pcalau12i

@pcalau12i@lemmygrad.ml

• ⁨Comment⁩ on ⁨It's not supposed to make sense...⁩ ⁨⁨4⁩ ⁨weeks⁩ ago⁩:

  I think it’s boring honestly. It’s a bit strange how like, the overwhelming majority of people either avoid interpreting quantum theory at all (“shut up and calculate”) or use it specifically as a springboard to justify either sci-fi nonsense (multiverses) or even straight8-up mystical nonsense (consciousness induced collapse). Meanwhile, every time there is a supposed “paradox” or “no-go theorem” showing you can’t have a relatively simple explanation for something, someone in the literature publishes a paper showing it’s false, and then only the paper showing how “weird” QM is gets media attention. I always find myself on the most extreme fringe of the fringe of thinking both that (1) we should try to interpret QM, and (2) we should be extremely conservative about our interpretation so we don’t give up classical intuitions unless we absolutely have to. That seems to be considered an extremist fringe position these days.

• ⁨Comment⁩ on ⁨It's not supposed to make sense...⁩ ⁨⁨4⁩ ⁨weeks⁩ ago⁩:

  The double-slit experiment doesn’t even require quantum mechanics. It can be explained classically and intuitively.

  It is helpful to think of a simpler case, the Mach-Zehnder interferometer, since it demonstrates the same effect but where where space is discretized to just two possible paths the particle can take and end up in, and so the path/position is typically described with just with a single qubit of information: |0⟩ and |1⟩.

  You can explain this entirely classical if you stop thinking of photons really as independent objects but just specific values propagating in a field, what are sometimes called modes. If you go to measure a photon and your measuring device registers a |1⟩, this is often interpreted as having detected the photon, but if it measures a |0⟩, this is often interpreted as not detecting a photon, but if the photons are just modes in a field, then |0⟩ does not mean you registered nothing, it means that you indeed measured the field but the field just so happens to have a value of |0⟩ at that location.

  Since fields are all-permeating, then describing two possible positions with |0⟩ and |1⟩ is misleading because there would be two modes in both possible positions, and each independently could have a value of |0⟩ or |1⟩, so it would be more accurate to describe the setup with two qubits worth of information, |00⟩, |01⟩, |10⟩, and |11⟩, which would represent a photon being on neither path, one path, the other path, or both paths (which indeed is physically possible in the real-world experiment).

  When systems are described with |0⟩ or |1⟩, that is to say, 1 qubit worth of information, that doesn’t mean they contain 1 bit of information. They actually contain as much as 3 as there are other bit values on orthogonal axes. You then find that the physical interaction between your measuring device and the mode perturbs one of the values on the orthogonal axis as information is propagating through the system, and this alters the outcome of the experiment.

  You can interpret the double-slit experiment in the exact same way, but the math gets a bit more hairy because it deals with continuous position, but the ultimate concept is the same.

  A measurement is a kind of physical interaction, and all physical interactions have to be specified by an operator, and not all operators are physically valid. Quantum theory simply doesn’t allow you to construct a physically valid operator whereby one system could interact with another to record its properties in a non-perturbing fashion. Any operator you construct to record one of its properties without perturbing it must necessarily perturb its other properties. Specifically, it perturbs any other property within the same noncommuting group.

  When the modes propagate from the two slits, your measurement of its position disturbs its momentum, and this random perturbation causes the momenta of the modes that were in phase with each other to longer be in phase. You can imagine two random strings which you don’t know what they are but you know they’re correlated with each other, so whatever is the values of the first one, whatever they are, they’d be correlated with the second. But then you randomly perturb one of them to randomly distribute its variables, and now they’re no longer correlated, and so when they come together and interact, they interact with each other differently.

  There’s a paper on this here and also a lecture on this here. You don’t have to go beyond the visualization or even mathematics of classical fields to understand the double-slit experiment.

• ⁨Comment⁩ on ⁨It's not supposed to make sense...⁩ ⁨⁨4⁩ ⁨weeks⁩ ago⁩:

  Why interpret it as either? The double-slit experiment can be given an entirely classical explanation. Such extravagances are not necessary.

