There is no “hard problem.” It’s made up. Nagel’s paper that Chalmers bases all his premises on is just awful and assumes for no reason at all that physical reality is something that exists entirely independently of one’s point of view within it, never justifies this bizarre claim and builds all of his arguments on top of it which then Chalmers cites as if they’re proven. “Consciousness” as Chalmers defines it doesn’t even exist and is just a fiction.

I feel like this is no different practically speaking than just saying its behavior is random, but anthropomorphizing it for some reason.

If there is an agent who is deciding it then that would show up in the statistics. Unless you’re saying there exists an agent who decides the outcomes but always just so happens to very conveniently decide they should be entirely random. lol

Many-worlds is nonsensical mumbo jumbo. It doesn’t even make sense without adding an additional unprovable postulate called the universal wave function. Every paper just has to assume it without deriving it from anywhere. If you take MWI and subtract away this arbitrary postulate then you get RQM. MWI - big psi = RQM. So RQM is inherently simpler.

Although the simplest explanation isn’t even RQM, but to drop the postulate that the world is time-asymmetric. If A causes B and B causes C, one of the assumptions of Bell’s theorem is that it would be invalid to say C causes B which then causes A, even though we can compute the time-reverse in quantum mechanics and there is nothing in the theory that tells us the time-reverse is not equally valid.

Indeed, that’s what unitary evolution means. Unitarity just means time-reversibility. You test if an operator is unitary by multiplying it by its own time-reverse, and if it gives you the identity matrix, meaning it completely cancels itself out, then it’s unitary.

If you just accept time-symmetry then it is just as valid to say A causes B as it is to say C causes B, as B is connected to both through a local causal chain of events. You can then imagine that if you compute A’s impact on B it has ambiguities, and if you compute C’s impact on B it also has ambiguities, but if you combine both together the ambiguities disappear and you get an absolutely deterministic value for B.

Indeed, it turns out quantum mechanics works precisely like this. If you compute the unitary evolution of a system from a known initial condition to an intermediate point, and the time-reverse of a known final condition to that intermediate point, you can then compute the values of all the observables at that intermediate point. If you repeat this process for all observables in the experiment, you will find that they evolve entirely locally and continuously. Entangled particles form their correlations when they locally interact, not when you later measure them.

But for some reason people would rather believe in an infinite multiverse than just accept that quantum mechanics is not a time-asymmetric theory.

cuz I would immediately die?

Speaking of predicting outcomes implies a forwards arrow of time. As far as we know, the arrow of time is a macroscopic feature of the universe and just doesn’t exist at a fundamental level. You cannot explain it with entropy without appealing to the past hypothesis, which then requires appealing to the Big Bang, which is in and of itself an appeal to general relativity, something which is not part of quantum mechanics.

Let’s say we happen to live in a universe where causality is genuinely indifferent to the arrow of time. This doesn’t mean such a universe would have retrocausality, because retrocausality is just causality with an arrow facing backwards. If its causal structure was genuinely independent of the arrow of time, then its causal structure would follow what the physicist Emily Adlam refers to as global determinism and an "all-at-once* structure of causality.

Such a causal model would require the universe’s future and past to follow certain global consistency rules, but each taken separately would not allow you to derive the outcomes of systems deterministically. You would only ever be able to describe the deterministic evolution of a system retrospecitvely, when you know its initial and final state, and then subject it to those consistency rules. Given science is usually driven by predictive theories, it would thus be useless in terms of making predictions, as in practice we’re usually only interested in making future predictions and not giving retrospective explanations.

If the initial conditions aren’t sufficient to predict the future, then any future prediction based on an initial state, not being sufficient to constrain the future state to a specific value, would lead to ambiguities, causing us to have to predict it probabilistically. And since physicists are very practically-minded, everyone would focus on the probabilistic forwards-evolution in time, and very few people would be that interested in reconstructing the state of the system retrospectively as it would have no practical predictive benefit.

I bring this all up because, as the physicists Ken Wharton, Roderick Sutherland, Titus Amza, Raylor Liu, and James Saslow have pointed out, you can quite easily reconstruct values for all the observables in the evolution of system retrospectively by analyzing its weak values, and those values appear to evolve entirely locally, deterministically, and continuously, but doing so requires conditioning on both the initial and final state of the system simultaneously and evolving both ends towards that intermediate point to arrive at the value of the observable at that intermediate point in time. You can therefore only do this retrospectively.

This is already built into the mathematics. You don’t have to add any additional assumptions. It is basically already a feature of quantum mechanics that if you evolve a known eigenstate at t=-1 and a known eigenstate at t=1 and evolve them towards each other simultaneously until they intersect at t=0, at the interaction you can seemingly compute the values of the observables at t=0. Even though the laws of quantum mechanics do not apply sufficient constraints to recover the observables when evolving them in a single direction in time, either forwards or backwards, if you do both simultaneously it gives you those sufficient constraints to determine a concrete value.

