Relativistic length contraction and magnetic force

[pengkuan]

length contraction and magnetic force.pdfMagnetism is intimately related to special relativity. Maxwell's equations are invariant under a Lorentz transformation; the electromagnetic wave equation gives the speed of light c. Many have explained magnetic force as a consequence of relativistic length contraction, for example Richard Feynman in page 13-8 of his ≪The Feynman Lectures on Physics, Volume II≫ and Steve Adams in page 266 in his ≪Relativity: An Introduction to Spacetime Physic≫. If magnetic force is really created by relativistic length contraction, we should be able to derive the expression for magnetic force from the length contraction formula. And indeed we can, as I will show below.

Please read the article at

PDF Relativistic length contraction and magnetic force URL deleted

Edited April 26, 2017 by pengkuan

[swansont]

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Moderator Note

Rule 2.7 dictates that discussion take place here

[pengkuan]

!

Moderator Note

Rule 2.7 dictates that discussion take place here

I'm sorry. I have uploaded the file here.

[pengkuan]

Length-contraction-magnetic-force between arbitrary currents

In ≪Relativistic length contraction and magnetic force≫ I have explained the mechanism of creation of magnetic force from Coulomb force and relativistic length contraction. For facilitating the understanding of this mechanism I used parallel current elements because the lengths are contracted in the direction of the currents. But real currents are rarely parallel, for example, dIa and dIb of the two circuits in Figure 1. For correctly applying length contraction on currents in any direction, we will consider conductor wires in their volume and apply length contraction on volume elements of the wires.

Please read the article here

Length-contraction-magnetic-force between arbitrary currents.pdf

[Mordred]

Thats actually not too bad an article just from a first glance. You obviously put a lot of work into it.

 

Will have to spend some more time reading it.

[pengkuan]

Thats actually not too bad an article just from a first glance. You obviously put a lot of work into it.

 

Will have to spend some more time reading it.

Thank you. My object is to derive the basic laws of magnetism from Coulomb's law and relativity, That is, Lorentz force and Faraday's law.

[KipIngram]

I have a book that does it that way, if I recall correctly. Principles of Electrodynamics by Melvin Schwartz. I always remember his opening sentence: "Electrodynamics is beautiful!"

[pengkuan]

I have a book that does it that way, if I recall correctly. Principles of Electrodynamics by Melvin Schwartz. I always remember his opening sentence: "Electrodynamics is beautiful!"

Thanks. I know that Feynman has explained this principle for infinitely long current.

[pengkuan]

Tangential magnetic force experiment with circular coil

If magnetic force is to respect Newton’s third law, there should be a recoil force on the vertical current which is Ft. This force is tangent to the current I1 and called tangential magnetic force. Some physicists claim that tangential magnetic force exists, this claim is supported by some experiments such as the rail gun recoil force shown by Peter Graneau and Ampère's hairpin experiment, see Lars Johansson’s paper. But these experiments did not convince the main stream physicists and tangential magnetic force is rejected. I have carried out an experiment to show tangential magnetic force acting on a circular coil.

Please read the attached document
Tangential magnetic force with round coil.pdf video url deleted

[swansont]

Tangential magnetic force experiment with circular coil

 

If magnetic force is to respect Newton’s third law, there should be a recoil force on the vertical current which is Ft. This force is tangent to the current I1 and called tangential magnetic force. Some physicists claim that tangential magnetic force exists, this claim is supported by some experiments such as the rail gun recoil force shown by Peter Graneau and Ampère's hairpin experiment, see Lars Johansson’s paper. But these experiments did not convince the main stream physicists and tangential magnetic force is rejected. I have carried out an experiment to show tangential magnetic force acting on a circular coil.

 

Please read the attached document

Tangential magnetic force with round coil.pdf video url deleted

 

!