• ⁨Comment⁩ on ⁨It's not supposed to make sense...⁩ ⁨⁨4⁩ ⁨weeks⁩ ago⁩:

  My impression from the literature is that superdeterminism is not the position of rejecting an asymmetrical arrow of time. In fact, it tries to build a model that can explain violations of Bell inequalities completely from the initial conditions evolved forwards in time.

  Let’s imagine you draw a coin from box A and it’s random, and you draw coins from box B and it’s random, but you find a peculiar feature where if you switch from A to B, the first coin you draw from B is always the last you drew from A, and then it goes back to being random. You repeat this many times and it always seems to hold. How is that possible if they’re independent of each other?

  Technically, no matter how many coins you draw, the probability of it occurring just by random chance is never zero. It might get really really low, but it’s not zero. A very specific initial configuration of the coins could reproduce that.

  Superdeterminism is just the idea that there are certain laws of physics that restrict the initial configurations of particles at the very beginning of the universe, the Big Bang, to guarantee their evolution would always maintain certain correlations that allow them to violate Bell inequalities. It’s not really an interpretation because it requires you to posit these laws, and so it really becomes a new theory since you have to introduce new postulates, but such a theory would in principle then allow you to evolve the system forwards from its initial conditions in time to explain every experimental outcome.

  As a side note, you can trivially explain violations of Bell inequalities in local realist terms without even introducing anything new to quantum theory just by abandoning the assumption of time-asymmetry. This is called the Two-State Vector Formalism and it’s been well-established in the literature for decades. If A causes B and B causes C, in the time-reverse, C causes B and B causes A. if you treat both as physically real, then B would have enough constraints placed upon it by A and C taken together (by evolving the wave function from both ends to where they meet at B) to violate Bell inequalities.

  That’s already pretty much a feature built-in to quantum theory and allows you to interpret it in local realist terms if you’d like, but it requires you to accept that the microscopic world is genuinely indifferent to the arrow-of-time and the time-forwards and the time-reversed evolution of a system are both physically real.

  However, this time-symmetric view is not superdeterminism. Superdeterminism is time-asymmetric just like most every other viewpoint (Copenhagen, MWI, pilot wave, objective collapse, etc). Causality goes in one temporal direction and not the other. The time-symmetric interpretation is its own thing and is mathematically equivalent to quantum mechanics so it is an actual interpretation and not another theory.

• ⁨Comment⁩ on ⁨It's not supposed to make sense...⁩ ⁨⁨4⁩ ⁨weeks⁩ ago⁩:

  The problem with pilot wave is it’s non-local, and so it contradicts with special relativity and cannot be made directly compatible with the predictions of quantum field theory. The only way to make it compatible would be to throw out special relativity and rewrite a whole new theory of spacetime with a preferred foliation built in that could reproduce the same predictions as special relativity, and so you end up basically having to rewrite all of physics from the ground-up.

  I also disagree that it’s intuitive. It’s intuitive when we’re talking about the trajectories of particles, but all its intuition disappears when we talk about any other property at all, like spin. You don’t even get a visualization of what’s going on at all when dealing with quantum circuits.

  Personally, I find the most intuitive interpretation a modification of the Two-State Vector Formalism where you replace the two state vectors with two vectors of expectation values. This gives you a very unambiguous and concrete picture of what’s going on. Due to the uncertainty principle, you always start with limited information on the system, you build out a list of expectation values assigned to each observable, and then take into account how those will swap around as the system evolves (for example, if you know X=+1 but don’t know Y, and an interaction has the effect of swapping X with Y, then now you know Y=+1 and don’t know X).

  This alone is sufficient to reproduce all of quantum mechanics, but it still doesn’t explain violations of Bell inequalities. You explain that by just introducing a second vector of expectation values to describe the final state of the system and evolve it backwards in time. This applies sufficient constraints on the system to explain violations of Bell inequalities in local realist terms, without having to introduce anything to the theory and with a largely classical picture.

• ⁨Comment⁩ on ⁨It's not supposed to make sense...⁩ ⁨⁨4⁩ ⁨weeks⁩ ago⁩:

  Quantum mechanics becomes massively simpler to interpret once you recognize that the wave function is just a compressed list of expectation values for the observables of a system. An expectation value is like a weighted probability. They can be negative because the measured values can be negative, such as fo qubits the measured values can be either +1 or -1, and if you weight by -1 then it can become negative. For example, an expectation value of -0.5 means there is a 25% chance of +1 and a 75% of -1.

