Schrödinger was not “rejecting” quantum mechanics, he was rejecting people treating things described in a superposition of states as literally existing in “two places at once.” And Schrödinger’s argument still holds up perfectly. What you are doing is equating a very dubious philosophical take on quantum mechanics with quantum mechanics itself, as if anyone who does not adhere to this dubious philosophical take is “denying quantum mechanics.” But this was not what Schrödinger was doing at all.

What you say here is a popular opinion, but it just doesn’t make any sense if you apply any scrutiny to it, which is what Schrödinger was trying to show. Quantum mechanics is a statistical theory where probability amplitudes are complex-valued, so things can have a -100% chance of occurring, or even a 100i% chance of occurring. This gives rise to interference effects which are unique to quantum mechanics. You interpret what these probabilities mean in physical reality based on how far they are away from zero (the further from zero, the more probable), but the negative signs allow for things to cancel out in ways that would not occur in normal probability theory, known as interference effects. Interference effects are the hallmark of quantum mechanics.

Because quantum probabilities have this difference, some people have wondered if maybe they are not probabilities at all but describe some sort of physical entity. If you believe this, then when you describe a particle as having a 50% probability of being here and a 50% probability of being there, then this is not just a statistical prediction but there must be some sort of “smeared out” entity that is both here and there simultaneously. Schrödinger showed that believing this leads to nonsense as you could trivially set up a chain reaction that scales up the effect of a single particle in a superposition of states to eventually affect a big system, forcing you to describe the big system, like a cat, in a superposition of states. If you believe particles really are “smeared out” here and there simultaneously, then you have to believe cats can be both “smeared out” here and there simultaneously.

Ironically, it was Schrödinger himself that spawned this way of thinking. Quantum mechanics was originally formulated without superposition in what is known as matrix mechanics. Matrix mechanics is complete, meaning, it fully makes all the same predictions as traditional quantum mechanics. It is a mathematically equivalent theory. Yet, what is different about it is that it does not include any sort of continuous evolution of a quantum state. It only describes discrete observables and how they change when they undergo discrete interactions.

Schrödinger did not like this on philosophical grounds due to the lack of continuity. There were discrete “gaps” between interactions. He criticized it saying that “I do not believe that the electron hops about like a flea” and came up with his famous wave equation as a replacement. This wave equation describes a list of probability amplitudes evolving like a wave in between interactions, and makes the same predictions as matrix mechanics. People then use the wave equation to argue that the particle literally becomes smeared out like a wave in between interactions.

However, Schrödinger later abandoned this point of view because it leads to nonsense. He pointed in one of his books that while his wave equation gets rid of the gaps in between interactions, it introduces a new gap in between the wave and the particle, as the moment you measure the wave it “jumps” into being a particle randomly, which is sometimes called the “collapse of the wave function.” This made even less sense because suddenly there is a special role for measurement. Take the cat example. Why doesn’t the cat’s observation of this wave not cause it to “collapse” but the person’s observation does? There is no special role for “measurement” in quantum mechanics, so it is unclear how to even answer this in the framework of quantum mechanics.

Schrödinger was thus arguing to go back to the position of treating quantum mechanics as a theory of discrete interactions. There are just “gaps” between interactions we cannot fill. The probability distribution does not represent a literal physical entity, it is just a predictive tool, a list of probabilities assigned to predict the outcome of an experiment. If we say a particle has a 50% chance of being here or a 50% chance of being there, it is just a prediction of where it will be if we were to measure it and shouldn’t be interpreted as the particle being literally smeared out between here and there at the same time.

There is no reason you have to actually believe particles can be smeared out between here and there at the same time. This is a philosophical interpretation which, if you believe it, it has an enormous amount of problems with it, such as what Schrödinger pointed out which ultimately gets to the heart of the measurement problem, but there are even larger problems. Wigner had also pointed out a paradox whereby two observers would assign different probability distributions to the same system. If it is merely probabilities, this isn’t a problem. If I flip a coin and look at the outcome and it’s heads, I would say it has a 100% chance of being heads because I saw it as heads, but if I asked you and covered it up so you did not see it, you would assign a 50% probability of it being heads or tails. If you believe the wave function represents a physical entity, then you could setup something similar in quantum mechanics whereby two different observers would describe two different waves, and so the physical shape of the wave would have to differ based on the observer.