Of course, there is no practical utility to this, but we should not necessarily confuse practicality with reality. Yes, being able to retrospectively reconstruct the system’s local and deterministic evolution is not practically useful as science is more about future prediction, but we shouldn’t declare from this practical choice that therefore the system has no deterministic dynamics, that it has no intermediate values and when it’s in a superposition of states it has no physical state at all or is literally equivalent to its probability distribution (a spread out wave in phase space). You are right that reconstructing the history of the system doesn’t help us predict outcomes better, but I don’t agree it doesn’t help us understand reality better.

Take all the “paradoxes” for example, like the Einstein-Podolsky-Rosen paradox or, my favorite, the Frauchiger–Renner paradox. These are more conceptual problems dealing with an understanding of reality and ultimately your answer to them doesn’t change what predictions you make with quantum mechanics in any way. Yet, I still think there is some benefit, maybe on a more philosophical level, of giving an answer to those paradoxes. If you reconstruct the history of the systems with weak values for example, then out falls very simple solutions to these conceptual problems because you can actually just look directly at how the observables change throughout the system as it evolves.

Not taking retrospection seriously as a tool of analysis leads to people believing in all sort of bizarre things like multiverses or physically collapsing wave functions, that all disappear if you just allow for retrospection to be a legitimate tool of analysis. It might not be as important as understanding the probabilistic structure of the theory that is needed for predictions, but it can still resolve confusions around the theory and what it implies about physical reality.

According to our current model, we would probably observe un-collapsed quantum field waves, which is a concept inaccessible from within the universe, and could very well just be an artifact of the model instead of ground truth.

It so strange to me that this is the popular way people think about quantum mechanics. Without reformulating quantum mechanics in any way or changing any of its postulates, the theory already allows you to recover the intermediate values of all the observables in any system through retrospection, and it evolves locally and deterministically.

The “spreading out as a wave” isn’t a physical thing, but an epistemic one. The uncertainty principle makes it such that you can’t accurately predict the outcome of certain interactions, and the probability distribution depends upon the phase, which is the relative orientation between your measurement basis and the property you’re trying to measure. The wave-like statistical behavior arises from the phase, and the wave function is just a statistical tool to keep track of the phase.

The “collapse” is not a physical process but a measurement update. Measurements aren’t fundamental to quantum mechanics. It is just that when you interact with something, you couple it to the environment, and this coupling leads to the effects of the phase spreading out to many particles in the environment. The spreading out of the influence of the phase dilutes its effects and renders it negligible to the statistics, and so the particle then briefly behaves more classically. That is why measurement causes the interference pattern to disappear in the double-slit experiment, not because of some physical “collapsing waves.”

People just ignore the fact that you can use weak values to reconstruct the values of the observables through any quantum experiment retrospectively, which is already a feature baked into the theory and not something you need to add, and then instead choose to believe that things are somehow spreading out as waves when you’re not looking at them, which leads to a whole host of paradoxes: the Einstein-Podolsky-Rosen paradox, the Wigner’s friend paradox, the Frauchiger-Renner paradox, etc.

Literally every paradox disappears if we stop pretending that systems are literally waves and that the wave-like behavior is just the result of the relationship between the phase and the statistical distribution of the system, and that the waves are ultimately a weakly emergent phenomena. We only see particle waves made up of particles. No one has ever seen a wave made up of nothing. Waves of light are made up of photons of light, and the wave-like behavior of the light is a weakly emergent property of the wave-like statistical distributions you get due to the relationship between the statistical uncertainty and the phase. It in no way implies everything is literally made up waves that are themselves made of nothing.

The decision that your brain’s decisions are due to chemical reactions, which itself would be due to chemicals reactions, is self-referential but not circular reasoning.

That’s a classical ambiguity, not a quantum ambiguity. It would be like if I placed a camera that recorded when cars arrived but I only gave you information on when it detected a car and at what time and no other information, not even providing you with the footage, and asked you to derive which car came first. You can’t because that’s not enough information.

The issue here isn’t a quantum mechanical one but due to the resolution of your detector. In principle if it was precise enough, because the radiation emanates from different points, you could figure out which one is first because there would be non-overlapping differences. This is just a practical issue due to the low resolution of the measuring device, and not a quantum mechanical ambiguity that couldn’t be resolved with a more precise measuring apparatus.

A more quantum mechanical example is something like if you apply the H operator twice in a row and then measure it, and then ask the value of the qubit after the first application. It would be in a superposition of states which describes both possibilities symmetrically so the wavefunction you derive from its forwards-in-time evolution is not enough to tell you anything about its observables at all, and if you try to measure it at the midpoint then you also alter the outcome at the final point, no matter how precise the measuring device is.

