# Fundamental properties of subatomic particles

• Amir Livne
In summary, the conversation discusses the properties and defining quantities of single particles in Newtonian gravitation and quantum mechanics. In QED, there are operators for mass and electric charge with an infinite set of eigenvalues. The concept of spin and its relation to these properties is also discussed, along with the number of linearly independent spin operators and the spectrum for a system with n electrons. The conversation also touches on the theory of electro-weak interactions and the Standard Model, questioning whether these models simply add on more degrees of freedom or if something more fundamental changes.
Amir Livne
A physics hobbyist such as myself, trying to understand high-energy experiments from the recent decades, often hears about symmetries in the model, conservation laws, Feynman diagrams and so on. These are all intuitive properties but very far from a basic world view of "what happens microscopically".

What I would like to ask, is what elementary quantities completely define the state of a single particle. In Newtonian gravitation these would be mass, position, and momentum. That's 7 real numbers, 6 of them unlimited and one restricted to positive values.

In QM things seem to be more difficult, and I understand much less. For a start, there is not isolated particle in vacuum, and even if there was, there would be no values for these properties. So instead - and my first question is whether this is an interesting property - I suggest counting operators whose eigenspaces are of dimension 1. These would include position and momentum, 6 operators with continuous spectrum. That's all there is for a free particle, meaning $$i\hbar\frac{\partial\Psi}{\partial t}=-\frac{\hbar^2}{2m}\nabla^2\Psi$$

What do you get for QED? As I understand, you have mass and electric charge, which are operators with discrete spectrum but an infinite set of eigenvalues. If you consider a state with a single electron it's in an eigenspace with one specific value for mass and electric charge. How does spin relate to this? I read everywhere that spin can be measured along any direction and give 2 values. But how many linearly independent spin operators are there? What is the spectrum for a system with n electrons (my common sense tells me n+1, but I don't know really know the physics)? And is there any other observable independent of the above?

The same question goes for the theory of electro-weak interactions and for the Standard Model. Do these models simple tack on more and more degrees of freedom on each particle, or does something more basic change? What are those parameters? Can extensions to the SM be state along the same lines? Like - "instead of being 3 independent neutrino operators, we now believe in stealth neutrinos so there are 4"

## 1. What are subatomic particles?

Subatomic particles are the smallest units of matter that make up atoms. They include protons, neutrons, and electrons.

## 2. What are the fundamental properties of subatomic particles?

The fundamental properties of subatomic particles include mass, charge, and spin. Protons have a positive charge, neutrons have no charge, and electrons have a negative charge. They all have a certain amount of mass and a spin value, which determines their angular momentum.

## 3. How do subatomic particles interact with each other?

Subatomic particles interact with each other through various fundamental forces, such as electromagnetic force, strong nuclear force, weak nuclear force, and gravity. These forces govern how particles interact and behave in the universe.

## 4. Can subatomic particles be broken down into smaller particles?

Yes, subatomic particles can be broken down into even smaller particles. For example, protons and neutrons are made up of smaller particles called quarks, and electrons are considered elementary particles with no substructure.

## 5. Why are subatomic particles important in understanding the universe?

Subatomic particles are important because they make up everything in the universe. By studying their properties and interactions, we can gain a better understanding of the fundamental laws of the universe and how everything is connected.

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