The Wu experiment conducted in 1956 is arguably the most important physics experiment conducted in the whole of the 20th century. If you read about it in wikipedia, for example, you will get a very clear idea of its importance, even if you don’t understand all the details (which I don’t). You will then be surprised to learn that Wu did not get a Nobel Prize for this work. When you discover that the two men who suggested the idea got the Nobel Prize, whereas the woman who designed, built and ran the experiment did not, you will no longer be surprised. You will be outraged.
Anyway, I don’t want to get into the politics of the Nobel Prizes, or the extreme irony of some of the awards (for example, the Nobel War Prizes). I want to explain how the interpretation of the results of the Wu experiment led the field of physics into a dead end, from which it cannot extricate itself. The interpretation of the results as being internal properties of the cobalt 60 atom, completely isolated from its surroundings, led to the Standard Model of Particle Physics that we have today. But you cannot isolate any experiment from gravity, and therefore the interpretation of the atom as being isolated from its surroundings is physically absurd.
If you think the atom is spinning in isolation from the rest of the universe, then you are in violation of Mach’s Principle. So let us see what happens if we analyse the Wu experiment with Mach’s Principle in mind, so that we couple the weak interaction to gravity, and interpret the results as being influenced by gravity. This will lead in a completely different direction of interpretation, not only for this experiment, but for the whole of the Standard Model. Mach’s Principle says that the atom can detect the rotation of the Earth around it. Wu’s experiment says that the atom does detect the rotation of the Earth around it.
That is the real significance of the Wu experiment. It underlines the importance of Mach’s Principle at the quantum level. Mach’s Principle is completely ignored in particle physics, and almost completely ignored in relativity. Until Mach’s Principle is incorporated into the foundations of quantum mechanics, no further progress in this area is possible.
The cobalt 60 atom, or the weak force in general, detects not only the rotation of the Earth on its own axis, but also detects the tidal forces of the Sun and the Moon. Because the theory has to be “renormalized” – which is code for using the symmetries of Hamilton’s equations to transform your coordinates to a different (usually hypothetical) “observer” – you don’t detect the sizes of anything, you just detect the directions they come from. So you detect the tilt of the Earth’s axis, and you detect the angle of inclination of the Moon’s orbit. That is all. You cannot detect anything else. Oh, apart from the latitude of the experiment, which tells you the direction of the centre of the Earth.
The Standard Model has been built to be (mostly) independent of the latitude, so we have two other angles to deal with. They have to be incorporated into the SM, if you refuse to couple the weak force to gravity. So they are. In fact, they are incorporated in very strange (pun intended) ways. The inclination of the Moon’s orbit appears in the fact that the mass ratio of charged to neutral kaons is the (average) cosine of the angle. Strange, but true. The kaons have strange quarks in them. No, I have not taken leave of my senses. I am not hallucinating. All I am doing is applying Mach’s Principle to the Standard Model. Somehow, the mainstream prefer to think that they can decouple their experiments completely from gravity, an assumption that is known to be false, rather than grapple with the confusing and counter-intuitive consequences of Mach’s Principle, rigorously applied.
The other angle appears in various places. For example, there is an angle called the “CP-violating phase”, which is also derived from properties of kaons, specifically the property that there are two orthogonal “states” which are distinguished by whether they decay into an even or odd number of pions. The experiment that detected this property sent some kaons, carefully cleaned to be purely odd, across the lab, and found some kaons had broken the rules and decayed into two pions instead of three. Naughty, naughty kaons! They must be punished! This was in the old days, before CP was outlawed, so you can imagine what happened. Nowadays, it’s just a phase they’re going through. Anyway, the actual angle that made its way into the SM (oh, dear, I’m going to get into trouble with these acronyms, aren’t I?) is the complement of the angle of tilt of the Earth’s axis. You see, the experiment cannot be isolated from gravity, so Mach’s Principle says it can detect the motion of the Earth. And it did. What it actually measured was the change in direction of the centre of the Earth. The angle of tilt arose from the theory by adding in the tides, that had been subtracted off by the interpretation of the Wu experiment.
Ah yes, you wanted to know where the electro-weak mixing angle came from, didn’t you? It’s the sum of the angle of tilt of the Earth’s axis, and the angle of inclination of the Moon’s orbit. Well, not exactly, because the particle experiments are more difficult to do than the astronomical ones, but it’s pretty close. So you see, the two angles that you must see in particle physics, simply from applying Mach’s Principle, do appear in the SM, individually and together. So why beat yourself up with SM and CP, just to avoid the Hamiltonian experience of putting yourself in someones else’s shoes?