The theories of weak and electroweak interaction have rarely been seriously critiqued. Both theories are very young, being about forty years old, but one would have liked to see a more rigorous analysis of both. Theories at this level are highly insulated, since those considered qualified to have an opinion include only a handful of top theorists. These top theorists define mainstream theory, they often work together, they are very authoritative, and—beyond a few meaningless bets—they rarely disagree publicly. If they argue about anything, it is only priority. For this reason, the method of modern physics is nearly monolithic, from the maths used and the assumptions made, to the role of science and the interpretation of history. Top physicists disagree about very little, and about almost nothing of fundamental importance.

We saw this clearly in the quick acceptance and immediate dogmatizing of electroweak theory at the end of the 20^th century. True, there was a period of indecision in the early 60’s, while the theorists sorted through new information from accelerators, but once the math was completed there was almost no opposition to the theory. In one way, this was not surprising, in that only a handful of people had the math and experimental knowledge to analyze the theory. But in another way it is shocking, since, as I will show, the theory is extremely speculative, it often or always uses the math as a cover for opacity, and in several places it diverges into outright irrationality and magic.

Only in the 20^th century were scientists finally able to achieve a complexity in math and terminology to allow them to avoid any and all critique and debate. Scientists have always attempted this, but in the past intelligent generalists always found a way in. Berkeley and Swift acted as gadflies to Newton, for instance. In fact, Newton met formidable critique from his own English colleagues (and Leibniz, of course), and the fight was both fierce and public. Until recently, this was the healthy norm. Popper was still pestering Einstein in the 1940’s. But now, the very exclusive club at the top of physics has shielded itself from external debate and critique, and this has allowed rot to set in. The pond has become too small, and too little fresh water flows in and out. Physicists have become warped by their own mathematical models, as well as by the perceived successes of their immediate predecessors, and they have quite literally left the path of reason.

As evidence for all this, let us start at Wikipedia. I like to critique Wikipedia pages for several reasons. One, all scientific topics are written by the universities and other institutions, and policed by them, so these pages are the perfect place to go to find the current fortified dogma. Two, Wikipedia is extremely influential. It is the most widely read of all the propagandized media sources that sell the current science product, dwarfing the numbers of Scientific American or Physical Review Letters or Physics Today or ArXiv. This is where the modern person goes for a quick education in the “hard” sciences. Three, despite the warnings on other pages—to tread with academic caution—the science pages really are representative of the standard model: they are well edited, extensive, and heavily policed, so you can be pretty sure you are getting the story right from the horse’s mouth. You may not get the whole story, but the story you get will be a professional gloss, fact-checked, sourced, and buffed to shine, likely with a sprinkling of diagrams and macromedia presentations.

The first thing we learn about the weak interaction from Wiki is that it is mediated by W and Z bosons. So we take that link to discover that bosons are mediating particles with huge masses, “heavier than entire atoms of iron.” The W boson is the mediator in beta decay, and its entire job is in facilitating the reversal of a quark. This reversal is called a flavor change, because the quark goes from being a down quark to being an up quark.

d → u + W^-

But why would we need a boson the size of an iron atom to flip a quark over? I don’t think anyone has ever bothered to ask that question. The mass of a quark is said to be about 4MeV; and of a W boson, about 80GeV. So the mediating particle outweighs the mediated particle by 20,000 to 1. That is like using an atomic bomb to flip your mattress. A tad more force than the job calls for. We will call that red flag number 1.

The W then decays into an electron and an antineutrino.

W^- → e + v

I keep looking at that decay and saying to myself, “AND!” Since the neutrino is said to weigh nothing and the electron weighs .5MeV, we have a slight imbalance here. That decay is not intended to be an equation, but still. We have a huge amount of energy coming from nowhere and then disappearing into nothing. We will call that red flag number 2.

Then we get a section on “predicting the W and Z.” Glashow, Weinberg, and Salam “predicted” them using an SU(2) gauge theory, but the bosons in a gauge theory must be massless. We must assume that the masses of the W and Z were “predicted” in some other way, then, since the gauge theory predicted zero masses. Wiki does not address this problem, but maybe we can clear it up later when we study the texts. Wiki only tells us that the symmetry of the gauge theory must be broken, to give the bosons mass, and that the Higgs mechanism does this job. So we take that link.

