L&FP 65d: Superposition and the wave function

_{kairosfocus

February 9, 2023

Physics}

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Hossenfelder is an instrumentalist, and emphasises that the superposition is an expression of a probability wave thus a prediction of observations not ultimate truth. Bonus, she brings in entanglement and the concept that it discusses correlated states, using radioactive decay as a case. However, all of this can help us address things like alleged clashes between Quantum Theory and Logic, cf our weak arguments discussion here. Q-Mech, of course, humbles us all. KF

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Q, pessimistic induction, as confessed similarly:
In the philosophy of science, the pessimistic induction, also known as the pessimistic meta-induction, is an argument which seeks to rebut scientific realism, particularly the scientific realist's notion of epistemic optimism. The pessimistic meta-induction is the argument that if past successful and accepted scientific theories were found to be false, we have no reason to believe the scientific realist's claim that our currently successful theories are approximately true.
That is probably an underlying influence. I hold, that theories are inferences to best current explanation and as such cannot be warranted to utter irreversible, incorrigible certainty. So, they may be reliable on a tested range, but are not absolute. Where, observations are far more certain, including the observation of reliability on a given gamut. See Newtonian Dynamics on such reliability. This is closely tied to my view that common sense knowledge is strictly a weak form, defeatable claim. KFkairosfocus_{February 13, 2023
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Q, Wiki confesses:
In philosophy of science and in epistemology, instrumentalism is a methodological view that ideas are useful instruments, and that the worth of an idea is based on how effective it is in explaining and predicting phenomena. According to instrumentalists, a successful scientific theory reveals nothing known either true or false about nature's unobservable objects, properties or processes.[1] Scientific theory is merely a tool whereby humans predict observations in a particular domain of nature by formulating laws, which state or summarize regularities, while theories themselves do not reveal supposedly hidden aspects of nature that somehow explain these laws.[2] Instrumentalism is a perspective originally introduced by Pierre Duhem in 1906.[2] Rejecting scientific realism's ambitions to uncover metaphysical truth about nature,[2] instrumentalism is usually categorized as an antirealism, although its mere lack of commitment to scientific theory's realism can be termed nonrealism. Instrumentalism merely bypasses debate concerning whether, for example, a particle spoken about in particle physics is a discrete entity enjoying individual existence, or is an excitation mode of a region of a field, or is something else altogether.[3][4][5] Instrumentalism holds that theoretical terms need only be useful to predict the phenomena, the observed outcomes.[3] There are multiple versions of instrumentalism.
KFkairosfocus_{February 13, 2023
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Bornagain77 @10, Regarding superposition as a tool, it's hard to imagine how Dr. Hossenfelder rationalizes these experimental results: https://www.newscientist.com/article/dn18669-first-quantum-effects-seen-in-visible-object/ https://physicsworld.com/a/quantum-effect-spotted-in-a-visible-object/ If you can see superposition with the naked eye, what more does she demand? Oh, and thanks for the link to the direct measurement of the wavefunction! I didn't know that this was possible. https://www.nature.com/articles/nature10120 -QQuerius_{February 9, 2023
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In fact, collapse of the ‘superposition’ wave function into a finite particle state of only one definite position, has now also been experimentally demonstrated. As the following article states, experiments have now demonstrated “the non-local, (i.e. beyond space and time), collapse of a (single) particle’s wave function”,, “the collapse of the wave function is a real effect”,, “the instantaneous non-local, (beyond space and time), collapse of the wave function to wherever the particle is detected”,, and “Through these different measurements, you see the wave function collapse in different ways, thus proving its existence and showing that Einstein was wrong.”,,
Quantum experiment verifies Einstein’s ‘spooky action at a distance’ – March 24, 2015 Excerpt: An experiment,, has for the first time demonstrated Albert Einstein’s original conception of “spooky action at a distance” using a single particle. ,,Professor Howard Wiseman and his experimental collaborators,, report their use of homodyne measurements to show what Einstein did not believe to be real, namely the non-local collapse of a (single) particle’s wave function.,, According to quantum mechanics, a single particle can be described by a wave function that spreads over arbitrarily large distances,,, ,, by splitting a single photon between two laboratories, scientists have used homodyne detectors—which measure wave-like properties—to show the collapse of the wave function is a real effect,, This phenomenon is explained in quantum theory,, the instantaneous non-local, (beyond space and time), collapse of the wave function to wherever the particle is detected.,,, “Einstein never accepted orthodox quantum mechanics and the original basis of his contention was this single-particle argument. This is why it is important to demonstrate non-local wave function collapse with a single particle,” says Professor Wiseman. “Einstein’s view was that the detection of the particle only ever at one point could be much better explained by the hypothesis that the particle is only ever at one point, without invoking the instantaneous collapse of the wave function to nothing at all other points. “However, rather than simply detecting the presence or absence of the particle, we used homodyne measurements enabling one party to make different measurements and the other, using quantum tomography, to test the effect of those choices.” “Through these different measurements, you see the wave function collapse in different ways, thus proving its existence and showing that Einstein was wrong.” http://phys.org/news/2015-03-quantum-einstein-spooky-action-distance.html (Of note: since the many worlds interpretation denies the reality of wave-function collapse, this experiment also falsifies the many worlds interpretation.)
