Uncertainty – The Key to Quantum Weirdness

All these fifty years of conscious brooding have brought me no nearer to the answer to the question, ‘What are light quanta?’ Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken.

                       Albert Einstein, 1954

As 1926 was coming to a close, the physics world lauded Erwin Schrodinger and his wave mechanics. Schrodinger’s purely mathematical tool was being used to probe the internal structure of the atom and to provide predictable experimental outcomes. However, some deep questions still remained – primarily with the idea of discontinuous movements of the electron within a hydrogen atom. Niels Bohr, champion of and chief spokesperson for quantum theory, had developed a model of the atom that explained spectral lines. This model required an electron to move to a higher energy level when absorbing a photon, and releasing a photon when it moved to a lower energy level. The point of contention is how the electron was moving. This quantum jumping, as Bohr called it was said to be instantaneous. And this did not sit well with classical minded physicists, including Schrodinger.

un_02
Source: Eureka Physics

At this point in time, Erwin Schrodinger favored the idea of ‘wave packets’, and that matter was simply a concentration of these packets. This allowed for a clearer picture of wave/particle duality. Schrodinger understood that there were many holes in this idea, but he believed they would be worked out over time. In August of 1926, he would meet up with Bohr and a man by the name of Werner Heisenberg in a debate that would send the understanding of quantum theory in a new direction.

Schrodinger would have nothing to do with this “damned quantum jumping” as he would later recall. His classical wave theory had continuity and was easy to visualize. But Bohr and Heisenberg held steadfast in their philosophical view that it was not possible to visualize such quantum phenomenon. The debate raged on, and neither side was able to convince the other. However, all three were moved by the debate…most notably Werner Heisenberg. He had long given up on classical space-time visualizations within the atom and instead relied on theory and results of laboratory experiments. But Schrodinger had forced him to step back and try to visualize at least some atomic aspects. And this would lead him to one of quantum physics’ most important discoveries.

Uncertainty

After the debate, Heisenberg began to ponder the path of an electron through a cloud chamber. This was an obvious way to visualize the position and momentum of an electron. Why could he not visualize such a path of the electron orbiting a hydrogen atom? After exchanging some correspondence with Wolfgang Pauli, he realized that he could reinterpret the square of the electron’s wave function. Instead of giving the probability of being in a specific state, this reinterpretation would give a probability of being in a particular location in the orbit of the atom. Doing so allowed Heisenberg to take Schrodinger’s wave mechanics and his insistence on being able to visualize the innards of atoms and apply his beloved matrix mechanics.

It was Pauli that would make the first connection between the position and momentum of the electron with wave mechanics. Viewing two electron waves on a collision path, one would find that each had a clear position (q) and momentum (p) while they are far apart. But as they come closer together, these values get ‘fuzzy’. He would write:

One may view the world with the p-eye and one may view it with the q-eye, but if one opens both eyes at the same time one becomes crazy.

Heisenberg took Pauli’s work and tried to describe the visible path of an electron in a cloud chamber. He would wrestle with this for a while before he began to ask himself some fundamental questions about what is meant by position. He realized that the position of the electron was only known because of the water droplets that condensed around its path. These droplets are much larger than the electron itself. While one might see the path readily by looking at the entire chamber, what happens when you zoom in? He realized that the position and momentum of the electron could not be known with infinite precision at the same time. Only an approximation could be measured. Heisenberg had discovered the uncertainty principle.

A Fundamental Limit of Measurement

After doing some quick math, Heisenberg found that the product of the uncertainties of an electron’s position and momentum could not be smaller than Planck’s constant. There is a fundamental limit to how accurately you can know the electron’s position and momentum. He illustrated his new findings with a few thought experiments, including the following:

un_01
Source: ChemWiki

Imagine we’re following the electron through our cloud chamber with a high powered microscope, and we wish to measure its position and velocity. The resolution of the microscope will increase with the frequency of radiation. So it would be most prudent to measure the position of the electron with a high frequency gamma ray. The problem is the gamma ray photon will affect the electron’s trajectory, which limits our ability to measure its velocity. The solution is to use lower energy radiation, so that the electron’s trajectory will not be affected by the photon. But lower energy means lower frequency. And because resolution is determined by the frequency, it limits our ability to measure its position. Which brings us back to where we started.

