Can the Lorentz Force be understood non-relativistically?

In summary, the force can only be understood in a relativistic context and is measured in a frame relative to that in which we measure E and B."
  • #1
RiemannLebesgueLemma
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I'm not sure if this belongs in special/general relativity or in this subforum.

I'm currently trying to refresh and strengthen my E&M, and I remembered that one thing that bugged me when I first learned about magnetism was the velocity in the Lorentz force,
$$\vec{F} = q\vec{v} \times \vec{B}$$.
It wasn't really clarified in the lecture video that I was watching, nor in my first-year E&M class, which reference frame this is valid in. I asked my professor at the time, and he gave me quite an unsatisfactory answer. My thinking was that, since E&M was developed before relativity, we should be able to understand this velocity in a non-relativistic context; this leads to some paradoxes, since, for example, we could entirely null the effect of a neutral wire on a moving charge just by boosting to the frame with the velocity of the charge carriers in the wire. If we don't consider Lorentz transformations, then the moving charge in the new frame sees only a neutral wire with no current, and thus should feel no force.

This led me to come to the kind of independent conclusion that the force can only be understood in a relativistic context, and that the full force,
$$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$
measures velocity in a frame relative to that in which we measure E and B.

This makes sense to me, but it doesn't seem like it is really highlighted in either Jackson or Griffiths. Purcell, after stating the force law, does stress that F, E, B and v must all be measured in the same inertial frame. Purcell also mentions in its introduction that Lorentz was close to the theory of relativity in his work on moving charges, which seems to suggest that this problem of velocity-dependence was one of the motivating factors for relativity.

Is it true that we can only understand the Lorentz force within the framework of special relativity? Also, if so, how did they account for magnetic forces before relativity?
 
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  • #2
RiemannLebesgueLemma said:
This led me to come to the kind of independent conclusion that the force can only be understood in a relativistic context, and that the full force,
$$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$
measures velocity in a frame relative to that in which we measure E and B.
In the pre-relativity days, physicists assumed the existence of a medium (the luminiferous aether) that defined a preferred reference frame for electromagnetism. My understanding is that ##\vec v## was assumed to be measured relative to the aether.
 
  • #3
Maxwell's equations did come before relativity. One can say special relativity was Einstein's solution to the riddles created by Maxwell's Equations.

https://en.wikipedia.org/wiki/Special_relativity said:
It was originally proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".[1] The inconsistency of Newtonian mechanics with Maxwell's equations of electromagnetism and the lack of experimental confirmation for a hypothesized luminiferous aether led to the development of special relativity, which corrects mechanics to handle situations involving motions at a significant fraction of the speed of light (known as relativistic velocities).
 
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1. What is the Lorentz Force?

The Lorentz Force refers to the force experienced by a charged particle moving through an electric and magnetic field. It is named after physicist Hendrik Lorentz and is a fundamental concept in electromagnetism.

2. Can the Lorentz Force be understood without considering relativity?

Yes, the Lorentz Force can be understood non-relativistically. This means that it can be explained using classical mechanics and does not require the theory of relativity.

3. What is the difference between the relativistic and non-relativistic understanding of the Lorentz Force?

The main difference between the two understandings is the inclusion of time dilation and length contraction in the relativistic explanation. In the non-relativistic understanding, these effects are not taken into account.

4. How is the Lorentz Force related to Newton's laws of motion?

The Lorentz Force is a combination of the electric and magnetic forces acting on a charged particle. It follows the principles of Newton's laws of motion, specifically the second law which states that the force acting on an object is equal to its mass multiplied by its acceleration.

5. Can the Lorentz Force be observed in everyday life?

Yes, the Lorentz Force can be observed in everyday life. A common example is the force experienced by a wire carrying current in a magnetic field, which causes it to move or rotate. This phenomenon is used in devices such as electric motors and generators.

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