Relativity fails with Magnetic Force

[martillo]

Here is presented a problem with the Magnetic Force where Relativity Theory fails:

Absolute Magnetic Force

A possible experiment is pointed out but the theoretical inconsistence is enough.

[martillo]

With thanks to "przyk" at SCI Forums I have realized that I was wrong in one point: actually the relativistic prediction do agree with the classical prediction. The relativistic electrodynamics with lenght and charge contraction with Lorentz Transform actually predict changing Electric and Magnetic Fields so that the the Force obtained is the same as in Classical Physics.

But the inconsistence rises then from the other point of view: Relativity states there are no privileged frames of reference and so in the presented problem there's a change in the real movement of the electron just because a change in the frame of observation (the observer)!

This is unsustainable...

What do Relativity defenders would argue now?

[martillo]

The problem have been re-written in the site.

[martillo]

Trying to clarify the thing better I'copying here what I have posted in other forum:

 

I will copy here what I have posted at SCI Forums what I think clarifies the thing better:

 

The point is that a change in the reference frame (the observer) cannot alter the behavior of the system ot phenomenon being analyzed. In other words the reality of the system/phenomenon cannot be changed and that is what is happening in the presented problem. By reality I mean all the characteristics and properties of the system/phenomenon itself.

If you change the reference frame you would get different expressions for many things as velocity, acceleration, the Force, etc but for example, as in our case, the relatrive movement between the electron and the beam of must be the same, but if you observe carefully the relativistic transformation of the frames you will find that they determine two different movements, two different phenomenons. This cannot happen.

 

In other words, in the problem the relativistic prediction is the same as the classical prediction, fine, but the classical prediction is that the isolated electron will behave differently in the two presented cases of the problem. Now, Classical Physics determines two different behaviors because it considers that if a new absolute velocity is given to the isolated electron and the beam then this actually is a new phenomenon, a new system whith justified different behavior.

Now how Relativity consider and justify the two cases? The relative initial velocity of the two cases is the same so they would represent the same phenomenon, the same system for Relativity, then, how two different behaviors (to match with the classical prediction) are justified? Remember that just a change in the freference frame have been done. Then how?

I don't understand. I see a big problem here.

[CraigD]

… Now, Classical Physics determines two different behaviors because it considers that if a new absolute velocity is given to the isolated electron and the beam then this actually is a new phenomenon, a new system whith justified different behavior.

Now how Relativity consider and justify the two cases? The relative initial velocity of the two cases is the same so they would represent the same phenomenon, the same system for Relativity, then, how two different behaviors (to match with the classical prediction) are justified? Remember that just a change in the freference frame have been done. Then how?

I don't understand. …

I think you confusion arises, martillo, in a faulty understanding of classical electromagnetism.

 

In the equation for the force acting upon a particle with charge [math]q[/math] and velocity [math]\mathbf{v}[/math] by magnetic field [math]\mathbf{B}[/math],

[math]\mathbf{F} = q\left( \mathbf{v} \times \mathbf{B} \right)[/math], (the Lorentz force)

which is the starting point of your page “absolute magnetic force”, the vector quantities [math]\mathbf{v}[/math] and [math]\mathbf{B}[/math] must be in the same coordinate frame.

 

So, in both of your examples, [math]\mathbf{v} = - \mathbf{v_1} = \mathbf{v_2} - \mathbf{w}[/math], and you conclusion that [math]\mathbf{F}[/math] is different for the 2 cases is incorrect.

 

Note that, except for cases where the magnitude of [math]\mathbf{v}[/math] in a large fraction of the speed of light, classical electromagnetism provides an adequate approximation of the more general relativistic electromagnetism. The Lorentz force formula remains usable in either case, because it describes only force, not the acceleration. All that’s necessary to calculate acceleration due to Lorentz force relativistically is to include the term for mass dilation,

[math]m = \frac{m_0}{\sqrt{1 - \left(\frac{|\mathbf{v}|}{c} \right)^2}}[/math]

in the classical equation for acceleration,

[math]\mathbf{A} = \frac{\mathbf{F}}{m}[/math].

 

Because the motion of charged particles such as electrons and protons are routinely and precisely observed, in devices from the most humble mass spectrometers to the most advanced cyclotron particle accelerators, relativity is very well confirmed by it.

 

I noticed another troubling sentence in your page (bolding mine):

Relativity applies Lorentz Transform with length and

charge contraction

in the beam of electrons.

Although you may not intend to apply otherwise, relativity describes mass dilation, and length contraction, but not any change in charge. For example, regardless of its velocity relative to an observer, the charge of an electron remains constant.

[martillo]

How could the velovity to be considered in the Lorentz Formula be v = v1 = v2-w if by definition that v must be the velocity of the moving isolated charge?

In Case 1 v = 0 and in Case 2 v = w.

and you conclusion that is different for the 2 cases is incorrect.

Well,then as in Case 1 the Magnetic Field and Force is zero the same would apply to Case 2 and further we would conclude that a line of current actually would never affect magnetically a near isolated charge. Absurd.

I think you confusion arises, martillo, in a faulty understanding of classical electromagnetism.

I think you must learn about real Magnetic Fields and Forces, I mean how the Magnetic Field and Force work in reallity.

 

May be you would like to perform the experiment to se what really happens...

I don't need to do this.

I noticed another troubling sentence in your page (bolding mine):

Relativity applies Lorentz Transform with length and charge contraction in the beam of electrons.

Although you may not intend to apply otherwise, relativity describes mass dilation, and length contraction, but not any change in charge. For example, regardless of its velocity relative to an observer, the charge of an electron remains constant.

You are right on this. I have corrected the page.