Please create an account to participate in the Slashdot moderation system

 



Forgot your password?
typodupeerror
×
Science

Why Even Physicists Still Don't Understand Quantum Theory 100 Years On (nature.com) 79

A century after quantum mechanics revolutionized physics, scientists still cannot agree on how the theory fundamentally works, despite its tremendous success in explaining natural phenomena and enabling modern technologies. The theory's central puzzle remains unresolved: the way quantum systems are described mathematically differs from what scientists observe when measuring them.

This has led to competing interpretations about whether quantum states represent physical reality or are merely tools for calculating probabilities. As researchers debate these foundational questions, quantum mechanics has enabled breakthroughs in particle physics, chemistry, and computing. It accurately predicts phenomena from the behavior of atoms to the properties of the Higgs boson, and underlies technologies like quantum computers and ultra-precise measurement devices. The field's inability to reach consensus on its foundations hasn't hindered its practical applications. Scientists continue to develop new quantum technologies even as they grapple with deep questions about measurement, locality, and the nature of reality that have persisted since Einstein and Bohr's famous debates in the 1920s and 1930s.

Why Even Physicists Still Don't Understand Quantum Theory 100 Years On

Comments Filter:
  • Humans used bows, and even thrown rocks effectively far before Newton's Laws of Motion.
    • by evanh ( 627108 ) on Monday February 03, 2025 @02:54PM (#65139099)

      That's the opposite process! Newton put paid to the questions rather than the other way around.

    • by Brain-Fu ( 1274756 ) on Monday February 03, 2025 @02:54PM (#65139105) Homepage Journal

      Yes, our brains evolved to understand the high-level phenomena that occur when uncountable numbers of atoms combine to form predatory animals. We are really good at understanding everything that hunter-gatherors need to understand. Unfortunately, the key principles at work in such an environment are all emergent phenomenon. The root causes work very differently.

      It is possible that our brains are simply ill-equipped to ever truly grasp the foundational aspects of physical reality. They may simply be too different from what we would consider "ordinary life" for us to get our heads around them. Of course, that is no reason to stop trying.

      But we DO live in a world where scientists still argue about things like whether numbers are real things with an independent existence of their own, or an imaginary tool our mind uses to understand real things. If we can't figure out something that basic, then we don't have a prayer of coming to agreement on the much more mysterious and complex observations of quantum physics.

      • by gweihir ( 88907 )

        Has somebody ever told you that Physicalism is belief and that you are giving pure speculation when you limit the human mind to the brain? In fact, there quite a few indicators that this is a faulty model, like consciousness (there is no mechanism for it in known Physics) and general intelligence (which may well also be impossible with known Physics)?

        But we DO live in a world where scientists still argue about things like whether numbers are real things with an independent existence of their own, or an imaginary tool our mind uses to understand real things.

        That is complete nonsense. No competent scientist would argue that numbers are elements of physical reality. They are a purely mental concept that requires _ab

        • by erice ( 13380 )

          Has somebody ever told you that Physicalism is belief and that you are giving pure speculation when you limit the human mind to the brain? In fact, there quite a few indicators that this is a faulty model, like consciousness (there is no mechanism for it in known Physics) and general intelligence (which may well also be impossible with known Physics)?

          We have no reliable definition for consciousness. Until we do, any attempt to explain how it works is premature. This is not a weakness of physics.

          General intelligence is a little better defined but I think society will still refine the term as technology advances to insure that no machine has it.

          • by gweihir ( 88907 )

            We have no reliable definition for consciousness. Until we do, any attempt to explain how it works is premature. This is not a weakness of physics.

            That is bullshit. Consciousness is real and hence no definition is needed. Incidentally there are quite a few descriptive definitions for it, just no Physical ones because this is one of the giant glaring holes in current Physics.

            General intelligence is a little better defined but I think society will still refine the term as technology advances to insure that no machine has it.

            Actually, it is not better described at all. Nobody knows what General Intelligence is. The only descriptions that exist for it are pure interface behaviors and the same is true for consciousness.

            • by erice ( 13380 )

              We have no reliable definition for consciousness. Until we do, any attempt to explain how it works is premature. This is not a weakness of physics.

              That is bullshit. Consciousness is real and hence no definition is needed. Incidentally there are quite a few descriptive definitions for it, just no Physical ones because this is one of the giant glaring holes in current Physics.