There are a lot more problems as well. A probability distribution scales up in terms of its dimensions exponentially. With a single bit, there are two possible outcomes, 0 and 1. With two bits, there’s four possible outcomes, 00, 01, 10, and 11. With three bits, eight outcomes. With four bits, sixteen outcomes. If we assign a probability amplitude to each possible outcome, then the number of degrees of freedom grows exponentially the more bits we have under consideration.

This is also true in quantum mechanics for the wave function, since it is again basically a list of probability amplitudes. If we treat the wave function as representing a physical wave, then this wave would not exist in our four-dimensional spacetime, but instead in an infinitely dimensional space known as a Hilbert space. If you want to believe the universe actually physically made up of infinitely dimensional waves, have at ya. But personally, I find it much easier to just treat a probability distribution as, well, a probability distribution.

What is it then? If you say it’s a wave, well, that wave is in Hilbert space which is infinitely dimensional, not in spacetime which is four dimensional, so what does it mean to say the wave is “going through” the slit if it doesn’t exist in spacetime? Personally, I think all the confusion around QM stems from trying to objectify a probability distribution, which is what people do when they claim it turns into a literal wave.

To be honest, I think it’s cheating. People are used to physics being continuous, but in quantum mechanics it is discrete. Schrodinger showed that if you take any operator and compute a derivative, you can “fill in the gaps” in between interactions, but this is just purely metaphysical. You never see these “in between” gaps. It’s just a nice little mathematical trick and nothing more. Even Schrodinger later abandoned this idea and admitted that trying to fill in the gaps between interactions just leads to confusion in his book Nature and the Greeks and Science and Humanism.

What’s even more problematic about this viewpoint is that Schrodinger’s wave equation is a result of a very particular mathematical formalism. It is not actually needed to make correct predictions. Heisenberg had developed what is known as matrix mechanics whereby you evolve the observables themselves rather than the state vector. Every time there is an interaction, you apply a discrete change to the observables. You always get the right statistical predictions and yet you don’t need the wave function at all.

The wave function is purely a result of a particular mathematical formalism and there is no reason to assign it ontological reality. Even then, if you have ever worked with quantum mechanics, it is quite apparent that the wave function is just a function for picking probability amplitudes from a state vector, and the state vector is merely a list of, well, probability amplitudes. Quantum mechanics is probabilistic so we assign things a list of probabilities. Treating a list of probabilities as if it has ontological existence doesn’t even make any sense, and it baffles me that it is so popular for people to do so.

This is why Hilbert space is infinitely dimensional. If I have a single qubit, there are two possible outcomes, 0 and 1. If I have two qubits, there are four possible outcomes, 00, 01, 10, and 11. If I have three qubits, there are eight possible outcomes, 000, 001, 010, 011, 100, 101, 110, and 111. If I assigned a probability amplitude to each event occurring, then the degrees of freedom would grow exponentially as I include more qubits into my system. The number of degrees of freedom are unbounded.

This is exactly how Hilbert space works. Interpreting this as a physical infinitely dimensional space where waves really propagate through it just makes absolutely no sense!

It is weird that you start by criticizing our physical theories being descriptions of reality then end criticizing the Copenhagen interpretation, since this is the Copenhagen interpretation, which says that physics is not about describing nature but describing what we can say about nature. It doesn’t make claims about underlying ontological reality but specifically says we cannot make those claims from physics and thus treats the maths in a more utilitarian fashion.

The only interpretation of quantum mechanics that actually tries to interpret it at face value as a theory of the natural world is relational quantum mechanics which isn’t that popular as most people dislike the notion of reality being relative all the way down. Almost all philosophers in academia define objective reality in terms of something being absolute and point-of-view independent, and so most academics struggle to comprehend what it even means to say that reality is relative all the way down, and thus interpreting quantum mechanics as a theory of nature at face-value is actually very unpopular.

All other interpretations either: (1) treat quantum mechanics as incomplete and therefore something needs to be added to it in order to complete it, such as hidden variables in the case of pilot wave theory or superdeterminism, or a universal psi with some underlying mathematics from which to derive the Born rule in the Many Worlds Interpretation, or (2) avoid saying anything about physical reality at all, such as Copenhagen or QBism.

