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B Any good lay explanation of the Schrödinger cat duality?

  1. Sep 2, 2016 #1
    Once again, I came across the notion (in a lay physics book by an academic) that two mutually exclusive states simultaneously exist until observed (based on the Schrödinger living/dead cat thought experiment), which, on its face, seems to me to belong to theology and not to science. That both mutually exclusive states are simultaneously possible is logical; but that both mutually exclusive states are being simultaneously fulfilled is not. Whether states are observed and whether an observer exists are irrelevant to the state of the states. I understand that the claim extends from two to three and to infinitely many states; I see that as just as illogical. (The latest source where I read of this is Neutrino Hunters: The Thrilling Chase For a Ghostly Particle to Unlock the Secrets of the Universe, by Ray Jayawardhana (author physics prof., York Univ.) (N.Y.: Scientific American / Farrar, Straus and Giroux, 1st ed. [1st printing?] hardback (ISBN 978-0-374-22063-1) 2013); the relevant passage is at p. 29 ("The determinism of classical mechanics gave way to mere statistical probabilities: instead of predicting definitive outcomes, quantum mechanics assigns likelihood to different results. That meant, as Erwin Schrödinger pointed out in a famous thought experiment, a cat in a box could be both alive and dead at the same time, until an observer intervenes by looking in."). I agree with the first quoted sentence but not the second in that we can grant that the probability of the first sentence has not been resolved but it does not follow that the two states are simultaneously fulfilled. To me, that's a non sequitur. It doesn't say, "could be either alive or dead"; it says, "both alive and dead at the same time".) I've seen similar statements several (maybe many) times in different science sources.

    But I gather my disagreement means that I don't know physics.

    Is there a reliable lay publication that sets out a proof for simultaneous preobservational existence of that which is mutually exclusive?

    I poked around this forum, which listed five topics as similar. <https://www.physicsforums.com/threads/schroedingers-cat-explanation.682271/#post-4329868> says many experiments prove this. I'd like to read about those, for example.

    I am not asking that someone explain the whole thing on this forum. I'm happy to read a book or an article or two or three by authors who are in one of these professions (not simply a professional writer, but a physicist or related academic). Do you know any you could recommend?
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  3. Sep 2, 2016 #2
    You have stumbled upon the fundamental concept of superposition in Quantum Mechanics. The problems you have stem from the problem of expressing QM in the usual language. You should replace the statement "state A and state B are simultaneously fulfilled" by "The state of the system is a superposition of the state A and the state B". Actually there are many ways to do this superposition, so even this is not precise enough. Roughly speaking this is because there are many way to assign relative probabilities to A and B.

    It is relevant to the state of the system whether observation has been made. In QM, measurement affects the state of the system. This is encoded in the Heisenberg uncertainty principle.

    I would advise you at the axiom of quantum mechanics that talks about the probability assigned to a state, and the axiom that talks about the way states change after measurement. Then the principle of superposition. There is mathematics, but it is not too hard if you are not trying to be technical. Even for a philosopher, if you are serious about this, mathematics is important. Lectures on quantum mechanics and quantum entanglement from Leonard Susskind on youtube will cover the basic mathematics as you go along.
  4. Sep 2, 2016 #3

    Simon Bridge

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    It is easy to get confused about this whole thing.

    It is not unusual to describe something as being in a superposition of other stuff ... for instance, a bishop, moving diagonally across the chessboard, find's it's movement in a superposition of sideways and vertical motion ... there is nothing profound about this: a rook moves in a superposition of two possible pure diagonal motions. It just means we can represent some things as combinations of other things ... the maths is covered in linear algebra concerning vectors and vector spaces if you want to see the details. The tricky part comes when you try to link two systems ... clearly the cat cannot move in both the alive and dead directions: they are not directions ferinstance.

    Usually a quantum 2-state system is not considered to consist of mutually exclusive states in the way you seem to think.
    A die thrown, while still in the air, may be considered, classically, to be in a superposition of 6 possible states. They do not become mutually exclusive until after the die lands - and the state is measured. Then you only see one. This would be somewhat analogous to the copenhagen idea of "collapsing the wavefunction" ... but not exactly because quantum statistics has different behaviour. Which exact superposition we use is called the representation of the state and we are free to choose whichever we want ... we could choose a representation where there is no superposition if we wanted. Faced with a sometimes infinite choice, we end up using the representation that makes the maths easy for what we want to describe.

