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:
Thank you, sir
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.
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.
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?
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.
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).
Ah, I guess I have to study Maxwell's again
Thank you for answering me sir
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