What we find is that the Higgs mechanism is a form of spontaneous symmetry breaking. What is spontaneous symmetry breaking? It is symmetry that is broken spontaneously. Something that happens spontaneously requires no mechanism, so the Higgs mechanism is a mechanism with no mechanism. In other words, the SU(2) problem is solved by calling it a symmetry, breaking it without a mechanism, and then calling that breaking a Higgs mechanism. That is red flag number four.

Wiki tells us that “the evidence for the Higgs mechanism is overwhelming,” but this evidence turns out to be evidence that particles near the predicted W and Z masses exist. So, we are to understand that because big particles exist for very short times, this means the SU(2) gauge theory can’t be correct in predicting zero masses. And this means that the gauge symmetry must be broken, which means that the theory must be correct.

That is so circular it is dizzying. All the fake Higgs mechanism does is allow you to break something you wanted to break, without having to give a mechanical reason for the breaking. It allows you to fudge your math while giving a fancy name to the fudging. But if your gauge theory requires you bypass it with a symmetry breaking, it could and probably does mean that your gauge theory isn’t any good to start with. Normally, if you develop equations that yield false predictions—like these zero boson masses—you must ditch the math. You don’t get to nail some jerry-rigged post hoc correction to it, in the form of a non-mechanical “field mechanism.”

There can be no evidence for the Higgs mechanism, since, as I just showed, the Higgs mechanism is not a mechanism. It is a spontaneous symmetry breaking, and you cannot have evidence for something that is spontaneous. All you do is say, “It happened, I had a theory for it, therefore I must be right.” It is strictly equivalent to saying, “I predict the Sun will rise tomorrow [after seeing the Sun rise everyday of your life], and I hypothesize that the reason it will rise is that it is filled with helium.” When it rises, you jump up with joy and claim that the evidence for your theory is overwhelming, since the Sun came up just as you predicted. Don’t you see that what these “physicists” have done is develop a math that doesn’t work, then said, “I predict that this math is broken and needs a fix. The fix is a spontaneously broken symmetry. Aha, here is a spontaneously broken symmetry that allows me to fix my math to any degree I want. So I must be right!”

Unfortunately, Mr. Higgs also predicted another particle, the Higgs boson. Glashow, Weinberg, and Salam probably would have preferred he hadn’t done that, since it requires another round of fudging, but these guys are good at making lemonade. They know that the odds are good that another big super-meson will be found, given enough energy in the accelerator, so they just bide their time. When a big particle is found, they can claim it. This time they are careful not to be too precise in their mass prediction, so that they can claim over a wide range of masses. Another benefit is that these particle accelerators employ a lot of physicists. So if the search is spun out another decade or two, so much the better.

Currently, this page at Wiki has a “General Discussion” section that I predict will soon be deleted. It will be deleted because it leaves some dirty laundry out in the open. I have already alerted you to huge piles of dirty laundry, but that was the sort of dirty laundry the standard model likes, because it causes confusion. The sort of dirty laundry the standard model does not like is information that allows a reader to see through the confusion, and this General Discussion section contains some of that information. Here is the laundry that will be deleted first:

Higgs' original article presenting the model was rejected by Physical Review Letters when first submitted, apparently because it did not predict any new detectable effects. So he added a sentence at the end, mentioning that it implies the existence of one or more new, massive scalar bosons, which do not form complete representations of the symmetry. These are the Higgs bosons.

The Higgs mechanism was incorporated into modern particle physics by Steven Weinberg and is an essential part of the Standard Model.

This is dirty laundry that really stinks, because it allows us to see how science really works. Higgs predicted nothing, but then, to save the publication, added a slapdash prediction of particles “which did not form complete representations of the symmetry.” This means that the particles were not a necessary outcome of the math. They were just a trial balloon, a piece of fluff up for the taking, a bit of bait on a hook. Weinberg saw the value of that bait, and swallowed it down. We will call that red flag number five.

