# Charge Invariance & Mass Dependence: Lorentz Transformations

• QuArK21343
In summary, the charge is Lorentz invariant, meaning it is a scalar and independent of the frame of reference. However, the mass of a particle is also a Lorentz invariant, despite the misconception that it is not. The concept of "relativistic mass" should be avoided, as it is misleading and arose from trying to make the relativistic expression for momentum look like the nonrelativistic formula. The Lorentz force equation also includes a combination of γ and e, but this should not be defined as "relativistic charge."

#### QuArK21343

Why is it that charge is Lorentz invariant (it's a scalar, independent of the frame of reference) whereas mass is not? Does this mean that the gravitational force a body exerts depends on the frame of reference, whereas the electric force doesn't?

The mass of a particle is also a Lorentz invariant. You may be thinking of the relativistic mass γm.

Ok, since this is new to me, could you clarify the difference between the two? Do you mean the rest mass is Lorentz invariant? Anyway, there is no analogue to relativistic mass as far as charge is concerned (no relativistic charge), right?

"Relativistic mass" is a highly misleading concept and should be avoided. Its use arose simply because the relativistic expression for the momentum happens to be p = γmv, and in trying to make look like the nonrelativistic formula it was written p = Mv where M = γm.

The Lorentz force equation can be written (τ is proper time)

dp/dτ = γe(E + v/c x B)

and sure enough there's the combination γe, but I would not recommend defining this as the "relativistic charge" either!

## 1. What is charge invariance?

Charge invariance refers to the principle that the total electric charge of a system remains constant, regardless of changes in position or motion. This is a fundamental concept in physics, particularly in the study of electromagnetism.

## 2. How does charge invariance relate to Lorentz transformations?

Charge invariance is a consequence of the Lorentz transformations, which are mathematical equations that describe how measurements of time and space change between reference frames moving at constant velocities relative to each other. These transformations are a crucial part of Einstein's theory of special relativity.

## 3. What is mass dependence in Lorentz transformations?

Mass dependence refers to the fact that the measurements of mass and energy of an object depend on the observer's reference frame. This means that the mass of an object can appear differently to different observers, depending on their relative velocities.

## 4. How does mass dependence affect the concept of charge invariance?

Mass dependence does not affect the principle of charge invariance, as the total charge of a system remains constant even when the mass of individual objects may appear different to different observers. However, mass dependence does play a role in the overall understanding of how physical quantities behave in different reference frames.

## 5. Are there any exceptions to the principle of charge invariance?

There are exceptions to the principle of charge invariance, particularly in the study of quantum mechanics where particles can have fractional or even zero charge. Additionally, in certain extreme conditions such as near black holes, the concept of charge invariance may not hold true. However, in most cases, charge invariance is a fundamental principle that holds true in the study of physics and electromagnetism.