, and you can compute the exact same results you would using the wave function.

The wave function is not even necessary for calculation, it's just more mathematically convenient because it's effectively a compressed form of the mathematically equivalent vector of expectation values. If you compute the vector of expectation values rather than the wave function, it becomes far more obvious that you're working with something epistemic, as you're basically just manipulating statistics, and you don't even need a Born rule because you're again just manipulating a list of expectation values, so at the end of the calculation you are left with a list of expectation values, which already gives you the statistics on the final results directly. All complex numbers also disappear, they are purely an artifact of mathematical compression.

In a time-symmetric approach, you can also evolve the list of expectation values from both ends until they meet at an intermediate point, and you find that this applies enough constraints to the system to compute what are called weak values. The weak values then can be shown to evolve locally and continuously, describable with differential equations, and at any point you can compute the expectation values directly from the weak values using the Aharonov-Bergmann-Lebowitz rule. You also can compute the weak values using two state vectors rather than vectors of expectation values and get the same results, so it's sometimes called the Two-State Vector Formalism.

Hence, the information needed to explain the probability distribution of the particles is locally available at the particles and doesn't need any sort of "spooky action at a distance" or treating anything as if it's in multiple places at once or spread out as waves that "collapse" when measured.

When you expand the operators out so that they act directly on expectation values, then suddenly quantum theory becomes rather simple and intuitive. There are rules that govern what kind of operators you can construct, they have to be time-reversible, preserve handedness, and be completely positive. This limitation disallows you from constructing a non-perturbing operator, and thus it's trivial to prove that any operator that describes the interaction between a measuring device and a particle must perturb the properties of the particle it is *not* measuring.

This is why you have to do statistics. Not because the particles are in all places at once, but because every time you measure a property, the physical interaction also perturbs the other properties you did not measure. If you measure position, you perturb its momentum, if you measure X, you perturb Y and Z.

That's where "wave function collapse" comes from. Nothing is collapsing. If I know Z=+1 but don't know X or Y, and I measure X anyways, I will measure something I can only at best describe statistically beforehand. After I measure X, let's say I learn it is X=-1, then I also have perturbed Z and Y in the process, so I no longer know if it's true that Z=+1.

This is not spooky but you can reproduce such an effect classically. Indeed, many aspects of quantum theory deemed "spooky" can be trivially reproduced in a classical model: double-slit experiment, Elitzur–Vaidman paradox, Deutsch's algorithm, superdense coding, quantum encryption and key distribution, etc.

It's only in the *contextual* cases, like in the GHZ paradox or the Frauchiger-Renner paradox that you actually find it hard to explain classically, but these also become trivially easy to explain the moment you abandon the additional postulate of imposing time-asymmetry onto quantum theory that is mathematically impossible to derive from the postulates of the theory. Drop that postulate, compute the weak values, and then you will see very clearly how the information locally evolves through the system and why the correlations are what they are.

It seems almost everyone comes in one of two flavors. The first flavor is "shut up and calculate." No one can understand quantum theory, so don't bother. The other flavor is using it as a springboard to justify sci-fi beliefs, like a multiverse, or straight-up mystical beliefs, like somehow consciousness has something to do with it. Despite the fact that much simpler explanations that are borderline classical have existed in the literature for decades, despite the fact the fact that every supposed "paradox" has been given simple explanations, the science media only ever reports on the wacky "paradoxes" that supposedly disprove there's objective reality or some nonsense like that, while most people remain unaware of the responses.

EPR
At the EPR (spooky action-at-a-distance, quantum entanglement) the distance doesn't play any role.
Distance is no matter. Interactions occur instantaneously.
This is possible if the speed of particles is faster than the constant speed c=1.
Atom, electron and wave.
An electron has no specific location in an atom.
In an atom the electron's action is explained by Schrödinger Ψ wave equation,
where the electron "waves" and creates "wave-clouds".
To define the electron, one needs to use the Born square-rule ( |ψ|²) of the probability
of finding an electron at a particular place (x) and time (t) inside the atom.