Some will say that the Higgs mechanism does provide a mechanism once joined to the gauged theory, since a broken symmetry that is gauged means that the vacuum is charged. Charge is a mechanism. But this is another fudge because 1) charge is not mechanical in QED. Even before we got to the Higgs field, charge was mediated by virtual photons. Virtual photons are non-mechanical. In fact, they are mystical. They mediate forces spontaneously, with no energy transfer, and so are a mathematical and physical cheat. 2) You cannot assign charge to the vacuum, since that is assigning characteristics to the void. One of the first postulates of physics is that you cannot assign extension, force, motion, or acceleration to nothing. For charge to be mechanical, it would have to have extension or motion. All virtual particles and fields are brazen cheats. Higgs’ field, like Dirac’s field, is a bald mathematical cheat. The only way to hope to hide this is to cover it with thick blankets of advanced math. That is what the Abelian, non-Abelian, and Affine models do. They misdirect you into mathematical symbolisms as fast as possible, to divert you from the realization that all this math is based on big cheats at the axiomatic level. Red flag number six.

So let us return to the W and Z page, on our way back to the Weak Force page. In a section on “discovery,” we discover this:

The huge Gargamelle bubble chamber photographed the tracks of a few electrons suddenly starting to move, seemingly of their own accord. This is interpreted as a neutrino interacting with the electron by the exchange of an unseen Z boson. The neutrino is otherwise undetectable, so the only observable effect is the momentum imparted to the electron by the interaction.

That is supposed to be a discovery of proof of weak interaction? That looks to me like a discovery of “a few electrons suddenly starting to move.” Why should we interpret it their way rather than any other way? No neutrino or Z is detected, as they admit, so this is hypothetical in the extreme. Is this what the other page meant by “overwhelming evidence” for the Higgs mechanism? Red flag number seven.

Well, no, we get some other evidence. We are told that the W and Z bosons were detected in 1983 by Carlo Rubbia. Problem is, this experiment only detected a particle, it did not tell us that it was a boson or that it was taking part in any weak mediation. Since I have shown that large mesons can be predicted by other simpler methods (stacked spins), this particle detection is not proof of weak interaction or of the Higgs mechanism. It is only indication of a large particle or two. Red flag number eight.

To understand why the weak interaction was initially proposed, we have to go back to 1957, the year that Yang and Lee were proven correct in their belief that beta decay violated parity. A parity violation means that beta decay works only on left-handed particles or right handed anti-particles. A theory was needed to explain why this was true. After a decade of fumbling, Glashow, Weinberg, and Salam provided the theory, using a whole mess of sloppy renormalized math to provide us with both a parity loss and a charge conjugation loss. I have already shown big red flags with their axioms, including giving charge to the vacuum and breaking parity “spontaneously” with no mechanism, but there are many others. Just as an example, we get this from the Wiki page:

However, at low energies, one of the Higgs fields acquires a vacuum expectation value and the gauge symmetry is spontaneously broken down to the symmetry of electromagnetism. This symmetry breaking would produce three massless Goldstone bosons but they are "eaten" by three of the photon-like fields through the Higgs mechanism, giving them mass. These three fields become the W^-, W⁺, and Z bosons of the weak interaction, while the fourth gauge field which remains massless is the photon of electromagnetism.

Does anyone really think that sounds like physics? A field “eats” a massless particle, thereby giving it mass?

Let us go to the texts to see if we can get clarification on any of this. Let us first look at Steven Weinberg’s The Quantum Theory of Fields, a very famous book that is often used as a textbook in graduate courses. Weinberg devotes most of the first 18 chapters to pseudo-mathematical formalisms, but in section 19.2, ironically titled Degenerate Vacua, we finally get some theory. Weinberg says,

We do not have to look far for examples of spontaneous symmetry breaking. Consider a chair. The equations governing the atoms of the chair are rotationally symmetric, but a solution of these equations, the actual chair, has a definite orientation in space.

That quote will serve as a perfect introduction to the nowhere land that is modern particle physics. Weinberg, a Nobel Prize Winner, doesn’t even understand what a conservation or symmetry law is. Classically, it was thought that parity was conserved because spin is an energy state. To conserve energy, you must have an equal number of left and right spins. As a matter of angular momentum, every left spin cancels a right spin of the same size, and sums to zero. If they were created from nothing, as in a Big Bang, they must sum to nothing, so we assume an equal number of left and right spins, at the quantum level. We also expect interactions to conserve parity, in that we expect that anything we can do left to right, we should also be able to do right to left. Unless we discover a mechanical reason that CCW is not just as good as CW in some experiment, we assume that they are equivalent.

Now, we have discovered that parity is not conserved in some quantum interactions, because some things like beta decay are preferential to one spin over another. We assume there is a reason for this. The electroweak theory supplies a mystical and non-mechanical reason for it and I will offer a simple mechanical reason for it below, but we know that parity is not conserved.

