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.
This is not the case.
This is a simple example of how hard quantum mechanics is to think about.
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.
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.
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.
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.
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.
Which, if you are going to take this position, applies just as much to neutrons as to photons. The only evidence we have for either of those being "particles" is such detections. So either you should withdraw your claim that neutrons are particles, or you should admit that photons are. You can't pick and choose.
Composite fermion systems may act as bosons and be "squeezed." Bose-Einstein condensates are an example of this.
The wave-like properties of all fermions can be explained with any variant of the many-worlds interpretation (MWI) that you prefer.
Essentially in MWI each neutron in each universe is a point (actually three because of the quarks), but that point is not in the same place in all universes. The "closer" a parallel universe is, the closer the neutrons are to each other spatially. The universes aren't discrete, they form a continuum that is locally smooth, forming a differentiable manifold.
It's the distribution across the parallel universes that's continuous and wave-like, not the individual neutrons! The wave mechanics of QM is simply a description of the cross-universe distribution of neutrons interacting with the cross-universe distribution of other particles.
This was not the initial mental model developed in the early days of quantum mechanics. The founders of the theory flatly rejected MWI based on largely religious objections. It's absurd if you think about it, but the weird and complex mathematics of QM is simply a product of these people pretending parallel worlds don't exist.
It's a way of pretending functions can have multiple values in one place without actually admitting that this requires additional dimensions, otherwise they're not mathematical functions!
They also like to pretend that scalars have probability distributions... except sometimes when interacting with other probability distributions that magically stop being distributed at the same time.
In computer terms: This is like someone pretending that arrays are passed into a function using a CPU register that can have many values at the same time. It's just absurd.
Note that MWI as originally formulated by Everett does not work this way. Eg quoting from the Discussion section of his thesis:
> [I]t seems to us to be much easier to understand particle aspects from a wave picture (concentrated wave packets) than it is to understand wave aspects (diffraction, interference, etc.) from a particle picture.
or
> This view [ie Everett's view, as described in the thesis] also corresponds most closely with that held by Schrödinger.
The main point of MWI is not to go back to a more classical picture of point particles, but to remove wave-function collapse and Heisenberg cut from the description.
Quantum Mechanics is actually incredibly conservative, with theoreticians simply refusing to abandon notions shown to be incompatible with reality for over a century now.
Same with Spin. Okay, so particles aren't literally spinning spheres. We get it. Stop pretending they are and then Spin won't be so mysterious any more!
It’s just an evocative name?
Okay then, if it's impossible, don't print what it isn't. Put down in writing what it is. That is all.
However, unlike the operators for the usual sense of angular momentum, there are additional solutions that appear, which have the half-integer spins.
And, in a sense the spin contributes to the angular momentum.
I don’t see a problem with saying “it is in some ways kind of like if it were spinning, but it isn’t quite the same. Here is the math to describe it, and how that math is like and how it is unlike something spinning.” . It seems better than just saying “here is the math which describes it”.
I don’t think your classical CPU analogy is really applicable here.
The wave function is exactly that, many values describing the probability of the particle in space. The act of measurement is what sets the value of the wave function. Take the classic electron diffraction experiment. It’s not the measurement that defines the wave-like property there.
Take tunneling through a potential barrier, why can the particle tunnel? Tunneling is a consequence of the wave function defining the probability of particle in all space.
In the last few decades especially the "publish or perish" culture of academia in general (not just in the physics departments) has lead to a perverse incentive to make mundane topics seem more impressive by deliberately overcomplicating the mathematics.
Similarly, if you read through most (95-99%) of high-energy physics papers, they aren't even remotely connected to reality. They're advancing the state of the art for some obscure corner of mathematics for the solution to some simplified model which itself is an abstraction of an abstraction.
It is astonishingly difficult to find "down to earth" mathematics for just about anything related to theoretical physics.
Meanwhile, a lot of what physics "does" is actually very simple mathematically, it's just that that simplicity is intractable symbolically. (Nonlinear differential equations are notoriously difficult to solve algebraically, but relatively straightforward numerically.)
If you think about it, particle physics must be simple because while the Universe contains advanced maths degrees, it doesn't have one. A particle zipping around and bouncing off of things doesn't solve monstrously complicated Feynman Integrals moment-to-moment! The rules it follows can't possibly be that complex.
Sure, but could it be that Feynman Integrals are one of the least complex measurable predictions/calculation of those simpler, underlying rules, potentially acting in dimensions we can't measure?
