I am factually correct, I am not here to “debate,” I am telling you how the theory works. When two systems interact such that they become statistically correlated with one another and knowing the state of one tells you the state of the other, it is no longer valid to assign a state vector to the system subsystems that are part of the interaction individually, you have to assign it to the system as a whole. When you do a partial trace on the system individually to get a reduced density matrix for the two systems, if they are perfectly entangled, then you end with a density matrix without coherence terms and thus without interference effects.

This is absolutely entanglement, this is what entanglement is. I am not misunderstanding what entanglement is, if you think what I have described here is not entanglement but a superposition of states then you don’t know what a superposition of states is. Yes, an entangled state would be in a superposition of states, but it would be a superposition of states which can only be applied to both correlated systems together and not to the individual subsystems.

Let’s say R = 1/sqrt(2) and Alice sends Bob a qubit. If the qubit has a probability of 1 of being the value 1 and Alice applies the Hadamard gate, it changes to R probability of being 0 and -R probability of being 1. In this state, if Bob were to apply a second Hadamard gate, then it undoes the first Hadamard gate and so it would have a probability of 1 of being a value of 1 due to interference effects.

However, if an eavesdropper, let’s call them Eve, measures the qubit in transit, because R and -R are equal distances from the origin, it would have an equal chance of being 0 or 1. Let’s say it’s 1. From their point of view, they would then update their probability distribution to be a probability of 1 of being the value 1 and send it off to Bob. When Bob applies the second Hadamard gate, it would then have a probability of R for being 0 and a probability of -R for being 1, and thus what should’ve been deterministic is now random noise for Bob.

Yet, this description only works from Eve’s point of view. From Alice and Bob’s point of view, neither of them measured the particle in transit, so when Bob received it, it still is probabilistic with an equal chance of being 0 and 1. So why does Bob still predict that interference effects will be lost if it is still probabilistic for him?

Because when Eve interacts with the qubit, from Alice and Bob’s perspective, it is no longer valid to assign a state vector to the qubit on its own. Eve and the qubit become correlated with one another. For Eve to know the particle’s state, there has to be some correlation between something in Eve’s brain (or, more directly, her measuring device) and the state of the particle. They are thus entangled with one another and Alice and Bob would have to assign the state vector to Eve and the qubit taken together and not to the individual parts.

Eve and the qubit taken together would have a probability distribution of R for the qubit being 0 and Eve knowing the qubit is 0, and a probability of -R of the qubit being 1 and Eve knowing the qubit is 1. There is still interference effects but only of the whole system taken together. Yet, Bob does not receive Eve and the qubit taken together. He receives only the qubit, so this probability distribution is no longer applicable to the qubit.

He instead has to do a partial trace to trace out (ignore) Eve from the equation to know how his qubit alone would behave. When he does this, he finds that the probability distribution has changed to 0.5 for 0 and 0.5 for 1. In the density matrix representation, you will see that the density matrix has all zeroes for the coherences. This is a classical probability distribution, something that cannot exhibit interference effects.

Bob simply cannot explain why his qubit loses its interference effects by Eve measuring it without Bob taking into account entanglement, at least within the framework of quantum theory. That is just how the theory works. The explanation from Eve’s perspective simply does not work for Bob in quantum mechanics. Reducing the state vector simultaneously between two different perspectives is known as an objective collapse model and makes different statistical predictions than quantum mechanics. It would not merely be an alternative interpretation but an alternative theory.

Eve explains the loss of coherence due to her reducing the state vector due to seeing a definite outcome for the qubit, and Bob explains the loss of coherence due to Eve becoming entangled with the qubit which leads to decoherence as doing a partial trace to trace out (ignore) Eve gives a reduced density matrix for the qubit whereby the coherence terms are zero.

You can break elliptic curve cryptography with quantum computers. Post-quantum cryptography is instead based on something called the lattice problem, sometimes called lattice-based cryptography.

Personally, I think there is a much bigger issue with the quantum internet that is often not discussed and it’s not just noise.

