Understanding why Einstein found Maxwell's electrodynamics not relativistic

In summary: Maxwell's equation for electromotive force (equation D in the paper): "electromotive force" and "electric field" are synonymous. For in the equation, electromotive force at any point is a vector quantity, and it gives rise to current; that is the definition of an electric field.
  • #36
GregAshmore said:
But I'm not sure why I'm not contradicting you. You said, "Although the energy does come from the B field, the force and the B field are not the same thing and are in fact not even proportional." I countered, "On inspection, it appears as though the force is proportional to the strength of the magnetic field." I expected you to tell me I am wrong. Instead you agreed with me.
A vector has a magnitude (strength) and a direction. So one vector (force) can be proportional to the strength (your claim) of another vector (B field) while not being proportional (my claim) to the other vector (B field) if they point in different directions. A closer inspection would show that they don't point in the same direction.

However, this is a minor point. The more important point is the one about work over closed paths.
 
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  • #37
DaleSpam said:
This is easy enough to check. The Lorentz force is given by [itex]f=q(E+v \times B)[/itex]. When we do a Galilean boost by a velocity u then q is unchanged as are E, and B, but v transforms to v+u. So in the boosted frame [itex]f=q(E+(v+u) \times B)[/itex] which is not the same as in the original frame. So the electromotive force is definitely not invariant wrt a Galilean transform.
So, if we return to this post and use the correct pair of Galilean transforms we get the following (in units where c=1):

Magnetic limit:
[itex]E' = E + u \times B[/itex]
[itex]B' = B[/itex]
[itex]f'=q(E' + v \times B') = q(E + u \times B + (v + u) \times B) \neq f[/itex]

Electric limit:
[itex]E' = E [/itex]
[itex]B' = B - u \times E[/itex]
[itex]f'=q(E' + v \times B') = q(E + (v + u) \times (B - u \times E)) \neq f[/itex]

So the Lorentz force is not Galilean invariant under either limit. For Einstein's scenario, clearly the magnetic limit is the appropriate one. For the special case of u=-v which he described f'=f even though it is not, in general, invariant.
 
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<h2>1. Why did Einstein find Maxwell's electrodynamics not relativistic?</h2><p>Einstein found Maxwell's electrodynamics not relativistic because it did not take into account the principle of relativity, which states that the laws of physics should be the same for all observers in uniform motion.</p><h2>2. How did Einstein's theory of relativity differ from Maxwell's electrodynamics?</h2><p>Einstein's theory of relativity introduced the concept of space-time and the idea that the laws of physics are the same for all observers in all frames of reference. This was a departure from Maxwell's electrodynamics, which did not consider the effects of motion on the laws of physics.</p><h2>3. What was the impact of Einstein's theory of relativity on Maxwell's electrodynamics?</h2><p>Einstein's theory of relativity revolutionized our understanding of space and time and showed that Maxwell's electrodynamics needed to be modified in order to be consistent with the principles of relativity. This led to the development of the special theory of relativity, which explained the behavior of objects moving at high speeds.</p><h2>4. How did Einstein's theory of relativity change our understanding of the universe?</h2><p>Einstein's theory of relativity fundamentally changed our understanding of the universe by showing that space and time are not absolute, but are relative to the observer's frame of reference. It also introduced the concept of gravity as the curvature of space-time, which revolutionized our understanding of the force that governs the motion of objects in the universe.</p><h2>5. What are some real-world applications of Einstein's theory of relativity?</h2><p>Einstein's theory of relativity has been confirmed through numerous experiments and has many practical applications. Some examples include GPS technology, which relies on the principles of relativity to accurately determine locations on Earth, and nuclear energy, which is based on the famous equation E=mc^2 derived from Einstein's theory. It has also had a significant impact on our understanding of the universe and has led to advancements in fields such as astrophysics and cosmology.</p>

1. Why did Einstein find Maxwell's electrodynamics not relativistic?

Einstein found Maxwell's electrodynamics not relativistic because it did not take into account the principle of relativity, which states that the laws of physics should be the same for all observers in uniform motion.

2. How did Einstein's theory of relativity differ from Maxwell's electrodynamics?

Einstein's theory of relativity introduced the concept of space-time and the idea that the laws of physics are the same for all observers in all frames of reference. This was a departure from Maxwell's electrodynamics, which did not consider the effects of motion on the laws of physics.

3. What was the impact of Einstein's theory of relativity on Maxwell's electrodynamics?

Einstein's theory of relativity revolutionized our understanding of space and time and showed that Maxwell's electrodynamics needed to be modified in order to be consistent with the principles of relativity. This led to the development of the special theory of relativity, which explained the behavior of objects moving at high speeds.

4. How did Einstein's theory of relativity change our understanding of the universe?

Einstein's theory of relativity fundamentally changed our understanding of the universe by showing that space and time are not absolute, but are relative to the observer's frame of reference. It also introduced the concept of gravity as the curvature of space-time, which revolutionized our understanding of the force that governs the motion of objects in the universe.

5. What are some real-world applications of Einstein's theory of relativity?

Einstein's theory of relativity has been confirmed through numerous experiments and has many practical applications. Some examples include GPS technology, which relies on the principles of relativity to accurately determine locations on Earth, and nuclear energy, which is based on the famous equation E=mc^2 derived from Einstein's theory. It has also had a significant impact on our understanding of the universe and has led to advancements in fields such as astrophysics and cosmology.

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