[amihart]

EPR At the EPR (spooky action-at-a-distance, quantum entanglement) the distance doesn't play any role. Distance is no matter. Interactions occur instantaneously.

No evidence of that. The EPR paradox was meant as a criticism of people who believe in ψ-completeness, as an appeal to absurdity, not an argument in favor of believing there is literally spooky action. The EPR paradox can be seen as a general no-go theorem against local Ψ-ontic interpretations.

This is possible if the speed of particles is faster than the constant speed c=1.

Well, all our current physics rely on the assumption that nothing is faster than the speed of light. Extraordinary claims require extraordinary evidence. If you want to claim otherwise, I'd need something major to convince me.

Atom, electron and wave. An electron has no specific location in an atom. In an atom the electron's action is explained by Schrödinger Ψ wave equation,
where the electron "waves" and creates "wave-clouds". To define the electron, one needs to use the Born square-rule ( |ψ|²) of the probability of finding an electron at a particular place (x) and time (t) inside the atom.

ψ is just a condensed list of expectation values, not even necessary for the calculation, but useful for mathematical expedience. Interpreting a probability distribution as physical, as if the particle is actually smeared out across the distribution, is a rather arbitrary deviation as to how statistics are interpreted in every other field of science, it requires a special rule specific to quantum mechanics, for some reason. It also leads to confusion, like the Schrodinger's cat paradox, where you have to genuinely believe a cat can become smeared out as a wave, the EPR paradox, where you have to believe in faster-than-light effects that have ambiguous causal order, and the Wigner's friend paradox, where you have to believe that reality is entirely physically different depending upon perspectives so much so that in one perspective a whole human being may be genuinely physically smeared out as a wave whereas in their own perspective they are not.

All these paradoxes arise from an arbitrary postulate of creating a special rule for how to interpret statistics in quantum theory which you wouldn't apply anywhere else. It's not necessary and just overcomplicates things.

[Atla]

The weirdness of quantum theory is largely self-imposed. The EPR paper demonstrates that if you believe the wave function is a complete description of the physical system, it leads to absurdities. Ever since Bell's theorem, people just accepted that maybe quantum mechanics is absurd, and so they started to adopt viewpoints of nonlocal collapsing wavefunctions, things not having properties until you measure them, or even an ever-branching multiverse.

But Bell's theorem has a bit of major flaw.

Let N denote a specification of all the beables, of some theory, belonging to the overlap of the backward light cones of spacelike separated regions 1 and 2. Let A be a specification of some beables from the remainder of the backward light cone of 1, and B of some beables in the region 2. Then in a locally causal theory {A|A, N, B} = {A|A, N} (2) whenever both probabilities are given by the theory.

Notice how Bell talks about "backwards light cones." How on earth, given the postulates of quantum mechanics alone, can you mathematically derive the "backwardness" of a light cone? Every operator in quantum mechanics is time-symmetric, that's one of its foundational postulates. There is no way within quantum theory to distinguish between one light cone as the "backward" one as opposed to the other. The rest of what Bell wrote is great, just delete the word "backward," then his formulation of causality is consistent with the postulates of quantum theory, but then violations of Bell inequalities don't become an issue nor contradict with local realism in any way. The supposed conflict between local realism and Bell's theorem is mathematically impossible to derive from the postulates of quantum mechanics, and requires you to introduce an additional postulate outside of the theory.

Of course, that's not to say that speaking of the asymmetry of time is meaningless, but it's ultimately a macroscopic feature of the universe, as it requires referencing the past hypothesis to make sense of it, which is a feature of general relativity and can't be derived from the postulates of quantum theory (to our knowledge). It's physically real, but macroscopic. If you zoom in on little particles buzzing around, you can't tell whether or not their buzzing around is going forwards in time or in the reverse. It's a meaningless concept at such a scale.