Imagine, for example, I were to offer you two algorithms. One can encrypt things so well that it would take a hundred trillion years for even a superadvanced quantum computer to break the encryption, and it almost has no overhead. The other is truly unbreakable even in an infinite amount of time, but it has a huge amount of overhead to the point that it will cut your bandwidth in half.

Which would you pick?

In practice, there is no difference between an algorithm that cannot be broken for trillions of years, and an algorithm that cannot be broken at all. But, in practice, cutting your internet bandwidth in half is a massive downside. The tradeoff just isn’t worth it.

All quantum “internet” algorithms suffer from this problem. There is always some massive practical tradeoff for a purely theoretical benefit. Even if we make it perfectly noise-free and entirely solve the noise problem, there would still be no practical reason at all to adopt the quantum internet.

The problem with the one-time pads is that they’re also the most inefficient cipher. If we switched to them for internet communication (ceteris paribus), it would basically cut internet bandwidth in half overnight. Even moreso, it’s a symmetric cipher, and symmetric ciphers cannot be broken by quantum computers. Ciphers like AES256 are considered still quantum-computer-proof. This means that you would be cutting the internet bandwidth in half for purely theoretical benefits that people wouldn’t notice in practice. The only people I could imagine finding this interesting are overly paranoid governments as there are no practical benefits.

It also really isn’t a selling point for quantum key distribution that it can reliably detect an eavesdropper. Modern cryptography does not care about detecting eavesdroppers. When two people are exchanging keys with a Diffie-Hellman key exchange, eavesdroppers are allowed to eavesdrop all they wish, but they cannot make sense of the data in transit. The problem with quantum key distribution is that it is worse than this, it cannot prevent an eavesdropper from seeing the transmitted key, it just discards it if they do. This to me seems like it would make it a bit harder to scale, although not impossible, because anyone can deny service just by observing the packets of data in transit.

Although, the bigger issue that nobody seems to talk about is that quantum key distribution, just like the Diffie-Hellman algorithm, is susceptible to a man-in-the-middle attack. Yes, it prevents an eavesdropper between two nodes, but if the eavesdropper sets themselves up as a third node pretending to be different nodes when queried from either end, they could trivially defeat quantum key distribution. Although, Diffie-Hellman is also susceptible to this, so that is not surprising.

What is surprising is that with Diffie-Hellman (or more commonly its elliptic curve brethren), we solve this using digital signatures which are part of public key infrastructure. With quantum mechanics, however, the only equivalent to digital signatures relies on the No-cloning Theorem. The No-cloning Theorem says if I gave you a qubit and you don’t know it is prepared, nothing you can do to it can tell you its quantum state, which requires knowledge of how it was prepared. You can use the fact only a single person can be aware of its quantum state as a form of a digital signature.

The thing is, however, the No-cloning Theorem only holds true for a single qubit. If I prepared a million qubits all the same way and handed them to you, you could derive its quantum state by doing different measurements on each qubit. Even though you could use this for digital signatures, those digital signatures would have to be disposable. If you made too many copies of them, they could be reverse-engineered. This presents a problem for using them as part of public key infrastructure as public key infrastructure requires those keys to be, well, public, meaning anyone can take a copy, and so infinite copy-ability is a requirement.

This makes quantum key distribution only reliable if you combine it with quantum digital signatures, but when you do that, it no longer becomes possible to scale it to some sort of “quantum internet.” It, again, might be something useful an overly paranoid government could use internally as part of their own small-scale intranet, but it would just be too impractical without any noticeable benefits for anyone outside of that. As, again, all this is for purely theoretical benefits, not anything you’d notice in the real world, as things like AES256 are already considered uncrackable in practice.

Entanglement plays a key role.

Any time you talk about “measurement” this is just observation, and the result of an observation is to reduce the state vector, which is just a list of complex-valued probability amplitudes. The fact they are complex numbers gives rise to interference effects. When the eavesdropper observes definite outcome, you no longer need to treat it as probabilistic anymore, you can therefore reduce the state vector by updating your probabilities to simply 100% for the outcome you saw. The number 100% has no negative or imaginary components, and so it cannot exhibit interference effects.