  It’s like, if I know for certain that X=+1 but I have no idea what Y is, and the physical system interacts with something that we know will have the effect of swapping its X and Y components around, then this would also swap my uncertainty around so now I would know that Y=+1 without knowing what X is. Hence, if you don’t know the complete initial conditions of a system, you can represent it with a list of all of possible observables and assign each one an expectation value related to your certainty of measuring that value, and then compute how that certainty is shifted around as the system evolves.

  The wave function then just becomes a compressed form of this. For qubits, the expectation value vector grows at a rate of 4^N where N is the number of qubits, but the uncertainty principle limits the total bits of information you can have at a single time to 2^N, so the vector is usually mostly empty (a lot of zeros). This allows you to mathematically compress it down to a wave function that also grows by 2^N, making it the most concise way to represent this.

  But the notation often confuses people, they think it means particles are in two places at once, that qubits are 0 and 1 at the same time, that there is some “collapse” that happens when you make a measurement, and they frequently ask what the imaginary components mean. But all this confusion just stems from notation. Any wave function can be expanded into a real-valued list of expectation values and you can evolve that through the system rather than the wave function and compute the same results, and then the confusion of what it represents disappears.

  When you write it out in this expanded form, it’s also clear why the uncertainty principle exists in the first place. A measurement is a kind of physical interaction between a record-keeping system and the recorded system, and it should result in information from the recorded system being copied onto the record-keeping system. Physical interactions are described by an operator, and quantum theory has certain restrictions on qualifies as a physically valid operator: it has to be time-reversible, preserve handedness, be completely positive, etc, and these restrictions prevent you from constructing an operator that can copy a value of an observable from one system onto another in a way that doesn’t perturb the its other observables.

  Most things in quantum theory that are considered “weird” are just misunderstandings, some of which can even be reproduced classically. Things like double-slit, Mach–Zehnder interferometer, the Elitzur–Vaidman “paradox,” the Wigner’s friend “paradox,” the Schrodinger’s cat “paradox,” the Deutsch algorithm, quantum encryption and key distribution, quantum superdense coding, etc, can all be explained entirely classically just by clearing up some confusion about the notation.

  This narrows it down to only a small number of things that genuinely raise an eyebrow, those being cases that exhibit what is sometimes called quantum contextuality, such as violations of Bell inequalities. It inherently requires a non-classical explanation for this, but I don’t think that also means it can’t be something understandable.

  The simplest explanation I have found in the literature is that of time-symmetry. It is a requirement in quantum mechanics that every operator is time-symmetric, and that famously leads to the problem of establishing an arrow of time in quantum theory. Rather than taking it to be a problem, we can instead presume that there is a good reason nature demands all its microscopic operators are time-symmetric: because the arrow of time is a macroscopic phenomena, not a microscopic one.

  If you have a set of interactions between microscopic particles where A causes B and B causes C, if I played the video in the reverse, it is mathematically just as valid to say that C causes B and B causes A. Most people then introduce an additional postulate that says “even though it is mathematically valid, it’s not physically valid, we should only take the evolution of the system in a single direction of time seriously.” You can’t derive that postulate from quantum theory, you just have to take it on faith.

  If we drop that postulate and take the local evolution of the system seriously in both its time-forwards evolution and its time-reversed evolution, then you can explain violations of Bell inequalities without having to add anything to the theory at all, and interpret it completely in intuitive local realist terms. You do this using the Two-State Vector Formalism where all you do is compute the evolution of the wave function (or expectation values) from both ends until they meet at an intermediate point, and that gives you enough constraints to deterministically derive a weak value at that point. The weak value is a physical variable that evolves locally and deterministically with the system and contains sufficient information to determine its expectation values.

  You still can’t always assign a definite value, but these expectation values are epistemic, there is no contradiction with there being a definite value as the weak value contains all the information needed for the correct expectation values, and therefore the correct probability distribution, locally within the particle.

