Lorentz Force Paradox

[eram]

I think you are mixing up a Lorentz force and Lorentz transfomation, or not.

The problem is that in the example you gave in the opening post below, the charged ball is not moving reltive to the magnetic field of the magnet.., so there is no Lorentz force.



The last part of the example, below is where the problem begins...



Bob is moving relative to both the charged ball and the magnetic field, he sees them both just setting there in space, as he whizzes by. If he and Sam are looking at their watches, they may notice that their watches don't match.., i.e. some time dilation.., but neither Bob or Sam see the charged ball moving through a magnetic field, so no Lorentz force...

From Wiki,
... the Lorentz force is the force on a point charge due to electromagnetic fields. If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force ...​

The point charge.., the charged ball in your example is at rest relative to the magnetic field, as seen by both Bob and Sam.

it goes back to the debate of what the ambiguously labelled "v" stands for.

though this implies that the magnetic field of the magnet has a velocity in Bob's frame. Hmm...


i've heard another example involving the magnet generating an electric field which balances out the Lorentz force. which is a completely different explanation. are both right?

 

[OnlyMe]

it goes back to the debate of what the ambiguously labelled "v" stands for.

though this implies that the magnetic field of the magnet has a velocity in Bob's frame. Hmm...


i've heard another example involving the magnet generating an electric field which balances out the Lorentz force. which is a completely different explanation. are both right?

The Lorentz force reduces to whether the charge has a velocity (v) relative to the magnetic/electric field.

It has nothing to do with the velocity of Bob, an observer.

In the example you set up the charge and the magnetic field have no velocity relative to one another, from any frame of reference. You specifically set them at rest in Sam's frame of reference.

Przyk gave a short and simple explanation and Tach has tried to show you the math. I have tried to reason it out with you. I don't know what else to say, othe than...

From your hypothetical there is no motion between the charge and the magnetic field.., and that is where the Lorentz force comes from.., the motion of a charged particle through a magnetic/electric field.

 

[eram]

The Lorentz force reduces to whether the charge has a velocity (v) relative to the magnetic/electric field.

It has nothing to do with the velocity of Bob, an observer.

In the example you set up the charge and the magnetic field have no velocity relative to one another, from any frame of reference. You specifically set them at rest in Sam's frame of reference.

Przyk gave a short and simple explanation and Tach has tried to show you the math. I have tried to reason it out with you. I don't know what else to say, othe than...

From your hypothetical there is no motion between the charge and the magnetic field.., and that is where the Lorentz force comes from.., the motion of a charged particle through a magnetic/electric field.

already got that.

Pryzk actually gave me the alt solution i mentioned in #41

Well, i guess we can live with two different explanations.

 

[brucep]

t's imagine two people, Sam and Bob, who are floating in deep space. Both are in an inertial frame.

A very powerful magnet is floating next to Sam, at rest. There is a stationary charged ball floating in the magnetic field. Since both the magnet and the charged ball are at rest w.r.t. Sam, the charged ball experiences no force, and it just floats there.


However, Bob is whizzing past Sam at a high velocity. The charged ball has a velocity w.r.t. to Bob's inertial frame. Bob would see that a Lorentz force is acting on the charged ball, and even see the ball move around in circles.


Imagine the awkward conversation between Bob and Sam afterwards.

Bob: Hey did you see that charged ball whipping about in a flurry!?

Sam: I don't know what you're talking about. :crazy: That ball was perfectly still. Are you high? :m:

Bob: I swear! I saw it with my own two eyes! :wtf:

Sam: I'm going to get you a pair of spectacles. :facepalm:

Events in spacetime are invariant. IE not frame dependent.
The 'ball floating in the magnetic field' is a spacetime event.
For your 'spacetime event' 2 sets of measurements are made. Sam's set of measurements are made while at rest with the 'magnetic field with the ball floating in it', Bob's set of measurement are made while in relative motion with the 'magnetic field with the ball floating in it'. Using the relativistic transformation equations both Sam and Bob will agree with measurements made in the proper frame of the spacetime event 'ball floating in the magnetic field'. Empirical observation [measurements]. Not 'seeing'.