It is this loss of interference which is ultimately detectable on the other end. If you apply a Hadamard gate to a qubit, you get a state vector that represents equal probabilities for 0 or 1, but in a way that could exhibit interference with later interactions. Such as, if you applied a second Hadamard gate, it would return to its original state due to interference. If you had a qubit that was prepared with a 50% probability of being 0 or 1 but without interference terms (coherences), then applying a second Hadamard gate would not return it to its original state but instead just give you a random output.

Hence, if qubits have undergone decoherence, i.e., if they have lost their ability to interfere with themselves, this is detectable. Obvious example is the double-slit experiment, you get real distinct outcomes by a change in the pattern on the screen if the photons can interfere with themselves or if they cannot. Quantum key distribution detects if an observer made a measurement in transit by relying on decoherence. Half the qubits a Hadamard gate is randomly applied, half they are not, and which it is applied to and which it is not is not revealed until after the communication is complete. If the recipient receives a qubit that had a Hadamard gate applied to it, they have to apply it again themselves to cancel it out, but they don’t know which ones they need to apply it to until the full qubits are transmitted and this is revealed.

That means at random, half they receive they need to just read as-is, and another half they need to rely on interference effects to move them back into their original state. Any person who intercepts this by measuring it would cause it to decohere by their measurement and thus when the recipient applies the Hadamard gate a second time to cancel out the first, they get random noise rather than it actually cancelling it out. The recipient receiving random noise when they should be getting definite values is how you detect if there is an eavesdropper.

What does this have to do with entanglement? If we just talk about “measuring a state” then quantum mechanics would be a rather paradoxical and inconsistent theory. If the eavesdropper measured the state and updated the probability distribution to 100% and thus destroyed its interference effects, the non-eavesdroppers did not measure the state, so it should still be probabilistic, and at face value, this seems to imply it should still exhibit interference effects from the non-eavesdroppers’ perspective.

A popular way to get around this is to claim that the act of measurement is something “special” which always destroys the quantum probabilities and forces it into a definite state. That means the moment the eavesdropper makes the measurement, it takes on a definite value for all observers, and from the non-eavesdroppers’ perspective, they only describe it still as probabilistic due to their ignorance of the outcome. At that point, it would have a definite value, but they just don’t know what it is.

However, if you believe that, then that is not quantum mechanics and in fact makes entirely different statistical predictions to quantum mechanics. In quantum mechanics, if two systems interact, they become entangled with one another. They still exhibit interference effects as a whole as an entangled system. There is no “special” interaction, such as a measurement, which forces a definite outcome. Indeed, if you try to introduce a “special” interaction, you get different statistical predictions than quantum mechanics actually makes.

This is because in quantum mechanics, every interaction leads to growing the scale of entanglement, and so the interference effects never go away, just spread out. If you introduce a “special” interaction such as a measurement whereby it forces things into a definite value for all observers, then you are inherently suggesting there is a limitation to this scale of entanglement. There is some cut-off point whereby interference effects can no longer be scaled passed that, and because we can detect if a system exhibits interference effects or not (that’s what quantum key distribution is based on), then such an alternative theory (called an objective collapse model) would necessarily have to make differ from quantum mechanics in its numerical predictions.

The actual answer to this seeming paradox is provided by quantum mechanics itself: entanglement. When the eavesdropper observes the qubit in transit, for the perspective of the non-eavesdroppers, the eavesdropper would become entangled with the qubit. It then no longer becomes valid in quantum mechanics to assign the state vector to the eavesdropper and the qubit separately, but only them together as an entangled system. However, the recipient does not receive both the qubit and the eavesdropper, they only receive the qubit. If they want to know how the qubit behaves, they have to do a partial trace to trace out (ignore) the eavesdropper, and when they do this, they find that the qubit’s state is still probabilistic, but it is a probability distribution with only terms between 0% and 100%, that is to say, no negatives or imaginary components, and thus it cannot exhibit interference effects.