Let’s say the initial state is at time t=x, the final state is at time t=z, and the state we’re interested in is at time t=y where x < y < z.

In classical mechanics you condition on the initial known state at t=x and evolve it up to the state you’re interested in at t=y. This works because the initial state is a sufficient constraint in order to guarantee only one possible outcome in classical mechanics, and so you don’t need to know the final state ahead of time at t=z.

This does not work in quantum mechanics because evolving time in a single direction gives you ambiguities due to the uncertainty principle. In quantum mechanics you have to condition on the known initial state at t=x and the known final state at t=z, and then evolve the initial state forwards in time from t=x to t=y and the final state backwards in time from t=z to t=y where they meet.

Both directions together provide sufficient constraints to give you a value for the observable.

I can’t explain it in more detail than that without giving you the mathematics. What you are asking is ultimately a mathematical question and so it demands a mathematical answer.

I am not that good with abstract language. It helps to put it into more logical terms.

It sounds like what you are saying is that you begin with something a superposition of states like (1/√2)(|0⟩ + |1⟩) which we could achieve with the H operator applied to |0⟩ and then you make that be the cause of something else which we would achieve with the CX operator and would give us (1/√2)(|00⟩ + |11⟩) and then measure it. We can call these t=0 starting in the |00⟩ state, then t=1 we apply H operator to the least significant, and then t=2 is the CX operator with the control on the least significant.

I can’t answer it for the two cats literally because they are made up it a gorillion particles and computing it for all of them would be computationally impossible. But in this simple case you would just compute the weak values which requires you to also condition on the final state which in this case the final states could be |00⟩ or |11⟩. For each observable, let’s say we’re interested in the one at t=x, you construct your final state vector by starting on this final state, specifically its Hermitian transpose, and multiplying it by the reversed unitary evolution from t=2 to t=x and multiply that by the observable then multiply that by the forwards-in-time evolution from t=0 to t=x multiplied by the initial state, and then normalize the whole thing by dividing it by the Hermitian transpose of the final state times the whole reverse time evolution from t=2 to t=0 and then by the final state.

In the case where the measured state at t=3 is |00⟩ we get for the observables (most significant followed by least significant)…

• t=0: (0,0,+1);(+1,+i,+1)
• t=1: (0,0,+1);(+1,-i,+1)
• t=2: (0,0,+1);(0,0,+1)

In the case where the measured state at t=3 is |11⟩ we get for the observables…

• t=0: (0,0,+1);(-1,-i,+1)
• t=1: (0,0,+1);(+1,+i,-1)
• t=2: (0,0,-1);(0,0,-1)

The values |0⟩ and |1⟩ just mean that the Z observable has a value of +1 or -1, so if we just look at the values of the Z observables we can rewrite this in something a bit more readable.

• |00⟩ → |00⟩ → |00⟩
• |00⟩ → |01⟩ → |11⟩

Even though the initial conditions both began at |00⟩ they have different values on their other observables which then plays a role in subsequent interactions. The least significant qubit in the case where the final state is |00⟩ begins with a different signage on its Y observable than in the case when the outcome is |11⟩. That causes the H opreator to have a different impact, in one case it flips the least significant qubit and in another case it does not. If it gets flipped then, since it is the control for the CX operator, it will flip the most significant qubit as well, but if it’s not then it won’t flip it.

Notice how there is also no t=3, because t=3 is when we measure, and the algorithm guarantees that the values are always in the state you will measure before you measure them. So your measurement does reveal what is really there.

If we say |0⟩ = no sleepy gas is released and the cat is awake, and |1⟩ = sleepy gas is released and the cat go sleepy time, then in the case where both cats are observed to be awake when you opened the box, at t=1: |00⟩ meaning the first one’s sleepy gas didn’t get released, and so at t=2: |00⟩ it doesn’t cause the other one’s to get released. In the case where both cats are observed to be asleep when you open the box, then t=1: |01⟩ meaning the first one’s did get released, and at t=2: |11⟩ that causes the second’s to be released.

When you compute this algorithm you find that the values of the observables are always set locally. Whenever two particles interact such that they become entangled, then they will form correlations for their observables in that moment and not later when you measure them, and you can even figure out what those values specifically are.

To borrow an analogy I heard from the physicist Emily Adlam, causality in quantum mechanics is akin to filling out a Sudoku puzzle. The global rules and some “known” values constrains the puzzle so that you are only capable of filling in very specific values, and so the “known” values plus the rules determine the rest of the values. If you are given the initial and final conditions as your “known” values plus the laws of quantum mechanics as the global rules constraining the system, then there is only one way you can fill in these numbers, those being the values for the observables.

