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>Mathematical models such as quantum mechanics and general relativity work, extraordinarily well. But they aren’t real in the same sense that neutrons and neuro

>Mathematical models such as quantum mechanics and general relativity work, extraordinarily well. But they aren’t real in the same sense that neutrons and neurons are real Why not? When you really get down to it, aren't both neutrons and neurons ultimately also models? When most people think of a neutron, they think of a classical particle, yet we know experimentally that there is no such thing.

uoaei 6y ago
Yeah the author is assuming that "neutrons" have definite boundaries and are unambiguously distinguishable from the soup they inhabit. This is not the case. This is a simple example of how hard quantum mechanics is to think about.
- jiggawatts 6y ago
  Neutrons are countable with integers. Waves -- even in classical mechanics -- are not "countable", and are best represented in physical models with a continuum, such as field of real numbers. They're fundamentally different. Quantum Mechanics glosses over this difference because when it was developed, this was too hard to deal with. A lot of people who briefly studied QM at an undergraduate level assume that it "keeps going" and is applicable to all small-scale processes. In reality, it is not applicable to a wide range of phenomena, including explaining why particles come in countable units. Similarly, the "infinite size" of electron clouds or the probability distributions of particles such as neutrons are a mathematical shortcut that was explicitly called out as such in the first QM papers. After a century, people just forgot and assumed that QM has a direct correspondence to reality, when it is a simplified abstraction designed to be analytically tractable. Lastly, many people think that QM predicts that EM waves come in "countable" units called photons. This isn't true in general, and again, was called out as a simplification for the treatment of the emission and absorption of EM waves by atomic matter specifically. Atoms have electron orbitals that can take on only specific values, hence they can only absorb or emit EM waves with specific values. This is not a property shared with free particles or other fields that interact electromagnetically. QM pedagogy needs to be rethought from the ground up, because nobody seems to be learning QM, but instead they're internalising a limited model they don't actually understand.
  - aeternum 6y ago
    My understanding is that quantization does come from the Schrodinger equation. Specifically, it comes from solving the wave equation given the boundary conditions, and those boundary conditions are fixed by the constraint that the square of the wave function (the probability of finding a particle somewhere = 1.
    - jiggawatts 6y ago
      Yes, that's the "particles in a box" model, such as the famous black-body experiment that involved light bouncing around inside a container with a tiny hole in the side for taking measurements of the glow inside. Similarly, atoms can be thought of as a "spherical box", the boundary in this case is a full revolution around the potential well. The thing is: Not everything is a box, hence the abstract model that uses photons as a shorthand for the behaviour of the EM field in a box isn't fully general, and simply doesn't apply outside of those scenarios. That doesn't stop the vast majority of people talking about photons (and bosonic particles in general) as if they're individually countable things zipping around in free space. Neutrons can be counted like this. Photons can't.
      - aeternum 6y ago
        Interesting, thanks for explaining
      - pdonis 6y ago
