# Question on color states

• metroplex021
In summary, the conversation discusses the concept of symmetries in particle dynamics and how they relate to defining different states or particles. The main point of contention is whether the dynamics can distinguish between states of different spin or color, and how this affects our understanding of particles. The expert provides an explanation for why we consider the two spin states of an electron as one particle, but the three color states of a quark as different particles. They argue that this distinction is somewhat arbitrary and based on which symmetries are spontaneously broken.

#### metroplex021

Hi folks,

I was just reading about symmetries, and why we say that the two spin states of the electron are states of the same particle, while we are free to say that the two strong isospin states define tow different types of particle. According to the book I'm reading, we must attribute two spin states to one and the same particle because the dynamics can distinguish between states of different spin (the triplet state having a different energy than the singlet state, for example). But that made me think: what about color? We say that e.g. each quark has 3 color states, but can be the dynamics distinguish between these states?

Any thoughts much appreciated!

The book is blowing smoke at you. The real reason is that strong isospin isn't an exact symmetry so particles related to each other through an isospin transformation will have different properties. The neutron is heavier than the proton and doesn't have a charge, for instance

Well, to be fair the book was stating how things looked from the perspective of strong-interaction theory alone (so no EM charge yet). And it doesn't seem so crazy: for consider the following. Given that particle dynamics is sensitive to spin, we can dynamically distinguish between the spin-up and spin-down states of a given particle: these two states are eigenstates of Sz. Then we can define a spin-flip operator, Sx, which relates these physically distinct states to one another and as such can be seen as a real physical operation (instead of just a piece of mathematical formalism). But then since Sx is a real physical operator, we must be able to ascribe physical states of Sx to the particle we started with; but then these will be superpositions of the Sz eigenstates (owing to the non-commutativity), so that we must be able to ascribe both spin states to the same particle (insofar as that's exactly what the superposition says is going on). So it seems that where the dynamics can distinguish between two states, we *must* be able to ascribe each of those states to one and the same particle, and hence we cannot that each state denotes a different particle. My question is then just this: one what grounds do we say that there are 3 states to each of the 6 quarks, not 3x6 different types of quark? Do the QCD dynamics distinguish the three states, or not?

My answer is the same it was before. What we decide to call different states of a particle and what we decide to call different particles is somewhat arbitrary. The (left handed) electron and the neutrino are related to each other by a weak isospin transformation and we call them separate particles. That's entirely equivalent to the fact that a blue-up quark is related to a red-up quark by a color transformation and we call them two states of a single particle. Why? well the weak isospin is spontaneously broken and the color symmetry isn't, so electrons and neutrinos acquire different properties. There is nothing particularly fundamental about that choice.

## 1. What is the significance of color states in science?

Color states refer to the different forms or states of matter that are characterized by distinct colors. Understanding these color states can provide valuable insights into the properties and behavior of various materials.

## 2. How many color states are there?

There are three main color states in science: solid, liquid, and gas. However, there are also other color states, such as plasma and Bose-Einstein condensate, that are less commonly studied.

## 3. What causes a material to change color states?

The change in color states is primarily caused by changes in temperature and pressure. As these factors change, the arrangement of molecules or atoms within a material also changes, resulting in a different color state.

## 4. Can a material exist in more than one color state at the same time?

Yes, some materials can exist in multiple color states simultaneously. For example, water can exist as a solid (ice), liquid, or gas (water vapor) depending on its temperature and pressure.

## 5. How do color states affect the properties of a material?

The color state of a material can greatly influence its physical and chemical properties. For example, a solid material is typically more rigid and has a fixed shape and volume, while a gas is more fluid and can fill the space it occupies. Understanding these differences is crucial in many scientific fields, such as materials science and chemistry.