Since the wave function is now experimentally shown to be an objectively real feature of reality, and not just to be some abstract 'mathematical tool' as Hossenfelder holds, then it is interesting to look at the mathematical definition of the wave function. The wave function is mathematically defined as being in an 'infinite dimensional' state which takes an infinite amount of information to describe properly.
Why do we need infinite-dimensional Hilbert spaces in physics? You need an infinite dimensional Hilbert space to represent a wavefunction of any continuous observable (like position for example).,,, However, these are all ugly and artificial schemes, and there is very little reason to prefer them over the perfectly reasonable standard Schrödinger theory, which is why we use infinite-dimensional Hilbert spaces in everyday quantum mechanics. https://physics.stackexchange.com/questions/149786/why-do-we-need-infinite-dimensional-hilbert-spaces-in-physics Why does describing a quantum state take an infinite amount of information? Excerpt: Intuitively, things look pretty bad for Alice. She doesn’t know the state (of the wave function) of the qubit she has to send to Bob, and the laws of quantum mechanics prevent her from determining the state when she only has a single copy of (the wave function) in her possession. What’s worse, even if she did know the state (of the wave function), describing it precisely takes an infinite amount of classical information since (the wave function) takes values in a continuous space. So even if she did know (the wave function) it would take forever for Alice to describe the state to Bob. https://quantumcomputing.stackexchange.com/questions/14324/why-does-describing-a-quantum-state-take-an-infinite-amount-of-classical-informa
As is fairly obvious, the ‘infinite dimensional’ Hilbert space corresponds to the Theistic attribute of omnipresence. And the infinite information required to describe the ‘infinite dimensional’ wave function prior to collapse to its finite particle state corresponds to the Theistic attribute of omniscience. In essence, the infinite dimensional/infinite information wave function is, basically, mathematically described as being one of “God’s thoughts’ prior to its collapse to its finite ‘material’ state. Of supplemental note, It is also interesting to note that the collapse of the wave function, (which, I remind, has now been experimentally shown to be a real effect), fits very well into Aristotle and Aquinas's ancient 'first mover' argument for the existence of God, i.e. (reduction of potency to act).
Stephen Hawking: "Philosophy Is Dead" - Michael Egnor - August 3, 2015 Excerpt: The metaphysics of Aristotle and Aquinas is far and away the most successful framework on which to understand modern science, especially quantum mechanics. Heisenberg knew this (Link on site). Aristotle 2,300 years ago described the basics of collapse of the quantum waveform (reduction of potency to act),,, Real scientists have a meaningful understanding of natural philosophy as it relates to their work. No atheist scientist in the public spotlight today would pass a freshman philosophy class. Think Dawkins. Think Krauss. Think Myers. Think Moran. Think Novella. Think Coyne. Think Hawking. Our 21st-century scientific priesthood -- mostly atheists and materialists to the extent that their metaphysics is coherent enough to be described -- is dominated by half-educated technicians with publicists.,,, http://www.evolutionnews.org/2015/08/stephen_hawking_3098261.html What Is Matter? The Aristotelian Perspective - Michael Egnor - July 21, 2017 Excerpt: Heisenberg, almost alone among the great physicists of the quantum revolution, understood that the Aristotelian concept of potency and act was beautifully confirmed by quantum theory and evidence.,,, Heisenberg wrote: ,,,”The probability wave of Bohr, Kramers, Slater… was a quantitative version of the old concept of “potentia” in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality…The probability function combines objective and subjective elements,,,” Thus, the existence of potential quantum states described by Schrodinger’s equation (which is a probability function) are the potency (the “matter”) of the system, and the collapse of the quantum waveform is the reduction of potency to act. To an Aristotelian (like Heisenberg), quantum mechanics isn’t strange at all. https://evolutionnews.org/2017/07/what-is-matter-the-aristotelian-perspective/
Verse:
Job 38:19-20 “What is the way to the abode of light? And where does darkness reside? Can you take them to their places? Do you know the paths to their dwellings?”