              And that, is why you fail. If you can't define what you mean in way that you be tested, then "it is real" is just navel gazing nonsense. If we had clearly described behaviour that physics could not explain that would be a problem with physics. But we don't. We have multiple definitions that all boil down to "ghost in the machine". In terms of actually described behaviour, we have incomplete descriptions of the actions of neurons then many many poorly understood when understood at all aggregations leadin

        • Has somebody ever told you that Physicalism is belief and that you are giving pure speculation when you limit the human mind to the brain? In fact, there quite a few indicators that this is a faulty model, like consciousness (there is no mechanism for it in known Physics) and general intelligence (which may well also be impossible with known Physics)?

          This is arguing from ignorance. Remarks above are no different from dunno therefore could be aliens.

          The only reason why some people argue is that they cannot deal with the idea that a human mind may be more than a purely physical thing, with respect to currently known Physics. That is what happens when you argue from belief, not Science.

          Absent credible evidence of the same you should not expect anyone to care. There is an infinite field of possibilities anyone can dream up that likewise cannot be ruled out. Inability to prove a negative is not a valid reason for anyone to care.

          You know, like the religious fuckups do with their bizarre ideas of how things work. Physicalism is really not much better. It essentially is a more sophisticated version of "intelligent design" where the "God" becomes implicit. Just as stupid though.

          This is a specious and backwards statement. While it is not correct to assume there are no aliens the distinction is effectively moot so long as there remains no e

        • belief and that you are giving pure speculation when you limit the human mind to the brain?

          There is no evidence of the existence of anything other than this reality and physical universe. Actually the evidence show rather that our consciousness is the brain. Accidents, surgeries, etc can fundamentally alter your consciousness and in fact completely change you and your personality. Chemicals such as drugs can do the same.

        • by keltor ( 99721 ) *
          > That is complete nonsense. No competent scientist would argue that numbers are elements of physical reality. They are a purely mental concept that requires _abstraction_, which requires _insight_, and nobody knows how the human mind does it. Also note that most human minds struggle with the idea of numbers or do not get it at all .,.

          Combinatorist here ... even on the mathematics side of things, this is a deep pool and the bases of all math is a bunch of assumptions. Quantum mechanics really messes wit
          • Combinatorist here ... even on the mathematics side of things, this is a deep pool and the bases of all math is a bunch of assumptions. Quantum mechanics really messes with those assumptions because maybe 1+1=2 OR maybe it also is 1+1=3.

            No, quantum mechanics does not "mess" with the assumptions(*) of mathematics. Quite the contrary: quantum mechanics relies heavily on mathematics to calculate predictions. If suddenly 1+1 equaled 3, then you're not dealing with reality anymore, or at least with a number system that has any utility for quantum mechanics.

            Quantum mechanics has presented challenges to physicists and mathematicians, causing new branches of mathematics to be developed (e.g., theory of Hilbert spaces and applications of group theo

        • No competent scientist would argue that numbers are elements of physical reality.

          Oh it gets weirder than that. "Platonism" hold that numbers are "abstract objects" which means they don't have a physical existence but they nonetheless have a "real" existence that is completely independent of our thoughts about them. This is to say, even if no humans existed at all, and even if no conscious beings existed at all, numbers would still exist as real (but non-physical) things.

          The belief known as "Mathematicism"

        • by Potor ( 658520 )

          Has somebody ever told you that Physicalism is belief and that you are giving pure speculation when you limit the human mind to the brain? In fact, there quite a few indicators that this is a faulty model, like consciousness (there is no mechanism for it in known Physics) and general intelligence (which may well also be impossible with known Physics)?

          But we DO live in a world where scientists still argue about things like whether numbers are real things with an independent existence of their own, or an imaginary tool our mind uses to understand real things.

          That is complete nonsense. No competent scientist would argue that numbers are elements of physical reality.

          Numbers can be real - in fact, more real than mutable physical reality - without being "elements of physical reality." In fact, that has always been the claim of mathematical realism.

      • by jonadab ( 583620 )
        > But we DO live in a world where scientists still argue about things like whether numbers
        > are real things with an independent existence of their own, or an imaginary tool our
        > mind uses to understand real things.