    The idea with schodingers cat is to link a macroscopic state to a quantum system, then discuss the state of the system in terms of the state of the cat.
    It is not that the cat exists in a superposition, but that a quantum experiment is performed and the fate of the cat rests on the result of the experiment.
    Which is the whole point: the copenhagen interpretation would appear to conflate the cat with the quantum system, and opening the box with a measurement. So we need to be careful.

    You are aware that huge tracts have been written on the subject. I am not aware of any good lay publications on the matter at all. It is unclear how one could be written, sorry: you just have to learn the maths. There are plenty of bad ones however - they all talk about the cat being alive and dead at the same time or until someone looks - which sounds silly because it is: they got it wrong. What has happened is that we need a more careful language to talk about it.
  5. Sep 2, 2016 #4
    That is a very good point. If we are being pure mathematicians we care not about the representation, and superposition is a representation dependent concept. If we are being applied mathematicians, we choose the representation which makes calculations easier. If we are being experimentalists, we choose the representation that corresponds to the oservable we want to measure.
  6. Sep 6, 2016 #5
    If no one wrote it up right except with deep math, which I probably don't know well enough, maybe someone should write The Math of Schrödinger's Cat For Dummies or something but get it right this time. It might be a great tool for introducing high-level math.

    These are my views, and I hope to understand how quantum mechanics deals with this.

    Did an experiment confirm that multiple contradictory states existed at once until observed? Is it even possible to design such an experiment? One would have to leave a test object unobserved (unmeasured) and still observe (measure) it, itself a contradiction. If that experiment has been published, I'd like to read it; is there a reference to it?

    The chess piece can be moved as a result of what opportunities (including those from rules) it has. A knight can move both vertically and horizontally in the same move, but that's serially or equivalently; it's not moving both vertically and horizontally at the same point in time, although at that point it may be moving obliquely. Chess may be a weak analogy.

    To conclude that the die reaches its exclusive state not when it lands but when it lands and we look at it, we have to believe that our eyes do something to the die. Everything I know of eyes is that they receive inputs and send information about them to the brain, not the other way, except for reflections, too minor a factor.

    If a state exists only if observed, if a cat is either dead or alive only if measured, then, since I'm in the United States and I can't see China, China doesn't exist. Granted there are observers in and near China and we can construct a chain of observers all the way from there to me, why should I believe them? If there's no satellite today that can see the far side of the moon, then maybe the moon is a bowl, not a ball. The moon could be either a bowl or a ball but we don't know which yet (we used to know but maybe a meteor hit the far side yesterday and most of the moon disintegrated, somehow without affecting its orbit). The moon is not both until a satellite is able to observe. Saying otherwise quickly gets solipsistic.

    Superposition still is in an apparent conflict with logic: I have no problem with relative probabilities but I do have a problem with simultaneous occurrence of what can only occur one way, whichever way but only one way. But maybe this is all meant only to be metaphorical, in which case it doesn't need mathematical support but also then we can dismiss it as anything scientific in itself. But physicists apparently don't think so.

    Modeling on the cat, could we extend a dying person's life by not looking at them? Coroners estimate that an unobserved person died a certain number of hours prior to examination. That's incomplete data, but it suggests that extreme privacy (not looking) won't extend someone's life until just before the examination, unless coroners aren't telling us something.

    At the level of the extremely tiny, hardly any of us ever sees even indirect evidence of a single atomic particle, other than macro-level objects made entirely of atomic particles, but macro-level objects are not a prime subject of quantum mechanics. I gather an atomic particle of some kinds enters and exits existence without being observed. Some of them interact with other particles so the latter observably change positions, but our micro-level observations are comparatively rare; should that imply that there are very few atomic particles, not enough to make more than what we can see in the sky? I don't think so. I assume that all the stars that we once found are still there (other than a few that died or merged) even when we have no observer watching.

