# Lorentz force: absolute reference frame?

• mangoos
In summary: However, there are some invariant values, which all observers should agree on, such as 2\left(\vec{B}.\vec{B}-\frac{\vec{E}.\vec{E}}{c^{2}}\right) or \frac{4}{c}\vec{E}.\vec{B}B= v x q*k*d/r^2
mangoos
F= q(v x B)
B= v x q*k*d/r^2

It is a basic physics knowledge magnetic field forms around moving charge, it tell us magnetic field is zero when charge is not moving and strength of magnetic field increases as velocity increases, right? Magnetic potential vector field increases with "absolute velocity", not relative velocity. Perhaps I got the equations wrong, but if not what is that velocity relative to, Aether?

Two parallel wires:
http://www.magnet.fsu.edu/education/tutorials/java/parallelwires/

1.) velocity relative to field?
2.) velocity relative to wires?

Velocity is with respect to the frame in which E and B are measured.

Velocity is with respect to the frame in which E and B are measured.

What exactly is that frame, aether? Why two parallel electrons, without any relative velocity, attract more the faster they are going? You see the equations? There is no any relative velocity there, just "individual" velocity. - "Two electrons traveling in parallel with the same velocity, without any relative velocity, will attract more the faster they are moving." Do you know about this, you do not know or you claim is false? This Java applet demonstrates well known and easy to test experiment about Lorentz attraction and Ampere's law: http://www.magnet.fsu.edu/education/tutorials/java/parallelwires/

Parallel wires, what is the frame of reference:
1.) velocity relative to field?
2.) velocity relative to wires? Free parallel electrons (cathode ray), what is the frame of reference:
1.) velocity relative to field?
2.) velocity relative to aether /absolute_reference_frame /fixed_stars?

In different inertial reference frames, the two currents or charges produce different mixtures of E and B fields, such that the net effect is the same, after taking length contraction and time dilation into account where necessary.

The E and B fields transform together as a tensor (the electromagnetic field tensor) under the Lorentz transformation.

Magnetic potential vector field increases with "absolute velocity", not relative velocity.

Sounds like this is an assumption you are making?? just not true.

Vanadium, post # 2, IS correct.

If you fire a test charge with a velocity v relative to a point which has a magnetic field present, a sideways magnetic force acts on the particle. As the velocity (between the particle and the magnetic field at the point) decreases so does the force F. If the particle sits still at the point relative to the magnetic field, there is no force F (v is zero)...does that help??

Alternatively, you can complicate the whole scene and use any other reference frame and if you account for the relative motions can still arrive at a correction solution...but the fact that there is NO absolute reference frame means you can pick an easy one and work your solution from that one you chose...you will still get the correct answer because no frame is absolute...no frame is the "correct" frame...

"Is there the possibility of "absolute time" and check out the first page or so of posts...

For example, what is considered "magnetic force" with respect to one frame of reference, may look like "electric force" with respect to another frame of reference (or some combination of magnetic and electric force). However, there are some invariant values, which all observers should agree on, such as
$$2\left(\vec{B}.\vec{B}-\frac{\vec{E}.\vec{E}}{c^{2}}\right)$$

or

$$\frac{4}{c}\vec{E}.\vec{B}$$

mangoos said:
B= v x q*k*d/r^2
Your magnetic field for a moving charge is wrong. You have to use the Lienard-Wiechert magnetic field. Look at an advanced EM text.

jtbell said:
In different inertial reference frames, the two currents or charges produce different mixtures of E and B fields, such that the net effect is the same, after taking length contraction and time dilation into account where necessary.

The E and B fields transform together as a tensor (the electromagnetic field tensor) under the Lorentz transformation.

I'm not talking about different inertial reference, but about two electrons traveling ALONG each other, in PARALLEL, without any relative velocity. What is relative velocity of two particles traveling in parallel?- "Two electrons traveling in parallel with the same velocity, without any relative velocity, will attract more the faster they are moving." - Do you know about this, you do not know or you claim is false?

