In electromagnetism, is the magnetic field, generated by charges, relative to the observer?
Dear Thierry,
A few remarks about the dependence of B, the magnetic induction, and Bg, the gravito-magnetic induction, on the position of the observer.
1. A charged particle at rest relative to an inertial reference frame O is the source of an electric field. In O this field is completely characterized by the vector E. Relative to the particle, E is radial: it is centrifugal if the charge of the particle is positive and centripetal in the other case.
2. A charged particle moving relative to an inertial reference frame O is the source of an electromagnetic field. In O this field is completely characterized by the vector pair (E, B) that is mathematically described by Maxwell's equations: a set of four partial differential equations that describe how E and B vary in space due to their sources - the electric charge and the electric current - and how they are intertwined.
- If the particle is moving with constant velocity relative to O, the expressions of E and B can be deduced by the Lorentz transformations from the expression of E in the case of a particle that is at rest relative to O (1), what implies that they depend on the speed of their source relative to the observer.
- If the charged particle accelerates relative to O, it radiates electromagnetic energy, it is the source of an electromagnetic wave. The rate of energy flow per unit area in an electromagnetic wave can be described by the Poynting vector.
3. Eg - the gravitational field of a particle at rest relative to an inertial reference frame - is centripetal as in the case of the electric field generated by a negative charged particle. So the role played by the charge -q as the source of an EM field in the cases 1 and 2 is, in the context of GEM, played by the rest mass m0 of a particle as the source of its gravitational field. That implies that in the GEM version of Maxwell's laws -(4.pi.G).m0 plays the role that is played by (q/epsilon0) in EM. This also implies that the mathematical expressions for as well Eg as Bg depend on the inertial reference frame in which they are observed.
Dear Thierry,
Yes, the magnetic field appears always as the Lorentz transformation of the electric field associated to a given observer. This means that different observers moving at different relative velocities must measure different magnetic fields.
Dear Daniel,
Thank you for your reply.
I suppose that on the other hand, if we have a magnetic field somewhere, let's say, the magnetic field of the Earth, it doesn't really matter what is causing that magnetic field when we make experiments on it.
If what you said is true, what would be the velocity needed about the Earth in order to get a measured magnetic field equal to zero by compensation, and in which direction?
Dear Thierry,
To make zero the Earth magnetic field for one observer it is not easy at all. The question is that you need a system of charges moving to produce a magnetic field exactly to the value of the Local magnetic field of the Earth (0.5 Oersteds). The problem is that the magnetic field is not radial. The easiest is to the North or South poles for solving this difficulty. But the system of charges can chosen in very different forms.
Dear Daniel,
I was in fact only talking about the effect you described.
You wrote: "Yes, the magnetic field appears always as the Lorentz transformation of the electric field associated to a given observer. This means that different observers moving at different relative velocities must measure different magnetic fields."
That would mean that when someone is going at half the speed of the moving charge, it would measure half the magnetic field according to you, and if he goes at the same speed, there would no magnetic field be measured.
So, my question was entirely in that frame of reasoning. For the magnetic field of the Earth, it doesn't really matter what is causing that magnetic field when we make experiments on it.
The observer is however not necessarily a charge. I assume a neutral very tiny mass with a measuring device for magnetism.
The question was, in the frame of what you stated: if what you said is true, what would be the velocity of the observer needed about the Earth in order to get a measured magnetic field equal to zero by compensation, and in which direction?
Dear Thierry,
No. The things a little bit more complex. You write:
That would mean that when someone is going at half the speed of the moving charge, it would measure half the magnetic field according to you, and if he goes at the same speed, there would no magnetic field be measured.
1. The transformation of the fieds is something more complex that a linear transformation.
2. The electric and magnetic fields that I was speaking on were produced by electric charges with relative velocity respect to the observer. Notice that the relative velocity with respect a field is always the same and constant independently of the state of motion of the observer.
Dear Daniel,
So, you state not that "the magnetic field, generated by charges, is relative to the observer", in the concept of relativity, i.e. the equivalence between inertial reference frames, but you state that, for an observer that is moving at high speeds, rather in the order near the speed of light, there will be a different measurement of the magnetic fields, due to the effect by the Lorentz transformations.