        Mathematicians don't have to argue about that. Well, not in general. There are some arguments about whether certain specific *classes* of numbers are fundamental properties of the universe or, or made-up concepts (e.g., infinitessimals); but there's no question at all about the really i
      • It is quite funny, both posts above mine argue that it is obvious, but on different sides of the argument:

        gweihir: "That is complete nonsense. No competent scientist would argue that numbers are elements of physical reality. They are a purely mental concept that requires _abstraction_"

        jonadab: "Mathematicians don't have to argue about that. There are some arguments about whether certain specific *classes* of numbers are fundamental properties of the universe or, or made-up concepts (e.g., infinitesima
      • Yes, our brains evolved to understand the high-level phenomena that occur

        Our brains evolved to model reality. That's why they work well in novel situations we've never been exposed to in evolutionary scales. It's why we dominated all other forms of life, and then some, and have the capacity to turn around and say oh shit.
        The strategies and methods a person uses to fill in the gaps in the model is their prerogative, but we are 100% built for modeling reality.

        It is possible that our brains are simply ill-equipped to ever truly grasp the foundational aspects of physical reality. They may simply be too different from what we would consider "ordinary life" for us to get our heads around them. Of course, that is no reason to stop trying.

        It's kind of like the concept of Turing Completeness, your brain and the universe are Turing equivalent. You can always do

    • by Sique ( 173459 )
      And? Squids have really good eyesight, and they never had a Max Planck, that we know of. And bees have an incredible sense of smell without any lessons in Organic Chemistry.
    • Humans figure out how to throw a baseball naturally, with lots and lots of trial and error. Eventually they learn how to get that ball to get close to their target. Meanwhile, armies wanted to get their projectiles to land on their enemies more accurately. Expensive projectiles. Trial and error is not a good approach here, why send a thousand cannon balls that all miss when you can do some math to create a table and then look up the parameters to get the cannon balls there on the first try? Or maybe, le

    • by gweihir ( 88907 )

      True. But Quantum Theory is used for deep predictions which are experimentally out of reach at this time (and maybe forever). That is a different application. Of course many people massively overestimate the worth of the theory and essentially mistake it for a GUT (a "theory of everything", which we very much do not have), because there are not only the problems described in the article, there are some fundamental holes (for example quantum-gravity, general intelligence which at least some humans can use, c

  • by SoftwareArtist ( 1472499 ) on Monday February 03, 2025 @02:53PM (#65139097)

    The reason we don't understand it is simple: we have lots of theories that all make identical or almost identical predictions. (We call those theories "interpretations" of quantum mechanics.) Since they all explain the data equally well, we don't know which one is right. That doesn't stop lots of people from forming religious beliefs that one interpretation is obviously the right one.

    That's also why it doesn't stop us from solving practical problems. Since all the interpretations are equally good at predicting experiments, you can pick any one you want, and they all do a great job.

    • by giampy ( 592646 )

      Exactly!

    • Re: (Score:3, Insightful)

      by SpinyNorman ( 33776 )

      Interpretations play no part in predicting experimental outcomes, which is what the theory itself does. Interpretations are just ways of trying to understand it - trying to understand the relationship between the strangeness of quantum behavior and the classical world that we are familiar with.

    • by gweihir ( 88907 )

      That doesn't stop lots of people from forming religious beliefs that one interpretation is obviously the right one.

      Indeed. Or from claiming we know "everything". Which is very obviously not the case, we are obviously missing some very fundamental things. Making predictions, even with a known incomplete and flawed theory is still ok to do. But one must never forget they are predictions, not statements of truth, and must be verified against actual reality before they get validity. In a sense, predictions from theory only tell you what you should probably try in the real world.

    • by ceoyoyo ( 59147 )

      We have one theory that makes very good predictions. We have a bunch of stories we tell ourselves about it and call these "interpretations."

      The interpretations are stories, not theories. They don't make predictions, they're attempts we've made to use analogies to explain the predictions. There are several perfectly good interpretations too, we just don't like the implications.

    • by clovis ( 4684 )

      Quantum mechanics is easy to understand. All you have to do is understand photons and go from there, lol.

      • Quantum mechanics is easy to understand. All you have to do is understand photons and go from there, lol.

        I think I can safely say that nobody understands quantum mechanics. -- Richard Feynman

  • by Anonymous Coward

    The theory's central puzzle remains unresolved: the way quantum systems are described mathematically differs from what scientists observe when measuring them.

    What a horrible sentence. It pivots completely around the word "described" and they aren't even using it in a mathematical sense!