bornagain77_{February 9, 2023
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Sabine Hossenfelder is an instrumentalist who believes the wave function is just a "mathematical tool". And she also holds "superpositions are really not terribly interesting."
1:59 "Personally, I am an instrumentalist and I don’t assign any particular meaning to such a superposition. It’s merely a mathematical tool to make a prediction for a measurement outcome.",,, 3:27 "In some sense, I have to say, superpositions are really not terribly interesting.",,, - Sabine Hossenfelder - Understanding Quantum Mechanics #2: Superposition and Entanglement https://www.youtube.com/watch?v=j6Mw3_tOcNI
In the following article, (which is an excellent article for untangling much of the confusion surrounding quantum mechanics), the late Steven Weinberg, an atheist, clarifies exactly what is meant when a person says that they are a 'instrumentalist' in regards to quantum mechanics.
The Trouble with Quantum Mechanics - Steven Weinberg The instrumentalist approach is a descendant of the Copenhagen interpretation, but instead of imagining a boundary beyond which reality is not described by quantum mechanics, it rejects quantum mechanics altogether as a description of reality. There is still a wave function, but it is not real like a particle or a field. Instead it is merely an instrument that provides predictions of the probabilities of various outcomes when measurements are made. It seems to me that the trouble with this approach is not only that it gives up on an ancient aim of science: to say what is really going on out there. It is a surrender of a particularly unfortunate kind. In the instrumentalist approach, we have to assume, as fundamental laws of nature, the rules (such as the Born rule I mentioned earlier) for using the wave function to calculate the probabilities of various results when humans make measurements. Thus humans are brought into the laws of nature at the most fundamental level. According to Eugene Wigner, a pioneer of quantum mechanics, “it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness.”11 Thus the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else. It is not that we object to thinking about humans. Rather, we want to understand the relation of humans to nature, not just assuming the character of this relation by incorporating it in what we suppose are nature’s fundamental laws, but rather by deduction from laws that make no explicit reference to humans. We may in the end have to give up this goal, but I think not yet. Some physicists who adopt an instrumentalist approach argue that the probabilities we infer from the wave function are objective probabilities, independent of whether humans are making a measurement. I don’t find this tenable. In quantum mechanics these probabilities do not exist until people choose what to measure, such as the spin in one or another direction. Unlike the case of classical physics, a choice must be made, because in quantum mechanics not everything can be simultaneously measured. As Werner Heisenberg realized, a particle cannot have, at the same time, both a definite position and a definite velocity. The measuring of one precludes the measuring of the other. Likewise, if we know the wave function that describes the spin of an electron we can calculate the probability that the electron would have a positive spin in the north direction if that were measured, or the probability that the electron would have a positive spin in the east direction if that were measured, but we cannot ask about the probability of the spins being found positive in both directions because there is no state in which an electron has a definite spin in two different directions.,,, http://quantum.phys.unm.edu/466-17/QuantumMechanicsWeinberg.pdf
Since, as I showed yesterday, Hossenfelder, (because of her apriori commitment to atheistic naturalism), rejects the reality of free will in quantum mechanics, (in spite of empirical evidence from Zeilinger to the contrary),, https://uncommondescent.com/intelligent-design/lfp-65c-hossenfelder-on-the-rest-of-the-story-on-delayed-choice-quantum-eraser-exercises/#comment-775366 ,,, Since Hossenfelder rejects the reality of free will in quantum mechanics, then I hold Hossenfelder, via the process of elimination, to be an instrumentalist who holds that "the probabilities we infer from the wave function are objective probabilities, independent of whether humans are making a measurement." Yet, (as she was wrong in her rejection of the empirical evidence that confirmed the reality of free will in quantum mechanics), she is also wrong in her presupposition that "the probabilities we infer from the wave function are objective probabilities, independent of whether humans are making a measurement." As the following article states, "we cannot interpret the measurements as revealing some pre-existing properties of the system.” What’s more, the mathematical machinery for unfolding these probabilities can only be written down if you stipulate how you’re looking. If you do different measurements, you might calculate different probabilities, even though you seem to be examining the same system in both cases."
