bunchberry

@bunchberry@lemmy.world

• ⁨Comment⁩ on ⁨Test of a prototype quantum internet runs under New York City for half a month⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

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become statistically correlated with one another and knowing the state of one tells you the state of the other, it is no longer valid to assign a state vector to the system subsystems that are part of the interaction individually, you have to assign it to the system as a whole.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

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

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

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

  Yet, this description only works from Eve’s point of view. From Alice and Bob’s point of view, neither of them measured the particle in transit, so when Bob received it, it still is probabilistic with an equal chance of being 0 and 1. So why does Bob receive different outcomes?

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

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

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

  Bob simply cannot explain why his qubit loses its interference effects by Eve measuring it without entanglement, at least within the framework of quantum theory. That is just how the theory works.

• ⁨Comment⁩ on ⁨Quantum physics⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  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. You can also do a similar trick and derive continuous evolution of the observables in between interactions in matrix mechanics, but what you get is, again, observables continuously changing, not the evolution of a wave function.

  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.

• ⁨Comment⁩ on ⁨Test of a prototype quantum internet runs under New York City for half a month⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

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

• ⁨Comment⁩ on ⁨Test of a prototype quantum internet runs under New York City for half a month⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

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

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

  Which would you pick?

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

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

• ⁨Comment⁩ on ⁨Test of a prototype quantum internet runs under New York City for half a month⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

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

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

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

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

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

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

• ⁨Comment⁩ on ⁨Test of a prototype quantum internet runs under New York City for half a month⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  Entanglement plays a key role.

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

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

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

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

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

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

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

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

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

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

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

• ⁨Comment⁩ on ⁨Regarding this picture, where do you think quantum computers lie and why?⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

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

• ⁨Comment⁩ on ⁨Regarding this picture, where do you think quantum computers lie and why?⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  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.

• ⁨Comment⁩ on ⁨Regarding this picture, where do you think quantum computers lie and why?⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  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.

• ⁨Comment⁩ on ⁨Regarding this picture, where do you think quantum computers lie and why?⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  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.

• ⁨Comment⁩ on ⁨I don’t understand quantum physics⁩ ⁨⁨3⁩ ⁨months⁩ ago⁩:

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

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

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

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

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

  Although Pris disagrees with both of these positions and offers his own solution based on Jocelyn Benoist’s philosophy of contextual realism which is in turn based off of Ludwig Wittgenstein’s writings. Benoist has written extensively against all the arguments claiming that reality is invisible and has instead argued that what we experience is objective reality as it is exists independent of the observer but dependent upon the context of the experience. Thus he is critical of pretty much all of modern philosophers who overwhelmingly adhere either to metaphysical realism or to idealism.

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

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

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

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

  Everything is interpreted through this lens whereby nature is treated as context variant in this way, and it resolves all the paradoxes without introducing anything else. So if you can accept that one premise then everything else is explained.

• ⁨Comment⁩ on ⁨The reason why we never meet time travelers is because our civilization ends before the technology can come to fruition.⁩ ⁨⁨3⁩ ⁨months⁩ ago⁩:

  That’s actually not quite accurate, although that is how it is commonly interpreted. The reason it is not accurate is because Bell’s theorem simply doesn’t show there is no hidden variables and indeed even Bell himself states very clearly what the theorem proves in the conclusion of his paper.

  In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.[1]

  In other words, you can have hidden variables, but those hidden variables would not be Lorentz invariant. What is Lorentz invariance? Well, to be “invariant” basically means to be absolute, that is to say, unchanging based on reference frame. The term Lorentz here refers to Lorentz transformations under Minkowski space, i.e. the four-dimensional spacetime described by special relativity.

  This implies you can actually have hidden variables under one of two conditions:

  1. Those hidden variables are invariant under some other framework that is not special relativity, basically meaning the signals would have to travel faster than light and thus would contradict special relativity and you would need to replace it with some other framework.
  2. Those hidden variables are variant. That would mean they do indeed change based on reference frame. This would allow local hidden variable theories and thus even allow for current quantum mechanics to be interpreted as a statistical theory in a more classical sense as it even evades the PBR theorem.[2]

  The first view is unpopular because special relativity is the basis of quantum field theory, and thus contradicting it would contradict with one of our best theories of nature. There has been some fringe research into figuring out ways to reformulate special relativity to make it compatible with invariant hidden variables,[3] but given quantum mechanics has been around for over a century and nobody has figured this out, I wouldn’t get your hopes up.

