Dreadfully incorrect logic was used in trying to explain how and why a Neutron can Beta-Decay into a Proton and a Electron about every 15 minutes. During the 1920s, Physicists had discovered that the elementary particles Electrons, Protons and Neutrons each had a "Nuclear Spin" and all three surprised Physicists by having the exact same amount of this Nuclear Spin, of what is now commonly called "1/2 unit". When it was realized that every Neutron "came apart" into a Proton and an Electron, many Physicists had a natural averse reaction to that. There is a basic Law in Physics called the Conservation of Angular Momentum. The entire Physics Community was troubled by a particle (a Neutron) having a Spin of 1/2 unit somehow coming apart into TWO new particles, an Electron and a Proton, each of which definitely had a Spin of 1/2 unit. And so Physicists were constantly discussing whether they might have to discard a basic Law, that of Conservation of Angular Momentum. Some people today have applied "Revisionist History" in claiming that Pauli was instead explaining some problem in Energy Conservation, but that was not actually the case. His focus was entirely based on what he thought was an Angular Momentum Conservation issue. The Beta-Decay of Neutrons soon became the "Nuclear problem of the Decade". Wolfgang Pauli took the lead in this matter, and he soon gave a "major speech" where he "explained to the world" how this could happen. Pauli announced that he had discovered that a "new particle" (which was later called a Neutrino) was also created in every Beta-Decay process, and Pauli explained that Nuclear Spin was thereby conserved:
1/2 → 1/2 + 1/2 + -1/2 which is (Neutron) → (Proton) + (Electron) + (Anti-Neutrino). This Scalar Addition would have worked if Nuclear Spin had been Scalar quantities.
That was a logical blunder, in trying to do Vector Addition as though they were Scalar quantities. The graphic here shows the ACTUAL Vector Addition problem, where all three Spins happen to be Vectors of identical 1/2 Amplitude.
Nuclear Spin is a Vector quantity, actually Angular Momentum, and it is not a Scalar quantity as Wolfgang Pauli had incorrectly assumed in 1930. As a Vector, both Amplitude and Direction are important. Most High School students learn Vector Addition by two simple examples. You know that you can swim at 4 mph and you are standing on the edge of a river where the water flows at 3 mph. What is the fastest you could cross the river? And what direction do you need to swim in order to arrive at a McDonald's Restaurant which is exactly straight across from you. These problems seem simple but they cannot be solved with traditional Scalar Addition. You might think that you would swim either 7 mph or 1 mph, but neither would be true. You need to use Vector Addition to solve these problems. For the first problem, you would discover that you would need to "aim" straight across, but that you would arrive way downstream. For the McDonalds problem, you would discover that you need to "aim" quite far upstream. I won't solve it here, but it is pretty simple math, and the answer is that you would need to "aim" 36.87° upstream (a surprising but correct angle). You would be swimming for a LONG time to get to the McDonald's restaurant.
As shown above, a Vector Addition Diagram of the Nuclear Spin of a Neutron's Beta-Decay happens to be an equilateral triangle. A Neutron's Spin of 1/2 unit is one (red) side of that triangle with a Proton's Spin of 1/2 unit (green) and an Electron's Spin of 1/2 unit (blue) being the other two Vector sides. (as shown in this graphic). There is NO issue of any problem with Conservation of Angular Momentum regarding the Spin Vector of a Neutron and the consequent Spin Vectors of a Proton and Electron.
Wolfgang Pauli did not seem to know that and in incorrectly thinking along Scalar lines (only considering the amplitude with no direction), he dreamed up the need for Neutrinos (with another [Scalar] Spin of 1/2 unit). His (incorrect) Scalar thinking did not add up correctly as Scalar quantities, and so he thought he needed to invent a neutrino, for a single purpose, that of supplying an extra Scalar quantity of Nuclear Spin in order to comply with the Conservation of Angular Momentum. It therefore turned out that Pauli was trying to resolve a PROBLEM WHICH DID NOT ACTUALLY EVEN EXIST. He was smart and he certainly should have known better than to try to apply Scalar thinking and logic to Vector quantities. His explanation was interesting in that he described his neutrinos as having ZERO mass, ZERO electrical charge, ZERO size, and ZERO everything else, except for the 1/2 Nuclear Spin that he needed to try to justify his Scalar Addition problem.
