What is Symmetry Breaking?

[Rhondazvous]

I know that in Higgs Mechanism SB results in adding mass to gauge bosons.

1. Does that mean gauge bosons have some kind of symmetry?
2. Exactly how is it broken?
3. What is the connection between mass and symmetry?

[Jesster]

Oh, I thought this was going to be something about symmetry in art. I will take a big step back and let the science experts handle this one.

[Alex K]

Hold my beer while I go on a 10 hour monologue about my dissertation topic (gauge symmetry breaking)...

[Alex K]

Oh, I thought this was going to be something about symmetry in art. I will take a big step back and let the science experts handle this one.

My wife and I once worked out (for a public lecture of ours) how to explain gauge symmetry breaking by comparing it to color palettes in paintings, so...

[Rhondazvous]

Hold my beer while I go on a 10 hour monologue about my dissertation topic (gauge symmetry breaking)...

Drink your beer, daddy. Beer is the intelligent man's drink. It made Bud wiser.

---

Oh, I thought this was going to be something about symmetry in art. I will take a big step back and let the science experts handle this one.

My wife and I once worked out (for a public lecture of ours) how to explain gauge symmetry breaking by comparing it to color palettes in paintings, so...

Well, gluons are a type of gauge boson that is color charged. so it makes perfect sense. Don't tell me color charging has nothing to do with perceptible colors. I don't want to hear it.

[Alex K]

Symmetry breaking in the context your brought up (gauge bosons) refers to what is called "spontaneous symmetry breaking".

The short definition of this type of symmetry breaking is that the fundamental laws of nature have a symmetry, but the actual state in which the universe finds itself does not respect this symmetry. This way, one can kind of have the cake and eat it, too, by having the symmetry, but also being rid of it at the same time.

Examples
________

I simple everyday example would be if you put a thin round elastic stick (a straw or so) perfectly upright on a table and push on its top end. Initially it will be straight and perfectly symmetric because it doesn't point in any particular sideways direction. If you push hard enough, it will bend, and it will bend in a random direction - the rotation symmetry is gone because the stick bends in one specific direction. So, the laws governing the stick do not distinguish different directions, but the stick now does.

Another important example is ferromagnets. If you heat them up, the atoms is the material will spin in random directions and there is nothing in the magnetic material that says - this direction here is special. But when the material cools down, suddenly a magnetic field will build up, and it will show in one particular direction, like in our example with the stick. Once again, the laws governing the atoms in the magnet do not distinguish directions, but the concrete magnetic field does.

One last example of this type: A roulette table. All the numbers are equally likely because the thing is round. But as soon as the ball slows down, it will settle in one and one only. The symmetry is broken and one number is selected even though ideally, the construction of the roulette table does not prefer any particular number.

Connection to Particle Physics
______________________________

Those are all what is called spatial symmetries: before, the thing we look at has a rotation symmetry which is gone after the symmetry breaking occurs. These spatial symmetries also play a central role in particle physics, but the ones we are talking about in the context of the Higgs boson, gauge bosons and their masses are abstract symmetries which do not refer to rotations in ordinary space but rather in the space of particles. Such a rotation does not turn "up" into "right" and "right" into "down" in space, but it turns "up-quarks" into "down-quarks" and elecrons into neutrinos, as if the different types of particles were directions in a ficticious particle space. As long as this symmetry is perfectly intact (and I simplify a bit here), there would be no distinction between electrons and neutrinos because nature hasn't even decided yet what electromagnetism is, which of the gauge bosons that exist is actually the Z boson, the photon, the W boson. Only when the universe cooled sufficiently, did nature suddenly decide: this direction in particle space is the one with the electrically charged particles, and now you there, you are the photon, and you are the Z boson (to anthropomorphize the process a bit which should be right up your alley, Rhonda). So that is what actually happened when the universe cooled below, say, 100 trillion degrees after the big bang.