However, in that case, you state also that for low speeds, this difference of measurement of the magnetic field is rather negligible.
In your last sentence, if I understood it well, you state that a charge will undergo the same Lorentz forces w.r.t. the magnetic field, independently from the state of motion of a neutral observer
Is that correct?
Dear Thierry,
You have made a very far interpretation of my words. Magnetic field has two different sources: magnetic moments associated to spins and angular momentum (within matter) and the relative motion of electric charge respect to one observer. Your question was only about the last one of the relative motion of the electric charge, which is obviously producing magnetic fields, and I think that I have answered you. After that you introduced other examples that are obviously out of observing motions of electric charges and the answers are much more complex than a simple Lorentz transformation of fields.
The magnetic field or the electromagnetic field travel at the velocity of light and therefore they are out of the Lorentz transformations as dynamical objects. But if you put them as associated to currents then they transform under Lorentz transformations as you can find in any text book of electromagnetism. In such a case it is not logic to speak about magnetic field alone but about the electromagnetic field because simultaneously is transformed the electric field.
I think that these are very basic concepts that you have to have and I don't understand your interpretations of my words.
Dear Daniel,
My questions were not intended to interpret your words very far.
My questions are whether or not:
1) the magnetic field, generated by charges, is *not* relative to the observer, in the concept of relativity, i.e. the equivalence between inertial reference frames.
2) for a neutral observer that is moving at high speeds, rather in the order near the speed of light, there will be a different measurement of the magnetic (and electric) fields, due to the effect by the Lorentz transformations.
3) a charge will undergo the same Lorentz forces w.r.t. the magnetic field, independently from the state of motion of a neutral observer.
Dear Thierry,
I am not sure to understand you. The magnetic field changes with respecto to inertial observers moving at different relalative velocities. In fact not the fields which move at the velocity of the light but the sources associated to them, i.e. electric charges.
If you understand for neutral not charged, thus the observer can be neutral, altough it is not a necessary condition is it is enough far of the sources for assuming no electric interaction.
Dear Thierry,
A few remarks about the dependence of B, the magnetic induction, and Bg, the gravito-magnetic induction, on the position of the observer.
1. A charged particle at rest relative to an inertial reference frame O is the source of an electric field. In O this field is completely characterized by the vector E. Relative to the particle, E is radial: it is centrifugal if the charge of the particle is positive and centripetal in the other case.
2. A charged particle moving relative to an inertial reference frame O is the source of an electromagnetic field. In O this field is completely characterized by the vector pair (E, B) that is mathematically described by Maxwell's equations: a set of four partial differential equations that describe how E and B vary in space due to their sources - the electric charge and the electric current - and how they are intertwined.
- If the particle is moving with constant velocity relative to O, the expressions of E and B can be deduced by the Lorentz transformations from the expression of E in the case of a particle that is at rest relative to O (1), what implies that they depend on the speed of their source relative to the observer.
- If the charged particle accelerates relative to O, it radiates electromagnetic energy, it is the source of an electromagnetic wave. The rate of energy flow per unit area in an electromagnetic wave can be described by the Poynting vector.
3. Eg - the gravitational field of a particle at rest relative to an inertial reference frame - is centripetal as in the case of the electric field generated by a negative charged particle. So the role played by the charge -q as the source of an EM field in the cases 1 and 2 is, in the context of GEM, played by the rest mass m0 of a particle as the source of its gravitational field. That implies that in the GEM version of Maxwell's laws -(4.pi.G).m0 plays the role that is played by (q/epsilon0) in EM. This also implies that the mathematical expressions for as well Eg as Bg depend on the inertial reference frame in which they are observed.
Dear Antoine,
Welcome in this discussion.
You write : “A charged particle moving relative to an inertial reference frame O is the source of an electromagnetic field.”
Really? However, it is important to notice that a magnetic field is a real physical event and not a fictive event.
