Consistence problems and Introduction to relativity

[Feynmanfan]

Hello there!

In my last Electromagnetism lecture, the teacher explained that Newton's 3rd law doesn't work when we "sit" on a charged particle and move at the same velocity while another particle is moving at another v velocitiy perpendicular to ours.

How ist it that Newton doesn't work? And how do you explain that if we move along both particles (paralell velocity) the magnetic force is not seen.

I suspect that Einsten has something to do with this. Although I haven't taken a special relativity course yet, I read that Einstein came up with his ideas due to these problems in electrodynamics.

I'd be very grateful if you could help me understand this.

 

[HallsofIvy]

It's more a matter of "pre-Einstein". It was determined, experimentally, in the 19th century that the force on a charged particle due to a magnetic field depends on the velocity of the charged particle relative to the magnetic field. No relative motion- no force. Newton's third law (for every action there is an equal and opposite reaction) was a variation of "Galilean relativity": Since F= ma, force, and so any interaction between the experiment and the experimenter, depends upon acceleration- it is impossible to determine the speed of a room moving at a constant velocity by an experiment inside the room.
The fact that the force due to a magnetic field depends on velocity, not acceleration would appear to mean that by some kind of experiment with electro-magnetic fields, we could determine an "absolute" speed. Michaelson and Morley tried to do such an experiment and the rest is history.

 

[turin]

In my last Electromagnetism lecture, the teacher explained that Newton's 3rd law doesn't work when we "sit" on a charged particle and move at the same velocity while another particle is moving at another v velocitiy perpendicular to ours.

Here entereth field theory.

And how do you explain that if we move along both particles (paralell velocity) the magnetic force is not seen.

The magnetic force is not completely independent of the electric force. This is a clear consequence of special relativity. This was probably my favorite paradox, and it took me a long time to finally discover the answer. This paradox is actually treated, in various forms, by various people. If you do a search for "paradox" and then maybe "Lorentz force," or "magnetism," you will probably find your answer. Let me give it a brief attempt, motivated by Wolfgang Rindler's resolution.¹

Imagine a current carrying wire and a charge sitting next to the wire. There is no magnetic force in this case. Now, imagine that the charge moves along the axis of the wire. There is a magnetic force in this case. But this seems to violate the principle of relativity (Galilean) in that, you can transform to a frame in which the charge is at rest, and therefore should experience no force. Rindler's resolution: In this frame, there is a length contraction of the charge density in the wire in such a way that there is then more net opposite charge, which attracts the charge next to the wire. I have mixed feelings about this resolution (i.e. conservation of charge), but the point is that special relativity comes to the rescue (yee-ha).

¹ W. Rindler. Relativity: Special, General, and Cosmological. (Oxford Univ. Press, Inc., NY, 2001).

 

[Feynmanfan]

Thanks!

You were both very kind. I'll have a look that Relativity book.