    Quantum mechanics, that is to say the math, predicts observations and measurements flawlessly.
    It has never once given an incorrect answer.

    The actual puzzle is that it makes no sense why the math should work.

    Spin this ball around once and it has rotated 360 degrees. Spin this other ball around once and it only rotated 180 degrees and one of its fields is backwards. Spin it aroun

    • Re: (Score:3, Insightful)

      Quantum mechanics, that is to say the math, predicts observations and measurements flawlessly. It has never once given an incorrect answer.

      Quantum mechanics produces many results that are not correct on a macroscopic scale. We don't see superpositions, for example. Schrodinger's alive and dead cat is a classic thought experiment intended to illustrate the deficiencies in QM as a complete theory - not to imply that alive/dead cats are real.

      And spinors, which you are describing are not even quantum! They are a characteristic of electrons, but have no "quantum leaps" in their states buried anywhere in their math. You might has well try to compar

    • by jonadab ( 583620 )
      Your description isn't wrong. It's too unrelated to reality to be wrong. You're speaking in macroscopic terms, and it doesn't have anything to do with quantum mechanics.

      For example, you're trying to interpret the word "spin" based on the way we use it in the macroscopic world, with reference to objects that have a specific shape and thus can look or be different when viewed from different angles. Sub-atomic phenomena don't have shape in that sense. They don't have a front and back and sides that are dis
  • by bugs2squash ( 1132591 ) on Monday February 03, 2025 @02:59PM (#65139121)
    If you think you understand quantum mechanics then you don't, apparently so they're stuck in an understanding loop.
    • If you think you understand quantum mechanics then you don't, apparently so they're stuck in an understanding loop.

      I like to believe this means the more we understand about it, the more complex reality actually becomes thus you don’t. We need to stop now while we are ahead. /s

  • by AeiwiMaster ( 20560 ) on Monday February 03, 2025 @03:14PM (#65139163)

    I recently finished an article, which suggest gauge waves as a possible explanation
    underlying quantum mechanics, gravity and dark energy.
    See https://www.researchgate.net/p... [researchgate.net]
    I also suggest a gauge wave detector called a quantum lens, to experimental verify the predictions.
    I am currently looking for funding and a team to build the detector.

  • It's not the "theory" that physicists don't understand; it is quantum *mechanics* that is not fully understood. Each of the theories (mathematical models) was devised by physicists who understood perfectly well how the mathematics would work. But as pointed out in the body of the summary, not all of the models (theories) agree with each other, and none of them seems to agree exactly with all of the observations of quantum mechanics at work.

    Quantum theories are understood; quantum mechanics is not.
    • But as pointed out in the body of the summary, not all of the models (theories) agree with each other, and none of them seems to agree exactly with all of the observations of quantum mechanics at work.

      The model interpretation differences, for any practical difference able to be measured today or dug for in todays data, are nonexistent. That’s the problem, there is no way today, in some cases no conceivable way for the foreseeable future, to tell the difference between interpretation method and actual data. No experiment can be done so it limits understanding, at least until technology can catch up or some fundamental breakthrough in understanding comes along which is unlikely given the lack of da

      • ^wavelengths than the gravitational waves we detect now to get some clues..
      • But as pointed out in the body of the summary, not all of the models (theories) agree with each other, and none of them seems to agree exactly with all of the observations of quantum mechanics at work.

        The model interpretation differences, for any practical difference able to be measured today or dug for in todays data, are nonexistent. That’s the problem, there is no way today, in some cases no conceivable way for the foreseeable future, to tell the difference between interpretation method and actual data. No experiment can be done so it limits understanding, at least until technology can catch up or some fundamental breakthrough in understanding comes along which is unlikely given the lack of data. Small irregularities are sought after as the way to cement new physics understanding even if it’s just minute incremental understanding. We may need to move on to expanding gravitational astronomy frequencies to detect more types of phenomena with lower and higher wavelengths than the gravitational waves to get some clues but it’s looking like we are hitting a wall in fundamental theory. We will likely make future gains in software and modeling instead, kind of how we don’t need to understand physics itself better to really understand how humans work or animals or life works on a physical level. Knowing a slightly more accurate interpretation won’t improve protein folding, but better more powerful computing approaches will.

        tl;dr If we lived in a world where Sophons were real, it would look exactly like the one we live in. We are bugs.