Equations are clear about that: F= q(v x B); B= v x q*k*d/r^2
Naty1 said:
Sounds like this is an assumption you are making?? just not true.

I'm not making any assumptions, but observations. I'm talking about real world experiments and equations form textbooks.

- "Two electrons traveling in parallel with the same velocity, without any relative velocity, will attract more the faster they are moving." - Do you know about this, you do not know or you claim is false?

Equations are clear about that: F= q(v x B); B= v x q*k*d/r^2

What do you say is assumption? What is not true?
3DM@rk said:
For example, what is considered "magnetic force" with respect to one frame of reference, may look like "electric force" with respect to another frame of reference (or some combination of magnetic and electric force). However, there are some invariant values, which all observers should agree on, such as

- "Two electrons traveling in parallel with the same velocity, without any relative velocity, will attract more the faster they are moving." - Do you know about this, you do not know or you claim is false?

clem said:
Your magnetic field for a moving charge is wrong. You have to use the Lienard-Wiechert magnetic field. Look at an advanced EM text.

It is correct enough to demonstrate how it works, EXPERIMENTS CONFIRM THOSE EQUATIONS, this is general knowledge, high-school physics. This Java applet demonstrates well known and easy to test experiment about Lorentz attraction and Ampere's law: http://www.magnet.fsu.edu/education/...parallelwires/

Parallel wires, what is the frame of reference:
1.) velocity relative to field?
2.) velocity relative to wires?Free parallel electrons (cathode ray), what is the frame of reference:
1.) velocity relative to field?
2.) velocity relative to ...?

Parallel wires, what is the frame of reference:
1.) velocity relative to field?
2.) velocity relative to wires?

Free parallel electrons (cathode ray), what is the frame of reference:
1.) velocity relative to field?
2.) velocity relative to ...?

In ANY experiment the measurements are made in the frame of the measurer !

This can be any frame you choose. The whole point of relativity is that the results will be the same in any inertial frame - you don't need an absolute frame.

- "Two electrons traveling in parallel with the same velocity, without any relative velocity, will attract more the faster they are moving."

is this true?

Equations are clear about that: F= q(v x B); B= v x q*k*d/r^2

is this true?

is this not what is is called "electron coupling" in chemistry and QM?

Hi Nancy57, welcome to PF,

It looks like the OP has already left, but I thought I should post this link about http://physics.weber.edu/schroeder/mrr/MRRtalk.html" .

It is a pretty interesting derivation. Basically, you can think of magnetism as simply being a consequence of length contraction for moving charges. It is really pretty amazing when you think that a typical drift velocity for an electron in a wire is on the order of mm/s or less, and yet electromagnetism is such a strong force that the miniscule length contraction even at such a small speeds can cause such easily measurable results.

In any case, the bottom line is that not only is magnetism completely compatible with relativity, but relativity unites electrostatics and magnetism in a very elegant manner, showing that they are simply "two sides of the same coin" in a way that simply cannot be appreciated without relativity.

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"this is general knowledge, high-school physics."
That just means you have to go to graduate school or read an advanced EM text before you find out about the force between two moving charges.

- "Two electrons traveling in parallel with the same velocity, without any relative velocity, will attract more the faster they are moving."

Equations are clear about that: F= q(v x B); B= v x q*k*d/r^2
Experiments are clear about that: http://www.magnet.fsu.edu/education/tutorials/java/parallelwires/index.html

DaleSpam,

hi, thank you. i see what you're saying, i learned the same at my uni and there is no question about "everything is relative", but if above statement is true, if experiments measure attraction of parallel electrons, then what does that mean, what is their relative velocity relative to? before talking about theory and relativity we need to know about experimental facts and whether above statement is true or false?

Wikipedia and my physics textbook used at Auckland University -"PHYSICS for Scientists and Engineers with Modern Physics, Serway-Beichner, 2001", confirms above statement. however, they do not talk about reference frames at all, so they do not say anything that would directly resolve the question, still they confirm formulas and experimental results, what does that mean?

