Dear Thierry Dr Mees,

It is a very interesting question.We may hope for useful discussions on this topic.

Regards

You need to remember (and take account of) the return current that is travelling in the opposite direction around the electron beam. This doubles when the observer changes from being stationary to travelling with the non-relativistic electron beam, so probably eliminates the effect you were hoping to demonstrate!

Relativity probably needs to be considered anyway.

Dear Malcolm,

Thank you for your advice. The return current wire can be installed perpendicularly to the cathode ray, far enough from it, and than parallel to it, in order to get a rectangle setup. Then, the mesurements near the cathode ray will not be influenced.

A tricky problem - the electrons in the perpendicular wires will all be travelling backwards, as well as towards and away from the beam at either end.

What about an evenly distributed cylindrical return current, coaxial to the beam? It will cause no magnetic field at its inside, regardless of the observer's speed.

Then the radial currents at the ends remain. For a resting observer, they would act identically to mirrors, giving the image of an electron beam of infinite length. In a distance much larger than the radius of the return cylinder, their field should decrease proportionally to 1/r3, I guess (point-like source of static field => 1/r2; each current has a counterpart in opposite direction => 1/r3, at least). So, in principle, it should be possible to remove them so far that their contribution is neglectable, for both the resting as well as the moving observer, relative to the radial currents.

I'm not sure the ends look like mirrors. Also these walls would not be stationary but be moving, so if they do act like mirrors the images would be moving at twice the original electron speed, so not an infinite line of stationary charge

The problem now looks like a cylinder of current moving along, with closed walls of current also moving along with it, adding electrons to the beam at one end and taking them out of it at the other, so that the line of stationary electrons moves progressively further backwards as electrons are added at one end and removed at the other, without the electrons in between moving - a bit like a caterpillar track).

Are we allowed to suppose that some kind of demon glues the electrons together at the beginning of the beam, and another demon de-glues them at the end? In this way, the bundle of electrons would retain its diameter instead of spreading out.

Do we agree that the magnetic field measured by the moving observer vanishes? E. g. if measuring the Faraday effect inside a coil of suitable glass fiber surrounding the beam, there would be an effect (however small) in the resting coil but none in the coil moving with the electrons.

But the path of a free charged particle, for example, moving in the field(s) of the beam should be the same for both observers but be explained differently by the resting and the moving observer.

Dear Readers,

The Einstein's theory of relativity is the out come of the eltromagnetism.Therefore,It would be logical not have direct verification of the Lorentz invariance through an experimental set up on the basis of electrodynamics.Another observational problem is due to very large value of the speed of light c .Therefore, an observable is either very large or very small.Here, I would like to request the readers to see my work"Role of the principle of relativity:an approach Towards the relativity beyond the domain of physics",General Science Journal,6986,July 12,2017,to get more informations about an observable in the Einstein' Theory of Relativity.

Further,according to the theory of of relativity,the twice derivatives of the four electromagnetic potential with respect to the proper time must vanish in a Minkowski space whether, The space is free from inertial force or not.This implies that in a freely falling system,the path of a free particle and the path of a charged particle in presence of electromagnetic field ,both are same.This property may be considered as one of the direct observation of Lorentz invariance.

Regards

Hi Joerg

I'm not sure what your question means. I was responding to your description of a possible solution, trying to make sure that at least some of the complications involved were taken into account.

I do not believe that violation of Lorentz invariance will be demonstrated with electromagnetism - people cleverer than me have been trying to do that for over 100 years. I am trying to point out complications in this apparently simple thought experiment that mean the original conclusions may not be true.

Dear all,

Could the experiment be simplified as follows?

Let instead of a cathode beam, be used a long plastic rod, strongly charged by electrons.

Let the rod be moving and a Hall effect sensor standing still: let the magnetic field be measured.

Let the rod be moving and a Hall effect sensor moving parallelly at the same rate: let the magnetic field be measured.

The outcome will either be as relativity propones, or as I propose, independent from that (non-relativistic) motion.

It has been shown that the moving hall probe sees a distorted electric field from each electron, due to Special Relativity (SR), that gives the same measurement as the magnetic field due to the current when the rod is moving and the probe is stationary. i.e. magnetic field can be completely explained (effects calulated) by SR on the electric field of electrons. It is surprising but true that even at the very slow speed of conduction electrons Lorentz contraction gives the forces that we attribute to magnetic fields.

Dear Malcolm,

For a plastic rod that is charged negatively, how can SR explain the same measurement for the magnetic field when the rod is moving and the probe is stationary or both at the same velocity? And how can it explain the zero magnetic field if both are standing still?