    Instead of YouTube, I'd rather read. I can cope with some math. I hope someone knows of a title or an author or something.
  7. Sep 6, 2016 #6


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    Experiments have decisively confirmed that superposition really happens. For example, an electron can be in the state "superposition of spin-up and spin-down". That state has subtly different properties than the more classical-sounding "It is either spin-up or spin-down, but we don't know which because we haven't looked"; we've looked for those differences and found them. In no particular order, you might try:
    1) Google for "Bell's Theorem experiment"
    2) https://www.scientificamerican.com/media/pdf/197911_0158.pdf (but read the article not the subtitle)
    3) Our own Dr Chinese maintains a web site devoted to Bell's Theorem: http://www.drchinese.com/Bells_Theorem.htm. Look at the "Easy math" proof.
    However, superposition does not mean that "multiple contradictory states existed at once". I already mentioned the electron in a superposition of spin-up and spin-down; that state is not some impossible contradictory "up and down at the same time", it is the perfectly reasonable state "spin pointing left". Perhaps the best analogy for superposition is the way that a vector pointing northwest is a perfectly good vector in its own right, it is neither a vector pointing north nor a vector pointing west, but it is a superposition of those two different directions.
    No, for two reasons.
    First, in quantum mechanics the word "observation" does not mean that we (or any conscious observer) had to look to see what happened - any interaction between the quantum system and its environment counts as an "observation". (This confusing use of the word "observation" is an unfortunate historical accident, but once a word makes it into common usage it's impossible to get rid of it). Maintaining a superposition requires heroic efforts to isolate the quantum system from the environment; for example our experiments with electron spins are done in vacuum chambers to prevent the electrons from interacting with the air around us. The particles that make up a human body cannot be isolated from their environment (the body around them) without completely disassembling the body, so there is no chance of maintaining a superposition of "dead" and "not yet dead" and death will happen when it happens.

    Second, if we model on the cat we come to a different conclusion than you have. When Schrodinger proposed his thought experiment, he was not seriously suggesting that the cat would be in a superposition of dead and alive - neither he not any of his contemporaries believed any such thing. Instead, he was pointing out a problem in the then-current (1930ish) understanding of quantum mechanics, namely that QM seemed to suggest that such a superposition would arise. It took several decades more work to resolve this problem; you can google for "quantum decoherence" (although I must caution you that the math is somewhat daunting) or give David Lindley's excellent and layman-friendly book "Where does the weirdness go?" a try.
  8. Sep 7, 2016 #7

    Simon Bridge

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    I don't think the math is all that deep. You need linear algebra and an appreciation of probability. QM is a tweak on these.
    So, per your request:
    ... Linear Algebra for Dummies (helps to understand the concept of "superposition":
    ... For probability and statistics - I usually suggest John Allen Paulos' "Innumeracy" as a basic primer.
    The idea is to go for understanding rather than "knowing how to do the math".

    There is a quantum physics for dummies:

    ... Where does the wierdness go? is available very cheap:

    A more weighty approach comes from extending regular probability theory to allow for negative probabilities:

    It is not so much that nobody can write about Scrodinger's Cat without deep maths, just that what is required to provide a good treatment would no longer be a lay description. The thing to understand about QM is that it is a superset of the usual, everyday, mechanics and statistics that observant people get used to. It is needed because there are phenomena that cannot be described in regular everyday terms. A lay descrption is, pretty much by definition, putting it in regular everyday terms. See the problem?

    Answered post #6. The experiment confirms states which are best and most simply described as a superposition rather than a "we do not know"... usually described as "hidden variables" in physics.

    Sure ... notice though that a bishop will always have motion in a superposition of horizontal and vertical motion. Alternately, a rook moves in a superposition of possible bishop moves.
    This is a poor analogy to QM, but may help you realize a bit about superposition.

    Which is why we do not make that conclusion.

    In physics this is usually represented as a problem of measurement.
    making a measurement involves some apparatus ... the apparatus interacts with what we want to know about in some way, and, later, tells us about it.
    The measurement is usually considered to have occurred sometime during the initial interaction, which can be arbitrarily complicated.
    We do not have to look at the apparatus for the measurement to have taken place.... and there are long stories about how the experimenter comes back the next day, takes the printout but, without looking at it, puts it in his pocket and forgets about it for many years ... and so on, and asks: when did the measurement happen? When did the wave function, in the copenhagen interretation, "collapse" occur?
    As Nugatory points out, people now talk about "decoherence".

    Mathematics does not need to represent something that exists in reality though.
    A typical superposition introduced to students, without worrying about entanglement just yet, is the K0 meson and it's antiparticle.
    This is something you can look up.

    The everyday World is the domain of classical mechanics - usually Newtonian. Classical mechanics is an emergent effect of quantum mechanics - in the simplest form: it is what happens on average over a very large number of trials. When you have large numbers of interacting particles things tend to average out also, so the odd, non-everyday, stuff appears as a fuzzyness at the edges.
    It is possible to carefully arrange things so that quantum mechanical statistics have a clearly odd macroscopic result: feynman's favorite example involves removing most of the surface of a plane mirror to maximize the strength of the reflection (but only for one color).