Moderator Note

You need to stick to the topic of the discussion, and remind you yet again of rule 2.7

 

Further tangents will simply be hidden with no warnings

[pengkuan]

Continuous rotation of a circular coil experiment

There is a long standing debate about whether tangential magnetic force exists. In «Tangential magnetic force experiment with circular coil» I discussed this force and presented an experiment that showed the action of this force. But, as the rotation of the coil in that experiment was limited to a small angle, it does not show that tangential force exists all over the coil. So, I have carried out the present experiment that shows continuous rotation of the coil to make clear that tangential force has the same value around the coil

Please read this article

Continuous rotation of a circular coil experiment.pdf

[Tim88]

Thanks, it's an interesting topic! You write:

 

"Since the charge density of a moving charged rod increases with velocity, the free electrons in a
conductor wire will also have a higher density when a current circulates in the wire. Indeed, electric
current is a moving line of electrons or charge. Thus, the free electrons will have higher density than
the positive charge of the wire. So, the wire will appear charged and exert a Coulomb force on a
charge located nearby."

 

I have seen such exposes in the past, and they could never convince me; here's why. Before I read any further, please clarify how you think that the charge density in a closed loop can be increased that way. As you surely know, following Lenz law one can induce a current with its corresponding magnetic field in such things as a single current loop or a piece of metal. I suppose that necessarily the total charge - and thus the charge density - cannot be altered.

[pengkuan]

Thanks, it's an interesting topic! You write:

 

"Since the charge density of a moving charged rod increases with velocity, the free electrons in a

conductor wire will also have a higher density when a current circulates in the wire. Indeed, electric

current is a moving line of electrons or charge. Thus, the free electrons will have higher density than

the positive charge of the wire. So, the wire will appear charged and exert a Coulomb force on a

charge located nearby."

 

I have seen such exposes in the past, and they could never convince me; here's why. Before I read any further, please clarify how you think that the charge density in a closed loop can be increased that way. As you surely know, following Lenz law one can induce a current with its corresponding magnetic field in such things as a single current loop or a piece of metal. I suppose that necessarily the total charge - and thus the charge density - cannot be altered.

Thanks for discussing this point. This is indeed a subtil relativistic phenomenon. How does the density of charge change while their number does not increase.

 

One explanation could be that the length of the moving system of reference contract, not only locally, but globally. Let us see a circular circuit in which the electron move at the same speed. At any point, the length is contracted in the same ratio. So, the total length of the circle made by the moving electrons is:

[latex]l_{e}=l_{0}/\gamma[/latex]

where [latex]l_{0}[/latex] is the length of the circuit and [latex]l_{e}[/latex] the length of the moving circle of electrons. The contraction of the total length makes their density bigger in the fixed system.

 

But how can the same circle have 2 different length? I think General relativity can explain this. In fact, Einstein used the system of a rotating disc to study General relativity. He solved the problem of the incompatibility of length of the 2 systems by stating that the space is curved in the moving system. Around a star, the circular trajectory of a planet has a length in the gravitational field which is different from that in a flat space.

 

In the case of current, the space of the moving electrons is curved and its apparent length is contracted everywhere in the fixed system. Then, the density of the electrons is higher in the fixed system. The moving system is a circle of a disc's system whose curvature is proportional to the speed of the electrons.

 

One may think that curvature of space is farfetched to explain the length of electrons' system. But this is one of possible explanation which is accepted for gravitational field.

[Tim88]

Thanks for discussing this point. This is indeed a subtil relativistic phenomenon. How does the density of charge change while their number does not increase.

 

One explanation could be that the length of the moving system of reference contract, not only locally, but globally. Let us see a circular circuit in which the electron move at the same speed. At any point, the length is contracted in the same ratio. So, the total length of the circle made by the moving electrons is:

[latex]l_{e}=l_{0}/\gamma[/latex]

where [latex]l_{0}[/latex] is the length of the circuit and [latex]l_{e}[/latex] the length of the moving circle of electrons. The contraction of the total length makes their density bigger in the fixed system.