This means the following: Let there be an unique large object in the whole universe with a charge, and one very tiny, neutral observer.
1) Let the observer and the large charge be mutually at rest. Will there be a magnetic field? No. Will this observer detect a magnetic field? No.
2) Let the observer and the large charge have a mutual velocity. Will there be a magnetic field? No! Will this observer detect a magnetic field? No, except if it carries a charge by itself!
Why?
Because a magnetic field is a real, physical phenomenon that occurs only between two charges with a mutual velocity. The observer is of no utility to determine that.
On the other hand, let there be only two mutually moving charges in the universe. Let we focus on the magnetic field that is formed about the first charged object.
1) Let the observer be at rest w.r.t. that first charged object. Will this observer detect the magnetic field of that first object? Yes!
2) Let the observer be at a non-relativistic speed w.r.t. that first charged object. Will the observer detect a different magnetic field now? No, it will be totally negligible!
3) Let the observer approach that charge at a high speed. Will the observer detect a different magnetic field now? Yes, the detection will be altered by the action of retardation by the speed of light, usually seen as a “relativistic effect”.
You see, dear Antoine, that magnetism is a real physical event and not a fictive event. The value is not dependent from relativity in the sense of the choice of the inertial frame.
Dear Thierry,
A charged particle manifests itself in space by creating and maintaining a substantial (real) presence that we call "an electromagnetic field". We can mathematically describe that field relative to an inertial reference frame O.
- If the particle is at rest relative to O, the field is completely characterized by the vector E. In that context we talk about an "electric field". An observer in O can deduce E from the force F exerted by the field on a test charge q: F = q.E
- If the particle is moving relative to O, we have to introduce the vector pair (E, B) to completely characterize the field. In that context we talk about an "electromagnetic field" and an observer in O can deduce E from the force FE (the electric force) exerted by the field on a test charge q at rest relative to O: FE = q.E. And next he can deduce B from the force F (the Lorentz force) exerted on the test charge q moving with velocity v relative to O from FB = q.(v x B) = F - FE (FB is the magnetic force).
To illustrate the role of the reference frame, we consider a positive and a negative particle (A and B) anchored on a table in an elevator that is going up with constant velocity relative to the earth . For an observer in that elevator the particles are both at rest and there is only an electric interaction between them. For an observer outside the elevator both particles are moving with constant velocity. So, particle B is moving in the electromagnetic field created by particle A: it is exposed to the superposition of an electric force and a magnetic force. A detailed analysis [1] shows that the magnetic force reduces the attraction between the particles, more concrete that the effective force between them is reduced with a factor [1 - (v/c)2]1/2
Conclusion: The (real) medium that mediates in the interaction between electrically charged particles is the electromagnetic field. The way it manifests itself depends on the inertial reference system of the observer.
[1] R.G. - A. Acke: Electro-magnetism explained by the theory of informatons-2 (§5.3.3)
Dear Antoine,
Gedanke experimenten are the ideal way to make believe wrong things.
Let us take something more concrete instead: lightning.
Lightning is made of electrons, they should strongly mutually repel.
Why doesn't lightning strongly spreads and widens? That is because the electron beam is moving at a considerable velocity, and creates a magnetic field w.r.t. the Earth's gravity field.
This magnetic field is circular about the electron beam, and every electron of that beam is influenced by that magnetic field, spites that this electron is going at the same speed as the rest of the beam. Why?
Indeed, if the magnetic field would suddenly disappear by the presence of the one isolated electron of that beam, this would lead to a contradiction, because there would then be a physical vanishing of the physical reality of the magnetic field, just by the presence of that single electron. Consequently, the magnetic field remains to exist of course, and the isolated electron gets a Lorentz force by that magnetic field and its velocity. F = q (E + v x B).
The resulting Lorentz force is pointing inwards the beam.
Hence, the lightning beam is tightly hold together, and doesn't widens much.
The speed of a neutral observer will change nothing about that.
Hence, there is no Lorentz invariance whatsoever.