Heisenberg would go on to show that it is fundamentally impossible to observe (or visualize, for that matter) an electron in the orbit of an atom, and that he and Bohr were right all along. His uncertainty principle and its fundamental limitation on measurement would go on to shape quantum theory for the next several decades. It would later be applied to the concepts of energy and time, allowing “virtual” particles to blink in and out of existence, using uncertainty to escape conservation laws. This would become the basis of QED, or quantum electrodynamics.

Author’s Opinion

I’ve read several books about Quantum Theory and even performed some basic experiments. While I will not pretend to understand even a fraction of the rigorous mathematics behind the theory, I can confidently state that anyone with an interest and desire to learn most of the basic aspects of the theory can do so.

One of my gripes with these books is that they tend to start off in Chapter 01 with explaining the concept of wave/particle duality, known as complementarity. This is utterly baffling to anyone new to the theory. How can something that looks like little baseballs be the same thing as what one sees when they toss a pebble into a pond? I would argue that they should first teach the uncertainty principle and focus on the idea of limitation of measurement. It’s not confusing, but fairly straight forward and anyone can grasp the idea without much effort. Once one understands that the location of a moving “tiny baseball” can only be known with a probability less than 100%, it becomes much easier to visualize wave/particle duality. The particle is there and real, just like a little baseball. But because of uncertainty in measurement, it is impossible to actually know it’s there1. We are forced to say that there is a probability it is here, and a probability it is over there. This probability is spread out in the form of a wave. This is why tiny particles display wave-like characteristics when you try to observe (or measure) them. You end up only seeing or measuring this wave of probability, because that’s all that you can see or measure.

So by understanding the above, looking at wave/particle duality is much easier, in my opinion. Understanding uncertainty in measurement is the key to all of the quantum weirdness.

1The question of if a quantum scale object can be considered actually ‘there’, even if it is impossible to know if it’s ‘there’ is a hotly debated subject that continues to this day. Albert Einstein refused to give up causality and held on to his belief that the universe is deterministic in nature (that means the object is really there even though we can’t measure it). While Niels Bohr and Werner Heisenberg pushed the idea that if you can’t measure and know that the object is there, to say that it is there is nonsensical. They believed that on the quantum scale, things like causality and determinism simply cannot exist. I will climb out on a yagi and say that modern quantum mechanics and experiments suggest that Einstein was wrong. It would appear that the quantum tree does not make a sound if no one is there to hear it.

Sources

The Quantum Story, by Jim Baggott. Chapters 9 &10  ISBN-978-0199566846

52 thoughts on “Uncertainty – The Key to Quantum Weirdness

      1. No need to postulate actually being able to measure superposition in USB-A at room temperature, as this is quite a difficult experiment involving laser-cooling and magnetic traps for macroscopic connectors.
        As a matter of fact, this behaviour is a quite elementary result of USB type A connectors, like most other commonly used connectors (e.g. the three-row DE-15 connectors used for VGA), being fermions: they are spin 1/2 connectors, and as such have 720° rotational symmetry, not 360°. See eg https://en.wikipedia.org/wiki/Spin-%C2%BD
        This, btw, is in contrast to bosonic connectors like 3.5mm audio plugs or DC barrel connectors, which, being of spin 0, do not have a preferred axis.

        Of course for *micro* USB, the phenomenon described above by Evaprototype is quite readily observable in even only slightly chilly environments.

      2. Oh, and as an interesting and not very widely known factoid, this is also the primary reason USB-C took so bloody long. It is highly nontrivial to engineer reliable spin 2 (i.e. gravitonic!) connectors that have 180° symmetry. I still cant wrap my head around how Apple managed to pull this off so effortlessly with magsafe, lightning etc! They must have some amazing IP still slumbering in Steve Jobs’s alien spaceship…

  1. “If you think you understand quantum mechanics, you don’t understand quantum mechanics.”–Richard Feynman, et. al.
    On being asked to prepare a lecture on why spin-one-half particles obey Fermi-Dirac statistics, Feynman said, “I’ll prepare a freshman lecture on it.” But he came back a few days later to say, “I couldn’t do it. I couldn’t reduce it to the freshman level. That means we don’t really understand it.”
    “The universe is not only queerer than we imagine, but queerer than we can imagine.” JBS Haldane, 1927

  2. “Heisenberg would go on to show that it is fundamentally impossible to observe (or visualize, for that matter) an electron in the orbit of an atom”

    Heisenberg would go on to show that it is fundamentally impossible to observe an electron in the orbit of an atom by using only photons. FTFY.