There is additional statistical scientific and precise mathematical evidence that Neutrinos do not exist inside atomic nuclei in the highly respected NIST data resource. Here are two related articles.
Nuclear Physics May be Fairly Simple
Nuclear Physics - Statistical Analysis of Isotope Masses
Wolfgang Pauli was one of the most brilliant men ever, one of a handful of men who developed Nuclear Physics, but in 1930, it appears that he made an enormous logical blunder when he speculated that Neutrinos MUST be necessary inside atomic nuclei!
There is a curious simple but huge flaw in Nuclear Physics today regarding this incorrect reasoning of Pauli (for which he even later received the Nobel Prize in Physics in 1945.) Nuclear Spin is a Vector quantity, actually Angular Momentum, which every beginning Physics student knows! It is not a Scalar quantity like most of the things we encounter in normal life. The difference is that every Vector quantity has both an Amplitude and a Direction, while all Scalar quantities only have Amplitude and they do not have any defined direction. Examples are speed, which is a Scalar, and velocity, which is a Vector, the difference being that velocity tells you what direction the object is moving in, along with its speed.
Physicists (should) all know that any quantity like Nuclear Spin is necessarily a Vector, where both the rate of rotation is specified, as well as the orientation, which is defined by the direction of the spin axis. We say the Earth has a Spin Vector of "once a day" rotational speed and a direction of exactly due north. If the Earth's spin Vector were pointed south instead, that would tell us the Earth was spinning the other way around.
During the 1920s, Physicists discovered that all nuclear particles have Angular Momentum or Spin Vectors. They were mostly concerned with one specific object, the Neutron, which was known to spontaneously decay into a Proton and an Electron with a half-life of around 15 minutes. More confusing yet, the Proton and Electron tended to quickly fuse back together to reform a Neutron.
Physics has long been based on several Conservation Laws, including one of Conservation of Angular Momentum.
By about 1929, it was firmly known that each Proton, each Electron and each Neutron all had the exact same amount of "Nuclear Spin". This Spin is described as being 1/2 unit of Spin, using an actual scientific quantity of Angular Momentum defined as Planck's Constant divided by (2 * Pi), or h/2 π or h-bar.
Many Physicists repeated the same experiment where a Neutron spontaneously "Beta-Decayed" into a Proton and an Electron, and everyone was uncomfortable with the result. Pauli was one of the leading Physicists who was troubled by a Neutron starting out with a Spin of 1/2, and coming apart into two particles, a Proton with a Spin of 1/2 and an Electron with a Spin of 1/2. It was (incorrectly) thought that this violated the Conservation of Angular Momentum. And so Wolfgang Pauli dreamed up a new particle, which became known as a Neutrino (or, in this specific case, an Anti-Neutrino), which he said had no electrical charge, no mass, no size and only a single characteristic, its Nuclear Spin of 1/2 unit.
In other words, the only reason that the Neutrino was even speculated to exist was for the single purpose of trying to resolve a CONSERVATION PROBLEM WHICH DID NOT ACTUALLY EVEN EXIST. There has never been any other reason suggested as to why Neutrinos should even exist!
Therefore, Pauli publicly announced that he had the explanation for how Angular Momentum could be Conserved when a Neutron decayed. He explained (wrongly) that the Neutron broke apart into three particles and not just the obvious two, that is:
Neutron → Proton + Electron + (anti-)Neutrino
He then explained that Nuclear Spin was conserved:
1/2 → 1/2 + 1/2 + -1/2
where the Neutrino involved was actually an Anti-Neutrino, meaning that it spins in the opposite direction so that the Spin Vector is in the opposite direction (and therefore the minus sign), which he needed for his Scalar Addition to work.
Everyone was thrilled that the brilliant Wolfgang Pauli had solved the biggest nuclear problem of the day! To this day, in 2018, everyone still absolutely accepts Pauli's explanation, as he was one of a handful of Physicists, with Einstein and Bohr, who was researching Nuclear Physics. Therefore, no one questions Pauli's announcement that there must be Neutrinos, in order to explain the Nuclear Spin Conservation issue of a Neutron's beta-decay.
For bizarre reasons that are beyond me, the brilliant Wolfgang Pauli and all Physicists since him seem to assume the Nuclear Spin is a Scalar quantity, which would then require the speculation of a Neutrino's existence, with a Spin of 1/2, to Conserve Spin by a Scalar addition of 1/2 = 1/2 + 1/2 - 1/2.