 

[eram]

Events in spacetime are invariant. IE not frame dependent.
The 'ball floating in the magnetic field' is a spacetime event.
For your 'spacetime event' 2 sets of measurements are made. Sam's set of measurements are made while at rest with the 'magnetic field with the ball floating in it', Bob's set of measurement are made while in relative motion with the 'magnetic field with the ball floating in it'. Using the relativistic transformation equations both Sam and Bob will agree with measurements made in the proper frame of the spacetime event 'ball floating in the magnetic field'. Empirical observation [measurements]. Not 'seeing'.

i had the idea that the lorentz force itself was a relativistic effect and frame dependent. But events must be frame independent.

So whether its because the ball is moving together with the field lines and experiences no force, or that the magnet balances the force with an electric field, we can't tell.

 

[brucep]

i had the idea that the lorentz force itself was a relativistic effect and frame dependent. But events must be frame independent.

So whether its because the ball is moving together with the field lines and experiences no force, or that the magnet balances the force with an electric field, we can't tell.

No, events in spacetime are not frame dependent. Events that happen in spacetime are invariant. I'm not guessing about this. Read page 2-1 thru 2-4 in chapter 2, 'Curving', Taylor and Wheeler Exploring Black Holes.
http://www.eftaylor.com/pub/chapter2.pdf
Further study material.
http://www.eftaylor.com/download.html#general_relativity

For instance: Sam measures the length of his penis while standing in his bathroom. Sam measures 6 inches. Bob goes flying by at .9c and measures the length of Sam's penis to be 2.61534 inches. When Sam and Bob get back together Bob starts laughing about how small Sam's penis is. Sam says "idiot wind you forgot to do the transformation back to the event proper frame to where, and when, I measured my penis in my bathroom". If events were frame dependent then we could say the actual length of Sam's penis can be both 6 inches and 2.611534 inches. The shorter length measured is the result of the relativistic effect called length contraction. If Bob had done the transformation to the events proper frame he would realize that Sam's penis was measured to be 6 inches when and where the event occurred. Sam's measurement is a proper frame invariant measurement. Bob's measurement is a remote coordinate frame dependent measurement.

 

[eram]

No, events in spacetime are not frame dependent. Events that happen in spacetime are invariant. I'm not guessing about this. Read page 2-1 thru 2-4 in chapter 2, 'Curving', Taylor and Wheeler Exploring Black Holes.
http://www.eftaylor.com/pub/chapter2.pdf
Further study material.
http://www.eftaylor.com/download.html#general_relativity

For instance: Sam measures the length of his penis while standing in his bathroom. Sam measures 6 inches. Bob goes flying by at .9c and measures the length of Sam's penis to be 2.61534 inches. When Sam and Bob get back together Bob starts laughing about how small Sam's penis is. Sam says "idiot wind you forgot to do the transformation back to the event proper frame to where, and when, I measured my penis in my bathroom". If events were frame dependent then we could say the actual length of Sam's penis can be both 6 inches and 2.611534 inches. The shorter length measured is the result of the relativistic effect called length contraction. If Bob had done the transformation to the events proper frame he would realize that Sam's penis was measured to be 6 inches when and where the event occurred. Sam's measurement is a proper frame invariant measurement. Bob's measurement is a remote coordinate frame dependent measurement.

you need new glasses too? I said "But events must be frame independent."

 

[brucep]

you need new glasses too? I said "But events must be frame independent."

I don't need new glasses. But I did misread what you said. Sorry for that. The links are very good and there's 3 chapters of 'Spacetime Physics', with answer to chapter problems.

 

[eram]

I don't need new glasses. But I did misread what you said. Sorry for that. The links are very good and there's 3 chapters of 'Spacetime Physics', with answer to chapter problems.

ef taylor looks pretty classic. i'll check it out.

 

[Aqueous Id]

ef taylor looks pretty classic. i'll check it out.

Hi, eram. So did you figure out what the velocity vector v is?

For the stationary observer the charge has no velocity. For the moving observer (say he's approaching the scene of our electromagnetic crime) he sees everything closing on him at the same speed. All objects appear to be approaching him at the exact same speed. Furthermore, he doesn't see the charge moving transversely with respect to the field. v is the velocity vector between the charge q and the B field. It's zero whether you're stationary or not. Both observers see that there is zero velocity between the charge and the field, therefore v x B is zero, and to each of them it also appears to be zero since neither observer sees the charge moving with respect to their observed "location" of the B field.

Hope that helps.

 

[brucep]

ef taylor looks pretty classic. i'll check it out.