    This may give you a better idea of what quantum mechanics can talk about... though it's a video series.

    To have an effect, it has to interact with something.
    See "Casimir effect" for how we establish particles popping in and out of existence unobserved.

    If it does not interact with anything, that is the same as saying it was not there. The QM says there is a probability of a particle being there.
    But sure: just because you don't see it don't mean it ain't there. Something like a star is a lot of particles interacting with each other ... we may not be looking at it, but all those particles are observed.
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  9. Sep 7, 2016 #8

    At first glance, this is very helpful. I'll follow up.

    I've long ago lost count of how many times I had read that one electron went to two places at once and similar statements about cats, worlds, and universes. I'm beginning to wonder how many academic authors have been putting this stuff into lay books for decades because their lay editors thought we lay readers would be amazed by it and therefore buy more books. although maybe I'm being too conspiratorial. Maybe lay book authors, even academics writing for laity, got caught up on the amazing concept that the public had already heard of and was fascinated by and the new authors lost the nuances of the reason for it. And thanks for the alert about the SciAm subhead; Wikipedia quotes it and attributes it to Bernard d'Espagnat, so I'll likely check if that's really his or an SA editor's statement.

    I'd begun thinking that our understanding of logic was not yet complete or our computerized closed-source math had an unresolved error that was waiting to be dug up, because there shouldn't be any space left between atomic particles as they all start occupying multiple loci, whereas my body temperature is nowhere near absolute zero. Your description of superposition is more consistent with how I usually experience the universe. I understood that an "observer" was a hypothetical figure of speech, like the observer said to ride on a beam of light, who, if human, could not exist at that speed; your explanation of "observer" is even more reasonable.

    Thank you immensely. It'll take me time to get through this but it took me time to get to where I was questioning whether what I was reading was really amazing or just impossible. I can afford to pour some more time in. Maybe the chess knight (supra) is not so bad for an analogy. Thank you for shining some light on this and pointing me to a few readable things. Two of the authors have especially good credentials for this, so I'll start with them, then dig into the third. I've started already.

    @Simon Bridge:

    Yes, it would be a challenge to write the noneveryday in everyday experiential terms. An illustration of a four-spatial-dimensional hypercube drawn on a two-dimensional sheet of paper really only works if it gets us imagining and thinking, since it can't be accurate by itself. On the other hand, describing color to someone who has been totally blind since birth, even though they actually may experience color (depending on physically why they're blind) may be too hard. I often learn a subject by reading several overlapping sources by different authors who may have some disagreements with each other. I'm not sure the writing is impossible but I couldn't do it myself now so maybe I'll realize later that it is impossible.

    On the experiment, yes, #6.

    On chess, I think I'm grasping what "superposition" really means, it's making more sense, and I'm waiting to read more.

    On the die, fair enough. I'll be reading. I'm understanding a wider scope for "observer" now.

    The pocketed results: I'd say twice, once when the device that made the printout did its measuring and then when the experimenter read and judged the printout's contents. But that may not be a QM answer.

    I understand that the math of the geometry of four or more spatial dimensions was invented a hundred years before a practical use was found for it, so, yes, math can describe what is physically yet unknown. And maybe a simple case of math describing what apparently can never exist is the math of infinity: space may be infinite but at least (I think) there is not (and I think there cannot be) an infinite quantity of matter.

    I'd have to look into how reflecting occurs to see what would be odd about Feynman's example. I guess he was talking about a degree of thinness we might not now have the technology to perform. As a practical matter, though, I recall from a few decades ago that high-quality camera lenses sometimes had a trade-off between sharpness and color fidelity, and a lens element (usually one glass piece) often had a complex coating to handle color.

    "If it does not interact with anything, that is the same as saying it was not there." Yes, in the practical sense that if someone says it was there and someone else says "prove it" the positive-claimant will be stymied. If I tell people there's a two-ton elephant on my head but no one can see it, I'd better remember that people have been locked up for saying less.

    Yes, I getting that observation means more than I had thought.

    It's tiresome that obsolete interpretations reappear as if never replaced, sort of like saying that the brontosaurus existed as such and that Pluto is still a planet. We lay peple have the burden of sorting it out. And it's harder because, in general, it's scientifically legitimate to reopen old questions; I think at least one experiment to try again to find ether (as a medium for light) was conducted in the 1960s, after Einstein had died (it didn't find it).