Mysterious Quantum Rule Reconstructed From Scratch - Philip Ball - February 13, 2019 Excerpt: Yet the arbitrariness of the Born rule is perhaps the least odd thing about it. In most physics equations, the variables refer to objective properties of the system they are describing: the mass or velocity of bodies in Newton’s laws of motion, for instance. But according to Born, the wave function is not like this. It’s not obvious whether it says anything about the quantum entity itself — such as where it is at any moment in time. Rather, it tells us what we might see if we choose to look. It points in the wrong direction: not down toward the system being studied, but up toward the observer’s experience of it. “What makes quantum theory puzzling is not so much the Born rule as a way of computing probabilities,” Chiribella said, “but the fact that we cannot interpret the measurements as revealing some pre-existing properties of the system.” What’s more, the mathematical machinery for unfolding these probabilities can only be written down if you stipulate how you’re looking. If you do different measurements, you might calculate different probabilities, even though you seem to be examining the same system in both cases.,,, https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/
Moreover, Hossenfelder's belief that the wave function is just an abstract 'mathematical tool' is also now experimentally shown to be a wrong belief. Specifically, “superposition" of the wave function is now experimentally shown to be physically real, and to not be merely an abstract 'mathematical tool' as Hossenfelder holds.
Direct measurement of the quantum wavefunction – June 2011 Excerpt: The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition.,,, Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way through weak measurement so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. http://www.nature.com/nature/journal/v474/n7350/full/nature10120.html The Weak Measurement in Quantum Mechanics – 2012 Excerpt: The basic idea of the weak measurement is that the interaction (or disturbance) between the measuring apparatus and the observed system or particle is so weak, that the wave function does not collapse but continues on unchanged. In other words, a weak measurement is one in which the coupling between the measuring device and the observable to be measured is so weak that the uncertainty in a single measurement is large compared with the separation between the eigenvalues of the observable [2]. http://www-f1.ijs.si/~ramsak/seminarji/KnaflicSibka.pdf
As the following article states, "For nearly a century physicists have argued about whether the wave function is a real part of the world or just a mathematical tool.,,, Eric Cavalcanti,, Alessandro Fedrizzi,, and their colleagues have made a measurement of the reality of the quantum wave function. Their results rule out a large class of interpretations of quantum mechanics and suggest that if there is any objective description of the world, the famous wave function is part of it",,,
Wave function gets real in quantum experiment – February 2, 2015 Excerpt: It underpins the whole theory of quantum mechanics, but does it exist? For nearly a century physicists have argued about whether the wave function is a real part of the world or just a mathematical tool. Now, the first experiment in years to draw a line in the quantum sand suggests we should take it seriously. The wave function helps predict the results of quantum experiments with incredible accuracy. But it describes a world where particles have fuzzy properties – for example, existing in two places at the same time. Erwin Schrödinger argued in 1935 that treating the wave function as a real thing leads to the perplexing situation where a cat in a box can be both dead and alive, until someone opens the box and observes it. Those who want an objective description of the world – one that doesn’t depend on how you’re looking at it – have two options. They can accept that the wave function is real and that the cat is both dead and alive. Or they can argue that the wave function is just a mathematical tool, which represents our lack of knowledge about the status of the poor cat, sometimes called the “epistemic interpretation”. This was the interpretation favoured by Albert Einstein, who allegedly asked, “Do you really believe the moon exists only when you look at it?” The trouble is, very few experiments have been performed that can rule versions of quantum mechanics in or out. Previous work that claimed to propose a way to test whether the wave function is real made a splash in the physics community but turned out to be based on improper assumptions, and no one ever ran the experiment. What a state Now, Eric Cavalcanti at the University of Sydney and Alessandro Fedrizzi at the University of Queensland, both in Australia, and their colleagues have made a measurement of the reality of the quantum wave function. Their results rule out a large class of interpretations of quantum mechanics and suggest that if there is any objective description of the world, the famous wave function is part of it: Schrödinger’s cat actually is both dead and alive.,,, There may still be a way to distinguish quantum states from each other that their experiment didn’t capture. But Howard Wiseman from Griffith University in Brisbane, Australia, says that shouldn’t weaken the results. “It’s saying there’s definitely some reality to the wave function,” he says. “You have to admit that to some extent there’s some reality to the wave function, so if you’ve gone that far, why don’t you just go the whole way?” http://www.newscientist.com/article/dn26893-wave-function-gets-real-in-quantum-experiment.html
bornagain77_{February 9, 2023
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JVL @6,
QM is just us limited, barely-out-of-the-caves humans trying to make sense of what we observe and discern when we are probably only seeing part of the shadow of the entire picture (like your Platonic (or was it Socratic?) cave analogy). Some bits of the universe we have learned to model (which is what QM is, a mathematical model) fairly well so that we get dependable, predictable, exploitable results. We also know that every single mathematical model we have invented/discovered has turned out to be limited and is eventually supplanted by another messier, more complicated model.
