Electromagnetism, Relativity, Force, Space ?

[Flea]

Hey there!

I was just listening to Richard Feynman on the way home and hit yet another issue I have with relativity... I'd be most thankful for any input! :)

So, suppose we got two charged particles moving parallel to each other. A charged particle has an electrical field - if it's moving, this field changes, which in turn leads to a magnetic field.
Having both particles move parallel to each other we get a force between them - they'll move towards each other.

Now... let's sit on one of those particles. Relativity says that there will be no magnetic field then because, from our point of view in time and space, they are not moving.

So what now - are they moving towards each other, or not?

The only answer that I could think of is this: they are both standing still and moving towards each other at the same time... depending on where you are as observer? Is this the concept behind time/space dilation or contraction?

Thanks for your time!

 

[bcrowell]

http://www.lightandmatter.com/html_books/genrel/ch04/ch04.html#Section4.2

See subsection 4.2.4.

 

[starthaus]

So what now - are they moving towards each other, or not?

Between two charged particles you always have an electrostatic force.
The force exists whether or not the particles are moving wrt. each other.
The force is attractive only if the particles have oposing polarity charges, otherwise it is repulsive.
So ,you will need to reflect on what does your post have to do with relativity?

 

[GRDixon]

Now... let's sit on one of those particles. Relativity says that there will be no magnetic field then because, from our point of view in time and space, they are not moving.

So what now - are they moving towards each other, or not?

The particles will only momentarily be at rest in the inertial frame that moves along in their direction of motion (relative to the original frame). In their momentarily rest frame there will still be an electric field, and they will start drifting toward one another.

 

[bcrowell]

So ,you will need to reflect on what does your post have to do with relativity?

It has to do with relativity for the reasons discussed in the link at #2.

The particles will only momentarily be at rest in the inertial frame that moves along in their direction of motion (relative to the original frame). In their momentarily rest frame there will still be an electric field, and they will start drifting toward one another.

The OP actually wasn't really very clear about whether s/he intended the charges to be like or opposite.

Assuming opposite charges, we have the following:

In frame A, where they're initially at rest, they accelerate toward one another. There is initially an electric field but no magnetic field. The electric field is responsible for their accelerations.

In frame B, where they're moving, there is initially both an electric field and a magnetic field. The electrical interaction is attractive, just as in frame A. The magnetic interaction is repulsive, but is weaker than the electrical one. Therefore the net interaction is attractive, and an observer in frame B agrees with an observer in frame A that the particles approach one another and collide.

Reading over the OP's #1, it's not clear to me why the OP seems to be ignoring the electrical interaction in frame A.

A charged particle has an electrical field - if it's moving, this field changes, which in turn leads to a magnetic field.

It's true that there is electromagnetic induction in frame B. However, there is also a magnetic field simply because the charges are moving; currents make magnetic fields.

 

[starthaus]

It has to do with relativity for the reasons discussed in the link at #2.

My point was that for same charges, the particles repulse each other and his scenario is false, relativity or not.

 

[bcrowell]

My point was that for same charges, the particles repulse each other and his scenario is false, relativity or not.

True. If the charges are alike, then all the signs of the interactions in #5 have to be reversed, but there is still no paradox. Anyway, it looks like the OP hasn't come back to look at the answers to his/her question, so we'll probably never know what s/he intended.

 

[GRDixon]

Hey there!

So, suppose we got two charged particles moving parallel to each other. A charged particle has an electrical field - if it's moving, this field changes, which in turn leads to a magnetic field.
Having both particles move parallel to each other we get a force between them - they'll move towards each other.

Now... let's sit on one of those particles. Relativity says that there will be no magnetic field then because, from our point of view in time and space, they are not moving.

So what now - are they moving towards each other, or not?

The only answer that I could think of is this: they are both standing still and moving towards each other at the same time... depending on where you are as observer? Is this the concept behind time/space dilation or contraction?

Thanks for your time!

Although they may momentarily be at rest in an inertial frame, they are accelerating in all inertial frames. At any time t+dt pr t-dt they will be moving toward one another. The point is that they are not doing both AT THE SAME TIME. I don't see how this effect contributes to time/space dilation/contraction.

 

[GRDixon]

In frame B, where they're moving, there is initially both an electric field and a magnetic field. The electrical interaction is attractive, just as in frame A. The magnetic interaction is repulsive, but is weaker than the electrical one. Therefore the net interaction is attractive, and an observer in frame B agrees with an observer in frame A that the particles approach one another and collide.

.

Well put. Here's a tickler: suppose the charges are held apart and at rest by a spring (viewed from their rest frame). If the apparatus is viewed from a second inertial frame, relative to which everything moves, can conclusions about the spring "constant" be drawn?