Dear Thierry,
I agree: the speed of the observer does not affect the facts. However, this does not mean that the speed of the inertial reference system that is connected to the observer doesn't affect the description of the facts.
As a result of the fact that the two observers in the example of the imaginary elevator (it can also be a rocket) observe the same phenomenon (the interaction between charged particles) in different inertial reference systems, the force between the particles is for the one observer (who is on earth) smaller than for the other (who is in the elevator). If the particles were free, they would move towards each other and finally collide. Because of the smaller force that process would take a longer time on the watch of the observer on earth than on that of the observer in the elevator, what is in line with the Lorentz transformations.
Because the phenomenon of lightning is very complex, I would rather focus on the example of an electron beam composed of electrons that travel with constant speed in vacuum. It is a fact that such a beam diverges because of the mutual repulsion of the particles. Relative to an observer that travels with the speed of the electrons there is only the electrical repulsion between the particles, but relative to an observer on earth this repulsion is reduced by the effect of the magnetic force (each particle moves in the electro-magnetic field generated by the others) with a factor [1 - (v/c)2]1/2. That implies that the phenomenon of a certain increase of the radius of the beam takes more time on the watch of the observer on earth than on that of the observer that travels with the beam, what is in line with the Lorentz transformations.
Yes, Thierry .
Because the Electromagnetic theory (Maxwell's theory) is invariant to the Lorentz transform, and thus relative to any observer.
All the best
Dear Ioseph,
Imagine a beam (bundle) of electrons at a certain, non-relativistic speed.
This beam of electrons will be encircled by a magnetic field. If we add one electron to this bundle at the same speed, this electron will undergo that magnetic field and thus get a Lorentz-force that is pushing inwards the bundle, which keeps the bundle a bit better together, instead of strongly spreading it due to repel forces.
It is not so that the additional electron would detect no magnetic field because it is traveling at the same speed of the bundle.
Hence, for non-relativistic speeds, this is totally independent form the observer. The magnetic field field will be measured by the observer according to the laws of electromagnetism, depending from its distance to the beam.
No Lorentz invariance exists, since the ultimate electron that we added to the bundle at the same speed detects the full magnetic field.
For relativistic speeds, the calculus depends from a number of parameters, and this will alter the measured magnetic field. In some cases, a factor sqrt(1-v2/c2) has to be used.
Charges moving with respect to the lab or rest frame create a magnetic field(in that frame). Using the right hand with thumb along charged current direction, the fingers give the magnetic field which wraps
around the charged current. Magnetic field lines do not terminate but wrap around div(B) =0. In a current carrying coil, this all adds up and a magnetic field threads through the coil, going all the way around.
Subject to frame transformations described by antoine; in a different frame you would see a different mixture of E and B fields. In SR the allowed frames move at constant speeds with respect to each other.
Dear Juan,
You write: "in a different frame you would see a different mixture of E and B fields. In SR the allowed frames move at constant speeds with respect to each other.".
Oh yes? Really? Can you cite any reliable observational evidence of your claim?
How would a tiny observer, without a charge, be able to turn a part of an important diverging E field into a rotating B field or vice-versa, when the observer has a non-relativistic speed?
How would a tiny observer that contains a single test-electron, be able to suddenly undergo, from an important electron beam with a (E,B) set, a totally different Lorentz force when it is moving at a different speed, except by the change of its speed in the equation vxB ?
"Hence, the lightning beam is tightly hold together"
Dear Thierry,
good idea! This certainly applies as well to an electron beam that will maintain its shape independently of the observer position and velocity. From where do the electrons know that they are moving? What is their reference? Is it something like an "ether"?
Dear Johan,
You write: "This certainly applies as well to an electron beam that will maintain its shape independently of the observer position and velocity."
Indeed! It has nothing to do with the observer.
You write : "From where do the electrons know that they are moving? What is their reference? Is it something like an "ether"?"
The Earth is a gigantic source of ions, which account for a physical reference field to which the lightning is moving.
The magnetic field can only exist if two physical fields are mutually moving. That's why the beam of electrons is better held together.