  In terms of computation, it’s very simple, because for the time-reverse evolution you just treat the final state as the initial state and then apply the operators in reverse with their time-symmetric equivalents (Hermitian transpose) and then the weak value equation looks exactly like the expectation value equation except rather than having the same wave function on both ends of the observable, you have the reverse-evolved wave function on one end of the observable and the forwards-evolved wave function on the other.

  Nothing about this is hard to visualize because you just imagine playing a moving forwards and also playing it in the reverse, and in both directions you get a local causal chain of interactions between the particles. If A causes B and B causes C in the time-forwards movie, playing the movie in reverse you will see C cause B which then causes A. That means B is both caused by A and C, and thus is influenced by both through a local chain of interactions. There is nothing “special” going on in the backwards evolution, the laws of physics are symmetrical to visually it is not distinguishable from its forwards evolution, so you visualize it the exact same way.

  That is enough to explain QM in local realist terms, and has been well-established in the literature for decades, but people often seem to favor explanations that are impossible to visualize, like treating the wave function as a literal object despite it being, at times, even infinite-dimensional or even believing we all live in an infinite-dimensional multiverse.

• ⁨Comment⁩ on ⁨ETERNAL TORMENT⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  There are no “paradoxes of quantum mechanics.” QM is a perfectly internally consistent theory. Most so-called “paradoxes” are just caused by people not understanding it.

  QM is both probabilistic and, in its own and very unique way, relative. Probability on its own isn’t confusing, if the world was just fundamentally random you could still describe it in the language of classical probability theory and it wouldn’t be that difficult. If it was just relative, it can still be a bit of a mind-bender like special relativity with its own faux paradoxes (like the twin “paradox”) that people struggle with, but ultimately people digest it and move on.

  But QM is probabilistic and relative, and for most people this becomes very confusing, because it means a particle can take on a physical value in one perspective while not having taken on a physical value in another (why is called the relativity of facts in the literature), and not only that, but because it’s fundamentally random, if you apply a transformation to try to mathematically place yourself in another perspective, you don’t get definite values but only probabilistic ones, albeit not in a superposition of states.

  For example, the famous “Wigner’s friend paradox” claims there is a “paradox” because you can setup an experiment whereby Wigner’s friend would assign a particle a real physical value whereas Wigner would be unable to from his perspective and would have to assign an entangled superposition of states to both his friend and the particle taken together, which has no clear physical meaning.

  However, what the supposed “paradox” misses is that it’s not paradoxical at all, it’s just relative. Wigner can apply a transformation in Hilbert space to compute the perspective of his friend, and what he would get out of that is a description of the particle that is probabilistic but not in a superposition of states. It’s still random because nature is fundamentally random so he cannot predict what his friend would see with absolute certainty, but he can predict it probabilistic, and since this probability is not a superposition of states, what’s called a maximally mixed state, which is basically a classical probability distribution.

  But you only get those classical distributions after applying the transformation to the correct perspective where such a distribution is to be found, i.e. what the mathematics of the theory literally implies is that only under some perspectives (defined in terms of any physical system at all, kind of like a frame of reference, nothing to do with human observers) are the physical properties of the system actually realized, while under some other perspectives, the properties just aren’t physically there.

  The Schrodinger’s cat “paradox” is another example of a faux paradox. People repeat it as if it is meant to explain how “weird” QM is, but when Schrodinger put it forward in his paper “The Present Situation in Quantum Mechanics,” he was using it to mock the idea of particles literally being in two states at once, by pointing out that if you believe this, then a chain reaction caused by that particle would force you to conclude cats can be in two states at once, which, to him, was obviously silly.

  If the properties of particles only exist in some perspectives and aren’t absolute, then a particle can’t meaningfully have “individually,” that is to say, you can’t define it in complete isolation. In his book “Science and Humanism,” Schrodinger talks about how, in classical theory, we like to imagine particles as having their own individual existence, moving around from interaction to interaction, carrying their properties with themselves at all times. But, as Schrodinger points out, you cannot actually empirically verify this.

  If you believe particles have continued existence in between interactions, this is only possible if the existence of their properties are not relative so they can be meaningfully considered to continue to exist even when entirely isolated. Yet, if they are isolated, then by definition, they are not interacting with anything, including a measuring device, so you can never actually empirically verify they have a kind of autonomous individual existence.

