# An infinite progression of 'meta charge'

• Phrak
In summary, the conversation discusses the various conserved charges in electromagnetism, including the Lorentz covariant vector \ J^{\mu} which is a derivative of the Maxwell tensor, F^{\mu\nu}. The Maxwell tensor is defined in terms of the electric and magnetic potentials, \ (\phi ,\textbf{A}), and the electric charge is a second derivative of the potential field \ A^{\nu}=(\phi,\textbf{A}). It is also mentioned that there is a quantity K^{\mu} which is conserved and can be obtained by applying the same function, f, on J^{\nu}. The physical significance of this charge, \ K^0, is unclear.
Phrak
There are many conserved charges in electromagnetism besides electric charge.

The electric charge and current combine to form a Lorentz covariant vector, $$\ J^{\mu} = (\rho, \textbf{J})$$.

This vector is a derivative of the the Maxwell tensor, $$F^{\mu\nu}$$. (More specifically, a derivative of $$\ \epsilon_{\rho\sigma\mu\nu} F^{\mu\nu}$$.)

The Maxwell tensor can be defined in terms of the electric and magnetic potentials, $$\ (\phi ,\textbf{A})$$, so that $$\ J^{\mu}$$ is also a function of $$(\phi,\textbf{A})$$

Without distraction by the mathematical details, the electric charge, is a second derivative of the potential field, $$\ A^{\nu}=(\phi,\textbf{A})$$ :

$$J^{\mu} = f(A^{\nu})$$​

Applying the same function, f, it's immediately apparent that a quantity K, is conserved as well,

$$K^{\mu} = f(J^{\nu})$$​

I can't imagine the physical significance of the charge, $$\ K^0$$ if there is one. $$(\rho,\textbf{J})$$ would be required to be twice differentiable over space and time.

Here appears to be this persistent stuff, whatever it is. It it, in general, nonzero. It never goes away, but we don't seem to notice it. Does it have a name?

BTW, there should be an infinite sequence of these 'charges,' $$f^{n}(A^{\mu})$$, n=0,1,2,...

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Anyone there?

I find this concept of an infinite progression of 'meta charge' intriguing. It suggests that there may be more to the concept of charge in electromagnetism than we currently understand. The fact that there are many conserved charges besides electric charge highlights the complexity of electromagnetism and the need for further investigation and understanding.

The idea that the electric charge is a second derivative of the potential field is also interesting. It implies that there may be deeper connections between these fundamental concepts in electromagnetism. It also raises questions about the physical significance of this 'meta charge' and whether it has any practical applications.

The suggestion of an infinite sequence of 'charges' adds another layer of complexity to the concept of charge in electromagnetism. It raises the question of whether there could be an infinite number of conserved charges and what their properties might be.

Overall, this content presents intriguing ideas and raises important questions about the nature of charge in electromagnetism. I would be eager to explore these concepts further and see how they fit into our current understanding of electromagnetism.

## 1. What is an infinite progression of 'meta charge'?

An infinite progression of 'meta charge' is a theoretical concept in physics that describes a never-ending sequence of energy charges that continuously increase in magnitude. It is based on the idea that there are infinitely small units of charge that make up matter and energy.

## 2. How does an infinite progression of 'meta charge' differ from traditional notions of charge?

Unlike traditional notions of charge, which involve discrete, measurable units, an infinite progression of 'meta charge' is a continuous and unbounded concept. This means that there is no limit to the amount of charge that can be present and that it can exist in infinitesimally small increments.

## 3. What implications does an infinite progression of 'meta charge' have on our understanding of the universe?

An infinite progression of 'meta charge' challenges our current understanding of the fundamental building blocks of the universe and the laws of physics that govern them. It suggests that there may be an infinite amount of energy and matter in the universe, and that the concept of infinity may be more prevalent than we previously thought.

## 4. How is an infinite progression of 'meta charge' related to other theories, such as string theory and loop quantum gravity?

An infinite progression of 'meta charge' is a concept that is often explored in theories such as string theory and loop quantum gravity, which aim to unify the laws of physics and reconcile the discrepancies between quantum mechanics and general relativity. These theories often incorporate the concept of infinitely small units of charge to explain the behavior of matter and energy at a fundamental level.

## 5. Is there any evidence to support the existence of an infinite progression of 'meta charge'?

Currently, there is no direct evidence to support the existence of an infinite progression of 'meta charge'. However, some theories and experiments, such as the Casimir effect, suggest that there may be an underlying energy at the quantum level that is continuously increasing and infinite in nature.

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