Since you talk about “free will,” I suppose you are talking about superdeterminism? Superdeterminism works by pointing out that at the Big Bang, everything was localized to a single place, and thus locally causally connected, so all apparent nonlocality could be explained if the correlations between things were all established at the Big Bang. The problem with this point of view, however, is that it only works if you know the initial configuration of all particles in the universe and a supercomputer powerful to trace them out to modern day.

Without it, you cannot actually predict any of these correlations ahead of time. You have to just assume that the particles “know” how to correlate to one another at a distance even though you cannot account for how this happens. Mathematically, this would be the same as a nonlocal hidden variable theory. While you might have a nice underlying philosophical story to go along with it as to how it isn’t truly nonlocal, the maths would still run into contradictions with special relativity. You would find it difficult to construe the maths in such a way that the hidden variables would be Lorentz invariant.

Superdeterministic models thus struggle to ever get off the ground. They only all exist as toy models. None of them can reproduce all the predictions of quantum field theory, which requires more than just accounting for quantum mechanics, but doing so in a way that is also compatible with special relativity.

You don’t have to be sorry, that was stupid of me to write that.

Because the same functionality would be available as a cloud service (like AI now). This reduces costs and the need to carry liquid nitrogen around.

Okay, you are just misrepresenting my argument at this point.

Why are you isolating a single algorithm? There are tons of them that speed up various aspects of linear algebra and not just that single one, and many improvements to these algorithms since they were first introduced, there are a lot more in the literature than just in the popular consciousness.

The point is not that it will speed up every major calculation, but these are calculations that could be made use of, and there will likely even be more similar algorithms discovered if quantum computers are more commonplace. There is a whole branch of research called quantum machine learning that is centered solely around figuring out how to make use of these algorithms to provide performance benefits for machine learning algorithms.

If they would offer speed benefits, then why wouldn’t you want to have the chip that offers the speed benefits in your phone? Of course, in practical terms, we likely will not have this due to the difficulty and expense of quantum chips, and the fact they currently have to be cooled below to near zero degrees Kelvin. But your argument suggests that if somehow consumers could have access to technology in their phone that would offer performance benefits to their software that they wouldn’t want it.

That just makes no sense to me. The issue is not that quantum computers could not offer performance benefits in theory. The issue is more about whether or not the theory can be implemented in practical engineering terms, as well as a cost-to-performance ratio. The engineering would have to be good enough to both bring the price down and make the performance benefits high enough to make it worth it.

It is the same with GPUs. A GPU can only speed up certain problems, and it would thus be even more inefficient to try and force every calculation through the GPU. You have libraries that only call the GPU when it is needed for certain calculations. This ends up offering major performance benefits and if the price of the GPU is low enough and the performance benefits high enough to match what the consumers want, they will buy it. We also have separate AI chips now as well which are making their way into some phones. While there’s no reason at the current moment to believe we will see quantum technology shrunk small and cheap enough to show up in consumer phones, if hypothetically that was the case, I don’t see why consumers wouldn’t want it.

I am sure clever software developers would figure out how to make use of them if they were available like that. They likely will not be available like that any time in the near future, if ever, but assuming they are, there would probably be a lot of interesting use cases for them that have not even been thought of yet. They will likely remain something largely used by businesses but in my view it will be mostly because of practical concerns. The benefits of them won’t outweigh the cost anytime soon.

Uh… one of those algorithms in your list is literally for speeding up linear algebra. Do you think just because it sounds technical it’s “businessy”? All modern technology is technical, that’s what technology is. It would be like someone saying, “GPUs would be useless to regular people because all they mainly do is speed up matrix multiplication. Who cares about that except for businesses?” Many of these algorithms here offer potential speedup for linear algebra operations. That is the basis of both graphics and AI. One of those algorithms is even for machine learning in that list. There are various algorithms for potentially speeding up matrix multiplication in the linear. It’s huge for regular consumers… assuming the technology could ever progress to come to regular consumers.

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.

A person who would state they fully understand quantum mechanics is the last person i would trust to have any understanding of it.

