# Charge Invariance: Argument Explained

• quasar987
In summary, the argument presented by the professor is that if charge were not frame invariant, a moving neutral object would become charged, which is not something that is observed. However, the missing piece in the argument is that if charge varies with speed and both positive and negative charges vary equally in magnitude, then the object would remain neutral. This argument also involves Gauss's Law and the relationship between charge invariance and atom neutrality. Another argument in favor of charge invariance is the electrical neutrality of atoms, where electrons move at different velocities around the nucleus. However, some are uncomfortable with this argument as it implies viewing electrons as moving at a particular speed. The argument for charge invariance is also supported by the 4D equivalent of
quasar987
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Today my professor gave us an argument in favor of why charge was frame invariant. It went like "if it were not, then moving neutral object would become charged, which is not something that we observe". It's not exactly that and it made sense at the time, but I'm missing a piece in the argument because if charge varies with speed and + and - charge varie equally in magnitude, then the object remains neutral.

So what is this argument exactly if you know of it? (it also involved gauss's law I think)

Think of a stationary wire with current flowing through it. The simplest model of that is a bunch of negative charges moving through a fixed lattice of positive charges. So if charge changed with speed, the wire's total charge would depend on the voltage applied to it.

So the wire would become charged as soon as we apply a voltage, which is something we do not observe.

quasar987 said:
So the wire would become charged as soon as we apply a voltage, which is something we do not observe.

Right. And since there are so many charges in a wire, even a tiny imbalance would be detectable.

quasar987 said:
So the wire would become charged as soon as we apply a voltage, which is something we do not observe.
No, it wouldn't. Any effect would be canceled immediately by a change of the number of electrons in the wire.

charge invariance and atom neutrality

quasar987 said:
Today my professor gave us an argument in favor of why charge was frame invariant. It went like "if it were not, then moving neutral object would become charged, which is not something that we observe". It's not exactly that and it made sense at the time, but I'm missing a piece in the argument because if charge varies with speed and + and - charge varie equally in magnitude, then the object remains neutral.

So what is this argument exactly if you know of it? (it also involved gauss's law I think)

I think that the most convincing argument is the electrical neutrality of an atom in which electrons move with different velocities arround the nucleus
Do you consider that charge invariance and the postulates of special relativity are sufficient for deriving the fundamental equations of relativistic eloctrodynamics without involving Maxwell? I am convinced.
The best things a physicist can offer to another one are information and criticism

Ich said:
No, it wouldn't. Any effect would be canceled immediately by a change of the number of electrons in the wire.

Why would the number of electrons change significantly? Suppose the wire had negligible capacitance.

Anyway, I just looked this up in Feynman's lectures where I remembered the topic being discussed. He uses the argument that the conduction electrons and everything else in a conductor move at different speeds just due to temperature. So heating something up (or cooling it) would change its total charge if there were any speed-dependence.

I'm a little uncomfortable with bernhard's argument because I don't really like viewing electrons in atoms as moving at any particular speed. It's not clear that a (semi)classical description has any meaning at that level.

Stingray said:
I'm a little uncomfortable with bernhard's argument because I don't really like viewing electrons in atoms as moving at any particular speed. It's not clear that a (semi)classical description has any meaning at that level.
Then you're probably not comfortable with Feynman's argument either, since it implies viewing the electrons in the conductor as moving at a particular speed.

quasar987 said:
Then you're probably not comfortable with Feynman's argument either, since it implies viewing the electrons in the conductor as moving at a particular speed.

True, but I am more comfortable with it. Classical statistical mechanics makes a lot of accurate predictions even when it is being applied to a bunch of objects that aren't quite classical themselves. But there really isn't much at all about individual atoms that can be described classically.

quasar987 said:
Today my professor gave us an argument in favor of why charge was frame invariant. It went like "if it were not, then moving neutral object would become charged, which is not something that we observe". It's not exactly that and it made sense at the time, but I'm missing a piece in the argument because if charge varies with speed and + and - charge varie equally in magnitude, then the object remains neutral.

So what is this argument exactly if you know of it? (it also involved gauss's law I think)
That charge is invariant is proven in several EM textbooks, using the 4D equivalent of Gauss's law. See for instance, Panofsky & Phillips,
"Classical E & M" or Franklin, "Classical Electromagnetism".

quasar987 said:
Today my professor gave us an argument in favor of why charge was frame invariant. It went like "if it were not, then moving neutral object would become charged, which is not something that we observe". It's not exactly that and it made sense at the time, but I'm missing a piece in the argument because if charge varies with speed and + and - charge varie equally in magnitude, then the object remains neutral.

So what is this argument exactly if you know of it? (it also involved gauss's law I think)

So what is magnetism than? I thought that magnetic efects come from changes of charges magnitudes as observed in different frames...

I can not agree with the argument of your professor - the moving neutral object consists of both + and - charges, so if both move with the same velocities with respect to the rest frame there is no efect obverved.

quasar987 said:
...but I'm missing a piece in the argument because if charge varies with speed and + and - charge varie equally in magnitude..
Why would you expect them to vary equally?

I was only saying that the fact that a moving neutral body remains neutral does not prove that charge is invariant. It could be that + and - both change equally in magnitude so as to keep the object neutral.

## 1. What is charge invariance?

Charge invariance is a concept in physics that states that the total electric charge in a closed system remains constant, regardless of any physical or chemical changes that occur within the system.

## 2. What is the significance of charge invariance?

The principle of charge invariance is a fundamental law of nature that plays a crucial role in understanding various physical phenomena, such as electromagnetic interactions and conservation of energy.

## 3. How is charge invariance related to the conservation of charge?

Charge invariance and conservation of charge are closely related concepts. Charge invariance states that the total electric charge in a closed system remains constant, while the conservation of charge states that charge cannot be created or destroyed, only transferred from one object to another.

## 4. What is the argument behind charge invariance?

The argument behind charge invariance is based on the principle of Noether's theorem, which states that for every continuous symmetry in a physical system, there is a corresponding conserved quantity. In the case of charge invariance, the symmetry is related to the conservation of electric charge.

## 5. How is charge invariance tested and verified?

Charge invariance has been extensively tested and verified through various experiments, including studies on electromagnetic interactions, particle collisions, and quantum field theory. These experiments have consistently shown that the total electric charge in a closed system remains constant, providing strong evidence for the principle of charge invariance.

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