"The Magnetic force has a strange directional character.. Magnetism is in reality a relativistic effect of electricity." -Richard P. Feynmanpic.twitter.com/rF3WZVbHg1
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The above equation depends of the velocity of the particle.
Naïvely, 2 observers then wouldn't agree on the resultant motion of the particle
However Einstein showed that the E&M fields transform *into* one another so that the 2 observers agree on the particle's trajectorypic.twitter.com/hBJ2n20v1r
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(obs.1) may say that an E force accelerated the particle (obs.2) will say no, there was actually an M force present too This suggests we're talking about E&M all wrong, and we should really be referring to a *single* object
That object is called the EM Field Strength Tensorpic.twitter.com/DtTIdANojp
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"What led me more or less directly to the Special Theory of Relativity was the conviction that the electromotive force acting on a body in motion in a Magnetic field was nothing else but an Electric field. " -Albert Einstein
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That interesting...and deep.
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Now we are talking!
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An interesting aspect is that only for some special electromagnetic fields there exists an observer for which the field is purely electric or purely magnetic.
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Okay but doesn't the cross product transform incorrectly under reflections when compared to magnetic fields? Using the wedge product to create bivectors which represent magnetic fields gives the right answer in 3d, and extends naturally higher.
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If you use bivectors for magnetic fields B (which transform correctly) and vectors for electric fields E, then you can also add those two fields together as F= E+B without destroying the individual information of both. Source: Vector and Geometric Calculus by Alan Macdonald.
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