If you just stick with the mathematics of quantum theory at face value and don't try to introduce extra postulates on top of it, then the supposed weirdness to a significant degree goes away. There is no need to pretend that particles are in multiple places at once until you measure them, the wave function just becomes an epistemic description.

Indeed, one thing most believers in the non-epistemic wave function love to sweep under the rug is that any wave function can be expanded out into a list of expectation values for all of the observables of the system, and you can also expand out all unitary operators to apply directly to the list of expectation values rather than to the wave function, and you can compute the exact same results you would using the wave function.

The wave function is not even necessary for calculation, it's just more mathematically convenient because it's effectively a compressed form of the mathematically equivalent vector of expectation values. If you compute the vector of expectation values rather than the wave function, it becomes far more obvious that you're working with something epistemic, as you're basically just manipulating statistics, and you don't even need a Born rule because you're again just manipulating a list of expectation values, so at the end of the calculation you are left with a list of expectation values, which already gives you the statistics on the final results directly. All complex numbers also disappear, they are purely an artifact of mathematical compression.

In a time-symmetric approach, you can also evolve the list of expectation values from both ends until they meet at an intermediate point, and you find that this applies enough constraints to the system to compute what are called weak values. The weak values then can be shown to evolve locally and continuously, describable with differential equations, and at any point you can compute the expectation values directly from the weak values using the Aharonov-Bergmann-Lebowitz rule. You also can compute the weak values using two state vectors rather than vectors of expectation values and get the same results, so it's sometimes called the Two-State Vector Formalism.

Hence, the information needed to explain the probability distribution of the particles is locally available at the particles and doesn't need any sort of "spooky action at a distance" or treating anything as if it's in multiple places at once or spread out as waves that "collapse" when measured.

When you expand the operators out so that they act directly on expectation values, then suddenly quantum theory becomes rather simple and intuitive. There are rules that govern what kind of operators you can construct, they have to be time-reversible, preserve handedness, and be completely positive. This limitation disallows you from constructing a non-perturbing operator, and thus it's trivial to prove that any operator that describes the interaction between a measuring device and a particle must perturb the properties of the particle it is *not* measuring.

This is why you have to do statistics. Not because the particles are in all places at once, but because every time you measure a property, the physical interaction also perturbs the other properties you did not measure. If you measure position, you perturb its momentum, if you measure X, you perturb Y and Z.

That's where "wave function collapse" comes from. Nothing is collapsing. If I know Z=+1 but don't know X or Y, and I measure X anyways, I will measure something I can only at best describe statistically beforehand. After I measure X, let's say I learn it is X=-1, then I also have perturbed Z and Y in the process, so I no longer know if it's true that Z=+1.

This is not spooky but you can reproduce such an effect classically. Indeed, many aspects of quantum theory deemed "spooky" can be trivially reproduced in a classical model: double-slit experiment, Elitzur–Vaidman paradox, Deutsch's algorithm, superdense coding, quantum encryption and key distribution, etc.

It's only in the *contextual* cases, like in the GHZ paradox or the Frauchiger-Renner paradox that you actually find it hard to explain classically, but these also become trivially easy to explain the moment you abandon the additional postulate of imposing time-asymmetry onto quantum theory that is mathematically impossible to derive from the postulates of the theory. Drop that postulate, compute the weak values, and then you will see very clearly how the information locally evolves through the system and why the correlations are what they are.

It seems almost everyone comes in one of two flavors. The first flavor is "shut up and calculate." No one can understand quantum theory, so don't bother. The other flavor is using it as a springboard to justify sci-fi beliefs, like a multiverse, or straight-up mystical beliefs, like somehow consciousness has something to do with it. Despite the fact that much simpler explanations that are borderline classical have existed in the literature for decades, despite the fact the fact that every supposed "paradox" has been given simple explanations, the science media only ever reports on the wacky "paradoxes" that supposedly disprove there's objective reality or some nonsense like that, while most people remain unaware of the responses.