However, this has absolutely nothing to do with chairs, and the fact that Weinberg would say such a thing is frightening. Weinberg implies that because we have a chair facing west, and not one facing east, we have a parity imbalance: that one chair has literally lopsided the entire universe. This requires a quantum explanation, and that explanation is a spontaneously broken symmetry.

The gods of physics would let Weinberg’s three sentences stand as a refutation of the entire book, but my readers will not, so I will slog on. Weinberg continues,

A spontaneously broken symmetry in field theory is always associated with a degeneracy of vacuum states.

What is a degeneracy of vacuum states?

For the vacuum the expectation value of [a set of scalar fields] must be at a minimum of the vacuum energy…. We are not yet ready to conclude that in such cases the symmetry is broken, because we have not yet ruled out the possibility that the true vacuum is a linear superposition of vacuum states in which [the summed scalar fields] has various expectation values, which would respect the assumed symmetry.

So, a degeneracy of vacuum states is the fall of these expectation values into a non-zero minimum, this minimum corresponding to a state of broken symmetry.

To pull that apart and put it into standard English, Weinberg is assuming what he is trying to prove. Rather than assume that the vacuum is a nothing, with only one possible state—zero—and with no expectation values above zero (which is of course the logical assumption), Weinberg assumes that the vacuum can have a range of non-zero states, giving both it and his fields a non-zero energy. Weinberg then plays with this possible range of energies, assigning a possible quantum effective action to the field and then looking at various ways it might create parity or subvert parity.

Since any expectation value above zero for the vacuum is just daydreaming, Weinberg is free to choose either parity or non-parity. Due to Yang and Lee’s finding, he chooses non-parity, which implies that his non-zero vacuum degenerates to the minimum.

He then applies this to the chair!

Spontaneous symmetry breaking actually occurs only for idealized systems that are infinitely large.

So a chair is an idealized system that is infinitely large!

The appearance of broken symmetry for a chair arises because it has a macroscopic moment of inertia I, so that its ground state is part of a tower of rotationally excited states whose energies are separated by only tiny amounts, of order h²/I. This gives the state vector of the chair an exquisite sensitivity to external perturbations; even very weak external fields will shift the energy by much more than the energy difference of these rotational level. In consequence, any rotationally asymmetrical external field will cause the ground state or any other state of the chair with definite angular momentum numbers rapidly to develop components with other angular momentum quantum numbers. The states of the chair that are relatively stable with respect to small external perturbations are not those with definite angular momentum quantum numbers, but rather those with a definite orientation, in which the rotational symmetry of the underlying theory is broken.

And you thought my papers were hard to read. The reason this is so hard to make sense of is that Weinberg is not really talking about symmetry here. He is talking about something called decoherence, and you have to know that to make any sense out of this paragraph. He is trying to explain to himself why the chair is not a probability or an expectation value: why its wave function has collapsed into a definite state. Quantum math works by proposing a range of states, this range determined by the uncertainty principle. This is what Weinberg did with the vacuum: he assigned it a range of states and then pushed that range based on the non-parity knowledge of Yang and Lee. This is how quantum physicists work. But the chair is not a range of states, it is a state. To degenerate or collapse into this ground state, or decohere from the probability cloud into the definite chair we see and experience, the chair has to interact with its surroundings. The chair is most stable when the surroundings are stable (having “a definite orientation”); so the chair aligns itself to this definite orientation. In doing so, it breaks the underlying symmetry. Or this is Weinberg’s argument.

This paragraph is interesting from a theoretical standpoint because it means that Weinberg believes that the chair is not just probabilistic as a matter of definite position; he believes it is probabilistic in spin orientation. He even talks about the macroscopic moment of inertia. This is doubly and triply weird, because the chair has no macroscopic angular motion. The chair may be facing east or west, but there is no indication it is spinning, either clockwise or counter. Even if it were, there is no physical reason to believe that a chair spinning clockwise should have a preponderance of quanta in it spinning clockwise. I don’t believe QED has ever shown that it is impossible to propose a macro-object spinning CW, with all constituent quanta spinning CCW. But clearly Weinberg is making this assumption.

Regardless, his whole discussion is just more proof that Weinberg doesn’t understand parity conservation or symmetry to begin with. Spin parity was never thought to apply to macro-objects, by anyone with any sense. A chair facing or spinning in one direction is not a fundamental energy state of the universe, and the Big Bang doesn’t care if you have five chairs spinning left and four spinning right. The Big Bang didn’t create chairs directly out of the void, so we don’t have to conserve chairs.