Sorry about the dumb misread but I still kinda like the example I wrote down. Both those books are my favorite. Exploring Black Holes 2nd edition is scheduled to be shipped on November 1st. The 1st edition has 5 chapter and 7 projects. The 2nd edition has 17 chapters. I'm guessing they mean 17 total chapters + projects. Looks like I'm going to have to brush up on the calculus. Maybe I should revisit my reading comprehension skill level also.

 

[brucep]

Hi, eram. So did you figure out what the velocity vector v is?

For the stationary observer the charge has no velocity. For the moving observer (say he's approaching the scene of our electromagnetic crime) he sees everything closing on him at the same speed. All objects appear to be approaching him at the exact same speed. Furthermore, he doesn't see the charge moving transversely with respect to the field. v is the velocity vector between the charge q and the B field. It's zero whether you're stationary or not. Both observers see that there is zero velocity between the charge and the field, therefore v x B is zero, and to each of them it also appears to be zero since neither observer sees the charge moving with respect to their observed "location" of the B field.

Hope that helps.

The science of relativity theory isn't about 'seeing' or 'appearances' it's about empirical measurements.

 

[eram]

Sorry about the dumb misread but I still kinda like the example I wrote down. Both those books are my favorite. Exploring Black Holes 2nd edition is scheduled to be shipped on November 1st. The 1st edition has 5 chapter and 7 projects. The 2nd edition has 17 chapters. I'm guessing they mean 17 total chapters + projects. Looks like I'm going to have to brush up on the calculus. Maybe I should revisit my reading comprehension skill level also.

interesting.




okay this thread has lasted long enough.

unfortunately i'm just as confused as i was before.

 

[eram]

this sortof implies that magnetic fields have velocities, not something usually associated with them. Also, i have received two different explanations.

 

[Tach]

this sortof implies that magnetic fields have velocities, not something usually associated with them. Also, i have received two different explanations.

I see that you are still trolling on this subject. The Lorentz force is the resultant of RELATIVE motion between charged particles and the e-m field. On one hand you claim that you don't have time to go to school and study, on the other hand you spam 5-6 threads at a time.

 

[eram]

im not trolling, and you always deftly sidestep like a politician. I do have a lot of questions on my mind at any given time. i just check on the forums every now and then. The forums yield mixed results.

and you shouldnt be getting so personal with me. Heh. Even my mother's nagging isnt that bad.

 

[OnlyMe]

this sortof implies that magnetic fields have velocities, not something usually associated with them. Also, i have received two different explanations.

You began the thread with a powerful magnet and a charged ball.., floating at rest in space (at rest relative to each other).

In that situation, relative to each other the magnetic field does not have a velocity.

However, if you move the magnet, the magnetic field associated with it, moves with it. In that case the magnetic field has a velocity.., relative to any frame of reference where the magnet has a velocity...

 

[eram]

got it. Though i feel like the discussion is not going into the "fine print" so to speak. Like not referring to some of my questions on the nature of magnets. the fact that i have received two different explanations makes it really confusing. But nevermind.

 

[Tach]

got it. Though i feel like the discussion is not going into the "fine print" so to speak. Like not referring to some of my questions on the nature of magnets. the fact that i have received two different explanations makes it really confusing. But nevermind.

A problem can have multiple valid solutions, it behooves on you to try understanding (at least) one.

 

[OnlyMe]

got it. Though i feel like the discussion is not going into the "fine print" so to speak. Like not referring to some of my questions on the nature of magnets. the fact that i have received two different explanations makes it really confusing. But nevermind.

Eram, I think you were referring to the following post by przyk as the alternate solution,

Yes, but you are also supposed to take into account the velocity of the magnet with respect to Bob's frame. Ultimately the resolution to your paradox is that the electric and magnetic fields are frame-dependent quantities. The magnet may produce a purely magnetic field in Sam's frame, but in Bob's frame the magnet will actually be surrounded by both nonzero magnetic and electric fields, and it'll work out in such a way that the net Lorentz force on the charged ball is zero.

I don't think przyk was saying anything different than others. He just says yes, you do have to take into account the magnet's velocity relative to Bob.., but you also have to account for the velocity of the ball relative to Bob.

It does not matter if you look at the velocity of the magnet and the ball from any frame of reference, what is important is their velocity relative to eachother.

The magnet and the ball are at rest relative to eachother, no matter what other frame of reference you measure their velocity from. If you handed the ball to Bob and left the magnet floating in space! as Bob and the ball speed past, then there would be an interaction between the field of the magnet and the ball.....

Maybe, I am wrong and this has nothing to do with your question. I could just misunderstand what you are referring to.