    This is my biggest gripe about quantum physics, the “light speed” limit, and other asinine unproven assumptions. We know about planck scale. That is, we’ve proven (with math) that there must be packets many many orders of magnitude smaller than what we’ve been able to observe, in order for us to have observed the things we have observed. Given this information, to assume that there is nothing in between the scale of leptons and planck scale, is just plain stupid.

    I wish there were a less inflamatory word, but stupid fits. “exhibiting the quality of having been done by someone lacking in intelligence”, since the obvious oversight is so obvious, as well as secondary definition “Characterized by or in a state of stupor; paralysed.” which is exhibited with the phrase “fundamentally impossible”. They’ve given up. They’ve stopped thinking. Not because they’ve proven something, but because they reached the limits of their own (limited) imaginations.

    Disagree? Tell me all about neutrinos. Go on. Tell me everything we as humanity know about them. Then tell me again that we are certain there is nothing smaller, or that goes faster than light speed. Tell me exactly how we’re certain. Because we’re fucking not.

    1. Thank you! One of my biggest gripes about the last several decades of physics, is that there are far too many results defining what we “can’t” do. As a hacker (and someone who studied physics in college), it galls me. An important part of both fields is cleverly working around limitations, and it seems quite clear that many of the limitations in physics are properties of the measuring tool (i.e. light).

      For now, we may have to fudge around the limits (quantum squeezing of uncertainty, entangled particle tricks, etc.), until we can grok enough of what’s going on underneath to make practical use of it. But there are still too many obvious mysteries in physics to think we’ve run out of steam (or tools) yet.

    2. Light speed is not arbitrary and it isn’t just a property of light. EM is required to propagate in a vacuum at the maximum rate allowed by anything, including information. If something new is discovered let’s call it the damnthatsfastino, that could not travel faster than c, because if travelling faster than c were allowed, light would be forced to do it.

      This comes together in special relativity as everything always travels at c all of the time in 4D, which is why time slows down as an accelerating object approaches c – it’s literally travelling slower in the time direction.

      1. EM is required to propagate in a vacuum at the maximum rate allowed by anything, including information.
        So you are claiming there is no such thing as Dark Matter or Dark Energy? What about non-charged particles? What part do they play if EM is the Master Of Everything? For that matter, why should we assume that there is only “plus”, “minus”, and “neutral”. After all, they are merely distinctions and definitions of each other (this != that). To assume there is nothing else is unproven hubris.

        1. I say nothing about the existence of dark matter, dark energy or black swans, but if they exist, they must all be subject to the same laws of physics everything else is, including EM.

          Are these laws absolute? Finding a particle that travels faster than c in a vacuum would break physics theory into a million bits. It could not be patched up, it’s self consistent. You’d need a fresh theory that explains everything every bit of physics does now as well as why the old theory worked for everything except the new particle. It would need to fit with every bit of physics that’s been proved axiomatically and every practical experiment ever done.

          It’s more likely someone is going to take off my VR goggles, wish me better luck next time playing “Earth” while I dress in a boiler outfit attached to a Dwayne Dibbley ID card.

          1. No, it wouldn’t. Because “travel” doesn’t mean what you think it does.

            The speed of light is the fastest that information can travel in spacetime. But that doesn’t mean you can’t deform spacetime to make the trip be *less actual distance*. You’d never actually be travelling faster than a light beam running along with you. You’re just actually making the trip shorter.

            “but if they exist, they must all be subject to the same laws of physics everything else is, including EM.”

            It’s not electromagnetism. *Any* massless particle travels at the speed of light, because lacking mass, there’s literally nothing to slow you down.

          2. cyberteque, re swans – awesome. We only have white ones, which I guess is how this became a standard way to teach evidence (and lack of) based conclusions.

            Pat, travel in my book would be relative to the path the particle actually took. I’m sorry if I didn’t make that clear.

            “It’s not electromagnetism” – you mean *just* electromagnetism, it does fall from Maxwell separately.
            “*Any* massless particle” – you mean rest mass and I’m not just picking pointless holes.
            I personally find the Maxwell route more convincing. Physics is the same for all observers and therefore c? Cool. Particle has no rest mass therefore c, oh but what about mass energy? Oh still c, why doesn’t it make a difference? It just doesn’t mmkay. Possibly a feature of the way I was taught special relativity. Maxwell climbs into a train and plays chicken with Time and his laws hold and it’s Time that dodges out of the way with beta falling out of right angled triangle maths – awesome. It’s just a shame GR needed the maths jump it did.