I find this sentiment can lead to devolving into quantum woo and mysticism. If you think anyone trying to tell you quantum mechanics can be made sense of rationally must be wrong, then you implicitly are suggesting that quantum mechanics is something that cannot be made sense of, and thus it logically follows that people who are speaking in a way that does not make sense and have no expertise in the subject so they do not even claim to make sense are the more reliable sources.

It’s really a sentiment I am not a fan of. When we encounter difficult problems that seem mysterious to us, we should treat the mystery as an opportunity to learn. It is very enjoyable, in my view, to read all the different views people put forward to try and make sense of quantum mechanics, to understand it, and then to contemplate on what they have to offer. To me, the joy of a mystery is not to revel in the mystery, but to search for solutions for it, and I will say the academic literature is filled with pretty good accounts of QM these days. It’s been around for a century, a lot of ideas are very developed.

I also would not take the game Outer Wilds that seriously. It plays into the myth that quantum effects depend upon whether or not you are “looking,” which is simply not the case and largely a myth. You end up with very bizarre and misleading results from this, for example, in the part where you land on the quantum moon and have to look at the picture of it for it to not disappear because your vision is obscured by fog. This makes no sense in light of real physics because the fog is still part of the moon and your ship is still interacting with the fog, so there is no reason it should hop to somewhere else.

Now quantum science isn’t exactly philosophy, ive always been interested in philosophy but its by studying quantum mechanics, inspired by that game that i learned about the mechanic of emerging properties. I think on a video about the dual slit experiment.

The double-slit experiment is a great example of something often misunderstood as somehow evidence observation plays some fundamental role in quantum mechanics. Yes, if you observe the path the two particles take through the slits, the interference pattern disappears. Yet, you can also trivially prove in a few line of calculation that if the particle interacts with a single other particle when it passes through the two slits then it would also lead to a destruction of the interference effects.

You model this by computing what is called a density matrix for both the particle going through the two slits and the particle it interacts with, and then you do what is called a partial trace whereby you “trace out” the particle it interacts with giving you a reduced density matrix of only the particle that passes through the two slits, and you find as a result of interacting with another particle its coherence terms would reduce to zero, i.e. it would decohere and thus lose the ability to interfere with itself.

If a single particle interaction can do this, then it is not surprising it interacting with a whole measuring device can do this. It has nothing to do with humans looking at it.

At that point i did not yet know that emergence was already a known topic in philosophy just quantum science, because i still tried to avoid external influences but it really was the breakthrough I needed and i have gained many new insights from this knowledge since.

Eh, you should be reading books and papers in the literature if you are serious about this topic. I agree that a lot of philosophy out there is bad so sometimes external influences can be negative, but the solution to that shouldn’t be to entirely avoid reading anything at all, but to dig through the trash to find the hidden gems.

My views when it comes to philosophy are pretty fringe as most academics believe the human brain can transcend reality and I reject this notion, and I find most philosophy falls right into place if you reject this notion. However, because my views are a bit fringe, I do find most philosophical literature out there unhelpful, but I don’t entirely not engage with it. I have found plenty of philosophers and physicists who have significantly helped develop my views, such as Jocelyn Benoist, Carlo Rovelli, Francois-Igor Pris, and Alexander Bogdanov.

This is why many philosophers came to criticize metaphysical logic in the 1800s, viewing it as dealing with absolutes when reality does not actually exist in absolutes, stating that we need some other logical system which could deal with the “fuzziness” of reality more accurately. That was the origin of the notion of dialectical logic from philosophers like Hegel and Engels, which caught on with some popularity in the east but then was mostly forgotten in the west outside of some fringe sections of academia. Even long prior to Bell’s theorem, the physicist Dmitry Blokhintsev, who adhered to this dialectical materialist mode of thought, wrote a whole book on quantum mechanics where the first part he discusses the need to abandon the false illusion of the rigidity and concreteness of reality and shows how this is an illusion even in the classical sciences where everything has uncertainty, all predictions eventually break down, nothing is never possible to actually fully separate something from its environment. These kinds of views heavily influenced the contemporary physicist Carlo Rovelli as well.

This is accurate, yes. The cat in the box is conscious presumably, in my opinion of cats at least, but still can be “not an observer” from the POV of the scientist observing the experiment from outside the box.