 

But how can the same circle have 2 different length? I think General relativity can explain this. In fact, Einstein used the system of a rotating disc to study General relativity. He solved the problem of the incompatibility of length of the 2 systems by stating that the space is curved in the moving system. Around a star, the circular trajectory of a planet has a length in the gravitational field which is different from that in a flat space.

 

In the case of current, the space of the moving electrons is curved and its apparent length is contracted everywhere in the fixed system. Then, the density of the electrons is higher in the fixed system. The moving system is a circle of a disc's system whose curvature is proportional to the speed of the electrons.

 

One may think that curvature of space is farfetched to explain the length of electrons' system. But this is one of possible explanation which is accepted for gravitational field.

 

I'm afraid that that's not going to work; and I don't know why you think that it would be needed.

SR is supposed to be self consistent, without gravitational fields. SR is based in part on Maxwell's theory, which includes magnetic fields.

 

Further, GR was (and is) not needed for the rotating disc, and there is no need to use a rotating frame, with possibly confusing nomenclature. The rotating disc and length contraction effects are perfectly understood from the point of view of a non-rotating reference system, without invoking any "curvature" or terms like that. That is also the reference frame that I used in my description. In the non rotating frame, a stationary wire is not expected to length contract due to the motion of electrons; and in any case, the ratio of electrons to protons remains the same so that their density would change equally.

 

Meanwhile I thought of an even simpler example: two equal charges moving in parallel, like this:

 

o ->

o ->

 

According to SR, the force between those charges decreases with speed. However, the Coulomb force between them does not change with speed (only with distance), and obviously the number of charges does not change with speed.

[pengkuan]

 

I'm afraid that that's not going to work; and I don't know why you think that it would be needed.

SR is supposed to be self consistent, without gravitational fields. SR is based in part on Maxwell's theory, which includes magnetic fields.

 

Further, GR was (and is) not needed for the rotating disc, and there is no need to use a rotating frame, with possibly confusing nomenclature. The rotating disc and length contraction effects are perfectly understood from the point of view of a non-rotating reference system, without invoking any "curvature" or terms like that. That is also the reference frame that I used in my description. In the non rotating frame, a stationary wire is not expected to length contract due to the motion of electrons; and in any case, the ratio of electrons to protons remains the same so that their density would change equally.

 

Meanwhile I thought of an even simpler example: two equal charges moving in parallel, like this:

 

o ->

o ->

 

According to SR, the force between those charges decreases with speed. However, the Coulomb force between them does not change with speed (only with distance), and obviously the number of charges does not change with speed.

Just about GR and rotating disc which are the point of this discussion. GR is generally thought as specific to gravitational field and in an electric circuit there is not this GR. I cited GR just to illustrate non-euclidean geometry. I apology for confusing the subject by using the word GR. It is in fact not GR, but non-euclidean geometry or metric of a rotating disc that solves this problem.

 

The system of a rotating disc is indeed a non-euclidean space and a rotating circle in this geometry does not has the same length than the same circle in a stationary state. See https://en.wikipedia.org/wiki/Ehrenfest_paradox.

 

I use non-euclidean geometry to explain that the same number of charged particles in a same lengthed circle can have different density because the lengths are evaluated in 2 different spaces using 2 differents metrics, one euclidean the other non-euclidean.

 

I agree that this explanation does not convince everyone.

[Tim88]

[..] I use non-euclidean geometry to explain that the same number of charged particles in a same lengthed circle can have different density because the lengths are evaluated in 2 different spaces using 2 differents metrics, one euclidean the other non-euclidean.

 

I agree that this explanation does not convince everyone.

 

I suppose that that explanation does "not convince everyone", because, as I pointed out: "in any case, the ratio of electrons to protons remains the same so that their density would change equally". In other words, everything remains neutrally charged, no matter one's point of view. And that has to be so, for the question if there is a net force or not, cannot depend on one's point of view.

 

I look forward to comments on my even simpler example with just two charges.

