Relativistic Paradox (1 Viewer)

[milton]

A charged particle, say an electron, moving through an external magnetic field is deflected perpendicularly to the direction of the magnetic field and the direction of tis velocity (right hand push rule) because a moving charged particle induces a magnetic field which interacts with the external magnetic field to produce a force on this particle.

Now consider 2 electrons fired in the same direction with the same velocity (i.e. they're travelling parallel to each other). There will be a force that will cause the 2 electrons to be attracted to each other since they both produce magnetic fields (in a similar way to how 2 parallel conductors with currents going in the same direction will be attracted to each other).

Now consider the 2 electrons that are stationary. they will be repelled because they are like charges. Note that in the previous scenario that the 2 moving electrons could still be repelled, but they will be repelled less than if they were staionary.

Now, the problem- doesn't this violate the Principle of Relativity? that constant uniform motion cannot be detected with any experiment without reference to an outside point?

Consider the 2 electrons on a train moving at very fast constant velocity. There will be a force attracting the 2 electrons since they are moving very fast together, and an observer on the train can in fact determine that his frame of reference is not stationary.

This 'paradox' has been on my mind for quite some time now and my teacher has been unable to give an satisfactory answer. this could make einstein, newton, galileo wrong? lol

 

[insert-username]

Consider the 2 electrons on a train moving at very fast constant velocity. There will be a force attracting the 2 electrons since they are moving very fast together, and an observer on the train can in fact determine that his frame of reference is not stationary.

This is where I think it falls down. Magnetism is a relative effect - the electrons must be moving relative to their immediate surrounds to generate the electric current. If the train is moving at a very fast constant velocity and the electrons are stationary inside the train with an observer, the electrons are not moving relative to the observer and their immediate environment. Hence, they do not create a magnetic field and are not attracted to each other. If the train and electrons are stationary, same situation - no magnetic field, no attraction.

However, if the electrons are moving, they will attract each other whether or not the train is moving. So, no violation of the Principle of Relativity - either way, the observer on the train cannot tell the difference between constant velocity or no velocity, since the electrons will attract/repel each other exactly the same in either case.


I_F