  Schrodinger pointed out that many of the paradoxes in QM carry over from this Newtonian way of thinking, that particles move through space with their own individual properties like billiard balls flying around. If this were to be the case, then it should be possible to assign a complete “history” to the particle, that is to say, what its individual properties are at all moments in time without any gaps, yet, as he points out in that book, any attempt to fill in the “gaps” leads to contradiction.

  One of these contradictions is the famous “delayed choice” paradox, whereby if you imagine what the particle is doing “in flight” when you change your measurement settings, you have to conclude the particle somehow went back in time to rewrite the past to change what it is doing. However, from Schrodinger’s perspective, this is not a genuine “paradox” but just a flaw of actually interpreting the particle as having a Newtonian-style autonomous existence, of having “individuality” as he called it.

  He also points out in that book that when he originally developed the Schrodinger equation, the purpose was precisely to “fill in the gaps,” but he realized later that interpreting the evolution of the wave function according to the Schrodinger equation as a literal physical description of what’s going on is a mistake, because all you are doing is pushing the “gap” from those that exist between interactions in general to those that exist between measurement, and he saw no reason as to why “measurement” should play an important role in the theory. Given that it is possible t make all the same predictions without using the wave function (using a mathematical formalism called matrix mechanics), you don’t have to reify the wave function because it’s just a result of an arbitrarily chosen mathematical formalism, and so Schrodinger cautioned against reifying it, because it leads directly to the measurement problem.

  The EPR “paradox” is a metaphysical “paradox.” We know for certain QM is empirically local due to the no-communication theorem, which proves that no interaction a particle could undergo could ever cause an observation alteration in its entangled pair. Hence, if there is any nonlocality, it must be invisible to us, i.e. entirely metaphysical and not physical. The EPR paper reaches the “paradox” through a metaphysical criterion it states very clearly on the first page, which is to equate the ontology of a system to its eigenstates (to “certainty”). This makes it seem like the theory is nonlocal because entangled particles are not in eigenstates, but if you measure one, both are suddenly in eigenstates, which makes it seem like they both undergo an ontological transition simultaneously, transforming from not having a physical state to having one at the same time, regardless of distance.

  However, if particles only have properties relative to what they are physically interacting with, from that perspective, then ontology should be assigned to interaction, not to eigenstates. Indeed, assigning it to “certainty” as the EPR paper claims is a bit strange. If I flip a coin, even if I can predict the outcome with absolute certainty by knowing all of its initial conditions, that doesn’t mean the outcome actually already exists in physical reality. To exist in physical reality, the outcome must actually happen, i.e. the coin must actually land. Just because I can predict the particle’s state at a distance if I were to travel there and interact with it doesn’t mean it actually has a physical state from my perspective.

  I would recommend checking out this paper here which shows how a relative ontology avoids the “paradox” in EPR. I also wrote my own blog post here which if you go to the second half it shows some tables which walk through how the ontology differs between EPR and a relational ontology and how the former is clearly nonlocal while the latter is clearly local.

  Some people frame Bell’s theorem as a “paradox” that proves some sort of “nonlocality,” but if you understand the mathematics it’s clear that Bell’s theorem only implies nonlocality for hidden variable theories. QM isn’t a hidden variable theory. It’s only a difficulty that arises in alternative theories like pilot wave theory, which due to their nonlocal nature have to come up with a new theory of spacetime because they aren’t compatible with special relativity due to the speed of light limit. However, QM on its own, without hidden variables, is indeed compatible with special relativity, which forms the foundations of quantum field theory. This isn’t just my opinion, if you go read Bell’s own paper himself where he introduces the theorem, he is blatantly clear in the conclusion, in simple English language, that it only implies nonlocality for hidden variable theories, not for orthodox QM.

  Some “paradoxes” just are much more difficult to catch because they are misunderstandings of the mathematics which can get hairy at times. The famous Frauchiger–Renner “paradox” for example stems from incorrect reasoning across incompatible bases, a very subtle point lost in all the math. The Cheshire cat “paradox” tries to show particles can dissassicate from their properties, but those properties only “dissociate” across different experiments, meaning in no singular experiment are they observed to “dissociate.”