        > Neutrons can be counted like this. Photons can't. Yes, they can. There are detectors that detect individual, free photons, just as there are detectors that detect individual, free neutrons. There are many, many experiments that have been done using them.
        jiggawatts 6y ago
        The detectors themselves introduce the quantisation. If you think you can disentangle the QM properties of the detector from the QM properties of the thing being detected, please write a paper explaining how and collect your well-deserved Nobel prize.
- floxy 6y ago
  >assuming that "neutrons" have definite boundaries and are unambiguously distinguishable from the soup they inhabit. How do free neutrons, etc. work into this? https://en.wikipedia.org/wiki/Free_neutron_decay https://en.wikipedia.org/wiki/Free_neutron_decay
  - uoaei 6y ago
    This may help answer some of your question, though I recognize it does not address it directly: https://www.youtube.com/watch?v=MBnnXbOM5S4 https://www.youtube.com/watch?v=MBnnXbOM5S4 (3b1b on the Heisenberg uncertainty principle and how it arises) Think of a free neutron as the wave envelope, rather than any of the bumps in the wave.
- jayd16 6y ago
  Something doesn't have to have a definite boundary to exist and I don't think it really matters to the author's point. This may or may not have been intentional by the author but you could also interpret the sentence as referring to whatever it is that does exist that we label neutrons as opposed to the models we currently use to define that thing.
gnramires 6y ago
Indeed, and the Schrodinger equation is well behind Quantum Field Theory (the most modern quantum theory). In QFT, particles can be interpreted to not exist, only fields -- particles are just a fuzzy (imperfect) abstraction of "field excitations". Particles may exist in the path-integral formulation of QM however. But it known among physicists that particles or fields don't define what is real -- what it matters is that the models predict observations. It is irrelevant which model is 'true' -- if they give equivalent results, both can be said to be [indistinguishably] correct (in their relevant domain). The examples go back a long way too, e.g. with the Hamiltonian and Lagrangian formulations of classical mechanics (wildly different but compatible mathematical formulations) -- so the 'model paradigm' has been known to physicists for a while. I think in physics 'truth' is understood to be a (possibly non-unique) model that in principle would provide an exact prediction under ideal conditions, for a limited experiment. In our reality the ideal conditions are never going to be met. For example, we cannot ensure that a system has every atom in a certain position before performing an experiment (in fact the known quantum principles of physics themselves would contradict this); we might in theory know of a generalized state of a system (quantum superposition), but even then there are too many other assumptions (about experimental devices, about the individuals reading the experiments, about science as a whole) that go into the experimental paradigm. I still find truth (as given) a useful concept, as a metaphysical principle that reality exists and has some working real mechanism (defined as being mathematically describable) -- we may never we able to write it down or discover it entirely, but it exists. Try to imagine an universe that is indescribable in principle (yields contradiction). There must be a rule. It also sets the standard for our models. https://chem.tufts.edu/answersinscience/relativityofwrong.htm https://chem.tufts.edu/answersinscience/relativityofwrong.ht...
jayd16 6y ago
Without getting into the pedantics of the specific examples, I'm sure you intuitively understand the difference between a exact value and an approximation, likewise discrete values and a fitted curve. The argument is that models are only useful tools and should not be taken to be a full or only representation of the thing being studied.