That is not remotely true! Pauli had made an enormous logical blunder in assuming that Nuclear Spin is a Scalar quantity! Therefore, every Physicist today still buys into that wrong assumption!
As an actual Vector quantity, it is clear that THERE IS NO NEED TO DREAM UP A NEUTRINO IN ORDER TO CONSERVE NUCLEAR SPIN.
Consider a (red) Spin Vector of a Neutron, which has amplitude of "1/2 unit". (as shown in this graphic, to the upper right). The way Vector Addition works, is that two new Vectors can be formed from the original Vector, as long as they graphically add together, as the green (Proton Spin Vector) and blue (Electron Spin Vector) Vectors do in this graphic. In our example, the three Vectors form an equilateral triangle, meaning that all three Vectors shown have exactly the same amplitude.
This works the other way as well. Two Spin Vectors (with identical amplitude of 1/2 unit) (shown in green and blue in our graphic) which happen to be oriented at a space angle of 120 degrees from each other, can also add, as Vectors, to become a new Spin Vector (shown in red in our graphic.) The new Neutron Spin has exactly the same amplitude (1/2 unit) but is now at an orientation of a third side of an equilateral triangle. There is NO issue of any problem with Conservation of Angular Momentum regarding the Spin Vector of a Neutron and the consequent Spin Vectors of a Proton and Electron.
Vector addition therefore works both ways, and Vectors can point in either direction, so a Neutron spin can spawn two Vectors for a Proton and an Electron, or a Proton Spin and an Electron Spin can add to form a Neutron Spin Vector.
Note that the ONLY reason that Neutrinos supposedly need to exist is to Conserve Angular Momentum for Beta-Decays such as when a Neutron decays into a Proton and Electron (which we know happens!) There has never been any other reason to speculate that neutrinos even exist! Since Wolfgang Pauli had made such an enormous logical blunder in 1930 in his speculation, even that is not actually the case.
It is not as though neutrinos are really obvious objects. It was more than 25 years after Pauli had speculated the existence of neutrinos that the first experiment claimed to have detected any of them. Worse, such experiments, inside nuclear reactors, involved some rather creative speculations in making that claim.
How could any Physicist, then or now, believe that it was even needed to dream up a Neutrino, for the single purpose of Conserving Nuclear Spin? Yes, Wolfgang Pauli, who was really smart, dreamed up the existence of neutrinos to achieve this Scalar addition of the quantities which are actually Vectors, and apparently everyone just accepted that Pauli must be right! However, he wasn't!
In fact, whether a Neutron is Free-Ranging across a room or within any atomic nucleus, the Vector nature of Spin is such that the complete experimental explanation of the beta-decay of a Neutron is simple and obvious! Just two objects are created, the Proton and the Electron! Much of the past 80 years of nuclear Physics has been centered on all the complexities Pauli had made necessary by his wrong explanation of a Neutron's decay and his wrong speculation of there therefore needing to be Neutrinos!
Even as a First Year Physics student in 1963, I was bothered by one other assumption that struck me as peculiar! IF this is all just scalar additions, are all protons and neutrons and electrons all neatly lined-up with their spin axes like trillions of soldiers? Otherwise, do Physicists believe that a beta-decayed Neutron comes apart into two neatly lined-up Proton and Electron objects? Because, 15 minutes later, it is assumed that the Proton and Electron re-combine to form a Neutron again! Do people think they stay lined up for all that time? On the other hand, do people just never think about such things? Apparently so!
In fact, Pauli and Hideki and other early Physicists extended this (incorrect) logic into requiring a Strong Nuclear Force, to try to explain how any atomic nucleus could contain a lot of positively-charged Protons very close to each other, knowing that such objects were clearly known to strongly repel each other due to the electrostatic force and its inverse-square-law distance dependency. Therefore, Hideki and Pauli dreamed up another really dumb idea, that there is an (invisible) even more powerful force which only acts at incredibly short distances, in order to try to come up with some explanation for how the intense mutual electrostatic repulsion of Protons could be overcome. Some of my Physics Professors at the University of Chicago said that the Strong Force has a Inverse-Third-Power distance dependency. Others of those Physics Professors said that the Strong has an Inverse-Fifth-Power distance dependency. Worse, Hideki and Pauli and the others then also said that the Strong USUALLY acts as an attractive force but then if anything gets too close, it sometimes completely changes to become an intensely repulsive force. Hideki and Pauli and others also dreamed up an immense number of smaller particles (eventually called Pi-mesons or Pions), which supposedly whiz back and forth between Protons (and Neutrons) inside every atomic nucleus to (somehow) do this "Strong Nuclear Force."