[-edit-]

after 3-4 hours of searching the net i can not find any direct answers, however i double checked formulas and experimental studies with free electrons and electron beams, many of which speak of attraction, but still no mention of reference frames and why would electrons attract proportionally to their velocity, instead of their relative velocity.

however, i found this is actually an old argument between Lorentz and Einstein: "Lorentz contended against Einstein that there had to be a medium in which electro-magnetic waves exist and propagate, and that that would of necessity be an absolute frame of reference for the universe. Einstein won that dispute contending that electro-magnetic waves needed no medium and that there was no absolute frame of reference. But, that victory was in a conflict of Lorentz’s opinion opposed to Einstein’s opinion combined with Einstein’s substantial other successes and reputation. It was not a victory of solid reasoning nor demonstrated factual evidence... "

basically, i could not find any verified source and reference to address this question, can anyone provide concrete peer reviewed reference that addresses this particular case of Lorentz force, parallel electrons and reference frames?

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Nancy57 said:
i learned the same at my uni and there is no question about "everything is relative",
Be careful here. This is not correct. When physicists say "X is relative" that means that X is a quantity which is frame variant, or in other words the value of X will be different in different coordinate systems. There do exist many things which have the same value in different coordinate systems. Such things are called "frame invariant" and are not relative. Examples of frame invariant quantities are the spacetime interval, proper time, invariant mass, etc.

Nancy57 said:
i can not find any direct answers, however i double checked formulas and experimental studies with free electrons and electron beams, many of which speak of attraction, but still no mention of reference frames and why would electrons attract proportionally to their velocity, instead of their relative velocity.
I provided you a link above. The explanation you are looking for is in the section "transformation of electrostatic fields", but I would recommend reading the section "magnetism as a consequence of length contraction" first. The same author also has more extensive notes in .pdf form at http://physics.weber.edu/schroeder/mrr/MRRnotes.pdf

There is also http://farside.ph.utexas.edu/teaching/em/lectures/node106.html which is a more advanced treatment but has essentially the same information. You should especially look at the "Force on a moving charge" and the "Fields due to a moving charge" sections.

Once you feel comfortable with the link between the electric field, length contraction, and the magnetic field then if you still don't understand the specific case of two co-moving electrons I will be glad to help.

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There is also http://farside.ph.utexas.edu/teachin...s/node106.html which is a more advanced treatment but has essentially the same information. You should especially look at the "Force on a moving charge" and the "Fields due to a moving charge" sections.

Once you feel comfortable with the link between the electric field, length contraction, and the magnetic field then if you still don't understand the specific case of two co-moving electrons I will be glad to help.

thank you, but those links actually confirm Lorentz force and Biot–Savart law even more. i already do feel very comfortable with all of it since I've been working in the field for the last five years, as a software engineer for numerical modeling and analysis of electromagnetic interaction. i suppose you are referring me to Einstein's "Lorentz transformations"?

i believe i already know everything about all that, but the answer i have does not make sense and i can not perform physical experiments myself. so, if you have an understanding with which you can answer the question, then please do:
- "Two electrons traveling in parallel with the same velocity, without any relative velocity, will attract more the faster they are moving."

Equations are clear about that: F= q(v x B); B= v x q*k*d/r^2
Experiments are clear about that: http://www.magnet.fsu.edu/education/...res/index.html

according to your understanding, is this true or false?

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Nancy57 said:
thank you, but those links actually confirm Lorentz force and Biot–Savart law even more. i already do feel very comfortable with all of it since I've been working in the field for the last five years, as a software engineer for numerical modeling and analysis of electromagnetic interaction. i suppose you are referring me to Einstein's "Lorentz transformations"?

i believe i already know everything about all that, but the answer i have does not make sense and i can not perform physical experiments myself. so, if you have an understanding with which you can answer the question, then please do:
Of course those links confirm the Lorentz force and Biot-Savart law! I am glad you feel comfortable with them, but I think you missed the whole point. The point was not to contradict Lorentz force law or Biot-Savart, but to derive them using relativity.