      2. And along comes Alcubierre and says, “hey maybe we can work around this light speed limitation by warping *space* *itself*”, in accord with Einstein’s field equations:
        https://en.wikipedia.org/wiki/Alcubierre_drive

        Of course, you haven’t said why the speed of light is a property of the vaccuum, or why “empty” space should have permittivity or permeability, or a frothing Dirac-sea of virtual particles at all. And if that’s something that can be modulated, then so can the speed of light (which we know is possible in one direction, slower, by just adding matter). The Cosmological-Constant fudge-factor made it clear that there is plenty we don’t really understand space itself yet.

        And if we do discover a Damfastino (faster than c), then it wouldn’t be travelling via oscillations of the electric and magnetic fields. Which means it would have to be detected in some indirect way, or with non-EM based tools. And that’s the fundamental problem: EM-based tools (including our eyes) have been so useful and ubiquitous that we’re not really thinking enough about how non-EM things might work, or where/how to look for them.

        1. If you allow energy to go negative and mass to go negative then all kinds of amazing solutions are allowed even with basic physics. Perpetual motion machines for example, thermodynamics shouldn’t exist. The Alcubierre drive is massive overkill if you are going to allow negative energy machines. Weirdly if I said I was going to vent negative energy, a process that requires no effort, to heat my house for free people would think I was retarded, but a GR solution to a warp drive lacks the same ring of idiocy even though the requirement is the same. It can’t be tested, no one even knows how it could ever be built and it’s in conflict with a major result by Hawking as well as the grandfather paradox so the smart money is on that universe not being our universe.

          If “empty” space had no permittivity light would bounce off it, along with all charged matter, if I existed I like to think I’d call it the sky mirror. I’ve not put any restriction on the damnfastino, and when physics forbids something, the method does not matter.

          1. Sure, Alcubierre is totally speculative at this point. I merely point it out as an example of working around assumptions that seem iron-clad.

            But you are putting a restriction on the damnfastino: you’re assuming that it has a significant electro-weak interaction with free space. That position is roughly analogous to a blind person saying that no wave can travel faster than the speed of sound, because they haven’t discovered light yet. Just as neutrinos could pass thru your “sky mirror”, there could be FTL particles whizzing around you right now. But you wouldn’t know, because they would have to be mass-less, and have incredibly limited interactions with normal matter. The method absolutely matters, because it puts boundaries on what *exactly* is forbidden and why.

          2. Negative energy density doesn’t mean what you think it means. For an Alcubierre drive, all it really means is that it acts the opposite of matter (e.g. it would push things away, not pull them together).

            “but a GR solution to a warp drive lacks the same ring of idiocy even though the requirement is the same.”

            Yeah, it’s totally nuts! I mean, the idea that you have some negative pressure thing that causes space to expand, moving things apart faster than the speed of light. That’s just totally nuts!

            Before you go ahead and ridicule things, you might want to understand that there is, in fact, weirdness in the Universe.

          3. timrc,
            The Alcubierre drive is not an example of working around an iron clad rule, it hits it straight on. As a solution it’s impossible for more reasons than an abstract tachyon. Usually one impossibility is enough.

            I do not see the implicit electro-weak restriction, but if the particle doesn’t interact with any force then it isn’t forbidden on causality grounds. ‘Limited interaction’ is not the same as forbidden, space is not slowing it and the method does not matter. It’s like saying – yes thermodynamics says perpetual motion is impossible, but my machine does it a *new* way.

            Pat,
            Allowing properties of negative mass/energy in the Alcubierre drive may seem reasonable to you, but if negative mass/energy is allowed, it should be allowed everywhere. The inertia of negative mass does work against an applied force. Weirdness in QM is the norm but this is slight of mind.

            You should probably read through a page before linking to it, especially if you are trying to make someone look foolish. That page suggests that the growing universe appears to violate the second law of thermodynamics because moving from a perfect sphere to a complicated structure is a drop in entropy. It also suggests that the universe growing faster than the speed of light is like two planes flying away from each other at their maximum speed.

            I assume the point you believed was a devastating counter to my objections to negative energy is the ‘negative energy or positive pressure’ implicated in inflation theory, which takes place before the higher dimensions collapsed, when magnetic monopoles roam and for all I know goblins dip their toes in the primordial soup.