    Thank you for the additional bibliography. I'll look into it. I ought to be able to get somewhere with this now. Thank you, again.
  10. Sep 7, 2016 #9

    Simon Bridge

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    Oh that too, but I mean that things like schrodinger's cat need QM because physics before QM is incapable of explaining it. If it were possible to explain without QM, we would not need QM. This is not just a matter of being challenging, it means there is no possible way of giving a good description without QM.

    You don't normally need to - for instance, how do you know that your experience of a particular color is the same as other people's? How do you detect color-blindness? These are related questions.... but worthy of a different thread.
    One of the things that often comes up is the idea of having to demonstrate colors to people who do not use sight, but, say, sonar, to get around.
    There are established scientific ways to cope with this sort of problem.

    That is correct - the QM observation is when the wavefunction "collapses" (in the copenhagen interpretation). This would be the first one in the example ... you can check by making repeated measurements.
    So you may have a 2-state system for a single particle prepared in superposition of state 1 and state 2 ... then the state is measured, but the experimenter does not look at the readout... then measure the state again, and again... the first measurement collapses the system to either state 1 or state 2, subsequent measurements result in whatever state was collapsed to repeatedly.
    This dynamic is pretty much what beginning students of QM learn about first.

    Math includes imaginary and irrational numbers - these you do not find in Nature.
    The evidence currently points to a physical Universe that is flat and infinite ... this implies an infinite quantity of matter, which is used in some models.
    It is not usually useful to do the maths like that ... however, the maths of calculus regularly uses infinities.

    Nope - Feynman's mirror example is easily manufactured.

    Another way of putting it is that if there is no way to tell the difference between the thing that is claimed to exist and that thing not existing, then that is as good as saying that it does not exist.

    Aether is another thing that, if it is there, there is no way to detect it... ergo: not there. The math is identical so we accept the simplest model re Occam's razor.
    There have been a lot of attempts since the famous Michealson/Morley experiment and that experiment is repeated, as an exercize, by students all over the world every year.
    There are lots of pseudocience and non-science attempts too, so the topic is off-limits for PF.
    Which is a shame really since it is a nice illustration of the philosophy of science.

    The thing to remember about scientiifc models is that they are not generally throught to be True (watch the caps). More that they are the best and simplest explanations we have that are supported by the facts and have withstood repeated, diverse, and cunning, attempts to disprove them.

    Remember: It is easy to come up with models for physics that explain something otherwise hard ... the difficult part is beating current models in the rest of the categories. Good hunting with your reading.
  11. Sep 8, 2016 #10


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    In my view, this is not far from the truth. Let's take Special Relativity (SR) as an example. A serious text book on SR would:

    1a) Explain how classical physics had all the problems in terms of being unable to explain observed phenomena.

    2a) Show how SR is logical, consistent and precisely explains the observations.

    A popular book on SR may (depending on the author, as I wouldn't want to tar them all with the same brush):

    1b) Emphasise how SR shocked the classical physicist.

    2b) Emphasise how bizarre, paradoxical and just downright weird relativity is.

    I guess the belief is that to the the general public 2a is dry and boring; whereas, 2b is exciting and marketable. But, to the serious student, 2a is beautiful, enlightening and practical; whereas, 2b is spurious.
  12. Sep 8, 2016 #11


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    On the subject of QM, here's what my serious QM text book has to say about the uncertainty principle (UP). Rather than talk about the infamous cat he says:

    "You might wonder how the UP is enforced in the lab - why can't you determine the position and momentum of a particle? Niels Bohr was at pains to track down the mechanism by which the measurement of position destroys the previous value of momentum. The crux of the matter is that in order to determine the position of a particle, you have to poke it with something - shine light on it, say. But these photons impart to the particle a momentum you cannot control. His famous debates with Einstein include many delightful examples, showing in detail how experimental constraints enforce the UP."