(Imo this isn't the main quantum weirdness, that would be why or whether we humans perceive reality from a particle behaviour island.)

Anyway does the above mean that you explain the experimental evidence for nonlocal correlations with a universal, time-symmetric determinism, universal as in it also includes the quantum world?

[amihart]

Anyway does the above mean that you explain the experimental evidence for nonlocal correlations with a universal, time-symmetric determinism, universal as in it also includes the quantum world?

Since the Two-State Vector Formalism is mathematically equivalent to quantum mechanics and adds no additional postulate, it does not recover completely deterministic dynamics. The weak values evolve locally and continuously but they only serve as generators for expectation values which are still probabilistic. To recover complete determinism you would need to add some additional postulate to "choose" from the probability distribution.

The distinction here is between determinism and realism. Determinism being the idea that everything is, well, determined, and realism simply being that everything has a real value independent of measurement. TSVF and the time-symmetric interpretation is consistent with local realism because the particles have access to sufficient local information to explain the probability distribution, so it is local and realistic, but it is still probabilistic.

Indeed, even if you do add additional postulates, it can be difficult to consistently explain quantum theory deterministically. Pilot wave theory, for example, still has to resort to probability for particle creation. Whether or not it's probabilistic or deterministic is honestly not something I am particularly bothered by. It only becomes conceptually difficult to wrap your head around the moment you start to try and abandon realism. We interpret statistics the same exact way in every field of science, except for quantum mechanics, people want to introduce an extra postulate that creates an exception for quantum theory to interpret it differently, but in a local realist approach you don't need this exception.

It is still partially deterministic, however, and yes, that partial determinism does include the quantum world.

[Martin Peter Clarke]

Anyway does the above mean that you explain the experimental evidence for nonlocal correlations with a universal, time-symmetric determinism, universal as in it also includes the quantum world?

Since the Two-State Vector Formalism is mathematically equivalent to quantum mechanics and adds no additional postulate, it does not recover completely deterministic dynamics. The weak values evolve locally and continuously but they only serve as generators for expectation values which are still probabilistic. To recover complete determinism you would need to add some additional postulate to "choose" from the probability distribution.

The distinction here is between determinism and realism. Determinism being the idea that everything is, well, determined, and realism simply being that everything has a real value independent of measurement. TSVF and the time-symmetric interpretation is consistent with local realism because the particles have access to sufficient local information to explain the probability distribution, so it is local and realistic, but it is still probabilistic.

Indeed, even if you do add additional postulates, it can be difficult to consistently explain quantum theory deterministically. Pilot wave theory, for example, still has to resort to probability for particle creation. Whether or not it's probabilistic or deterministic is honestly not something I am particularly bothered by. It only becomes conceptually difficult to wrap your head around the moment you start to try and abandon realism. We interpret statistics the same exact way in every field of science, except for quantum mechanics, people want to introduce an extra postulate that creates an exception for quantum theory to interpret it differently, but in a local realist approach you don't need this exception.

It is still partially deterministic, however, and yes, that partial determinism does include the quantum world.

I'm 110% convinced that you are flawlessly correct. True. Semantic as well as syntactic, although I'm relying very mainly on the latter.

So, sorry to be so sodding dim, but when observation determines the immediately prior real indeterminate spin of one of a tangled pair, does experimentation empirically prove that the other is always pre-determined as opposite, to date? (And, of course, c is conserved).

[amihart]

So, sorry to be so sodding dim, but when observation determines the immediately prior real indeterminate spin of one of a tangled pair, does experimentation empirically prove that the other is always pre-determined as opposite, to date? (And, of course, c is conserved).