  The second view is unpopular because it can be shown to violate a more subtle intuition we all tend to have, but is taken for granted so much I’m not sure if there’s even a name for it. The intuition is that not only should there be no mathematical contradictions within a single given reference frame so that an observer will never see the laws of physics break down, but that there should additionally be no contradictions when all possible reference frames are considered simultaneously.

  It is not physically possible to observe all reference frames simulatenously, and thus one can argue that such an assumption should be abandoned because it is metaphysical and not something you can ever observe in practice.[4] Note that inconsistency between all reference frames considered simulatenously does not mean observers will disagree over the facts, because if one observer asks another for information about a measurement result, they are still acquiring information about that result from their reference frame, just indirectly, and thus they would never run into a disagreement in practice.

  However, people still tend to find it too intuitive to abandon this notion of simultaneous consistency, so it remains unpopular and most physicists choose to just interpret quantum mechanics as if there are no hidden variables at all. #1 you can argue is enforced by the evidence, but #2 is more of a philosophical position, so ultimately the view that there are no hidden variables is not “proven” but proven if you accept certain philosophical assumptions.

  There is actually a second way to restore local hidden variables which I did not go into detail here which is superdeterminism. Superdeterminism basically argues that if you did just have a theory which describes how particles behave now but a more holistic theory that includes the entire initial state of the universe going back to the Big Bang and tracing out how all particles evolved to the state they are now, you can place restrictions on how that system would develop that would such that it would always reproduce the correlations we see even with hidden variables that is indeed Lorentz invariant.

  Although, the obvious problem is that it would never actually be possible to have such a theory, we cannot know the complete initial configuration of all particles in the universe, and so it’s not obvious how you would derive the correlations between particles beforehand. You would instead have to just assume they “know” how to be correlated already, which makes them equivalent to nonlocal hidden variable theories, and thus it is not entirely clear how they could be made Lorentz invariant. Not sure if anyone’s ever put forward a complete model in this framework either, same issue with nonlocal hidden variable theories.

• ⁨Comment⁩ on ⁨The theory that we live in a simulation involves simulants running their own simulations; wouldn't that require impossibly more resources for the main sim?⁩ ⁨⁨4⁩ ⁨months⁩ ago⁩:

  If our technology is limited so we can never see beyond something, why even propose it exists? Bell’s theorem also demonstrates that if you do add hidden parameters, it would have to violate Lorentz invariance, meaning it would have to contradict with the predictions of our current best theories of the universe, like GR and QFT. Even as pure speculation it’s rather dubious as there’s no evidence that Lorentz invariance is ever violated.

• ⁨Comment⁩ on ⁨The theory that we live in a simulation involves simulants running their own simulations; wouldn't that require impossibly more resources for the main sim?⁩ ⁨⁨4⁩ ⁨months⁩ ago⁩:

  My issue it is similar: each “layer” of simulation would necessarily be far simpler than than the layer in which the simulation is built, and so complexity would drop down exponentially such that even an incredibly complex universe would not be able to support conscious beings in simulations within only a few layers. You could imagine that maybe the initial universe is so much more complex than our own that it could support millions of layers, but at that point you’re just guessing, as we have no reason to believe there is even a single layer above our own, and the whole notion that “we’re more likely to be an a simulation than not” just ceases to be true. You can’t actually put a number on it, or even a vague description like “more likely.” it’s ultimately a guess.

• ⁨Comment⁩ on ⁨The theory that we live in a simulation involves simulants running their own simulations; wouldn't that require impossibly more resources for the main sim?⁩ ⁨⁨4⁩ ⁨months⁩ ago⁩:

  I have never understood the argument that QM is evidence for a simulation because the universe is using less resources or something like that by not “rendering” things at that low of a level. The problem is that, yes, it’s probabilistic, but it is not merely probabilistic. We have probability in classical mechanics already like when dealing with gasses in statistical mechanics and we can model that just fine. Modeling wave functions is far more computationally expensive because they do not even exist in traditional spacetime but in an abstract Hilbert space that can grows in complexity exponentially faster than classical systems. That’s the whole reason for building quantum computers, it’s so much more computationally expensive to simulate this that it is more efficient just to have a machine that can do it.