As a Physics Major at the University of Chicago during the 1960s, I was told to always insist on absolute rigidity of my logic, but I was taught these very questionable speculations that seem to be rampant in the Physics community, then and now. Why don't other Physicists today see these same logical flaws which have troubled me during my whole 50-year career in Physics?
Disappointingly, modern Physics seems to have made many more assumptions and speculations upon which much of modern Physics is based, which may have been weak or even wrong. Nearly all of modern Physicists absolutely believe that our Sun creates astounding numbers of Neutrinos inside its core in the process of the nuclear fusion which produces the heat, light and energy upon which our lives depend. Different Physicists calculate different numbers of such Solar Neutrinos, but all such numbers are enormous. A popular claim is that "the Sun produces so many Neutrinos that 70 billion solar-originated neutrinos pass through every square centimeter of the surface of Earth (or your eyeball) every second." Alternately "The Sun creates and releases 4 * 1038 Neutrinos every second."
There are about 20 Neutrino telescope experiments now in operation. They all seem to agree in detecting fewer experimental results than they had expected. As has begun to be the "solution" to such "problems", another unsupported assumption was soon presented, and virtually immediately accepted by everyone. It is now believed that many of the (alleged) Solar (electron) neutrinos on their way to Earth spontaneously change into different (Muon or Tau) forms of Neutrinos, which they now (comfortably) accept as the reason why they detect fewer (electron) neutrinos than they had expected. That would be fine if there had been any actual logical reason for such transitions or if there had been any experimental confirmation for anyone ever having detected any such transition, but there has never been any such actual support. Such broadly accepted beliefs have seemingly been simply speculations without any hint of proof! Now, if it turns out those Neutrinos are not even actually created in nuclear decays and fusion, wow!
In any case, I have no grudge against Pauli! When I have examined such logical flaws as by Pauli (for which he was even given a Nobel Prize in Physics in 1945), I found a far simpler explanation of nearly everything in nuclear physics. In the late 1990s, I spent several years studying the highly respected NIST nuclear data and I found many wonderful mathematically precise statistical patterns in various groupings of their very precise Atomic Mass data for the thousands of Atomic Isotopes.
The implications are in many fields, and they took me several years (1996-2003) to analyze and digest. The Mass Defect Chart, which has always been ignored as being too complex to be beyond math, is actually pretty easily and simply accurately calculated, and by only simple quadratic equations! The Quantum Defect is NOT the irrational quantity that is ignored in Physics, but is instead a very precisely calculable quantity! It is even intimately related to something that Moseley discovered in 1913, which may suggest a weird new aspect of Physics, a quantity dependent on the square of the electrostatic charge of a nucleus! A rather comprehensive web-page on the patterns and results found in the NIST data is at http://mb-soft.com/public2/nuclei6.html named Statistical Analysis of Same-Atomic-Weight Isotopes.
One of the most powerful results of that research is that there appears to be NO statistical evidence that neutrons even exist within atomic nuclei! The materials are certainly there, but mathematically they appear to exist as separate Protons and Electrons rather than as bound Neutrons! IF they exist as the universally assumed Neutrons, then we expect to need to find rather large amounts of Neutron Self-Binding Energy (0.78235 MeV) inside every atomic nucleus which contains any Neutrons, and all that extra energy simply is not in the NIST data. We note here that an entire electron is only 0.511 MeV of energy, which we consider pretty easy to detect. That Neutron Self-Binding Energy also obviously Violates the Conservation of Energy inside nuclei. In fact, there appear to be specific patterns of motion of the (somewhat free-ranging) electrons inside atomic nuclei, where the negative charge of the electrons provides wonderful sources of nuclear stability! It is certainly recognized that every two Protons inside a specific atomic nucleus are SO close to each other that they exert immense repulsive electrostatic force on each other, constantly trying to push each other out of the nucleus. I found that if a single (negatively-charged) Electron happened to be at a location exactly midway between those two protons (at half the distance to each), there is then a net ATTRACTIVE force on both protons that is four times as strong (due to the inverse square law of electrostatic force). The tiny Electron could not stay at that exact midpoint for very long without collapsing the nucleus! However, I now believe that the intra-nuclear Electrons migrate between such midpoint locations, where each two protons inside an atomic nucleus repel each other for around 3/4 of the time, while the brief presence of the centerpoint electron enables the two protons to attract each other four times as strongly, for the other 1/4 of the time. This should result in the Protons vibrating with specific frequencies, which I believe are experimentally seen in some nuclei, and it therefore provides a stability or at least a meta-stability of the nuclei's structure, purely due to electrostatic forces of repulsion and attraction! No Strong Nuclear Force appears to be necessary at all to provide nuclear stability!