Quantum key distribution does indeed rely on entanglement as you cannot describe the algorithm consistently from all reference frames (within the framework of quantum mechanics and not implicitly abandoning quantum mechanics for an objective collapse theory) without taking into account entanglement. As I started with, the reduction of the wave function, which is a first-person description of an interaction (when there are 2 systems interacting and one is an observer describing the second), leads to decoherence. The third-person description of an interaction (when there are 3 systems and one is on the “outside” describing the other two systems interacting) is entanglement, and this also leads to decoherence.

You even say that “measurement changes the state”, but how do you derive that without entanglement? It is entanglement between the eavesdropper and the qubit that leads to a change in the reduced density matrix of the qubit on its own.

OrchOR makes way too many wild claims for there to easily be any evidence for it. Even if we discover quantum effects (in the sense of scalable interference effects which have absolutely not been demonstrated) in the brain that would just demonstrate there are quantum effects in the brain, OrchOR is filled with a lot of assumptions which go far beyond this and would not be anywhere near justified. One of them being its reliance on gravity-induced collapse, which is nonrelativistic, meaning it cannot reproduce the predictions of quantum field theory, our best theory of the natural world.

A theory is ultimately not just a list of facts but a collection of facts under a single philosophical interpretation of how they relate to one another. This is more of a philosophical issue, but even if OrchOR proves there is gravitational induced collapse and that there is quantum effects in the brain, we would still just take these two facts separately. OrchOR tries to unify them under some bizarre philosophical interpretation called the Penrose–Lucas argument that says because humans can believe things that are not proven, therefore human consciousness must be noncomputable, and because human consciousness is not computable, it must be reducible to something that you cannot algorithmically predict its outcome, which would be true of an objective collapse model. Ergo, wave function collapse causes consciousness.

Again, even if they proved that there is scalable quantum interference effects in the brain, even if they proved that there is gravitationally induced collapse, that alone does not demonstrate OrchOR unless you actually think the Penrose-Lucas argument makes sense. They would just be two facts which we would take separately as fact. It would just be a fact that there is gravitionally induced collapse, a fact that there is scalable quantum interference effects in the brain but there would be no reason to adopt any of their claims about “consciousness.”

But even then, there is still no strong evidence that the brain in any way makes use of quantum interference effects, only loose hints that it may or not be possible with microtubules, and there is definitely no evidence of the gravitationally induced collapse.

Both these figures are embarrassingly bad.

Hoffman confuses function for perception and constantly uses arguments demonstrating things can interpret reality incorrectly (which is purely a question of function) in order to argue they cannot perceive reality “as it is.,” which is a huge non-sequitur. He keeps going around promoting his “theorem” which supposedly “proves” this yet if you read his book where he explains his theorem it is again clearly about function as his theorem only shows that limitations in cognitive and sensory capabilities can lead something to interpret reality incorrectly yet he draws a wild conclusion which he never justifies that this means they do not perceive reality “as it is” at all.

Kastrup is also just incredibly boring because he never reads books so he is convinced the only two philosophical schools in the universe are his personal idealism and metaphysical realism, which the latter he constantly incorrectly calls “materialism” when not all materialist schools of thought are even metaphysically realist. Unless you are yourself a metaphysical realist, nothing Kastrup has ever written is interesting at all, because he just pretends you don’t exist.

Metaphysical realism is just a popular worldview in the west that most Laymen tend to naturally take on unwittingly. If you’re a person who has ever read books in your life, then you’d quickly notice that attacking metaphysical realism doesn’t get you to idealism, at best it gets you to metaphysical realism being not a coherent worldview… which that is the only thing I agree with Kastrup with.

Kastrup is entirely unconvincing because he pretends the only two schools of philosophy in the whole universe are his specific idealism and metaphysical realism which he falsely calls the latter “materialism.” He thus never feels the need to ever address anything outside of a critique of a single Laymen understanding of materialism which is more popular in western countries than eastern countries, ignoring the actual wealth of philosophical literature.