“Free will” usually refers to the belief that your decisions cannot be reduced to the laws of physics (e.g. people who say “do you really think your thoughts are just a bunch of chemical reactions in the brain???”), either because they can’t be reduced at all or that they operate according to their own independent logic. I see no reason to believe that and no evidence for it.

Some people try to bring up randomness but even if the universe is random that doesn’t get you to free will. Imagine if the state forced you to accept a job for life they choose when you turn 18, and they pick it with a random number generator. Is that free will? Of course not. Randomness is not relevant to free will. I think the confusion comes from the fact that we have two parallel debates of “free will vs determinism” and “randomness vs determinism” and people think they’re related, but in reality the term “determinism” means something different in both contexts.

In the “free will vs determinism” debate we are talking about nomological determinism, which is the idea that reality is reducible to the laws of physics and nothing more. Even if those laws may be random, it would still be incompatible with the philosophical notion of “free will” because it would still be ultimately the probabilistic mathematical laws that govern the chemical reactions in your brain that cause you to make decisions.

In the “randomness vs determinism” debate we are instead talking about absolute determinism, sometimes also called Laplacian determinism, which is the idea that if you fully know the initial state of the universe you could predict the future with absolute certainty.

These are two separate discussions and shouldn’t be confused with one another.

In a sense it is deterministic. It’s just when most people think of determinism, they think of conditioning on the initial state, and that this provides sufficient constraints to predict all future states. In quantum mechanics, conditioning on the initial state does not provide sufficient constraints to predict all future states and leads to ambiguities. However, if you condition on both the initial state and the final state, you appear to get determinstic values for all of the observables. It seems to be deterministic, just not forwards-in-time deterministic, but “all-at-once” deterministic. Laplace’s demon would just need to know the very initial conditions of the universe and the very final conditions.

Many Worlds is an incredibly bizarre point of view.

Quantum mechanics has two fundamental postulates, that being the Schrodinger equation and the Born rule. It’s impossible to get rid of the Born rule in quantum mechanics as shown by Gleason’s Theorem, it’s an inevitable consequence of the structure of the theory. But Schrodinger’s equation implies that systems can undergo unitary evolution in certain contexts, whereas the Born rule implies systems can undergo non-unitary evolution in other contexts.

If we just take this as true at face value, then it means the wave function is not fundamental because it can only model unitary evolution, hence why you need the measurement update hack to skip over non-unitary transformations. It is only a convenient shorthand for when you are solely dealing with unitary evolution. The density matrix is then more fundamental because it is a complete description which can model both unitary and non-unitary transformations without the need for measurement update, “collapse,” and does so continuously and linearly.

However, MWI proponents have a weird unexplained bias against the Born rule and love for unitary evolution, so they insist the Born rule must actually just be due to some error in measurement, and that everything actually evolves unitarily. This is trivially false if you just take quantum mechanics at face value. The mathematics at face value unequivocally tells you that both kinds of evolution can occur under different contexts.

MWI tries to escape this by pointing out that because it’s contextual, i.e. “perspectival,” you can imagine a kind of universal perspective where everything is unitary. For example, in the Wigner’s friend scenario, for his friend, he would describe the particle undergoing non-unitary evolution, but for Wigner, he would describe the system as still unitary from his “outside” perspective. Hence, you can imagine a cosmic, godlike perspective outside of everything, and from it, everything would always remain unitary.

The problem with this is Hilbert space isn’t a background space like Minkowski space where you can apply a perspective transformation to something independent of any physical object, which is possible with background spaces because they are defined independently of the relevant objects. Hilbert space is a constructed space which is defined dependently upon the relevant objects. Two different objects described with two different wave functions would be elements of different Hilbert spaces.

That means perspective transformations are only possible to the perspective of other objects within your defined Hilbert space, you cannot adopt a “view from nowhere” like you can with a background space, so there is just nothing in the mathematics of quantum mechanics that could ever allow you to mathematically derive this cosmic perspective of the universal wave function. You could not even define it, because, again, a Hilbert space is defined in terms of the objects it contains, and so a Hilbert space containing the whole universe would require knowing the whole universe to even define it.

The issue is that this “universal wave function” is neither mathematically definable nor derivable, so it only has to be postulated, as well as its mathematical properties postulates, as a matter of fiat. Every single paper on MWI ever just postulates it entirely by fiat and defines by fiat what its mathematical properties are. Because the Born rule is inevitable form the logical structure of quantum theory, these mathematical properties always include something basically just the same as the Born rule but in a more roundabout fashion.

None of this plays any empirical role in the real world. The only point of the universal wave function is so that whenever you perceive non-unitary evolution, you can clasp your hands together and pray, “I know from the viewpoint of the great universal wave function above that is watching over us all, it is still unitary!” If you believe this, it still doesn’t play any role in how you would carry out quantum mechanics, because you don’t have access to it, so you still have to treat it as if from your perspective it’s non-unitary.