When they were initially developed they were the result of empirical data, with no understanding or connection to anything else. With the advent of relativity however it became possible to actually derive magnetism as a direct result of the postulates of relativity. Thus, magnetism is not only completely compatible with relativity, but is in fact an inevitable logical consequence of relativity.

So the point is that since magnetism is a logical consequence of the postulates of relativity it certainly cannot be logically used to claim the existence of an aether frame.

Nancy57 said:
according to your understanding, is this true or false?
It is essentially correct, but poorly worded. Electrons are negatively charged and like charges repel, so two electrons repel each other. Due to relativity and magnetism (see the links I provided) the faster two co-moving electrons are traveling in a given inertial frame the less they repel in that frame. It is a direct consequence of length contraction, time dilation, etc.

DaleSpam said:
Due to relativity and magnetism (see the links I provided) the faster two co-moving electrons are traveling in a given inertial frame the less they repel in that frame. It is a direct consequence of length contraction, time dilation, etc.

thank you, we needed to agree on experimental facts. unfortunately, the length contraction and time dilation do not really address the obvious paradox, on the contrary, look how Wikipedia describes Lorentz transformation: "They form the mathematical basis for Albert Einstein's theory of special relativity. In 1905 Einstein derived them under the assumptions of the principle of relativity and the constancy of the speed of light in any inertial reference frame."

...what's worse, those formulas simply do not apply, nor work, while Lorentz and other classical physics equations work very well, they can actually model electron interaction and electron beams in magnetic field with the same results as experiments measure, stuff like this for example:

- can you point exactly what part about length contraction and time dilation explains the attraction of electrons traveling without any relative speed?

Nancy57 said:
...what's worse, those formulas simply do not apply, nor work,

Citation to experimental evidence published in peer-reviewed scientific literature, please?

jtbell said:
Citation to experimental evidence published in peer-reviewed scientific literature, please?

according to my understanding those equations simply do not apply.

are you saying 'Lorentz transformation' can be used to model individual electromagnetic interaction of moving charges? if anyone ever managed to document how to model interaction of moving charges using those formulas, published in peer-reviewed scientific literature, please let us know.

- can you point exactly what part about length contraction and time dilation explains the attraction of electrons traveling without any relative speed?

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Nancy57 said:
according to my understanding those equations simply do not apply.

are you saying 'Lorentz transformation' can be used to model individual electromagnetic interaction of moving charges? if anyone ever managed to document how to model interaction of moving charges using those formulas, published in peer-reviewed scientific literature, please let us know.

- can you point exactly what part about length contraction and time dilation explains the attraction of electrons traveling without any relative speed?

Relativistic electrodynamics can handle the problem and shows that there is no paradox. All intertial observers will see the same outcome. It's in any good textbook on the subject.

See for example chapter 12 of Griffiths, "Introduction to Electrodynamics."

## 1. What is the Lorentz force in an absolute reference frame?

The Lorentz force is the force experienced by a charged particle in an electric and magnetic field in an absolute reference frame. It is given by the equation F = q(E + v x B), where q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

## 2. How does the Lorentz force act on a charged particle in an absolute reference frame?

The Lorentz force acts perpendicular to both the electric and magnetic fields and is directly proportional to the charge of the particle and the magnitude of the fields. It also depends on the velocity of the particle, with a larger velocity resulting in a larger force.

## 3. What is the significance of the Lorentz force in electromagnetism?

The Lorentz force is a fundamental concept in electromagnetism and is used to explain the motion of charged particles in both electric and magnetic fields. It also plays a crucial role in the development of many technologies, such as electric motors and generators.

## 4. How does the Lorentz force differ from the Coulomb force?

The Lorentz force takes into account the effects of both electric and magnetic fields, whereas the Coulomb force only considers the effects of electric fields. Additionally, the Lorentz force is dependent on the velocity of the charged particle, while the Coulomb force is not.

## 5. Can the Lorentz force be applied to both moving and stationary charged particles?

Yes, the Lorentz force can be applied to both moving and stationary charged particles. However, for a stationary charged particle, the magnetic field has no effect on the force as the cross product between the velocity and magnetic field is zero.

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