# How Do Quark Matrix Masses Relate to Einstein's E=mc^2?

• Ruslan_Sharipov
In summary, the conversation discusses the relationship between matrix masses of quarks and Einstein's formula E=mc^2. The speaker explains that there is currently no understanding of where fermion masses come from and that even if the Higgs mechanism is correct, the values of the masses must still be questioned. They also note that energy is frame dependent while the masses in the matrix are frame independent, and ask if the speaker understands how this is resolved.
Ruslan_Sharipov
Recently I have managed to understand some basics of the Standard Model and even have written some note about it (see http://arxiv.org/abs/math.DG/0605709" ). The quark masses there are matrix quantities. Two tripples of quarks (the upper row - one from each generation and the lower row - one from each generation) have matix masses. I. e. the masses of 6 quarks are given by two 3x3 matrices. How such a matrix mass correlates with the famous Einsteins's formula E=mc^2. Especially its non-diagonal elements? I think this question is worth to discus here.

Ruslan Sharipov,
algebra & geometry group of Bashkir State University,
cell phone +7(917)476-93-48

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Ruslan_Sharipov said:
How such a matrix mass correlates with the famous Einsteins's formula E=mc^2.

It doesn't. We don't understand yet where the fermion masses come from. Even if the Higgs mechanism turns out to be correct, we still won't know what they are, because we will instead have to aks why the Yukawa couplings take on the values they do.

Incidentally, do you see a problem with what you wrote in your post? Energy is frame dependent, but the masses you wrote down in your matrix are frame independent. Do you understand how this is resolved?

The relationship between quark masses and the famous equation E=mc^2 is a fascinating topic in the field of particle physics. As you have noted, the masses of quarks are represented by matrix quantities, specifically two 3x3 matrices. This is because the Standard Model of particle physics predicts that quarks have mass due to their interactions with the Higgs field.

In order to understand how these matrix masses correlate with E=mc^2, we must first understand the meaning of each term in the equation. The symbol "E" represents energy, "m" represents mass, and "c" represents the speed of light. This equation states that energy and mass are equivalent and can be converted into one another.

In the context of quark masses, this means that the energy required to create a quark can also be converted into its mass. The non-diagonal elements of the matrix mass represent the interactions between different generations of quarks, which can also be thought of as the energy needed to create or transform a quark from one generation to another.

Furthermore, this equation also highlights the importance of the speed of light in understanding the relationship between quark masses and energy. The speed of light is a fundamental constant in the universe and plays a crucial role in determining the energy and mass of particles.

In summary, the matrix masses of quarks are directly related to the famous equation E=mc^2. They represent the energy required to create or transform quarks, and the non-diagonal elements of the matrix correspond to the interactions between different generations of quarks. The speed of light is a fundamental factor in understanding this relationship and plays a crucial role in determining the energy and mass of particles in the Standard Model. Thank you for bringing up this interesting topic for discussion.

## 1. What is a quark?

A quark is a fundamental particle that makes up protons, neutrons, and other subatomic particles. It is one of the building blocks of matter and cannot be broken down into smaller particles.

## 2. How do quark masses affect E=mc^2?

E=mc^2 is a famous equation in physics that relates energy (E), mass (m), and the speed of light (c). Quark masses are a component of the mass (m) in this equation, so they play a role in determining the amount of energy that can be produced from a given amount of mass.

## 3. Are all quarks the same mass?

No, there are six different types of quarks (up, down, charm, strange, top, and bottom), and each type has a different mass. The masses of quarks are relatively small compared to other particles, such as protons and electrons.

## 4. How do scientists determine the masses of quarks?

Scientists use a variety of experimental methods, such as particle accelerators, to study the behavior of particles and determine their masses. The masses of quarks are also predicted and refined using theoretical models and calculations.

## 5. Can quark masses change?

Yes, quark masses can change in certain physical processes, such as in particle collisions or in the extreme conditions of the early universe. However, the masses of quarks are considered to be fundamental properties and are not known to change under normal circumstances.

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