Symmetry and masses
___________________

What does this symmetry in particle space have to do with mass? First of all, you have to understand that these symmetries are absolutely crucial to describe the behavior of gauge bosons: when you postulate this kind of symmetry, you automatically get gauge bosons out of your theory which act like the mediator particles doing something with this symmetry. There is for example a symmetry between leptons and neutrinos, and the gauge boson which is connected to this symmetry is the W-Boson: it can turn leptons into neutrinos and vice versa, so whenever the gauge bosons are present, they kind of "turn the symmetry crank". So having this symmetry in your theory is absolutely crucial in order to have a consistent description of how gauge bosons interact with the fermions and themselves. The mathematics tells you, however, that the symmetry forbids the gauge bosons from having any mass (Why that is is not easily explained). But we know that some of them do have a mass, namely the Z boson and the W bosons. So how can you have the symmetry in your maths that makes it consistent, but at the same time give your gauge bosons mass which seems to be at odds with it? And that's where the spontaneous symmetry breaking comes in: it preserves the symmetry in the fundamental laws, but it is not there in the actual universe.

The thing that accomplishes this, that's the Higgs field. The higgs field is kind of like your roulette table, it has several differnet directions which are tied to the different directions in particle space, and when the universe cools, the higgs field decides which of the directions in particle space is special, just like a roulette ball coming to rest in one place. And that decides which of the particles become electrically neutral, and which become electrically charged. And once the higgs field chooses one direction in particle space, this violation of symmetry suddenly lets some of the gauge bosons have a mass - they basically get it automatically as soon as the symmetry is gone.

So that's the story.

[Alex K]

Hold my beer while I go on a 10 hour monologue about my dissertation topic (gauge symmetry breaking)...

Drink your beer, daddy. Beer is the intelligent man's drink. It made Bud wiser.

---

My wife and I once worked out (for a public lecture of ours) how to explain gauge symmetry breaking by comparing it to color palettes in paintings, so...

Well, gluons are a type of gauge boson that is color charged. so it makes perfect sense. Don't tell me color charging has nothing to do with perceptible colors. I don't want to hear it.

*lalalalalalalalala* It doesn't *lalalalalalala*

But you can try and make an analogy (that's how the name arose, because in the proton and neutron, red green and blue quarks combine to give you a color-neutral whole, just like when you mix red green and blue light you get white. )

[Rhondazvous]

Symmetry breaking in the context your brought up (gauge bosons) refers to what is called "spontaneous symmetry breaking".

The short definition of this type of symmetry breaking is that the fundamental laws of nature have a symmetry, but the actual state in which the universe finds itself does not respect this symmetry. This way, one can kind of have the cake and eat it, too, by having the symmetry, but also being rid of it at the same time.

Examples
________

I simple everyday example would be if you put a thin round elastic stick (a straw or so) perfectly upright on a table and push on its top end. Initially it will be straight and perfectly symmetric because it doesn't point in any particular sideways direction. If you push hard enough, it will bend, and it will bend in a random direction - the rotation symmetry is gone because the stick bends in one specific direction. So, the laws governing the stick do not distinguish different directions, but the stick now does.

Another important example is ferromagnets. If you heat them up, the atoms is the material will spin in random directions and there is nothing in the magnetic material that says - this direction here is special. But when the material cools down, suddenly a magnetic field will build up, and it will show in one particular direction, like in our example with the stick. Once again, the laws governing the atoms in the magnet do not distinguish directions, but the concrete magnetic field does.

One last example of this type: A roulette table. All the numbers are equally likely because the thing is round. But as soon as the ball slows down, it will settle in one and one only. The symmetry is broken and one number is selected even though ideally, the construction of the roulette table does not prefer any particular number.