Anyone who actually reads books on philosophy would inevitably find Kastrup to be incredibly unconvincing as he, by focusing primarily on a single school, never justifies many of his premises. He begins from the very beginning talking about “conscious experience” and whatnot when, if you’re not a metaphysical realist, that is what you are supposed to be arguing in the first place. Unless you’re already a dualist or metaphysical realist, if you are pretty much any other philosophical school like contextual realist, dialectical materialist, empiriomonist, etc, you probably already view reality as inherently observable, and thus perception is just reality from a particular point-of-view. It then becomes invalid to add qualifiers to it like “conscious experience” or “subjective experience” as reality itself cannot had qualifiers.

I mean, the whole notion of “subjective experience” goes back to Nagel who was a metaphysical realist through-and-through and wrote a whole paper defending that notion, “What is it like to be a Bat?”, and this is what Kastrup assumes his audience already agrees with from the get-go. He never addresses any of the criticisms of metaphysical realism but pretends like they don’t exist and he is the unique sole critic of it and constantly calls metaphysical realism “materialism” as if they’re the same philosophy at all. He then builds all of his arguments off of this premise.

For the first question, I would recommend reading the philosopher and physicist Francois-Igor Pris who not only seems to understand the deep philosophical origins of the problem, but also provides probably the simplest solution to it. Pris points out that we cannot treat the philosophical ramification in isolation, as if the difficulty in understanding quantum physics originates from quantum physics itself. It must originate from a framework in which we are trying to apply to quantum physics that just breaks down, and therefore it must originate from preconceived philosophical notions people have before even learning of quantum physics.

In other words, you have to go back to the drawing board, question very foundational philosophical notions. He believes that it originates from the belief in metaphysical realism in the traditional sense, which is the idea that there is an objective reality but it is purely metaphysical, i.e. entirely invisible because what we perceive is merely an illusion created by the conscious mind, but somehow it is given rise to by equivalent objects that are impossible to see. For example, if you have a concept of a rock in your mind, that concept “reflects” a rock that is impossible to see, what Kant had called the thing-in-itself. How can a reality that is impossible to observe ever “give rise to” what we observe? This is basically the mind-body problem.

Most academics refuse to put forward a coherent answer to this, and in a Newtonian framework it can be ignored. This problem resurfaces in quantum physics, because you have the same kind of problem yet again. What is a measurement if not an observation, and what is an observation if not an experience? You have a whole world of invisible waves floating around in Hilbert space that suddenly transform themselves into something we can observe (i.e. experience) the moment we attempt to look at them, i.e. they transform themselves suddenly into observable particles in spacetime the moment we look.

His point is ultimately that, because people push off coming up with a philosophical solution to the mind-body problem, when it resurfaces as the measurement problem, people have no idea how to even approach it. However, he also points out that any approach you do take ultimately parallels whatever solution you would take to the mind-body problem.

For example, eliminative materialists say the visible world does not actually exist but only the nonvisible world and that our belief we can experience things is an illusion. This parallels the Many Worlds Interpretation which gets rid of physical particles and thus gets rid of all observables and only has waves evolving in Hilbert space without observables. Idealists argue in favor of getting rid of invisible reality and just speak of the mind, which if you read the philosophical literature you will indeed find a lot of academics who are idealists who try to justify it with quantum mechanics.

Both of these positions are, in my view, problematic, and I like Pris’ his own solution based on Jocelyn Benoist’s philosophy of contextual realism which is in turn based off of Ludwig Wittgenstein’s writings. Benoist has written extensively against all the arguments claiming that reality is invisible and has instead argued that what we experience is objective reality as it is exists independent of the observer but dependent upon the context of the observation. Thus he is critical of pretty much all of modern philosophers who overwhelmingly adhere either to metaphysical realism or to idealism. There is no mind-body problem under this framework because reality was never invisible to begin with, so there is no “explanatory gap.”

Apply this thinking to quantum mechanics then it also provides a solution to the measurement problem that is probably the simplest and most intuitive and is very similar to Carlo Rovelli’s interpretation. Reality depends upon context all the way down, meaning that the properties of systems must be context variant. And that’s really the end of the story, no spooky action at a distance, no multiverse, no particles in two places at once, no language of observer-dependence, etc.

