New Explanation to How Newton's Third Law is Satisfied in Magnetism

[Mike Xander]

<Moderators note. Moved from the quoted thread to avoid detracting>

Proton 1 (p1) moving in the positive x direction, currently at some position on the positive x-axis. Proton 2 (p2) moving in the positive y direction, currently at some position on the positive y-axis.
The magnetic field of p1 at the position of p2 is in the positive z direction (Biot-Savart law). So the force on p2 is in the + x direction (Lorentz force).
The magnetic field of p2 at the position of p1 is in the - z direction. The force on p1 is in + y direction.
So the two forces are not opposite to each other.

Newton third law does apply in magnetism, and this is proved by applying the conservation of momentum principle. This will be clearer when the causes/origin of the magnetic force is understood as described in the work "Two new theories for the current charge relativity and the electric origin of the magnetic force between two filamentary current elements" by Shadid. Current elements produce spreading electric fields in the space that changes from inward to outward and outward to inward due to the position switching of the moving positive and negative in current elements. These changes produce discontinuity charges at changing points following Gauss law. These charges electrically interact with the moving charges in current elements to produce the magnetic force. The electrical interaction between current discontinuity charges and moving current charges satisfy Newton third law. So the Newton third law applies in magnetism. Also, this description applies for protons.

Below is a longer description of the electric origin of magnetic force written by Robert Spark to answer a similar question and I quote it here:
“This might be a long answer but hope it helps in resolving the curiosity about this controversial topic. A better understanding of the nature and origin of magnetic force is needed to understand how the Newton’s third law does not fail in magnetostatic. The conservation of momentum explanation is a solid proof that the third law is satisfied in magnetostatics but this explanation does not say HOW, some may make general statements such as “there are corresponding and opposite net forces and torques on the electromagnetic field” and this is not satisfying for me.

It is known that electric currents generate magnetic field/force but since these currents are electrically neutral the magnetic force and the electric force were treated as different aspects of the same subject. Therefore, the actual nature of magnetic field/force was a mystery.

A new work published recently provided a successful explanation to the origin of the magnetic force that is able to explain how the Newton’s third law is satisfied in magnetism, how opposite forces exist, and why they do not appear in some cases, and it was satisfying to me. Shadid in his work “Two new theories for the current charge relativity and the electric origin of the magnetic force” analyzed the electric field pattern spreading in the space due to the movement of electric current charges. Biot-Savart law and Magnetic force law depend on two properties of the current only: Amount and direction. So regardless how the current is generated, e.g., (moving negative charges, moving positive charges, or both moving positive and moving negative charges) as long as it has the same amount and direction it will produce the same magnetic field/force effect in the space. This effect is studied using the minimum possible equal amount of positive and negative charges moving in opposite directions that is needed to produce the current. This minimum amount is obtained when these charges are moving at the maximum possible speed, which is at the speed of light.

In this situation, when the positive and negative charges switch positions in a current element due to their movement the spreading electric field changes from inward to outward and from outward to inward indicating the change of charge positions. This alternation in electric field produces discontinuity points in the spreading electric field. By applying Gauss law at these discontinuity points, the Gauss law indicates the existence of charges, referred to as discontinuity charges. These discontinuity charges surround current elements and are produced when charges move to carry on electric field changes in the space. These charges are partially explained by the photons that travel to indicate the changes in the electric field, these photons are assumed to be charged as assumed in Altschul’s work "Bound on the photon charge from the phase coherence of extragalactic radiation".

These discontinuity charges interact with the moving positive and negative charges in a current element to produce the magnetic force. By applying the electric force law on these interactions the exact magnetic force law and Biot-Savart law are derived as specified in the electromagnetic theory. So, moving electric charges of current elements interact with each other through discontinuity charges, since current elements are electrically neutral. The electric force between a current charge and a discontinuity charge obeys Newton's third law as in Coulomb’s law. The forces exerted on current charges allow the charges to produce either a non-zero or zero net force on the containing infinitesimal current element. This net force on the current element is the observed magnetic force. The produced net force is non-zero on the current element when the positive and negative charges push the current element in the same direction. The push occurs when the exerted forces are perpendicular to the motion direction of the charges and they are not allowed to move outside the containing filamentary current element, while they are free to move along that element. Notice that the push interaction between the current charges and the containing current element obeys Newton’s third law as in particles interaction. However, the net force is zero when these charges push the current element in opposite directions thereby canceling each other or when the exerted forces on the current charges are completely along the direction of movement for the charges so no push force is produced on the containing current element.