No, neutron observations in experiments are countable with integers. But the model that correctly predicts all those observations does not have "neutrons" that are countable with integers everywhere and at all times between observations.
> including explaining why particles come in countable units.
What observations of particles are you claiming that QM (which includes quantum field theory and the Standard Model of particle physics) cannot explain? I'm not aware of any.
> many people think that QM predicts that EM waves come in "countable" units called photons.
No, many people think that when you observe faint EM fields, those observations come in discrete units. When you shine very faint light through a two-slit apparatus onto a screen, you see individual dots on the screen as individual photons hit. The interference pattern that the wave model predicts only shows up over time in the pattern of the dots. Each individual photon observation is discrete. And that's what QM predicts. But QM does not say that there are always countable little photons everywhere and at all times between observations.
In the doubleslit experiment, can it be that the two slits set up magnetic or gravitational field that creates the interference pattern and photons are just a method to observe that pattern? Just like iron dust is used to see the magnetic lines that would exist regardless.
Physics equations don't have "if (...) { ... }" conditionals in them. The Universe doesn't seem to run on Boolean algebra!
The rules that govern neutrons either apply everywhere, or nowhere.
If the number of neutrons weren't so thoroughly tied to integer quantities, then deuterium could spontaneously convert to tritium and would decay at some non-zero rate.[1]
A mental model that I like to use (but certainly isn't mainstream) is to think of fermions as topological flaws, much like knots. In this model bosons are like wiggles in the rope.
I like this model because Fermions are very robust to outside interference except when interacting with other Fermions. This is much like knots in a rope. No amount of rope wiggling will ever undo a knot.[2] However, when two knots meet on a rope they obey a kind of "knot algebra" with strange and interesting rules. Preon and Rishon models are an attempt to formalise the mathematics of this, and work surprisingly well.
Continuous transformations of a topological flaw in a 3D volume of the "fabric" of the universe has Spin, which is hard to introduce otherwise. Topological flaws in crystals have even been used to model General Relativity!
Obviously, reality is not a 1-D rope with knots (tell the String Theorists that!). My model of this is a block universe where the parallel universes form a continuum. The knots are point-like only if you take a 3D spatial slice through the higher-dimensional block[3]. However, this point-like behaviour can never 100% manifest physically, because only interactions with other particles can ever be used by in-universe observers.[4] These particles in turn are a continuum across parallel universes. Thus any interaction is essentially the product of two continuous functions with each other, not infinitesimally small points bouncing off of each other.
I know this may seem a bit... "out there", but it's just a minor variation on MWI with elements of Rishon theory sprinkled on top.
[1] I'm obviously pulling this example out of a hat, but you get the idea. I'm not aware of any experiment that can demonstrate neutron number changing in any circumstance other than high energy collisions, or particle exchange between hadrons. A neutron floating about in space will remain a neutron. You won't get two neutrons suddenly turning up where you had one before. More importantly, you can certainly never have fractional neutrons. You can have a fractional expectation of finding a neutron, but you'll find a whole neutron.
[2] This begs the question of how photon-photon pair production can create an electron-positron pair out of nothing! This is like a sufficiently strong wave looping the string back on itself to produce a pair of opposite-handed knots. If separated you can call them two particles if you wish. If you bring them together they "annihilate" to form a rope that's locally highly curved. The curvature flattens, racing outwards as wiggles. These are the gamma rays produced by an positron-electron interaction. Similarly, long-wavelength wiggles move the whole knot around, but very short-wavelength wiggles can loop around the knot and through it. This could explain how some particles interact, but only above certain energy levels.
[3] A common mental model of MWI or parallel universes is something akin to pages of the book with slightly different content printed on each page. But this traps the physicist into thinking that spatial slices can only go parallel to the pages. In my model there's no preferred direction or "grain", so any slice is valid! This means that observers will disagree on essentially all measurements, including particle number. However, all observers will agree that particle numbers are quantised, and all observers agree that the particles follow the same rules. They just disagree about particle histories and particle futures.
[4] The refusal of some physicists to admit that everything obeys QM rules is a disease of the field. Either everything is QM or nothing is. QM experiments don't end at the bench top. The equipment, the physicist, everything is a part of the wave function. This insight is critical, and forms the basis of RQM and MWI, but not mainstream QM as taught in most universities.
But you'll get a proton, an electron and an anti-electron-neutrino. Possibly a photon as well. Remember, free neutrons only have a mean lifetime of less than 15min.
However, you'll still have three quarks either way.
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.
How do free neutrons, etc. work into this?
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.