“Consciousness” is not relevant here at all. You can write down the wave function of a system relative to a rock if you wanted, in a comparable way as writing down the velocity of a train from the “point of view” of a rock. It is coordinate. It has nothing to do with “consciousness.” The cat would perceive a definite state of the system from its reference frame, but the person outside the box would not until they interact with it.

QM is about quite a lot more than coordinate systems

Obviously QM is not just coordinate systems. The coordinate nature of quantum mechanics, the relative nature of it, is merely a property of the theory and not the whole theory. But the rest of the theory does not have any relevance to “consciousness.”

and in my opinion will make it look weird in retrospect once physics expands to a more coherent whole

The theory is fully coherent and internally consistent. It amazes me how many people choose to deny QM and always want to rush to change it. Your philosophy should be guided by the physical sciences, not the other way around. People see QM going against their basic intuitions and their first thought is it must be incomplete and needs to have additional complexity added to it to make it fit their intuitions, rather than just questioning that maybe their basic intuitions are wrong.

Your other comment was to a Wikipedia page which if you clicked the link on your own source it would’ve told you that the scientific consensus on that topic is that what you’re presenting is a misinterpretation.

• https://en.m.wikipedia.org/wiki/Delayed-choice_quantum_eraser#Consensus:_no_retrocausality

A simple search on YouTube could’ve also brought up several videos explaining this to you.

• https://www.youtube.com/watch?v=s5yON4Gs3D0
• https://www.youtube.com/watch?v=RQv5CVELG3U

Edit: Placing my response here as an edit since I don’t care to continue this conversation so I don’t want to notify.

Yes, that was what I said. Er, well… QM, as I understand it, doesn’t have to do anything with shifting coordinate systems per se (and in fact is still incompatible with relativity). They’re just sort of similar in that they both have to define some point of view and make everything else in the model relative to it. I’m still not sure why you brought coordinate systems into it.

A point of view is just a colloquial term to refer to a coordinate system. They are not coordinate in the exact same way but they are both coordinate.

My point was that communication of state to the observer in the system, or not, causes a difference in the outcome. And that from the general intuitions that drive almost all of the rest of physics, that’s weird and sort of should be impossible.

No, it doesn’t not, and you’re never demonstrated that.

Sure. How is it when combined with macro-scale intuition about the way natural laws work, or with general relativity?

We have never observed quantum effects on the scale where gravitational effects would also be observable, so such a theory, if we proposed one, would not be based on empirical evidence.

This is very, very very much not what I am doing. What did I say that gave you the impression I was adding anything to it?

You literally said in your own words we need to take additional things into account we currently are not. You’re now just doing a 180 and pretending you did not say what literally anyone can scroll up and see that you said.

I am not talking about anything about retrocausality here, except maybe accidentally.

Then you don’t understand the experiment since the only reason it is considered interesting is because if you interpret it in certain ways it seems to imply retrocausality. Literally no one has ever treated it as anything more than that. You are just making up your own wild implications from the experiment.

I was emphasizing the second paragraph; “wave behavior can be restored by erasing or otherwise making permanently unavailable the ‘which path’ information.”

The behavior of the system physically changes when it undergoes a physical interaction. How surprising!

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.

There is “observer-dependence” in quantum mechanics in a comparable way that there is observer-dependence in general relativity. It has nothing to do with some “fundamental role of consciousness” but comes from the fact that reality itself depends on how you look at it, it is reference frame dependent. The “observer” is just a chosen coordinate system in which to describe other things. I know, you probably got this from Kastrup too, right? Idealists have been getting desperate and resorting to quantum woo, pretending that something that changes based on coordinate system proves fundamental consciousnesses.

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.

Classical computers compute using 0s and 1s which refer to something physical like voltage levels of 0v or 3.3v respectively. Quantum computers also compute using 0s and 1s that also refers to something physical, like the spin of an electron which can only be up or down. Although these qubits differ because with a classical bit, there is just one thing to “look at” (called “observables”) if you want to know its value. If I want to know the voltage level is 0 or 1 I can just take out my multimeter and check. There is just one single observable.