uoaei 6y ago

Yeah the author is assuming that "neutrons" have definite boundaries and are unambiguously distinguishable from the soup they inhabit. This is not the case. This is a simple example of how hard quantum mechanics is to think about.

jiggawatts 6y ago
Neutrons are countable with integers. Waves -- even in classical mechanics -- are not "countable", and are best represented in physical models with a continuum, such as field of real numbers. They're fundamentally different. Quantum Mechanics glosses over this difference because when it was developed, this was too hard to deal with. A lot of people who briefly studied QM at an undergraduate level assume that it "keeps going" and is applicable to all small-scale processes. In reality, it is not applicable to a wide range of phenomena, including explaining why particles come in countable units. Similarly, the "infinite size" of electron clouds or the probability distributions of particles such as neutrons are a mathematical shortcut that was explicitly called out as such in the first QM papers. After a century, people just forgot and assumed that QM has a direct correspondence to reality, when it is a simplified abstraction designed to be analytically tractable. Lastly, many people think that QM predicts that EM waves come in "countable" units called photons. This isn't true in general, and again, was called out as a simplification for the treatment of the emission and absorption of EM waves by atomic matter specifically. Atoms have electron orbitals that can take on only specific values, hence they can only absorb or emit EM waves with specific values. This is not a property shared with free particles or other fields that interact electromagnetically. QM pedagogy needs to be rethought from the ground up, because nobody seems to be learning QM, but instead they're internalising a limited model they don't actually understand.
- aeternum 6y ago
  My understanding is that quantization does come from the Schrodinger equation. Specifically, it comes from solving the wave equation given the boundary conditions, and those boundary conditions are fixed by the constraint that the square of the wave function (the probability of finding a particle somewhere = 1.
  - jiggawatts 6y ago
    Yes, that's the "particles in a box" model, such as the famous black-body experiment that involved light bouncing around inside a container with a tiny hole in the side for taking measurements of the glow inside. Similarly, atoms can be thought of as a "spherical box", the boundary in this case is a full revolution around the potential well. The thing is: Not everything is a box, hence the abstract model that uses photons as a shorthand for the behaviour of the EM field in a box isn't fully general, and simply doesn't apply outside of those scenarios. That doesn't stop the vast majority of people talking about photons (and bosonic particles in general) as if they're individually countable things zipping around in free space. Neutrons can be counted like this. Photons can't.
    - aeternum 6y ago
      Interesting, thanks for explaining
    - pdonis 6y ago
      > Neutrons can be counted like this. Photons can't. Yes, they can. There are detectors that detect individual, free photons, just as there are detectors that detect individual, free neutrons. There are many, many experiments that have been done using them.
      - jiggawatts 6y ago
        The detectors themselves introduce the quantisation. If you think you can disentangle the QM properties of the detector from the QM properties of the thing being detected, please write a paper explaining how and collect your well-deserved Nobel prize.
floxy 6y ago
>assuming that "neutrons" have definite boundaries and are unambiguously distinguishable from the soup they inhabit. How do free neutrons, etc. work into this? https://en.wikipedia.org/wiki/Free_neutron_decay https://en.wikipedia.org/wiki/Free_neutron_decay
- uoaei 6y ago
  This may help answer some of your question, though I recognize it does not address it directly: https://www.youtube.com/watch?v=MBnnXbOM5S4 https://www.youtube.com/watch?v=MBnnXbOM5S4 (3b1b on the Heisenberg uncertainty principle and how it arises) Think of a free neutron as the wave envelope, rather than any of the bumps in the wave.
jayd16 6y ago
Something doesn't have to have a definite boundary to exist and I don't think it really matters to the author's point. This may or may not have been intentional by the author but you could also interpret the sentence as referring to whatever it is that does exist that we label neutrons as opposed to the models we currently use to define that thing.

gnramires 6y ago

Indeed, and the Schrodinger equation is well behind Quantum Field Theory (the most modern quantum theory). In QFT, particles can be interpreted to not exist, only fields -- particles are just a fuzzy (imperfect) abstraction of "field excitations". Particles may exist in the path-integral formulation of QM however. But it known among physicists that particles or fields don't define what is real -- what it matters is that the models predict observations. It is irrelevant which model is 'true' -- if they give equivalent results, both can be said to be [indistinguishably] correct (in their relevant domain). The examples go back a long way too, e.g. with the Hamiltonian and Lagrangian formulations of classical mechanics (wildly different but compatible mathematical formulations) -- so the 'model paradigm' has been known to physicists for a while. I think in physics 'truth' is understood to be a (possibly non-unique) model that in principle would provide an exact prediction under ideal conditions, for a limited experiment. In our reality the ideal conditions are never going to be met. For example, we cannot ensure that a system has every atom in a certain position before performing an experiment (in fact the known quantum principles of physics themselves would contradict this); we might in theory know of a generalized state of a system (quantum superposition), but even then there are too many other assumptions (about experimental devices, about the individuals reading the experiments, about science as a whole) that go into the experimental paradigm. I still find truth (as given) a useful concept, as a metaphysical principle that reality exists and has some working real mechanism (defined as being mathematically describable) -- we may never we able to write it down or discover it entirely, but it exists. Try to imagine an universe that is indescribable in principle (yields contradiction). There must be a rule. It also sets the standard for our models. https://chem.tufts.edu/answersinscience/relativityofwrong.htm https://chem.tufts.edu/answersinscience/relativityofwrong.ht...

jayd16 6y ago

Without getting into the pedantics of the specific examples, I'm sure you intuitively understand the difference between a exact value and an approximation, likewise discrete values and a fitted curve. The argument is that models are only useful tools and should not be taken to be a full or only representation of the thing being studied.