Dear Joerg,

You wrote: "Do we agree that the magnetic field measured by the moving observer vanishes?"

That is precisily the question that I would like to find out by experiment...

Since the electrons of a cathode ray are very fast, maybe it is easier to use a negatively charged plastic rod instead, and measure:

1) the magnetic field if both the rod and the sensor are standing still;

2) the magnetic field if both the rod and the sensor are moving at the same speed;

3) the magnetic field if either the rod or the sensor is moving.

When the probe is moving relative to the electrons it sees electrons moving backwards and it sees their electrostatic fields distorted by length contraction, which has the same effect as a magnetic field. When both are moving at the same same velocity or are stationary (the same thing) then there is no relativistic distortion.

See: . The Feynman Lectures on Physics (vol. 2, ch. 13-6) uses this method to derive the "magnetic" force on a moving charge next to a current-carrying wire. See also Haskell[9] and Landau.[10] (from Classical electromagnetism and special relativity page on Wikipedia.)

I originally read it in Electromagnetic Fields and Waves; Lorrain and Corson. It is usually calculated for the difference between stationary positive charges and moving negative charges, but the principle applies here too.

Dear Malcolm,

Sorry, but it is not about a wire but about a cathode ray or an electrically charged plastic rod. It is not about relativistic speeds, but about non-relativistic speeds.

Dear Thierry

Relativistic length contraction of electric fields gives the forces attributed to magnetic fields even for slow electrons - such as conduction electrons. You were talking about fast electrons a few posts up. Electrons are relativistic at about 500 kv voltage drop. The magnetic field equivalence will work in each case. The electrons in a charged rod or electron beam could be moving at any speed. This does not make the equivalence invalid.

Dear Malcolm,

"Relativistic length contraction of electric fields gives the forces attributed to magnetic fields"

Where is the direct observational evidence?

Finally, it is agreed that no direct proof of any Lorentz invariance exists?

Thierry

The deformation of electric fields of moving electrons has been calculated assuming Lorentz contraction, and the resulting forces on other moving electrons when both are surrounded by stationary positive charges; and the forces are identical to the forces calculated using the magnetic field description.

See, for example http://www.damtp.cam.ac.uk/user/db275/concepts/Lecture4.pdf

This shows that effects described by magnetic fields are entirely explained by electric fields with Lorentz contraction.

Dear Malcolm,

You show a link that is only a ad hoc calculation with the wrong phenomenology. Einstein's SRT is only an optical deformation of a light beam when sent from an inertial reference frame (IRF). That explains why he found a "longitudinal mass" and a "transverse mass".

It has nothing to do with electromagnetism, which are real force fields. A light beam is no force field and can not change anything.

Electromagnetic fields propagate at finite velocity, and the force field at a distance from the IRF produces a field that has a similar mathematical result as the Lorentz factor.

However, the phenomenology is totally different and is real.

SRT cannot give force fields, and it is just optics. It is apparent, while electromagnetism is real.

Regards,

Thierry De Mees

The only proof of anything existing is in the results of its existence. What Lorentz invariance predicts happens. In all cases where it has been used, in everyday engineering (satnav), and in high energy physics, for example, the results predicted by Lorentz invariance are correct within the accuracy of any measurement that has been made.

Dear Malcolm,

An empirical equation cannot justify an "explanation" that has not the least of a phenomenological substantiation.

For charges, electromagnetism possess the required phenomenological substantiation. SRT has not.

Best regards,

Thierry De Mees

I believe you will find that Maxwell's equations are the same as the relativistic Schrodinger equation of the photon, i.e Maxwell's equations can be generated from Schrodingers equation if Lorentz invariance is true. Electromagnetism is the combination of SRT and wave mechanics for massless particles.

https://en.wikipedia.org/wiki/Relativistic_wave_equations

Dear Malcolm,

Maxwell's equations are equivalences at one place and time. They are not causal, which means: the RHS is not causing the LHS. In order to make the equations causal, one must include distance, and automatically time before reaching the distance.

Therefore one must understand that both E fields and B fields are generated by charges. The retardation with which this happens is caused by the limited propagation speed "c".

Hence, by making Maxwell's equations causal, one gets automatically a Lorentz-like factor. However, the phenomenological origin has nothing to do with SRT, which is only optics by light between inertial reference frames.

Your Wikipedia link is plain wrong. It uses the SRT dogma which is utterly false in that context, as it is false in any context with charges. The correct context is the one that I have explained.

Best regards, Thierry De Mees