Whenever you describe physical reality, you have to pick a coordinate system as reality depends upon context and is not “absolute,” or as Rovelli would say, reality depends upon the relations of a system to every other system. Hence, if you want to describe a system, you have to pick a coordinate system under which it will be “observed,” kind of like a reference frame, but the object you choose as the basis of the coordinate system has to actually interact with the other object. The wave function then is just a way for accounting for the system’s context as it incorporates the relations between the system being used as the basis of the reference frame and the object that it will interact with.

Basically, it is not much different from Copenhagen, except “observer-dependence” is replaced by “context-dependence” as the properties of systems are context variant and any physical system, even a rock, can be used as the basis of the coordinate system. But, of course, if you want to predict what you will observe, then you always implicitly use your own context as the basis of the coordinate system. This is a realist stance, but not a metaphysical realist stance, because the states of particles are not absolute, there is no thing-in-itself, and the reality is precisely what you perceive and not some waves in Hilbert space beyond it (these are instead treated as tools for predicting what the value will be when you measure it, and not itself an entity). Although, it is only whether or not they have a property at all that is context variant.

If two observers have interacted with the same particle, they will agree as to its state, as you do not get disagreements of the actual values of those particles, only whether or not they have a state at all. They would not be verbal disagreements either, because if an observer measures the state of a particle then goes and tells it to someone else, then it also indirectly enters their context as they would become correlated with that particle through their friend. You only get disagreements if there is no contact. For example, Wigner’s friend paradox, where his friend has measured the particle but has not told him the results nor has he measured it himself, from his context it would indeed have no state.

The “collapse” would then not be a collapse of a physical “wave” but, again, reality is context variant, and so if you interact with a system, then it changes your relation to it, so you have to update the wave function to account for a change in context, kind of like if you change your reference frame in Galilean relativity. Everything is interpreted through this lens whereby nature is treated as context variant in this way, and it resolves all the paradoxes without introducing anything else. So if you can accept that one premise then everything else is explained. By abandoning metaphysical realism, it also simultaneously solves the other philosophical problems that originate from that point of view, i.e. the “hard problem” does not even make sense in a contextual realist framework and is not applicable.

Yes, there are a lot of intuitive understandings in the literature if you’re willing to look for it. The problem is that most people believe in a Newtonian view of the world which just is not compatible with quantum physics, so it requires you to alter some philosophical beliefs, and physics professors don’t really want to get into philosophical arguments, so it’s not really possible to reach a consensus on the question in physics departments. Even worse, there’s rarely a consensus on anything if you go to the philosophy department. So it’s not really that there are not very simple and intuitive ways to understand quantum mechanics, it’s that it’s not possible to get people to agree upon a way to interpret it, so there is a mentality to just avoid interpretation at all so that students don’t get distracted from actually understanding the math.

So… there are things that are either within the category of thought or not?

Objects are in the category of thought but not in some spatial “realm” or “world” of thought. It is definitional, linguistic, not a statement about ontology.

Is thought mutually exclusive to material? Is thought composed of material or the other way around? Or are they both the same?

From an a priori standpoint there is no material, there is just reality. Our understanding of material reality comes from an a posteriori standpoint of investing it, learning about it, forming laws etc, and we do come to understand thought from an a posteriori lens as something that can be observed and implemented in other systems.

Usually thought itself is not even considered as part of the so-called “hard problem” as that’s categorized into the “easy problem.”

That is the standard definition of idealism, is it not? That existence is immaterial?

They say existence is “mind” which includes both thought and experience which they both argue are products of the mind, and so if we start off with thought and experience as the foundations of philosophy then we’re never able to leave the mind. That’s how idealism works, the “thought” part of basically the “easy” problem and the “experience” part is what entails the “hard” problem since even idealists would concede that it is not difficult to conceive of constructing an intelligent machine that can reason, potentially even as good as humans can.

well IBM does have cloud accessible quantum computers that they don’t charge to use

I used those to teach myself some stuff about quantum information science

They’re just categorically different, there isn’t an “inside” or an “outside” in the sense of spatial structure as that is something derived a posteriori as part of thought.