The full details of the proof and calculation are a bit long; I gave a brief overview of it. Details can be found at http://ieeexplore.ieee.org/stamp...″

 

[Dale]

The authors of this paper seem to have not read much of the relevant literature for their theory. They seem to be unaware of four vectors in general and the fact that charge density and current density form a four vector with well known transformation properties. They also seem unaware that massless charged particles would make the electron highly unstable which is contrary to observation.

 

[Mike Xander]

The authors of this paper seem to have not read much of the relevant literature for their theory. They seem to be unaware of four vectors in general and the fact that charge density and current density form a four vector with well known transformation properties. They also seem unaware that massless charged particles would make the electron highly unstable which is contrary to observation.

After careful reading and understanding of the whole paper, I believe there is a confusion here.

For the first claim, the four vectors for charge density and current density specify the laws that cover the magnetic force and electric force in relative frames according to the relative charge density and current density observed in relative frames, but these laws do not specify the origin or nature of the magnetic force in these frames which is the topic of the paper, unless you are referring to the Lorentz length contraction approach which explains the magnetic force as a natural consequence of special relativity and purely electrostatic forces. This approach has three shortcomings: 1) It does not explain the force between two parallel current-wires as purely electrostatic; i.e., the force appears as purely magnetostatic in the ion frame, while the force appears as a combined magnetostatic and electrostatic in the electron frame, 2) It does not apply to a charged particle moving in a direction perpendicular to the current-carrying wire along either the same plane or the perpendicular plane for the current-carrying wire, 3) It raises questions about the electric charge for the wire, because if the wire with current flowing through is electrically neutral (this is what the derivation starts from) then the wire without current will become electrically charged in lab frame, and this is against the fact that a neutral wire keeps electrically neutral in lab frame whether having a current flowing through it or not.

More can be found in this regard in the work of Jefimenko “Is magnetic field due to an electric current a relativistic effect?” https://pdfs.semanticscholar.org/a53a/80483bdbbd610eb7e608fb47705022d3cbde.pdf

While, the work described in the paper “Two new theories for the current charge relativity and the electric origin of the magnetic force” addresses the shortcomings of the above approach as mentioned in its literature review and explains the magnetic force as purely electrostatic that is consistent with the laws specified in the EM theory in all frames.

For the second claim, the paper does not assume that electrons are running at the speed of light, actually they are assumed to be running at small speed in a current-carrying conductor. Light speed current is an equivalent theoretical representation to current flowing in a conductor or a current generated by a moving charge. Because the magnetic force law depends on two current characteristics: Amount and Direction, as specified in Biot-Savart law regardless of the nature for current generators. So currents of the same amount and direction generate the same magnetic force effect in the space. This effect is studied using the minimum possible equal amount of positive and negative charges moving in opposite directions that is needed to produce the current. This minimum amount is obtained when these charges are moving at the maximum possible speed, which is at the speed of light.

This study does not specify the nature of charge which is a question left for investigation. But aside from this work, and not making a claim, I would like to quote a part regarding photons and electrons from the Quantum electrodynamics theory that might be of interest for this topic: “The hypothesis of virtual photon exchanges explains how action at a distance occurs. Electrons interact through the exchange of virtual photons. Individual electrons are continuously emitting and reabsorbing virtual photons. They are surrounded by a cloud of virtual photons. Whenever another charged particle enters that cloud it will interact electrically (i.e. experience a force) by absorbing one of the virtual photons. The electron whose virtual photon is absorbed will also experience a force because the absorbed virtual photon will never return to balance the momentum lost by its original emission.” (From book "The Poetry of Physics and the Physics of Poetry" by Robert K. Logan) This might be interesting since photons that are making the cloud surrounding electrons run at the speed of light.

 

[Dale]

the four vectors for charge density and current density specify the laws that cover the magnetic force and electric force in relative frames according to the relative charge density and current density observed in relative frames, but these laws do not specify the origin or nature of the magnetic force in these frames

Sure they do. ##f_{\mu}=F_{\mu\nu} J^{\nu}## specifies the origin of the electromagnetic four force density in all frames.

This is well known material, so I am not sure why the author does not make use of it and even claims that it doesn't exist. I am assuming that the author is not being deliberately deceptive, which leaves only ignorance of the material.

the paper does not assume that electrons are running at the speed of light

The author explicitly lists massless charge carriers (moving at c) as assumption number three. The assumption of massless charges has been considered in the literature. It is contradicted by observation, specifically if there were a massless charge carrier then electrons would be unstable and would decay into it for the same reason that muons decay into electrons.

Again, this is in the literature and the author's lack of awareness substantially reduces the credibility of the work.

At this point, there doesn't seem to be anything further to discuss about this paper, so I am closing the thread. I am not familiar with IEEE Access, but judging from this paper its peer review process seems fatally flawed.