    • by gweihir ( 88907 )

      It actually is both. The theory is complex enough to not be fully understood in its implications and physical reality (and not only quantum mechanics) is not fully understood either. There is the missing quantum-gravity, for example, but there are also things like consciousness (which supposedly all humans have and some animals as well) and general intelligence (which some humans have, but apparently not that many). Incidentally, we do not understand life itself either at this time. It looks like life may b

    • Quantum mechanics is going to have to invent gravity, mass, inertia, and time.

      So far, it hasn't done all those things at the same time,

      Even the string theorists are finding it difficult to come up with those things, and they pretty much have the mathematics equivalent of an Anything Printer.

      Finding the Higgs didnt make this better.

      Probably going to find out we got sub-atomics all wrong, that we arent observing fundamental particles after all when "interactions" happen, that its literally just the in
  • But I recall one physicist basically saying of all the "explanations" and "interpretations" that he was just there to give working math models, not delve into the more essentially philosophical matters of what the "meaning" behind the math was.

    We see weird stuff at the edges of our ability to experiment and observe and we can to some extent model that weird stuff with math, but ultimately the weirdness drives us to want more satisfying understanding than just predicting behavior with math. Whether that's so

    • But I recall one physicist basically saying of all the "explanations" and "interpretations" that he was just there to give working math models, not delve into the more essentially philosophical matters of what the "meaning" behind the math was.

      This is the "shut up and calculate! [nature.com]" approach. I got to this article via a discussion [stackexchange.com] of who came up with the phrase. [Apparently it was the co-author of my favorite solid state textbook, rather than the co-author of my three favorite physics books]

    • by gweihir ( 88907 )

      That is pretty accurate. "Meaning" is pretty dangerous because it is subject to wishful thinking. Also with meaning come questions like consciousness and general intelligence and life itself, for which Physics has no answers. Most physicists do understand that and understand that their theory is likely fundamentally incomplete. But since they are interested in the theory, they work on that, because that is the only scientifically valid approach at this time. The real problem is that the press (and sometimes

  • by rossdee ( 243626 ) on Monday February 03, 2025 @03:44PM (#65139241)

    is the cat still in the box?

  • Math is used to calculate a solution. I don't believe the physical nature of the universe applies to our ideas of calculating solutions. It might be that everything in the universe is actually connected so trying to define individual systems at the quantum level is pointless and unobtainable. Fascinating to think about though.

    • It might be that everything in the universe is actually connected

      Reminds me of the One Electron Theory [wikipedia.org]

      I think the universe is probably mathematically sound. But the margin of error with the equipment we have far outweighs the minor differences between the mathematical models we have. We are currently out of technological means to verify any theory.

      • Thanks for the link, I've never stumbled across that.

      • by gweihir ( 88907 )

        I think the universe is probably mathematically sound.

        It cannot actually be. Only mathematical statements can be mathematically sound. But mathematical statement never apply to reality except by an intermediate interpretation step and that always loses precision and that loss is never zero and can be arbitrary large.

        Because theory (which essentially all boils down to mathematics, ultimately) is so hugely useful, some people start to forget what it is and mistake it for what it is not.

    • by gweihir ( 88907 )

      Possibly. We have very good calculations and very good solutions in mist cases were we apply that approach. But, so far, they always failed when we applied them to extreme circumstances. We see that with energy, speed, size and maybe see it with complexity (via QCs) in the future. Hence whatever we have is restricted to limited circumstances. Still exceptionally useful, but not a means to make fundamental claims.

      Incidentally, while everything may be connected and everything influences everything (an idea th

    • I don't believe the physical nature of the universe applies to our ideas of calculating solutions.

      I don't understand how you can say that. Scientists and engineers make a living doing what you believe is inapplicable. And they have demonstrated tremendous success at it.

      Or perhaps it's better said the other way around: our ideas of calculating solutions can in fact be applied to the physical nature of the universe with great success.

      As the saying goes, all models are wrong, but some are useful. It's remarkable that any models work as well as they do, but as long as they do work, let's keep using them.

  • Ultimately every theory of physics can be ”how, why” its way to the question “how and why does anything exist?” .. and if we knew THAT we wouldn’t need to know anything.

