Spontaneous Symmetry Breaking

In summary, the conversation discusses the concept of spontaneous symmetry breaking in physics, specifically in relation to the standard model and the existence of particles with mass. The speaker has some confusion regarding the idea that nature chooses just one solution, while the other person in the conversation explains that this is a result of symmetry breaking. They also touch on the idea that electrons and neutrinos are aspects of the same thing in the standard model.
  • #1
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I often have this problem when reading physics books (the kind I can understand) where, because I'm only in High school math, the author explains only in analogies, and the analogies sometimes don't make logical sense.

I'm reading Steven Weinberg's "Dreams of a Final Theory" and I got to the part where he describes spontaneous symmetry breaking. He says that the equations for the electron and neutrino fields (for example) are symmetrical, interchangable. But the solutions to the equations are not symmetrical, as he says "electrons and W and Z particles have mass, but neutrinos and photons do not." He explains this by saying that where you can mix up the fields you get multiple possible solutions (ex. a solution where an up quark has a higher mass than down, must also have a solution where down is higher than up). He then says "the difference between the two solutions would be simply a matter of which quark we chose to call up and down. Nature as we know it represents one solution of all the equations of the standard model." And then he goes on by how physics predicts a Higgs particle to explain this breaking.

But I'm not so sure this is true, given his description. It seems as though he just gave the answer. The equations can give either an electron with the properties we observe or with those of a neutrino because if it has the properties of a neutrino then we call it a neutrino. Nature is not one solution, but all of them, and that's why we have both electrons and neutrinos. It doesn't seem so far fetched to imagine that an electron and a neutrino are aspects of the same thing.

Obviously I'm misunderstanding him. If someone could explain how.
 
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  • #2
"Nature is not one solution, but all of them, and that's why we have both electrons and neutrinos."

Here is your problem, nature really does choose just one solution. Just think about the chair that you're sitting in right now, there isn't any reason why it should face one way or the other. All the directions are the same as far as the atoms that make up the chair are concerned, but the chair still faces in just one direction, that's symmetry breaking. Ferromagnetic domains do point in just one direction, one generator of the electroweak gauge group does remain unbroken by the Higgs, and so on. The fact of the matter is that nature does pick just one vacuum and that is the world we see at low energies. The fact that you call the massive particle an "electron" is irrelevant, the key is really that nature has got to have a massive particle no matter what you call it. Of course, electrons and neutrinos are "aspects of the same thing" in some very real sense. They form an SU(2) doublet in the standard model, and in the early universe before the Higgs acquired a vacuum expectation value, they were rather more similar than they appear now.
 
  • #3


I understand your confusion and frustration when reading about complex concepts in physics. Spontaneous symmetry breaking is indeed a difficult concept to grasp, especially with limited mathematical background.

First of all, it's important to understand that the concept of symmetry in physics refers to the invariance of physical laws under certain transformations. In the case of spontaneous symmetry breaking, we are talking about a situation where the underlying equations are symmetric, but the solutions to those equations are not. This means that there is a symmetry in the equations, but not in the solutions.

Now, let's take the example of the electron and neutrino fields. As Weinberg explains, the equations for these fields are symmetric, meaning that they can be interchanged without changing the outcome. However, when we look at the solutions to these equations, we see that the electron has mass while the neutrino does not. This is a breaking of the symmetry, as the solutions are not interchangeable. This is where the concept of "mixing" comes in - the equations allow for the possibility of mixing the fields, resulting in multiple solutions with different properties.

So, why do we observe electrons and neutrinos as separate particles with different properties? This is where the role of the Higgs particle comes in. The Higgs mechanism explains how the symmetry is broken in a way that allows for the mass of particles like the electron, while keeping other particles like the neutrino massless. This is where the Higgs field comes in - it interacts differently with different particles, resulting in the spontaneous symmetry breaking and giving mass to some particles while leaving others massless.

To address your last point, it's important to remember that nature is not just one solution, but a combination of all possible solutions to the equations. However, the specific solution that we observe in our universe is the one that breaks the symmetry in a way that allows for the existence of particles with mass. This is why we have electrons and neutrinos as separate particles, rather than just different aspects of the same thing.

I hope this explanation helps clarify the concept of spontaneous symmetry breaking for you. It's a complex concept, and it's completely understandable to struggle with it at first. Keep learning and asking questions, and you will continue to deepen your understanding of physics.
 

1. What is spontaneous symmetry breaking?

Spontaneous symmetry breaking is a phenomenon in physics where a system exhibits a symmetry in its underlying laws, but the state of the system does not reflect this symmetry. This means that the laws governing the system are symmetrical, but the actual state of the system is not.

2. How does spontaneous symmetry breaking occur?

Spontaneous symmetry breaking occurs when the energy of a system is lower in one state than in another, even though the laws governing the system are symmetrical. This leads to a spontaneous change in the system, breaking the symmetry and resulting in a new state of lower energy.

3. What are some examples of spontaneous symmetry breaking in nature?

One example of spontaneous symmetry breaking is the Higgs mechanism, which explains the origin of mass in elementary particles. Another example is the formation of a crystal lattice in a liquid, where the symmetry of the liquid is broken as it transitions to a solid state.

4. What are the implications of spontaneous symmetry breaking in particle physics?

Spontaneous symmetry breaking is a crucial concept in particle physics as it helps explain the origin of mass and the behavior of fundamental particles. It also plays a role in the Grand Unified Theory, which attempts to unify the four fundamental forces of nature.

5. Can spontaneous symmetry breaking be observed in everyday life?

While spontaneous symmetry breaking is mainly observed in the field of particle physics, it can also be observed in everyday life. Examples include the formation of snowflakes, the breaking of a pencil, and the magnetization of a material as it cools below its Curie temperature.

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