# Maxwell's equations and relativity

• Zac Einstein
In summary, Maxwell's equations relate to classical electromagnetism, and general relativity is a gravity theory that takes advantage of Maxwell's equations.
Zac Einstein
what is the connection between maxwell's equations and relativity?

Zac Einstein said:
what is the connection between maxwell's equations and relativity?

Using the framework of special relativity, you can construct a tensorial quantity called the electromagnetic field tensor. It unifies the Maxwell equations in an elegant way, showing that they are essentially part of one simple object. You should read this article for an introduction:

http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism" .

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Polyrhythmic said:
Using the framework of special relativity, you can construct a tensorial quantity called the electromagnetic field tensor. It unifies the Maxwell equations in an elegant way, showing that they are essentially part of one simple object. You should read this article for an introduction:

http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism" .

Thank you, sir

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Classical Newtonian mechanics is incompatible with Einsteinian relativity, so we basically have to re-write the laws of mechanics to make them relativistically correct.

Classical electromagnetism, on the other hand, is already compatible with Einsteinian relativity, so we don't have to re-write the laws of electromagnetism except to gain a more elegant formulation as Poly described.

Let's call electromagnetism based on Maxwell equations the igniting factor for a new theory of dynamics, the one put forth by Einstein, Poincare and Lorentz and later generalized by Einstein under the name of <General Relativity>.

In one phrase, special relativity emerged because of electrodynamics and is encoded in the 4 equations for the E and B fields.

Let's call electromagnetism based on Maxwell equations the igniting factor for a new theory of dynamics, the one put forth by Einstein, Poincare and Lorentz and later generalized by Einstein under the name of <General Relativity>.

In one phrase, special relativity emerged because of electrodynamics and is encoded in the 4 equations for the E and B fields.

Classical Newtonian mechanics is incompatible with Einsteinian relativity, so we basically have to re-write the laws of mechanics to make them relativistically correct.

General Relativity is another gravity theory...but why do some people still use Newton's law of gravity, according to General Relativity Newton didn't know how gravity works so Newton's law is not true.
Maxwell's equations doesn't agree with Newton's law too.
Right?

Zac Einstein said:
General Relativity is another gravity theory...but why do some people still use Newton's law of gravity, according to General Relativity Newton didn't know how gravity works so Newton's law is not true.
Maxwell's equations doesn't agree with Newton's law too.
Right?

Because Newton's law is a good and simple approximation to general relativity that is applicable in numerous situations. Just because a new theory is better, it doesn't mean the old one is completely false.
Maxwell's equations have nothing to to with Newton's law.

Polyrhythmic said:
Because Newton's law is a good and simple approximation to general relativity that is applicable in numerous situations. Just because a new theory is better, it doesn't mean the old one is completely false.
Maxwell's equations have nothing to to with Newton's law.

Yes sir, I didn't mean that it's completely false and if it was completely true Einstein didn't have to develop a new theory, am I right, sir?

You said "Maxwell's equations have nothing to to with Newton's law" how come that there's a connection between general relativity and Maxwell's and no connection between Maxwell's and Newton's law of gravity sir?

Zac Einstein said:
Yes sir, I didn't mean that it's completely false and if it was completely true Einstein didn't have to develop a new theory, am I right, sir?

Yes.

You said "Maxwell's equations have nothing to to with Newton's law" how come that there's a connection between general relativity and Maxwell's and no connection between Maxwell's and Newton's law of gravity sir?

Let's not mix theories here. Maxwell's equation can be formulated nicely in terms of special relativity. You interpret classical fields in terms of relativistic tensorial quantities and take advantage of an elegant formalism. This alone has nothing to do with gravity, neither with Newton's nor Einstein's equations.

Zac Einstein said:
General Relativity is another gravity theory.[...]

Not only that, it's much more, it's a theory of dynamics, which is a part of classical mechanics.
So it goes like:

Newtonian mechanics for inertial reference frames < Special Relativity < General Relativity

... < Electromagnetism in flat space-time < Electromagnetism in curved space-time ( = in the presence of gravity).

Let's not mix theories here. Maxwell's equation can be formulated nicely in terms of special relativity. You interpret classical fields in terms of relativistic tensorial quantities and take advantage of an elegant formalism. This alone has nothing to do with gravity, neither with Newton's nor Einstein's equations

Ah, I guess I have to study Maxwell's again

Thank you for answering me sir

## 1. What are Maxwell's equations and how are they related to relativity?

Maxwell's equations are a set of four equations that describe the behavior of electric and magnetic fields. They are closely related to relativity because they were used by Einstein to develop his theory of special relativity.

## 2. What is the significance of the speed of light in Maxwell's equations and relativity?

The speed of light, denoted by the constant c, is a fundamental value in both Maxwell's equations and relativity. It is the maximum speed at which any object or information can travel in the universe, and plays a crucial role in understanding the behavior of electric and magnetic fields as well as the effects of relativity.

## 3. Can Maxwell's equations be used to explain the phenomena of time dilation and length contraction in relativity?

Yes, Maxwell's equations are the basis for the theory of electromagnetism, which is one of the cornerstones of relativity. The equations describe the behavior of electric and magnetic fields in a uniform and consistent way, allowing for the prediction of time dilation and length contraction effects in moving frames of reference.

## 4. How do Maxwell's equations and relativity relate to each other in terms of the concept of a unified theory?

Maxwell's equations were developed in the 19th century and were later used by Einstein in his development of relativity in the 20th century. Both theories have been successful in describing the behavior of the universe at different scales, and many physicists believe that a unified theory combining both Maxwell's equations and relativity is necessary to fully understand the physical laws of the universe.

## 5. Are Maxwell's equations and relativity still relevant in modern science?

Yes, both Maxwell's equations and relativity are still highly relevant in modern science. They continue to be used in fields such as electromagnetism, particle physics, and astrophysics to make predictions and understand the behavior of the universe. In fact, many modern technologies, such as GPS systems, rely on the principles of relativity and electromagnetism to function accurately.

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