[pengkuan]

 

I suppose that that explanation does "not convince everyone", because, as I pointed out: "in any case, the ratio of electrons to protons remains the same so that their density would change equally". In other words, everything remains neutrally charged, no matter one's point of view. And that has to be so, for the question if there is a net force or not, cannot depend on one's point of view.

 

I look forward to comments on my even simpler example with just two charges.

It's OK that you are not convinced.

 

For the two charges, I do not see why the force between o and o moving i parallel decreases according to SR, since their distance is perpendicular to their velocity.

[Tim88]

It's OK that you are not convinced.

 

For the two charges, I do not see why the force between o and o moving i parallel decreases according to SR, since their distance is perpendicular to their velocity.

 

According to SR:

 

- in the frame S, according to which the charges are moving at high speed v, there is a magnetic field force that is opposite to the Coulomb force.

Consequently the charges deflect less fast at this high speed than at low speed.

 

- in the frame S', according to which the charges are not moving, there is no magnetic field and so they deflect fast.

 

This disagreement matches the Lorentz transformations; the same trajectory is predicted.

The main issue that I see here, is already present in your intro:

 

If magnetic force is really created by relativistic length contraction

 

According to SR, that is wrong - as I illustrated with the two parallel moving charges.

On hindsight, if I correctly perceive what you are trying to communicate here, I can probably phrase the central issue more briefly.

 

Discussions in this forum are supposed to be about classical theory; but happily, special relativity is compatible with classical electrodynamics.

According to two centuries of electrodynamics, when an uncharged electric wire is connected to an uncharged galvanic cell (an ordinary battery) then an electric current will flow through the wire. As measured in the lab, the wire will normally not have an electric field around it but it will have a magnetic field around it.

 

Is your theory in agreement with those basic observations?

[pengkuan]

 

According to SR:

 

- in the frame S, according to which the charges are moving at high speed v, there is a magnetic field force that is opposite to the Coulomb force.

Consequently the charges deflect less fast at this high speed than at low speed.

 

- in the frame S', according to which the charges are not moving, there is no magnetic field and so they deflect fast.

 

This disagreement matches the Lorentz transformations; the same trajectory is predicted.

The main issue that I see here, is already present in your intro:

 

 

In my article, SR is only mechanical, that is, length contraction and time dilation. Your are saying about relativistic electromagnetism which uses Lorentz force law in high speed. But this is not in my consideration. What I'm doing is to find magnetic effect from length contraction and Coulomb's law. So, a priori, there is not magnetic field in space and no relativistic electromagnetism at all. Electromagnetism comes after relativistic effect, not before.

 

According to SR, that is wrong - as I illustrated with the two parallel moving charges.

On hindsight, if I correctly perceive what you are trying to communicate here, I can probably phrase the central issue more briefly.

 

Discussions in this forum are supposed to be about classical theory; but happily, special relativity is compatible with classical electrodynamics.

According to two centuries of electrodynamics, when an uncharged electric wire is connected to an uncharged galvanic cell (an ordinary battery) then an electric current will flow through the wire. As measured in the lab, the wire will normally not have an electric field around it but it will have a magnetic field around it.

 

Is your theory in agreement with those basic observations?

 

The two parallel moving charges are not in the domain of my theory, but in the domain of classic relativistic electromagnetism.

 

What I'm doing is to compute a force on an element of current, which is acted by another element of current. This force integrated over a closed circuit equals that computed from Lorentz force law. So, this force is surely a magnetic force while magnetic field was not in the condition, which comes after the force on elements of current. Magnetic field is computed from the force, not the force computed from magnetic field. This is another approach of magnetism.

[Tim88]

With emphasis mine:

[..] What I'm doing is to find magnetic effect from length contraction and Coulomb's law. So, a priori, there is not magnetic field in space and no relativistic electromagnetism at all. Electromagnetism comes after relativistic effect, not before.