I’m not sure what it would even mean to say reality is “thought”. If I try my best to stop thinking about things does experiential reality just disappear? Not for me it doesn’t. Maybe for you.

What is thought of as opposed to thought itself must necessarily exist prior to the thought in order for it to enter into thought and be what is thought of in the first place. I mean, it’s just self-evident, is it not? If all thoughts cease, reality doesn’t disappear. It’s always there independent of whether or not thought is applied to it or not, whether or not there is an attempt to interpret it. It exists independent of any attempt made to formulate a subjective interpretation of it. That’s all that is meant here by “objective,” that reality is what it is entirely independent of what it is subjectively taken to be.

There is no mind-body problem in the first place. All dualisms and idealisms are circular as they start from the premise that reality is subject-dependent then work backwards from that conclusion, but they never justify that premise. Even many materialists fall for it.

We can’t see wave functions. It is a tool used to predict observations but itself cannot be observed, and cannot be an observable object as it exists in an abstract Hilbert space and not even in spacetime. It is only “space” in the sense of a state space, kind of like how if I have a radio with 4 knobs, I can describe the settings with a single point in a 4 dimensional space. That doesn’t mean the radio actually is a 4 dimensional object existing in this state space, it only means that we can represent that way for convenience, and the dimensions here moreso represent degrees of freedom.

If you believe everything is a wave function then you believe the whole universe is made out of things that cannot be observed. So how does that explain what we observe? Just leads to confusion. Confusion not caused by the mathematics but self-imposed. Nothing about the mathematics says you literally have to think everything is made out of waves. In fact, Heisenberg’s original formulation of quantum mechanics made all the same predictions yet this was before the Schrodinger equation was even invented.

People take the wave formulation way too literally and ultimately it just produces much of this confusion. They are misleadingly taught that you can think of things turning into waves by starting with the double-slit experiment, except it is horribly misleading because they think the interference pattern they’re seeing is the wave function. Yet, (1) the wave function is associated with individual particles, not the interference pattern which is formed by thousands, millions of particles. There is nothing wave-like visible with just a single particle experiment. (2) Even the interference pattern formed by millions of particles does not contain the information of the wave function, only a projection of it, sort of like its “shadow” as the imaginary terms are lost when you apply the Born rule to it and square it. (3) They also like to depict a literal wave moving through two slits, but again there are imaginary components which don’t map to anything physically real, and so the depiction is a lie as information has to be removed in order to actually display a wave on the screen.

The moment you look at literally anything that isn’t the double-slit experiment, the intuitive notion of imagining waves moving through space breaks down. Consider a quantum computer where the qubits are electrons with up or down spin representing 0 or 1. You can also represent the state of the quantum computer with a wave function, yet what does it even mean to imagine the computer’s internal state is a wave when there is nothing moving at all and the state of the quantum computer doesn’t even have position as one of its values? You can’t point to that wave even existing anywhere, you get lost in confusion if you try.

This cloud is described by a mathematical object called wave function. The Austrian physicist Erwin Schrödinger has written an equation describing its evolution in time. Quantum mechanics is often mistakenly identified with this equation. Schrödinger had hopes that the ‘wave’ could be used to explain the oddities of quantum theory: from those of the sea to electromagnetic ones, waves are something we understand well. Even today, some physicists try to understand quantum mechanics by thinking that reality is the Schrödinger wave. But Heisenberg and Dirac understood at once that this would not do.