Quantum physicists have been monumentally confused by their maths. That is why Weinberg’s book begins with 18 chapters of math. The math is primary, and then the theory is cobbled together around the math. But you can’t do theory this way, because you end up building grand edifices on infantile assumptions. We have seen that Weinberg builds his math and theory on the assumption that the vacuum has a possible range of non-zero states. That is like building a theory of entomology on the assumption that bugs have a range of transfinite IQ’s. No matter how much fancy math you bring to the problem, you will still look confused.

For instance, electroweak theory, like all quantum theory, is built on gauge fields. These gauge fields have built-in symmetries that have nothing to do with the various conservation laws. What physicists tried to do was to choose gauge fields that matched the symmetries they had found or hoped to find in their physical fields. QED began with the simplest field U(1), but the strong force and weak force had more symmetries and therefore required SU(2) and SU(3). Because these gauge fields were mathematical fields and not physical fields, and because they contained symmetries of their own, physicists soon got tangled up in the gauge fields. Later experiments would show that the symmetries in the math didn’t match the symmetries in nature, and the gauge field would have to be broken somehow, either by adding ghost fields or by subtracting symmetries by “breaking” them.

Any normal person who found that his mathematical field didn’t fit nature would get rid of the field altogether, choosing a math that was more transparent and less intrusive. But modern physicists are not normal people. They are very attached to their maths. So instead of ditching the entire set of gauge theories, they have preferred to paste them up and patch them and drill them full of holes. They push them and renormalize them and fluff them with make-believe fields and particles. Just as matter of mediating particles, quantum theory now has 12 gauge bosons, only three of which are known to exist, and only 1 of which has been well-linked to the theory. The eight gluons are completely theoretical, and only fill slots in the gauge theory. The three weak bosons apparently exist, but no experiment has tied them to beta decay, as I showed above. The photon is the only boson known to exist as a mediating particle, and it was known long before gauge theory entered the picture.

Amazingly, quantum theory has managed to get even this 1 boson wrong, since the boson of quantum theory is not a real photon: it is a virtual photon! QED couldn’t conserve energy with a real photon, so the virtual photon mediates charge without any transfer of energy. The virtual photon creates a zero-energy field and a zero-energy mediation: the photon does not bump the electron, it just whispers a message in its ear.

So, from a theoretical standpoint, the gauge groups are not the solution, they are part of the problem. We should be fitting the math to the particles, not the particles to the math. Quantum physicists claim over and over that their field is mainly experimental, but any cursory study of the history of the field shows this is not true. Quantum physics has always been primarily mathematical. A large part of 20^th century experiment was the search for particles to fill out the gauge groups, and the search continues.

Weinberg’s book proves this beyond any doubt. 99% of the book is couched in what I call leading math. The math has a mind of its own. It is not a tool, but a vehicle. You climb in and it takes you where it wants to go.

You have to search hard for any connection to reality in Weinberg’s book. In very few places does he step out of the math. Just as a knight never leaves the castle without his armor and a hooker never leaves the house without her lipstick, the physicist never leaves the house without his math. Weinberg is behind high walls of math on almost every page, and we see why in the rare instances he steps out. He steps out and begins conserving chairs.

To show an example of this, let us stay in chapter 19 and look at Goldstone bosons. Weinberg admits that Goldstone bosons “were first encountered in specific models by Goldstone and Nambu.” Notice they were not first encountered in experiments. No, they were encountered in the math. As a “proof” of their existence, Weinberg offers us a first equation in which action is invariant under a continuous symmetry, and in which a set of Hermitian scalar fields are subjected to infinitesimal transformations. This equation also includes it, a finite real matrix. To solve, he also needs the spacetime volume and the effective potential.

You will see below that I am able to analyze beta decay from nothing but a bald interaction. I don’t even have to be told all the particles present: I can deduce the others. Almost no math is involved. But quantum physicists never look at a problem without first loading it down with all the math they know. The first thing they do is write everything as integrals and/or partial derivatives, whether they need to or not. Then they bury their particles under matrices and action and Lagrangians and Hamiltonians and Hermitian operators and so on, as many as they can apply. Only then do they begin calculating.

