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rakeshsugirth
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How does Maxwell's electrodynamics contradict Newton's mechanics? I read the Maxwell's equations but i am not able to find how those eqns bring up the contradiction. Can anyone explain in detail?
This result would not contradict Newton if there were an aether that the wave traveled in.D H said:The electromagnetic wave equation is a consequence of Maxwell's equations,
[tex]\nabla^2 \mathbf E
= \mu_0\epsilon_0\frac{\partial^2}{\partial t^2}\mathbf E[/tex]
Neither the velocity of the emitter nor the velocity of the observer appear in this equation. This is where Maxwell's equations contradict Newtonian mechanics. The velocity of the emitter and the observer should appear in the wave equation per Newtonian mechanics. Newtonian mechanics is invariant with respect to the Galilean transform. Maxwell's equations are not.
CPL.Luke said:I wonder if you could formulate maxwell's equations in terms of force, this would make the contradiction obvious
or you can also get this from the force law,
F=qE +qv x B
now, if you apply a galilean transform on that
F=qE'+q(v+v')xB'=qE'+q(vxB')+q(v'xB')=mr''=qE+vxB
it shouldn't be to difficult to find the problems from there.
note: the E' and B' are the gallilean transform of the magnetic and electric fields, if you check out maxwell's equations you should find that its not possible for the gallilean transform to yield the same equations of motion.
Maxwell's theory of electromagnetism describes the relationship between electric and magnetic fields, while Newton's theory of mechanics explains the motion of objects in response to forces.
Maxwell's equations predict that electromagnetic waves, such as light, can travel through empty space without a medium, whereas Newton's laws state that an object cannot move without a force acting upon it.
Maxwell's theory of electromagnetism has been extensively tested and is widely accepted by the scientific community as the more accurate description of electromagnetic phenomena.
Yes, they can. While Newton's laws may not fully explain electromagnetic phenomena, they are still useful for describing the motion of objects in everyday scenarios. Maxwell's equations can also be derived from Newton's laws in certain situations.
Maxwell's theory of electromagnetism revolutionized the understanding of light and electricity, and paved the way for later discoveries such as radio and television. It also played a crucial role in the development of Einstein's theory of relativity.