Unified electrodynamic force
The magnetic force is a relativistic effect.
By Howard Johnson, PhD -- EDN, February 5, 2009
Fire two charged particles at the same moment, with the same initial velocity, into a perfect vacuum (Figure 1). The two particles, having the same electric charge, repel one another. This repelling electric force, F, makes the particle tracks diverge.
Given the magnitude of the electric force and the masses and internal velocities of the particles, you can, if you know a little college physics, predict the rate of divergence—but you'd be wrong. The actual particle tracks diverge at a slower rate than electric-field considerations alone predict.
If French physicist and mathematician Andrè-Marie Ampère were alive today, he would explain the diminished divergence as the result of magnetic forces. Ampère's laws describe a mechanical force that pulls together parallel wires carrying current in the same direction. Simplified to the case of only two charged particles moving in space, the pull of Ampère's magnetic force partly counteracts the electric repulsion to produce the actual trajectories shown in Figure 1.
Case closed? Hardly. Follow me to the next level.
Place yourself in a chair moving alongside the two particles. From your perspective, as the electron guns recede leftward, the two particles appear stationary. The only movement you perceive is their gradual vertical divergence. From your perspective, the particles have no horizontal motion, so there is no magnetic force. From your perspective in the chair, the particles diverge at a rate that solely their electric-field interactions determine.
Yet, from my perspective standing on the ground beside the electron guns, a magnetic force indeed seems to exist, and it slows the divergence of the two particles. Which of us is right?
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The key to this paradox may shock you because it sounds like the theme of a science-fiction novel: My time and your time are different. Your velocity induces a tiny dilation of your scale of time relative to mine. From my perspective, that time dilation slows your predicted rate of divergence just enough so that your rate precisely matches mine.
In this experiment, the choice of reference frame modulates the existence of the magnetic force. You can turn it on or off depending upon where you stand or sit. It is therefore not a “real” force. It is nothing more and nothing less than a direct consequence of Einstein's theory of relativity.
Standing on the ground observing the experiment, I can view the result in three ways:
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using the reference frame of your chair, computing a purely electric-field interaction, and adjusting the results to account for the relativistic time dilation between us;
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accepting at face value Ampère's fictional magnetic force as apparent from my perspective; or
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in full realization that only one force, the electric force, is in play, with its magnitude modified according to the relative velocities of the particles and observers involved.
Reference 1 outlines the third method. It makes interesting reading for those ready to embrace the full brilliance of relativity and the true meaning of the unified electrodynamic force. The treatment is highly mathematical.
The characterization of magnetic force as a relativistic effect in no way diminishes the importance of magnetic-field calculations in ordinary circuits. The magnetic-field illusion is an extremely useful means of understanding and designing all sorts of things—from motor-generators to high-speed transmission lines.
ReferenceFukai, Junichiro, A Promenade Along Electrodynamics, Vales Lake Publishing, 2003.
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Ths is obvious enough that I worked this out for myself as an undergraduate back in 1962, and obvious enough that none of my tutors thought that I'd done anything particularly clever.
It has never been spelled out in any of the physics texts that I've used, so I guess it has to rate as an obvious implication of special relativity.
Bill Sloman - 2009-26-12 20:33:00 PST -
could it be that the particles don't quite behave in a "perfect vacuum" as expected because the particles interact w/ the "aether" which is a BEC of e+ and e- ??? SMer's conveniently circumvent "aether" by saying the vacuum is full of "virtual particles" but that virtual concept is a virtual invention to avoid admitting they were virtually wrong (and so was Einstein - and he knew it) dismissing the aether concept at the beginning of the last century.
Barry Cullen - 2009-14-3 06:33:00 PDT -
Howard,
I really enjoyed your article, "Unified Electrodynamic Force". This really brings to light the genius of the creation of the universe. How weirld would it be if the same event appeared differently to observers in different frames of reference. To resolve this, Einstein proposed that time was different for different observers, an idea that was at first ridiculed. But nature has brilliantly worked it out such that no matter what the reference frame, the physics of an event remains constant.
Bob Blacka - 2009-18-2 06:48:00 PST -
I was quite surprised when I first realized the relativistic mechanism behind magnetism. This did not occur in college, but many years later when trying to explain the finer points of magnetism to my daughter. We hadn't used the "Feynman Lectures" in school, but I have enjoyed reading them from time to time "post graduation". I decided to read what Feynman had to say about magnetism when I stumbled into the ideas that Dr. Johnson describes. Point being the effects of special relativity do not have to involve extremely high velocities to be observed in every day life, and that if we're willing to compute relativistically magnetic force computations are unnecessary. But what surprised me the most is that neither my physics or E&M profs pointed out the special relativity connection. We certainly had been exposed to all the material: the beauty of that connection was just never made for us ....
Eric Beck - 2009-17-2 14:29:00 PST -
Nice stuff, the Dutch Hendrik Lorentz introduced this in 1892 already, but he did not made the conclusions Einstein did.
Still magnetic force is real, the electrons in copper wires move very slow (cm/sec order) due to current, and still they attract each other firmly.
Yes, and the same analogy applies to gravity:
if there is a magnetic force for moving electric fields, there is also a analogue force for masses.
Two masses attract each other, but when they travel at near light speed, there clocks go slower and they will
fall less fast to each other. For a non-moving observer
it looks like some repelling force slows there fall: The 'mass-magnetic' force! Howver it is many orders of magnitude weaker than the magnetic force...
See also gravitational waves.
Benjamin Perdeck - 2009-17-2 14:20:00 PST