The result of all this is that atomic nuclei seem to logically not contain Neutrinos at all, not to contain Neutrons at all, not to contain any Strong Nuclear Force, and not to contain massive numbers of Pions! I believe the NIST data clearly shows that atomic nuclei only contain Protons and an appropriate number of internally migrating Electrons.
My (nearby) academia.edu article Nuclear Physics May be Fairly Simple clarifies this.
The full analysis of the NIST data analysis is rather complex, but I believe it is strictly compliant with the Logic of Physics. That analysis of the NIST data for all the activities within atomic nuclei is at http://mb-soft.com/public2/nuclei6.html named Statistical Analysis of Same-Atomic-Weight Isotopes.
An unrelated matter regarding neutrinos is the common claim in Physics that the Sun's fusion activity produces "nearly all" of a spectacular number of neutrinos that supposedly penetrate through every square centimeter of the Earth's surface every second. An assumption is made that neutrinos penetrate essentially everything, even generally passing completely through the entire Earth as though it was not even here. An enormous logical error seems to be applied, which a brilliant astronomer named Heinrich Wilhelm Olbers postulated in 1826 regarding the night sky and the cumulative effect of all the stars that exist. Olbers did not understand why the night sky should not be brilliantly white, as no matter what direction you look, you should be looking exactly at the brilliant face of some star. Specifically regarding neutrinos, the Olbers' Paradox should even more obviously apply. No matter what direction we look, logic would seem to force believing that immense numbers of Neutrinos should be coming at us from every possible direction (from other stars). We on Earth should only be getting a tiny fraction of our Neutrinos from the Sun. However, all researchers think otherwise, where they only think of the Sun as producing all the Neutrinos they try to detect! (The Sun only represents about 1/200,000 of the total area of the sky. If Neutrinos actually exist, and if they are created by nuclear fusion inside every star, then why wouldn't we be receiving 200,000 times as many Neutrinos as "experts" claim are coming from our Sun?)
Seems like all sorts of wrong assumptions have been applied regarding neutrinos, which may not even exist at all! I also wonder about the logic of using neutrino detectors deep in mines. Doesn't the Earth have significant amounts of radioactive material inside it? What if some pocket of radioactive material happened to be just below where the mine and detector is? If Neutrinos actually exist, couldn't that mean that some sort of local source of neutrinos might exist, which would screw up experiments that only aspire to detect a few events per year?
Modern speculation in Physics now claims that 99% or 95% of everything which exists in the Universe is Neutrinos. Doesn't anyone know how to multiply any more? If the claim that the Fusion processes inside the Sun "always" create Neutrinos in creating the energy that the Sun radiates outward, the usual claim is that only a trillionth or less of the mass of the protons and electrons involved would be neutrinos. In the five-billion-year lifetime of the Sun, simple math shows that the Sun has never even created even one-Earth's worth of Neutrinos. Even if that speculative reasoning had any validity, simple math shows that the most of the entirety of the Universe which could now be Neutrinos, could not even be 0.0001% of whatever else is there. What possible logic could claim that it represents 99% or 95% of the Universe? Silly reasoning.
I apologize that this is a broad-ranging discussion, referring to a wide assortment of apparently weak assumptions by assorted Physicists. More complete and thorough discussions on each of the matters exist, in separate Articles and discussions of each issue, both within the web-pages of my mb-soft.com Domain and within my Articles in Academia.edu.
In order for Physics to advance, it is clearly important to only base knowledge on solid sources, and if sloppy logic has ever been applied, then our collective future may be cloudy! We should fix such flaws in logic!
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Carl W. Johnson, Theoretical Physicist, Physics Degree from University of Chicago