  3. “The foolish and wicked practice of profane cursing and swearing is a vice so mean and low that every person of sense and character detests and despises it.”–George Washington

    “A single profane expression betrays a [person’s] low breeding.”–Joseph Cook

    “Profanity is the effort of a feeble brain to express itself forcibly.”–Spencer Kimball

    “Rudeness is the weak [person’s] imitation of strength.” – Eric Hoffer

    1. “quoting people is how stupid people make themselves look smart and sound important without having to know or understand anything” — Lord Quantas de Fabrike

      https://yourlogicalfallacyis.com/tu-quoque

      It really annoys me when people completely ignore the content of what someone is saying just because of how they talk (type). It is a particularly repugnant form of ignorance.

      1. “I would like to take you seriously, but to do so would affront your intelligence.”–Wm. F. Buckley

        Poor, stoopid Winnie Churchill, who obviously didn’t know or understand anything…
        “It is a good thing for an uneducated man to read books of quotations. Bartlett’s Familiar Quotations is an admirable work, and I studied it intently. The quotations when engraved upon the memory give you good thoughts. They also make you anxious to read the authors and look for more.”–Winston Churchill

        Your acquiescence is particularly appreciated (“tu quoque”): “…It is a particularly repugnant form of ignorance.” As is the acceptance and defence of obscenities in trying to appear erudite; as well as an indication of “low breeding”.
        “Profanity is the Last Refuge of the Truly Ignorant”, including those who use it AND those who accept it.
        Blockhead, brain-dead millenial.

        Tu quoque. Verbum sedes sat sapientiae.
        Although it appears there ain’t many sapientiae around these parts.

        1. You are mean, which is just as bad as being rude, only with an additional and intentional insult. We are not your match in word parrying, and we don’t even think it is worthy of trying to become that, because our common idea is cooperation, sharing and building, not honing and storing our sharp and pointy idioms to be used to belittle others. It seems you came to plunder intellectual supremacy acknowledgement, yet we don’t cache that kind of treasures here – someone sold you a fake map. If you wish to stay among us uneducated idiots because perhaps we are cute playing with our toys, please consider changing your ways. If you are here just to rattle our collective cage, please leave. Either way, thank you for your visit.

    2. “Bollocks it does”. My brain’s not weak and I swear like a fucking trooper. There’s as much art and skill in swearing properly as there is in any other part of language.

      Interestingly, if you study that sort of thing, Gordon Ramsay, famous radgey-chef, can’t actually swear properly. He gets the basic grammar of saying “fuck” wrong. He also manages not to swear when he’s not allowed to. Which means he goes to special effort when he is expected to. Dickhead puts it on. They must have laughed him out of the changing room of whatever football team he was in.

  4. “How can something that looks like little baseballs be the same thing as what one sees when they toss a pebble into a pond?”

    Because it’s not a baseball! Who said anything about particles looking like baseballs?

    Wave/particle duality really isn’t weird magic. You see it all the time. Take a drum head, for instance. Whack it crazy, and it just bubbles around and wouldn’t really look like anything. Excite it at the right fundamental frequency, though, and you get a clear standing wave on the drum. That’s all it means. You’ve got a medium that you can only create discrete states in, and those discrete states are quanta. Nothing magic.

    I also have to say I that this comment: “and focus on the idea of limitation of measurement. ” – really misses the mark. It’s not a limitation of measurement. It’s a limitation of the *very idea of position and momentum in the first place*. Particles don’t really have position and momentum at all. All they have is a history of interactions with other particles. And when you quantize those interactions, that gets you the position/momentum uncertainty.

  5. “The particle is there and real, just like a little baseball. But because of uncertainty in measurement, it is impossible to actually know it’s there1. We are forced to say that there is a probability it is here, and a probability it is over there. This probability is spread out in the form of a wave. This is why tiny particles display wave-like characteristics when you try to observe (or measure) them.”

    Doesn’t the double-slit experiment disprove this “little baseball” analogy?

    1. Not really. There’s different ways you can approach it, but if you want to maintain your sanity, I suggest you think of particles as tiny baseballs, and their wave characteristics as waves of probability that corresponds to its location. If you try to locate the tiny baseball to see which slit it went through, then the wave characteristics goes away because you know where it is. This is usually refereed to as “collapse of the wave function”. If you do not try to see which slit it went through, then its location is governed by probability and you will observe wave like characteristics.