    • Here is an example to clarify my point .. You see a candle burning .. and you ask how, why .. then the answer is well there's is fuel and oxygen and heat .. the heat causes the combustion reaction .. well how, why does that happen .. well because of the molecular interaction .. how does that happen? Well because of the structure of its constituent atoms and the configuration of electrons. Well why does it have that structure .. then we can go to the arrangement of the protons and neutrons .. and for why tha

      • by gweihir ( 88907 )

        It is even worse: We do not actually know that physical reality exists. It is a useful model only. But the only thing we have are rather indirect and subjective observations. This gives raise to pretty stupid models like "we live in a simulation" (which is just a camouflaged religious idea), but the uncertainty such ideas exploit is real. And we have managed in modern Science to push the subjectivity wayyyy down when some approaches are used and make Science and Engineering (which is derived from Science) v

  • by Mordain ( 204988 ) on Monday February 03, 2025 @03:59PM (#65139279) Homepage

    We only have so many ways to measure what is happening at the subatomic level, so we have to infer relationships using a toolbox with a limited resolution, so to say. Granted, what we have determined so far is really impressive, but we may really need a new method or two to extract the actual mechanics of the system. It also doesn't help that the particles themselves act in ways that make it hard to capture their real state. Think of it as only being able to see a three dimensional system in two dimensions (so in reality we may just need the ability to observe higher dimensions).

    • by gweihir ( 88907 )

      You are certainly correct that long chains of assumptions are used in all of these observations. These assumptions are typically experimentally verified very well, but that can do only so much. Experiments do not give you truth, only indicators. While unlikely, it is quite possible that some even more visible effects have been overlooked or misattributed as a result.

  • I believe the next generation of scientists to enter the field will have an easier time with these concepts and each iteration will get better and better until understanding the C in E=MC^2 is as common as the theory of bacteria. Alot of Quantum physics deals with the concepts of abstraction and the concept of infinite. These are concepts that are easier to understand when you grew up with The Internet and are more niche if you grew up before Quantum theory and especially if you were born after most of the
  • .... is to make it less understandable?

  • "The theory's central puzzle remains unresolved: the way quantum systems are described mathematically differs from what scientists observe when measuring them."

    Someone is saying something wrong. Calculations of quantum system agree very well with measurements of quantum systems, otherwise we wouldn't use the calculations - and we do. The agreement between theory and experiment is tested to absolutely ridiculous levels of accuracy - like to ten (or more) digits.

    We may not be all in agreement of what the mode

  • Whenever I read about quantum physics, I find 10% explanation and 90% either history, or praise for this new thing and how great it is.
    I gave up on finding a good explainer
  • I took quantum mechanics in college 50 years ago. It was a requirement for a BS in Chemistry. I never had any idea what the hell was going on. First, it was obvious that I didn't even come close to having the math skills required to understand it. And second, it was obvious that I wasn't even expected to. So we learned about quantum mechanics. We learned about the Schrödinger equation and how we should feel intellectually inferior to physicists. But we also learned a lot about molecular orbital theory
  • Quantum theory contains two facts that are intolerable to most physicists. First, the observer is itself a quantum object. Most physicists insist on dealing with observers in classical terms despite knowing that this is false. A few insightful researchers addressed this issue head on, notably Sidney Coleman in his 1994 Dirac lecture âoeQuantum mechanics in your faceâ.

    Second, that QM is not a fundamental theory. The actual fundamental theory is quantum field theory, where particles are a derive

  • Some of the issues involve the attempts to map quantum scenarios onto the effects of the conscious mind, or even onto what is referred to as 'the observer' even if this is say, a measuring system.

    I have a problem with at least the term 'observer'. It implies something special beyond simple interaction, that there's some kind of observation to be made, as opposed to the effect simply manifesting based on the probability.

    The Schroedinger's Cat scenario was right as far as Schoedinger's scorn for the scenario

  • should have been the title here. Things must be getting tough there behind their paywall.
  • Classical mechanics does not match what we experience with our senses. It uses idealized mathematical concepts. But we experience real life in a fuzzy way.

    quotes are from the article:

    Whereas in classical physics, a particle such as an electron has a real, objective position and momentum at any given moment

    What is a particle in classical mechanics? An object with an exact location, zero volume, and therefore infinite density? Does this match what we experience in real-life? What is an object? A discontinuous distribution of matter in space, with an exact surface that separates matter from empty space? Those are obviously i

Wishing without work is like fishing without bait. -- Frank Tyger

Working...