All this is risible, since you can’t prove a particle with math. You can only prove a particle by studying nature. Weinberg is forced to admit this when, in chapter 21, he begins by “eliminating Goldstone bosons.” Yes, the particle he uses so much math to prove (twice) in chapter 19 has zero mass, and that doesn’t work as the mediator of the weak force. It doesn’t exist. He needs to go from zero mass to 80 GeV, and only a broken symmetry can achieve that sort of weight gain. So he proves a particle twice in one chapter and disproves it two chapters later.

Before we leave this text, let us ask if we find a prediction of the mass of the W particle. We do, in equation 21.3.36: W = ev/2sinθ, where e is the electron field, v is the vacuum expectation value, and the angle is the electroweak mixing angle. Weinberg develops v right out of the Fermi coupling constant, so that it has a value here of 247 GeV.

v ≈ 1/√G_F

The angle was taken from elastic scattering experiments between muon neutrinos and electrons, which gave a value for θ of about 28^o.

All of this is of great interest, because 1) there is no muon neutrino in beta decay, so the scattering angle of electrons and muon neutrinos don’t tell us anything about the scattering angles of protons and electrons, or electrons and electron antineutrinos. The electron antineutrino is about 80 times smaller than a muon neutrino, so it is hard to see how the scattering angles could be equivalent. It appears this angle was chosen after the fact, to match the data. Weinberg even admits it, since the angle wasn’t known until 1994. The W was discovered in 1983, remember. 2) Fermi gave the coupling value to the fermions, but Weinberg gives the derived value to the vacuum expectation. This means that the W particle comes right out of the vacuum, and the only reason it doesn’t have the full value of 247 GeV is that angle and its relation to the electron. We were initially shocked to find 80 GeV coming from nowhere, but we actually have 247 GeV coming from nowhere. Yes, Weinberg has magically called forth 247 GeV from the void, to explain one neutron decay, and no one has blinked an eye. He gives it back 10^-25 seconds later, so it is considered a borrowing, not a theft. But 247 GeV is not a little bump in the void; it is an absolute Everest.

One other thing to get in here, since it is very important. The symmetry breaking is local, not global. What does that mean? It means that Weinberg wanted to keep his magic as localized as possible. A global symmetry breaking might have unforeseen side-effects, warping the gauge theory in unwonted ways. But a local symmetry breaking affects only the vacuum at a single “point.” The symmetry is broken only within that hole that the W particle pops out of and back into. If we fill the hole back in fast enough, and divert the audience’s gaze with the right patter, we won’t have to admit that any rules were broken or that any symmetries really fell. We can solve the problem at hand, keep the math we want to keep, and hide the spilled milk in a 10^-25s rabbit hole.

Why did physics embrace this magic? Because Weinberg’s math is renormalizable (where Fermi’s was not) and because Weinberg’s math breaks the necessary symmetries. But since renormalization is hocus pocus, and since I will show below that the symmetries can be broken without invoking the vacuum, we have embraced this conjuring for no good reason, and to the eternal shame of the history of physics.

Let us now look at another text, Bryon Roe’s Particle Physics at the New Millennium. Roe is a bit more transparent than Weinberg. He gives away the farm a little more often. As we study this text, let us try to find an answer to this question: “Why is the weak force considered a force, one of the four fundamental forces of nature?” Wiki downgraded it to an “interaction” in the title of the page, but then re-boosted it to its original pre-eminence in the paragraph below the title. From what we have seen up to now, the weak interaction appears to be nothing more than a set of similar decays, linked by their parity breaking and by their use of big particles. Is this a fundamental force of nature?

Roe, like Weinberg, loses his balance most when talking about symmetry breaking. Roe doesn’t devolve into quite the strangeness of Weinberg: he illustrates the theory with wine glasses instead of chairs:

Imagine a dinner at a round table where the wine glasses are centered between pairs of diners. This is a symmetric situation and one doesn’t know whether to use the right or the left glass. However, as soon as one person at the table makes a choice, the symmetry is broken and glass for each person to use is determined. It is no longer right-left symmetric. Even though a Lagrangian has a particular symmetry, a ground state may have a lesser symmetry.¹

Directly after this Roe shows us some very short math for our Goldstone boson getting “eaten up by the gauge field” and thereby becoming massive. Remember above where I ridiculed the idea of a field giving mass to a massless theoretical particle, by eating it? Well, here is the math:²