Nicely articulated! What I'd like to see in QM, is much less speculation and ideological filtering (such as determinism at one end and trying to prove God exists on the other) together with more ideologically neutral experimentation. Mathematical models, as you noted, can't be trusted. They've not been very good for extrapolation, but are usually successful at interpolation. We should simply follow the data and create mathematical models on the basis of pragmatism and let philosophers rip each others' lungs out on the apparent implications for their entertainment. There are some amazing technologies that are currently being developed that make use of quantum effects, such as spin alignment. As you pointed out, we might not exactly understand why they work, but that's not going to stop us from making use of them. My favorite one has to do with new battery technologies that don't need to use rare earth elements. In case you're interested, it's also gratifying to know just how much positive impact cell phone access has provided for low-income farmers in developing nations. A great example of this involves apps for farmers in India, enabling them to compare prices offered by different wholesalers so as to foster true free-market competition between middlemen/wholesalers/retailers: https://www.thehindubusinessline.com/economy/agri-business/aggregator-platform-for-farmers-buyers-launched/article8855380.ece https://farmersbridge.org/about/ https://economictimes.indiatimes.com/industry/cons-products/food/organised-wholesalers-can-procure-goods-directly-from-farmers/articleshow/74976727.cms -QQuerius_{February 9, 2023
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Kairosfocus: precisely, humbling. And extremely challenging! There is still so much to discover and explore! And we have better and better tools for doing that. It's a great time to be alive.JVL_{February 9, 2023
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JVL, precisely, humbling. KFkairosfocus_{February 9, 2023
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Kairosfocus: it seems we need a nodding acquaintance. Including, learning why Q-Mech humbles us all. QM is just us limited, barely-out-of-the-caves humans trying to make sense of what we observe and discern when we are probably only seeing part of the shadow of the entire picture (like your Platonic (or was it Socratic?) cave analogy). Some bits of the universe we have learned to model (which is what QM is, a mathematical model) fairly well so that we get dependable, predictable, exploitable results. We also know that every single mathematical model we have invented/discovered has turned out to be limited and is eventually supplanted by another messier, more complicated model. The current models (like QM and relativity) are a far bit removed from common, everyday experiences and the math involved is beyond almost everyone's ken. So we trust the scientists to know what they are talking about but we trust the engineers even more 'cause they come up with clever exploitations of the models and we get GPS or transistors. Some of us kind of understand internal combustion engines but almost none of us really understand all the innards of our smart phones or computers. We turn them on, they do what it says on the tin . . . mostly. I only see that gulf of knowledge increasing. And that is not a good thing. But there's no real solution. It takes years of work and study to really grok the current models. What's it going to be like in the future? Then it probably will all seem like magic except for a select few. And they will become like gods. What did Dr Oppenheimer say: I have become death, the destroyer of worlds? From a Hindu scripture I think.JVL_{February 9, 2023
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Sev, yes. KFkairosfocus_{February 9, 2023
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JVL, quantum themes keep coming up, it seems we need a nodding acquaintance. Including, learning why Q-Mech humbles us all. KFkairosfocus_{February 9, 2023
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Q-Mech, of course, humbles us all. KF
Which is good since humility is good for the soul.Seversky_{February 9, 2023
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Not bad at all. Not sure what it has to do with ID but not bad.JVL_{February 9, 2023
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L&FP 65d: Superposition and the wave functionkairosfocus_{February 9, 2023
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