Knowledge can evolve nonlocally while the underlying physical dynamics the knowledge is describing evolves locally. Let me give an analogy. If I get a box with a pair of shoes in and take out the left shoe and send you the box, and it reaches you a thousand miles away, before you open the box, you have no idea what shoe is in there, but the moment you open it, you see the right shoe, but at the same time, you simultaneously know I must have the left shoe. Before opening the box, you'd assign the probabilities of me having the right or left shoe as 50/50 and you having the left/right shoe to 50/50, but the moment you open the box, you update both probabilities simultaneously for two objects at a distance.

This, of course, doesn't reflect anything physically changing nonlocally about the shoes. The underlying physical dynamics of the shoes are local. I took a shoe out of the box locally before I sent it to you, and it had to locally travel to you before you open it. The subjective update of knowledge is nonlocal, but that is just something subjective, it doesn't reflect anything nonlocally occurring in physically reality, as if the shoes literally existed in some indeterminate state of a 50/50 distribution until you open the box then suddenly they both physically transform into a determinate state. The update of the probabilities reflects no physical, objective change in the system, only a change in your subjective knowledge on the system.

Indeed, if you analyze the evolution of the weak values, you see that they behave like the shoes. If you entangle two qubits, their weak values become correlated at the moment the two qubits interact. In the GHZ experiment for example, you will find that the three qubits decide what values they will have the moment you entangle them, and not later when you measure them. The measurement just reveals a property that is already there.

That does not mean it reduces to an entirely classical experiment, because weak values are time-symmetrical. Take a simple case of the EPR paradox but with two qubits in a Bell state. If you measure them on the X basis, we know that XX=+1, so they are positively correlated, either being (+1)(+1) or (-1)(-1). Indeed, if you track the weak values, you find that whichever you measure, they will have "chosen" that value when they interact and become entangled, not later when you measure it, which is akin to the shoe analogy.

However, where it differs from the shoe analogy is that quantum mechanics also tells us that ZZ=+1 and YY=-1. If you look at the weak values in the case where you measure the qubits on the X basis, they do indeed "choose" appropriate values on the X basis when they interact, but they do not necessarily "choose" appropriate values on the Z or Y basis to match the other two equalities. Yet, if you instead choose to measure them on, let's say, the Y basis, they will "choose" specific opposing values on the Y basis when they locally interact and not later when you measure them.

What you choose to measure has an impact on the dynamics of the system you're measuring before it even reaches your measuring device. This seems like a contradiction if you impose a strict arrow of time on the system that says only its time-evolution in a single direction matters. Since the qubits interact and become entangled prior to you measuring them, if you believe in a strict arrow of time, you would expect that your choice of measurement could not have any impact on them. But if you drop the arrow of time postulate (which has no mathematical basis in quantum mechanics is more of a fuzzy philosophical idea), then you can also equally treat the final measurement as the beginning of the experiment and the flow towards the initial preparation from the final measurement as the forwards time evolution.

This time-reversal is both mathematically and physically valid in quantum theory because it is a time-symmetrical theory, and in the time-reversal the measurement would indeed be part of a local causal chain in the past light cone of qubits and thus can impact what they "choose" when they locally interact with each other. Indeed, all Bell tests, from Bell's original theorem, to the CHSH inequalities, to the GHZ experiment, these all require you to bring the measurement results to a single locality in order to verify the violations of the inequalities, yet the moment you do, if you look at the time-reverse from that point going back to the past, then the violations of the inequalities becomes clearly and unambiguously a local phenomena.

It only appears nonlocal if you artificially declare that the time-reverse isn't valid, but to make this rigorous you need a mathematical derivation, or at the very least a mathematical definition, of the arrow of time. Some way to unambiguously distinguish between future and past light cones within the framework of quantum theory. No one in the literature has presented it, and so without it, there is no way to formulate the notion that causality in quantum mechanics only flows forwards in time, because the statement is meaningless without a way to distinguish "forwards" from "backwards." The notion that Bell's theorem violates local realism genuinely has no mathematical basis until someone plugs this hole.