With a qubit, there are actually three observables: σ_x, σ_y, and σ_z. You can think of a qubit like a sphere where you can measure it along its x, y, or z axis. These often correspond in real life to real rotations, for example, you can measure electron spin using something called Stern-Gerlach apparatus and you can measure a different axis by physically rotating the whole apparatus.

How can a single 0 or 1 be associated with three different observables? Well, the qubit can only have a single 0 or 1 at a time, so, let’s say, you measure its value on the z-axis, so you measure σ_z, and you get 0 or 1, then the qubit ceases to have values for σ_x or σ_y. They just don’t exist anymore. If you then go measure, let’s say, σ_x, then you will get something entirely random, and then the value for σ_z will cease to exist. So it can only hold one bit of information at a time, but measuring it on a different axis will “interfere” with that information.

It’s thus not possible to actually know the values for all the different observables because only one exists at a time, but you can also use them in logic gates where one depends on an axis with no value. For example, if you measure a qubit on the σ_z axis, you can then pass it through a logic gate where it will flip a second qubit or not flip it because on whether or not σ_x is 0 or 1. Of course, if you measured σ_z, then σ_x has no value, so you can’t say whether or not it will flip the other qubit, but you can say that they would be correlated with one another (if σ_x is 0 then it will not flip it, if it is 1 then it will, and thus they are related to one another). This is basically what entanglement is.

Because you cannot know the outcome when you have certain interactions like this, you can only model the system probabilistically based on the information you do know, and because measuring qubits on one axis erases its value on all others, then some information you know about the system can interfere with (cancel out) other information you know about it. Waves also can interfere with each other, and so oddly enough, it turns out you can model how your predictions of the system evolve over the computation using a wave function which then can be used to derive a probability distribution of the results.

What is even more interesting is that if you have a system like this where you have to model it using a wave function, it turns out it can in principle execute certain algorithms exponentially faster than classical computers. So they are definitely nowhere near the same as classical computers. Their complexity scales up exponentially when trying to simulate quantum computers on a classical computer. Every additional qubit doubles the complexity, and thus it becomes really difficult to even simulate small numbers of qubits. I built my own simulator in C and it uses 45 gigabytes of RAM to simulate just 16. I think the world record is literally only like 56.

I feel like there is a pretty big gap between understanding how logic gates and truth tables work and understanding the underlying physics of how modern processors work.

Even if you believe there really exists a “hard problem of consciousness,” even Chalmers admits such a thing would have to be fundamentally unobservable and indistinguishable from something that does not have it (see his p-zombie argument), so it could never be something discovered by the sciences, or something discovered at all. Believing there is something immaterial about consciousness inherently requires an a priori assumption and cannot be something derived from a posteriori observational evidence.

We feel conscious and have an internal experience

It does not make sense to add the qualifier “internal” unless it is being contrasted with “external.” It makes no sense to say “I’m inside this house” unless you’re contrasting it with “as opposed to outside the house.” Speaking of “internal experience” is a bit odd in my view because it implies there is such thing as an “external experience”. What would that even be?

What about the p-zombie, the human person who just doesn’t have an internal experience and just had a set of rules, but acts like every other human?

The p-zombie argument doesn’t make sense as you can only conceive of things that are remixes of what you’ve seen before. I have never seen a pink elephant but I’ve seen pink things and I’ve seen elephants so I can remix them in my mind and imagine it. But if you ask me to imagine an elephant a color I’ve never seen before? I just can’t do it, I wouldn’t even know what that means. Indeed, a person blind since birth cannot “see” at all, not in their imagination, not even in their dreams.

The p-zombie argument asks us to conceive of two people that are not observably different in every way yet still different because one is lacking some property that the other has. But if you’re claiming you can conceive of this, I just don’t believe you. You’re probably playing some mental tricks on yourself to make you think you can conceive of it but you cannot. If there is nothing observably different about them then there is nothing conceivably different about them either.

What about a cat, who apparently has a less complex internal experience, but seems to act like we’d expect if it has something like that? What about a tick, or a louse? What about a water bear? A tree? A paramecium? A bacteria? A computer program?