What I'm doing is to compute a force on an element of current, which is acted by another element of current. This force integrated over a closed circuit equals that computed from Lorentz force law. So, this force is surely a magnetic force while magnetic field was not in the condition, which comes after the force on elements of current. Magnetic field is computed from the force, not the force computed from magnetic field. This is another approach of magnetism.

 

As I indicated, it looks to me that it's not just "another approach", but really a different theory.

I repeat: according to two centuries of electrodynamics, when an uncharged electric wire is connected to an uncharged galvanic cell (an ordinary battery) then an electric current will flow through the wire. As measured in the lab, the wire will normally not have an electric field around it (except for the field necessary to sustain the current) but it will have a magnetic field around it.

 

Apparently you now confirmed that your theory disagrees with classical electrodynamics. In particular, you seem to predict for measurements in the "laboratory" frame, on a current carrying wire in rest in the lab:

the wire will appear charged and exert a Coulomb force on a charge located nearby.

I think that two centuries of experiments disagree with that. And as you showed to be handy in doing your own experiments, you can check it for yourself.

Edited July 4, 2017 by Tim88

[pengkuan]

As I indicated, it looks to me that it's not just "another approach", but really a different theory.

I repeat: according to two centuries of electrodynamics, when an uncharged electric wire is connected to an uncharged galvanic cell (an ordinary battery) then an electric current will flow through the wire. As measured in the lab, the wire will normally not have an electric field around it (except for the field necessary to sustain the current) but it will have a magnetic field around it.

 

Apparently you now confirmed that your theory disagrees with classical electrodynamics. In particular, you seem to predict for measurements in the "laboratory" frame, on a current carrying wire in rest in the lab:

I think that two centuries of experiments disagree with that. And as you showed to be handy in doing your own experiments, you can check it for yourself.

Yes, any new theory originates from new approach. As I stated, electrons goes under relativistic length contraction and make the wire seems to have excess of charge, a current carrying wire will create an electric field around.

 

The fact that such electric field is not predicted by classic theory does not mean that this field does not exist. Simply in 200 years, no one has tested this, at least no experiment subsists in textbook. It is a good idea to do an experiment to show this field. I will do it in the future.

 

My last experiment showed that tangential magnetic force exists, which is in contradiction with classic electromagnetic theory. So, it would not be totally surprising if this electric field shows up,

[pengkuan]

Coulomb magnetic force

The relativistic length contraction effect and changing distance effect produce 2 different magnetic forces. Together they form complete magnetic force. 
I have derived 2 magnetic forces with Coulomb’s law and charges’ velocity. The first force dFlc is derived in «Length-contraction magnetic-force between arbitrary currents». The second force dFcd is derived in «Changing distance effect». dFlc and dFcd are added together to give the expression for complete magnetic force dFcm.

Please read the attachment 
Coulomb magnetic force.pdf

Changing distance effect.pdf

[pengkuan]

Plasma under Coulomb magnetic force
Nuclear fusion reactors use strong magnetic field to confine plasma in reaction chambers. The magnetic field is so designed that plasma should follow field lines which do not encounter the chambers’ wall. But it seems that a mysterious force pushes plasma off its track. For explaining this force, Coulomb magnetic force law for plasma is derived.

Please read the article at 
Plasma under Coulomb magnetic force 
Plasma under Coulomb magnetic force.pdf

[pengkuan]

Showing tangential magnetic force by experiment 
Theoretical explanation of tangential magnetic force and the experiment of rotating coil. Tangential magnetic force is tangent to the current on which it acts. For the classical theory this force does not exist. However, my experiment « Continuous rotation of a circular coil experiment » showed that a force tangent to the current must be there. If tangential magnetic force exists, why was it not detected in almost 200 years? 

Please read the article
Showing tangential magnetic force by experiment.pdf

[pengkuan]

Longitudinal magnetic force and high field magnet

Theoretical explanation of longitudinal magnetic force and its practical application in high field magnet.

Please read the article below 
Longitudinal magnetic force.pdf