I don't fully understand the forces at play which require a left hand thread on the left pedal
Jobst Brandt no doubt wrote more comprehensively and forthrightly on this. On the face of it, it seems as though a left-hand pedal should have a right-hand thread, because the rotation of the crank when pedalling would seem to risk loosening a left-hand thread (assuming the pedal bearings were stiff), whereas a right-hand thread would screw itself into the crank while pedalling.
That much is true but it's an oversimplification, because we have overlooked the great force from the rider's leg, plus the fact that at a micro level, threads just don't fit together that accurately.
What happens is that the effort of pushing on the pedal causes a small amount of deflection of the pedal's thread in the crank - in essence, the two are no longer exactly concentric. Under the action of pedalling, the radial force on the pedal spindle maintains this eccentricity, and it results in an effect called mechanical precession (same but different from, say, gyroscopic precession or the precession of the equinoxes). The effect of this is that the pedal thread will ever so slowly roll around inside the crank thread, and this action runs in the direction opposite to pedalling. Thus, the thread of a left-hand pedal must be made left-handed to counter loosening through precession rather than loosening through seized spindle bearings. The same applies for the right-hand pedal.
Of course, if we had a conical interface and a securing nut, like every car axle, this particular problem would go away, and pedals could all be made identical left and right. The problem though would become one of less trivial pedal removal.
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