Why Need Covarient Form of Electrodynamics?

• B
• physicist 12345
In summary: If you are using the 3-vector form of the equation, there is no...temporal component?No, there is no temporal component in the 3-vector form of the equation.
physicist 12345
hello this is my first topic here and i hope good discussion or answer to my question

As i understand the Maxwell equation keep its form in all frames so why i need to make a covarient formulation form of electrodynamics ?

for example what the covarient form of continuity equation give me !

physicist 12345 said:
this is my first topic here

Welcome to PF! Please note that the thread levels ("B", "I", and "A") are meant to show the level of your background knowledge in the subject matter. Based on your post, I have changed the level of this thread to "B".

physicist 12345 said:
the Maxwell equation keep its form in all frames

Yes, provided we transform all quantities appropriately.

physicist 12345 said:
why i need to make a covarient formulation form of electrodynamics ?

I assume that by "covariant formulation" you mean a formulation in terms of 4-vectors and 4-scalars instead of 3-vectors and 3-scalars. The reason this is done is that it makes it much easier to transform all quantities appropriately, and to see explicitly how the laws remain invariant under Lorentz transformations.

physicist 12345 said:
what the covarient form of continuity equation give me

This is easily found by looking in textbooks or online resources. It is much too broad a subject for a PF thread; once you have taken some time to build your background knowledge, you should be able to ask a more specific question.

vanhees71
thank you very much for quick answer

my question about continuity equation not about the difference but i ask what i get from the covarient form instead of usual form (how i benefit from writing it in covarient form)

also as you say that new formulation to make work much easier then if we use the ordinary (not modified equations) we will get the same results
(i.e i use the same form of Maxwell equation in different frames )

physicist 12345 said:
as you say that new formulation to make work much easier then if we use the ordinary (not modified equations) we will get the same results
(i.e i use the same form of Maxwell equation in different frames )

I don't understand what you mean by this. Maxwell's Equations already take the same form in different frames, whether you use 3-vectors and 3-scalars or 4-vectors and 4-scalars to express them, as long as you transform between frames using the Lorentz transformations for all quantities. That's what you were saying in the OP when you said "the Maxwell equation keep its form in all frames".

I meant by two forms the equations in attached photo (i meant covarience form and usual handing form)

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physicist 12345 said:
I meant by two forms the equations in attached photo (i meant covarience form and usual handing form)

These are two forms of the continuity equation, not Maxwell's Equations. The advantage of using the 4-vector form should be obvious.

then the advantage of using 4- vector is just simplifying the transformation ??

physicist 12345 said:
i ask what i get from the covarient form instead of usual form
You get two things. First, you get brevity. Second, by writing it in covariant form you can immediately use any coordinates you like. For instance, suppose you want to use Maxwell's equations in spherical coordinates. The covariant form allows you to immediately use the same laws as you normally would use.

vanhees71
physicist 12345 said:
then the advantage of using 4- vector is just simplifying the transformation ?

And making the Lorentz invariance more explicit, because the covariant quantities are always just one symbol; in the continuity equation, you have just ##J^a## instead of having to remember that the pair ##\rho, \vec{J}## go together.

vanhees71 and physicist 12345
Dale said:
You get two things. First, you get brevity. Second, by writing it in covariant form you can immediately use any coordinates you like. For instance, suppose you want to use Maxwell's equations in spherical coordinates. The covariant form allows you to immediately use the same laws as you normally would use.

then the covariant form is that which keep its form under transformation (is that which is invariant)

physicist 12345 said:
then the covariant form is that which keep its form under transformation
Yes, that is what covariant means in this context.

PeterDonis said:
And making the Lorentz invariance more explicit, because the covariant quantities are always just one symbol; in the continuity equation, you have just ##J^a## instead of having to remember that the pair ##\rho, \vec{J}## go together.
PeterDonis said:
And making the Lorentz invariance more explicit, because the covariant quantities are always just one symbol; in the continuity equation, you have just ##J^a## instead of having to remember that the pair ##\rho, \vec{J}## go together.
but the density (rho) is still exist as a temporal component of the current denisty

Dale said:
Yes, that is what covariant means in this context.

Also could i think that covariance is the generalization of electrodynamic laws in diffrent frames ?

physicist 12345 said:
the density (rho) is still exist as a temporal component of the current denisty

If you are using the 3-vector form of the equation, there is no "temporal component of the current density", because there is no "current density" 4-vector. There is just the charge density ##\rho## and the current density 3-vector ##\vec{J}##. And they just happen to get mixed up together in Lorentz transformations.

PeterDonis said:
If you are using the 3-vector form of the equation, there is no "temporal component of the current density", because there is no "current density" 4-vector. There is just the charge density ##\rho## and the current density 3-vector ##\vec{J}##. And they just happen to get mixed up together in Lorentz transformations.

it seems that i benefit from this discussion ,, i don't want to waste your time more than that but i want to thank u for your time .. i will read more and may return to ask you again ,,, deep thanks

You're welcome!

physicist 12345

1. Why is covariant form of electrodynamics important?

The covariant form of electrodynamics is important because it allows us to describe electromagnetic phenomena in a way that is consistent with the principles of special relativity. This is necessary because the traditional formulation of electromagnetism, known as the Maxwell's equations, is not invariant under Lorentz transformations.

2. What is the difference between covariant and contravariant form of electrodynamics?

The covariant form of electrodynamics uses four-vectors, which are quantities that transform in a specific way under Lorentz transformations, to describe electromagnetic quantities. The contravariant form, on the other hand, uses four-vectors with an opposite transformation rule. In essence, the difference lies in the direction of the transformation.

3. Can the covariant form of electrodynamics be applied to all electromagnetic phenomena?

Yes, the covariant form of electrodynamics can be applied to all electromagnetic phenomena. It is a more general and fundamental formulation that can be used to describe all types of electromagnetic interactions, including those involving particles with high velocities.

4. How does the covariant form of electrodynamics relate to other fundamental theories?

The covariant form of electrodynamics is closely related to other fundamental theories, such as special relativity and quantum mechanics. It is a crucial component in the development of quantum field theory, which is the framework used to describe the interactions of particles and fields in a relativistic manner.

5. What are some practical applications of the covariant form of electrodynamics?

The covariant form of electrodynamics has many practical applications, including in the fields of particle physics, astrophysics, and engineering. It is used to accurately describe the behavior of particles at high energies, as well as the behavior of electromagnetic fields in complex systems. It is also used in the development of advanced technologies, such as particle accelerators and electromagnetic devices.

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