To view Schrödinger’s wave as something real is to give it too much weight – it doesn’t help us to understand the theory; on the contrary, it leads to greater confusion. Except for special cases, the Schrödinger wave is not in physical space, and this divests it of all its intuitive character. But the main reason why Schrödinger’s wave is a bad image of reality is the fact that, when a particle collides with something else, it is always at a point: it is never spread out in space like a wave. If we conceive an electron as a wave, we get in trouble explaining how this wave instantly concentrates to a point at each collision. Schrödinger’s wave is not a useful representation of reality: it is an aid to calculation which permits us to predict with some degree of precision where the electron will reappear. The reality of the electron is not a wave: it is how it manifests itself in interactions

— Carlo Rovelli, “Reality is Not What it Seems”

It is more intuitive to not think of wave functions as entities at all. But people have this very specific mathematical notation so burned into their heads from the repeated uses of the double-slit experiment that it is very difficult to get it out of their heads. Not only did Heisenberg instead use matrix transformation rather than the Schrodinger equation to represent QM, but it is also possible to represent quantum mechanics in even a third mathematical formulation known as the ensemble in phase space formulation.

The point here is that the Schrodinger equation is just one mathematical formalism in which there are multiple mathematically equivalent ways to formulate quantum mechanics, and so treating these wave functions wave really existing waves moving through a Hilbert space which you try to imagine as something like our own spacetime seems to be putting too much weight on a very specific formalism and ultimately is the source of a lot of the confusion. Describing the whole universe as thus a giant wave in Hilbert space evolving according to the Schrodinger equation is thus rather dubious, especially since these are entirely metaphysical constructs without any observable properties.

The traditional notion of cause and effect is not something all philosophers even agree upon, I mean many materialist philosophers largely rejected the notion of simple cause-and-effect chains that go back to the “first cause” since the 1800s, and that idea is still pretty popular in some eastern countries.

For example, in China they teach “dialectical materialist” philosophy part of required “common core” in universities for any degree, and that philosophical school sees cause and effect as in a sense dependent upon point of view, that an effect being described as a particular cause is just a way of looking at things, and the same relationship under a different point of view may in fact reverse what is considered the cause and the effect, viewing the effect as the cause and vice-versa. Other points of view may even ascribe entirely different things as the cause.

It has a very holistic view of the material world so there really is no single cause to any effect, so what you choose to identify as the cause is more of a label placed by an individual based on causes that are relevant to them and not necessarily because those are truly the only causes. In a more holistic view of nature, Laplacian-style determinism doesn’t even make sense because it implies nature is reducible down to separable causes which can all be isolated from the rest and their properties can then be fully accounted for, allowing one to predict the future with certainty.

However, in a more holistic view of nature, it makes no sense to speak of the universe being reducible to separable causes as, again, what we label as causes are human constructs and the universe is not actually separable. In fact, the physicists Dmitry Blokhintsev had written a paper in response to a paper Albert Einstein wrote criticizing Einstein’s distaste for quantum mechanics as based on his adherence to the notion of separability which stems from Newtonian and Kantian philosophy, something which dialectical materialists, which Blokhintsev self-identified as, had rejected on philosophical grounds.

He wrote this paper many many years prior to the publication of Bell’s theorem which showed that giving up on separability (and by extension absolute determinism) really is a necessity in quantum mechanics. Blokhintsev would then go on to write a whole book called The Philosophy of Quantum Mechanics where in it he argues that separability in nature is an illusion and under a more holistic picture absolute determinism makes no sense, again, purely from materialistic grounds.

The point I’m making is ultimately just that a lot of the properties people try to ascribe to “materialists” or “naturalists” which then later try to show quantum mechanics is in contradiction with, they seem to forget that these are large umbrella philosophies with many different sects and there have been materialist philosophers criticizing absolute determinism as even being a meaningful concept since at least the 1800s.

I agree experience is incalculable but not because it is some special immaterial substance but because experience just is objective reality from a particular context frame. I can do all the calculations I want on a piece of paper describing the properties of fire, but the paper it’s written on won’t suddenly burst into flames. A description of an object will never converge into a real object, and by no means will descriptions of reality ever become reality itself. The notion that experience is incalculable is just uninteresting. Of course, we can say the same about the wave function. We use it as a tool to predict where we will see real particles. You also cannot compute the real particles from the wave function either because it’s not a real entity but a description of relationships between observations (i.e. experiences) of real things.