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Physics, Astronomy & Cosmology / What's the paradox involving two moving parallel electrons?
« on: 07/06/2008 16:08:19 »
To rephrase what everyone else has said (broken down into steps)
(1) Special relativity tells us that if put an experiment on a train and run it past our observer at high speeds, he sees the experiment happening more slowly than it would appear to if the train is still.
(2) In order to test this paradox, we put two electrons on a table on the train some distance apart. To someone onboard the train with them, they appear to repel entirely because of electrical forces since they're sitting still onboard the train. They therefore move apart.
(3a) To an observer outside the train, because the experiment appears to slow down (special relativity), the electrons appear to move apart more slowly. However, he can explain this entirely by understanding the electric repulsion on the train and then applying relativity to slow the effects down.
(3b) If the outside observer doesn't know about relativity (and electromagnetism was formulated before relativity), he can explain the "slowing down" as a result of the magnetic fields/forces that are generated by the motion of the electrons which oppose the electric "push" apart.
(4) The paradox is: if you use the magnetic field explanation instead of relativity, why does one observer see a magnetic field and the other not? How can a field just vanish like that? The resolution is that magnetic fields have a deep connection to relativity, and that you can describe the situation here without them if you understand the relativity going on.
(1) Special relativity tells us that if put an experiment on a train and run it past our observer at high speeds, he sees the experiment happening more slowly than it would appear to if the train is still.
(2) In order to test this paradox, we put two electrons on a table on the train some distance apart. To someone onboard the train with them, they appear to repel entirely because of electrical forces since they're sitting still onboard the train. They therefore move apart.
(3a) To an observer outside the train, because the experiment appears to slow down (special relativity), the electrons appear to move apart more slowly. However, he can explain this entirely by understanding the electric repulsion on the train and then applying relativity to slow the effects down.
(3b) If the outside observer doesn't know about relativity (and electromagnetism was formulated before relativity), he can explain the "slowing down" as a result of the magnetic fields/forces that are generated by the motion of the electrons which oppose the electric "push" apart.
(4) The paradox is: if you use the magnetic field explanation instead of relativity, why does one observer see a magnetic field and the other not? How can a field just vanish like that? The resolution is that magnetic fields have a deep connection to relativity, and that you can describe the situation here without them if you understand the relativity going on.
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