This is what Thomas Nagel and David Chalmers ask and then settles on “mammals only” because they have an unjustified mammalian bias. Like I said, there is no “internal” experience, there is just experience. Nagel and Chalmers both rely on an unjustified premise that “point-of-view” is unique to mammalian brains because supposedly objective reality is point-of-view independent and since experience clearly has an aspect of point-of-view then that means experience too must be a product purely of mammalian brains, and then demands the “physicalists” prove how non-experiential reality gives rise to the experiential realm.

But the entire premise is arbitrary and wrong. Objective reality is not point-of-view independent. In general relativity, reality literally change depending on your point-of-view. Time passes a bit faster for people standing up than people sitting down, lengths of rulers can change between observers, velocity of objects can change as well. Relational quantum mechanics goes even further and shows that all variable properties of particles depend upon point-of-view.

The idea that objective reality is point-of-view independent is just entirely false. It is point-of-view dependent all the way down. Experience is just objective reality as it actually exists independent of the observer but dependent upon the point-of-view in which they occupy. It has nothing to do with mammalian brains, “consciousness,” or subjectivity. If reality is point-of-view dependent all the way down, then it is not even possible to conceive of an intelligent being that would occupy a unique point-of-view, because everything occupies their own unique point-of-view, even a rock. It’s not a byproduct of the “conscious mind” but just a property of objective reality: experience is objective reality independent of the observer, but dependent upon the context of that experience.

There’s a continuum one could construct that includes all those things and ranks them by how similar their behaviors are to ours, and calls the things close to us conscious and the things farther away not, but the line is ever going to be fuzzy. There’s no categorical difference that separates one end of the spectrum from the other, it’s just about picking where to put the line.

When you go down this continuum what gradually disappears is cognition, that is to say, the ability to think about, reflect upon, be self-aware of, one’s point-of-view. The point-of-viewness of reality, or more simply the contextual nature of reality, does not disappear at any point. Only the ability to talk about it disappears. A rock cannot tell you anything about what it’s like to be a rock from its context, it has no ability to reflect upon the point-of-view it occupies.

Although you’re right there is no hard-and-fast line for cognition, but that’s true of anything in nature. There’s no hard-and-fast line for anything. Take a cat for example, where does the cat begin and end, both in space in time? Create a rigorous definition of its borders. You won’t be able to do it. All our conceptions are human creations and therefore a bit fuzzy. Reality is infinitely complex and we cannot deal with the infinite complexity all at once so we break it up into chunks that are easier to work with: cats, dogs, trees, red, blue, hydrogen, helium, etc. But you always find when you look at these things a little more closely that their nature as discrete “things” becomes rather fuzzy and disappears.

You should look into contextual realism. You might find it interesting. It is a philosophical school from the philosopher Jocelyn Benoist that basically argues that the best way to solve most of the major philosophical problems and paradoxes (i.e. mind-body problem) is to presume the natural world is context variant all the way down, i.e. there simply is no reality independent of specifying some sort of context under which it is described (kind of like a reference frame).

The physicist Francois-Igor Pris points out that if you apply this thinking to quantum mechanics, then the confusion around interpreting it entirely disappears, because the wave function clearly just becomes a way of accounting for the context under which an observer is observing a system, and that value definiteness is just a context variant property, i.e. two people occupying two different contexts will not always describe the system as having the same definite values, but may describe some as indefinite which the other person describes as definite.

“Observation” is just an interaction, and by interacting with a system you are by definition changing your context, and thus you have to change your accounting for your context (i.e. the wave function) in order to make future predictions. Updating the wave function then just becomes like taring a scale, that is to say, it is like re-centering or “zeroing” your coordinate system, and isn’t “collapsing” anything physical. There is no observer-dependence in the sense that observers are somehow fundamental to nature, only that systems depend upon context and so naturally as an observer describing a system you have to take this into account.

Quantum mechanics is incompatible with general relativity, it is perfectly compatible with special relativity, however. I mean, that is literally what quantum field theory is, the unification of special relativity and quantum mechanics into a single framework. You can indeed integrate all aspects of relativity into quantum mechanics just fine except for gravity. It’s more that quantum mechanics is incompatible with gravity and less that it is incompatible with relativity, as all the other aspects we associate with relativity are still part of quantum field theory, like the passage of time being relative, relativity of simultaneity, length contraction, etc.