    So, it's not so weird as a cat that's alive and dead at the same time, after all!
  13. Sep 8, 2016 #12


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    The trick is the other way around. One should emphasize

    2b') How bizzare, paradoxical and just downright weird Newtonian action at a distance is.
  14. Sep 8, 2016 #13


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    Schrodinger's cat is not a good example because it has a perfectly satisfactory classical explanation: the atom decays, the decay products trigger the detector, the signal from the detector activates the mechanism that breaks the vial of cyanide, and the unfortunate cat dies. As I pointed out above, Schodinger didn't invent the thought experiment to explain quantum mechanics, but to point out the inability of 1930s-vintage QM to properly describe cats in gas chambers.
  15. Sep 8, 2016 #14


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    It's not impossible that the subhead also reflects d'Espagnat's thinking at the time (although I wouldn't trust wikipedia on the subject - the anonymous wikipedian's source might well be the SA article) but either way it's beside the point.

    Superposition ("there is a state that is neither A nor B, but that when measured will always yield one or the other with probabilities that can be calculated from that state") can be valid and experimentally tested for whether consciousness is required to collapse the alternatives or not.
  16. Sep 8, 2016 #15


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    Well, now I'm very interested in finding an experimental test "for whether consciousness is required to collapse the alternatives or not." How should it be possible that "the collapse" happens only due to a consciousness taking note of an experimental result? This would imply that something happens to the setup an arbitrarily long time after an experiment is finished. Suppose at the LHC they had written the results leading to the discovery of the Higgs boson to their storage and nobody had looked at them yet and CERN had decided to dismantle the LHC, the detectors and everything. Do you think that now, when somebody with a consciousness analyses these stored data, something happens to the dismantled CERN or the decaying Higgs boson? Seriously? Well, then for me it's an example how dangerous philosophy can be to the sanity of scholars working in this field... ;-)).
  17. Sep 8, 2016 #16
    The quote being "The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict with quantum mechanics and with facts established by experiment."? I asked Bernard d'Espagnat last year (3 June 2015) whether he still adhered to it and he replied his view on that hasn't changed. Unfortunately Bernard died 1st August 2015, so I cannot undertake any more email correspondence with him. :(
  18. Sep 8, 2016 #17
    Yes, @StevieTNZ, that's the quote. SA is not reckless, so they probably let an article author veto the title and subheads, but perhaps a nuance is erroneous. Besides, science often advances beyond a scientist, perhaps the most famous example being, approximately, Einstein's rejection of QM. The Wikipedia quote (@StevieTNZ and @Nugatory) is attributed to the SciAm article and appears at https://en.wikipedia.org/wiki/Bernard_d'Espagnat at least as of yesterday and today. I haven't read much of the SciAm article (or, for that matter, much of Wikipedia on any related subject (Wikipedia considers itself an unreliable source on all subjects and does not allow citing Wikipedia as a source in a Wikipedia article, other than cross-linking)).

    I agree, @Simon Bridge. Someone once told me that the theory/ies of gravity is not absolutely true but is the best explanation for the known data, and, if someone can come up with a better explanation, so be it. Nonetheless, whoever proposes an alternative for a heavily-validated theorem will have an uphill struggle if they are not to fail. Anyway, I'm not planning on breaking any ground, just on learning. And agreed that QM, like many new sciences, are needed to explain known data. And I was not intending to invoke pseudoscience/nonscience or an exercise; I recall reading that it was a serious experiment, perhaps not exactly a replication of Michelson's-Morley's work but with the same goal, and I think done at Columbia University, but finding a citation now would likely be very time-consuming and it's not that important; the point I was making that that was part of is still valid (some experiments are scientifically rerun and that can be legitimate, even though it burdens people who don't follow the field as closely as others do).

    @vanhees71 on editing a book for a reversal: Good idea. I think it's been tried and it may be hard to keep people taking you seriously and maybe that's why it's not done that often, but that's just a guess.
  19. Sep 8, 2016 #18
    My understanding is uncertainty arises because position and momentum are not pre-existing properties intrinsic to the particle. You can control the macroscopic measuring device's disturbance of the particle's momentum by measuring the particle's position less precisely. Even if you have only a vague idea of any particle's position (and hence you are causing almost no disturbance), if you measure a sufficiently large ensemble of particles, you can measure both position and momentum of the ensemble simultaneously to hypothetically any degree of precision.
  20. Sep 8, 2016 #19

    Stephen Tashi

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  21. Sep 8, 2016 #20
    There is a difference between saying only what you know, and saying that only what you know is true. The first is positivism, the second is vulgar positivism. There is a current of the second in certain discussions about QM. The cat is either dead or alive. We have powerful equations that tell us the probability of either. Before you open the box, the cat is either dead or alive. When you open the box, the cat is still either dead or alive, only now you'll find out which.
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