Connection to Particle Physics
______________________________

Those are all what is called spatial symmetries: before, the thing we look at has a rotation symmetry which is gone after the symmetry breaking occurs. These spatial symmetries also play a central role in particle physics, but the ones we are talking about in the context of the Higgs boson, gauge bosons and their masses are abstract symmetries which do not refer to rotations in ordinary space but rather in the space of particles. Such a rotation does not turn "up" into "right" and "right" into "down" in space, but it turns "up-quarks" into "down-quarks" and elecrons into neutrinos, as if the different types of particles were directions in a ficticious particle space. As long as this symmetry is perfectly intact (and I simplify a bit here), there would be no distinction between electrons and neutrinos because nature hasn't even decided yet what electromagnetism is, which of the gauge bosons that exist is actually the Z boson, the photon, the W boson. Only when the universe cooled sufficiently, did nature suddenly decide: this direction in particle space is the one with the electrically charged particles, and now you there, you are the photon, and you are the Z boson (to anthropomorphize the process a bit which should be right up your alley, Rhonda). So that is what actually happened when the universe cooled below, say, 100 trillion degrees after the big bang.

Symmetry and masses
___________________

What does this symmetry in particle space have to do with mass? First of all, you have to understand that these symmetries are absolutely crucial to describe the behavior of gauge bosons: when you postulate this kind of symmetry, you automatically get gauge bosons out of your theory which act like the mediator particles doing something with this symmetry. There is for example a symmetry between leptons and neutrinos, and the gauge boson which is connected to this symmetry is the W-Boson: it can turn leptons into neutrinos and vice versa, so whenever the gauge bosons are present, they kind of "turn the symmetry crank". So having this symmetry in your theory is absolutely crucial in order to have a consistent description of how gauge bosons interact with the fermions and themselves. The mathematics tells you, however, that the symmetry forbids the gauge bosons from having any mass (Why that is is not easily explained). But we know that some of them do have a mass, namely the Z boson and the W bosons. So how can you have the symmetry in your maths that makes it consistent, but at the same time give your gauge bosons mass which seems to be at odds with it? And that's where the spontaneous symmetry breaking comes in: it preserves the symmetry in the fundamental laws, but it is not there in the actual universe.

The thing that accomplishes this, that's the Higgs field. The higgs field is kind of like your roulette table, it has several differnet directions which are tied to the different directions in particle space, and when the universe cools, the higgs field decides which of the directions in particle space is special, just like a roulette ball coming to rest in one place. And that decides which of the particles become electrically neutral, and which become electrically charged. And once the higgs field chooses one direction in particle space, this violation of symmetry suddenly lets some of the gauge bosons have a mass - they basically get it automatically as soon as the symmetry is gone.

So that's the story.

Yalza! I think we've been here before in Queen when we used W bosons to turn positrons into electrons. I like that the knowledge builds on itself.

I still get a little glitch in my understanding.
1.I thought that the W boson acts like a catalyst when it turns the positron into a neutrino, isn't it annihilated? How then can it gain mass?

2. I understand that your colleagues detest the term "God particle" when referring to the Higgs boson. would they also object to using the term "primordial soup" to refer to the absolute symmetry that doesn't differentiate one particle from another?

3. If I put a Higgs boson and a gauge boson in a"room" together, how will the Higgs boson react to the gauge boson in a symmetry breaking episode?

[Rhondazvous]

Bringing these last questions up for you Alex or Brewer or Vorlon. My official brain team.

[Alex K]

Yalza! I think we've been here before in Queen when we used W bosons to turn positrons into electrons. I like that the knowledge builds on itself.

I still get a little glitch in my understanding.
1.I thought that the W boson acts like a catalyst when it turns the positron into a neutrino, isn't it annihilated? How then can it gain mass?

2. I understand that your colleagues detest the term "God particle" when referring to the Higgs boson. would they also object to using the term "primordial soup" to refer to the absolute symmetry that doesn't differentiate one particle from another?

3. If I put a Higgs boson and a gauge boson in a"room" together, how will the Higgs boson react to the gauge boson in a symmetry breaking episode?

1. Yes it is annihilated. Whatever energy is carried by the W boson is then inherited by the new particle. But the W bosons e.g. causing beta decay are what is called virtual W bosons which do not have to carry all the energy that would usually come with its assigned mass via E=mc^2.

2. The name God particle is stupid because the name in no way adequately represents what the particle does, but primordial soup is ok I think.

3. The higgs boson would be absorbed by the gauge boson and vanish, but that only ç if it is a massive gauge boson.