Maxwell vs Newton: Contradictions in Electrodynamics and Mechanics

[rakeshsugirth]

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?

 

[D H]

The electromagnetic wave equation is a consequence of Maxwell's equations,

$$\nabla^2 \mathbf E<br /> = \mu_0\epsilon_0\frac{\partial^2}{\partial t^2}\mathbf E$$

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]

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.

 

[Meir Achuz]

The electromagnetic wave equation is a consequence of Maxwell's equations,

$$\nabla^2 \mathbf E<br /> = \mu_0\epsilon_0\frac{\partial^2}{\partial t^2}\mathbf E$$

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.

This result would not contradict Newton if there were an aether that the wave traveled in.
Sound waves have a velocity that does not depend on the emitter or observer.

 

[Meir Achuz]

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.

These equations are correct up to relativistic corrections of order (v/c)^2, so were not found experimentally to be wanting until late in the game.

 

[Meir Achuz]

There were three early problems in reconciling Maxwell with Newton, two and a half of them not seen until after Maxwell's death. He died with the belief that he and Newton were compatible.

1. No consistent theoretical equation could be found for the force between two moving charges. All the great men-- Gauss, Weber, etc. tried and failed. Even though the (v/c)^2 terms could not be measured, they could not be made consistent. This convinced Maxwell, in his last published sentence, to conclude that his equations should only be applied in the rest system of the aether.

2. The EM prediction of radiation from atoms (I don't think Maxwell did this.) was inconsistent with the Rutherford model of the atom (of course, unknown to Maxwell).
EM theory predicted a very short atomic lifetime and a continuous spectrum.

3. The movement of the Earth through aether should be detectable either by the MM experiment attempting to measure the speed of light relative to the aether, or the
Trouton-Noble experiment to measure the movement of a capacitor through the aether.
Each experiment proved negative, refuting the aether model.

Points 1 and 3 contradicted Galilean invariance, while point 2 was purely experimental.

Interestingly, in titling his paper "The electrodynamics of moving bodies", Einstein based his theory on explaining point 1, even though he used the constancy of c to get to his equations.