      1. Nonono.

        Don’t think of it as a baseball. It’s not a baseball! Think of it like a standing wave on a drum head, oscillating around but *confined* – not spreading out like someone dropping a rock in a pond. (What’s doing the confining? That’s the mass of the particle – it’s being confined by space itself.)

        Now imagine pushing opening up the ‘confinement’ on one side, as it’s still excited. That’s like accelerating the particle, letting it move.. The standing wave starts rippling out on the side you opened. OK, so you’ve got a double slit experiment then, and it diffracts through the double slit.

        What about the “try to locate the tiny baseball”? Locating the quanta means *interacting* with it, so it’s like setting up *more* confined standing-wave patterns at each of the slits. Depending on how the phase of those oscillating patterns at the slits are interacting with your “propagating” wave, one of them interacts (or neither! no one said the particle always gets through!) and the interaction produces a *new* standing wave, starting out from that point.

        The wave characteristics don’t go away ‘magically.’ Interacting in the one slit *tells* you about both the incoming quanta and your measurement apparatus. The ‘collapse of the wavefunction’ is just the collapse of *your uncertainty* about the initial state of the particle.

  6. still, there is something to be said about the ‘classical’ mathematical introductions to quantum mechanics. For example it really helps to have some intuition of Fourier transforms of different 1-dimensional complex functions, and how scaling etc affects the Fourier transform of different example functions. Then postulating that a quantum wave function in one domain (say position space) implies a corresponding wave function in the impulse domain, namely the Fourier transform. Then all the previous intuition about Fourier transforms more quickly links to the quantum mechanics theory. For example making a gaussian wave packet smaller in one domain broadens the gaussian wave packet in the other. Also of interest is how while this is all true for single packets, it simultaneously tells us another mathematical fact should have a correspondence: the Fourier transform of an impulse train (i.e. arbitrarily sharp impulses)… is another impulse train! So the resolution tradeoff has at least some caveats when it comes to repetitive functions!

  7. After I read this article, I broke out my Quantum Mechanics book from undergrad, “Introduction to Quantum Mechanics, 2nd Ed.” by David J. Griffiths. This last half of this book spends a lot of time on formalism, however the first half of the book is quite good if you are interested in both learning the basic concepts AND how to do all of the associated math. Also, the book is written in a slightly-less-dry manner as compared to a normal textbook. If you want more than just a cursory overview of Quantum Mechanical concepts, it *may* be worth your time.

  8. Kudos to you for actually explaining where “uncertainty” actually comes from – too often I see the topic brought brought up and the limitation of how an “observation” actually works is completely glossed over.

  9. “It would appear that the quantum tree does not make a sound if no one is there to hear it.” Have you ever realise that where there are no ears, there’s never any sound, only motion?
    Indeed, if we define sound as the “pressure changes in an elastic medium capable of being detected by the ear.” The only thing that a falling tree does is create a “pressure changes” in the ambient atmosphere; which are eventually intercepted by ear lobes; concentrate by ear canals; transform into motion in inner ears by tympans; transmitted by small bones; which create waves in a the fluid inside cochleas; which are transduced into electrical signals by cilia; then transported by ear nerves to brains, where sound are produced.
    So, no brain, no sound. Only motion.
    It is the same with the moon, when there is nobody to look at it, there is no moon, only electromagnetic waves. Our brains create the “spatiotemporal objective” world in which we live.
    See agaudreault.com. I will not talk about this for the moment, only later in the conclusion of my dissertation: De evolutionibus res naturas.

  10. Uncertainty is not new to the author of a book. Characters have all kinds of undefined attributes that stay undefined unless those attributes are involved in a character’s interaction with the story. Bilbo Baggins’ short stature was a significant part of the story and consequently given form and is observed by both author and reader . Whether his belly button is an innie or an outie is undefined and exists in superposition between both states and will stay that way since Tolkin is done writing. I think reality is a lot like that, with many features defined and other not so well or at all. There is also a parallel between a logical and consistent story and a real world that is coherent and respects causation between events with both the natural world and the Author injecting effect. There is no real randomness, only events that are simply uncorrelated with anything we can control or observe including the actions of the Author’s “pen”. Of such things we observe the illusion of uncertainty. Unfortunately many people’s egos are WAY to big to accept the idea of being a mere character in someone else’s book, that someone being “the one who really exists”. That is unfortunate, considering this is the best explanation of life, the universe, and everything that I’ve been able to put together. (much better than 42 :-) )

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