This is of course also the reason why fast muons don't fall apart (don't desintegrate) quickly in the presence of the Earth's field, and that their lifetime augments: a magnetic field encircles it and a Lorentz force acts radially, inwards, holding it stable.
If you speak of aether, I would advocate that it is a hydraulic medium to which all masses and all ions collaborate ~q/R2 and ~M/R2.
Since the Earth's field of ions and mass is the reference field then, it is not surprizing that the aether's speed would be zero close to the Earth's surface and that Michelson-Morley experiments give a zero result.
"The Earth is a gigantic source of ions, which account for a physical reference field to which the lightning is moving."
Dear Thierry,
and what about an electron beam inside a high vacuum enclosure? Do you think a cathode ray tube won't work on a spacecraft far outside the reach of celestial bodies?
dear Johan, I think that one needs two charges at a mutual speed in order to get a magnetic field, which is standard Maxwellian electromagnetism.
I cannot answer the hypothetical question you ask, because it depends if the spacecraft alone can provide a reference field for the cathode ray and provide the required energy for the required magnetic field, assuming that only that spacecraft exists in the universe.
suppose a proton is moving to the right with velocity v, and also the frame is moving to the right with the same velocity.
then the proton is at rest in the frame and only has an electrical field radially outward.
Whereas if the proton moves and the frame does not move, then you get a magnetic field. The electric field is then more closely perpendicular to the direction of motion.
A lot of comon sense in this.
We are only talking about the fields produced by the charge, but not preexisting fields the
charge may be moving through. The charge does not interact with its own fields.
Otherwise there are forces invaldating the assumptions.
Dear Juan,
You write: “suppose a proton is moving to the right with velocity v, and also the frame is moving to the right with the same velocity, then the proton is at rest in the frame and only has an electrical field radially outward..../... A lot of comon sense in this.”
Which "common sense"? Does your “frame” have magic properties? Can you cite any reliable observational evidence of your claim?
How would you explain the Lorentz force on one of the protons of your proton beam, if your frame doesn't allegedly detect the magnetic field when it has the same speed of the beam? However, you pretend “if the proton moves and the frame does not move, then you get a magnetic field”.
So there is a magnetic field.
How would a tiny observer with a non-relativistic speed and without a charge, be able to turn a part of an important rotating B field that is created by a moving electron beam w.r.t. the Earth into a diverging E field or vice-versa, or make some part of the fields disappear?
"I think that one needs two charges at a mutual speed in order to get a magnetic field"
Dear Thierry,
I don't see any neccessity to think this way. An electron beam according to my understanding is composed of nothing else but electrons.
Another thought experiment: There are two equal charges at rest in a vacuum. An external observer will see them flying apart due to electrostatic repulsion. When speeding up the charges at the same rate on parallel lines, Lorentz type attraction forces will increase until they overcome static repulsion forces. In the latter case the observer will see the charges attracting each other. The observer, anyway, should be able to clearly differentiate the relative motions.
Dear Johan,
It can be shown [1] that - in the case of two equally charged particles that move along parallel paths with speed v - the magnetic component of the Lorentz force is (v/c)2-times the electric component of that force and that it is opposite to it. Because v cannot become larger than c, it is evident that the magnetic component cannot overcome the electric one.
Conclusion: the interaction between two charges with the same sign depends on their speed, but it is in all circumstances repulsive (and between two charges with opposite sign attractive)
[1] R.G. - A. Acke: ELECTROMAGNETISM EXPLAINED BY THE THEORY OF INFORMATONS-2(§5.3.3.2)
I do not have to explain any force because it is fields generated by the charge itself.
"the interaction between two charges with the same sign depends on their speed, but it is in all circumstances repulsive"
Dear Antoine,
shouldn't the electron beam fly apart then?
Dear Johan,
Because the electrons repel each other, the beam that they constitute always diverge. Because of the magnetic component of the Lorentz force, this happens to a lesser extent according as the electrons move faster, but there is always a certain degree of divergence. In a C.R.T. there is a focusing system to compensate for this effect.
Maybe an electron beam would fly apart, depends on distance and the initial momentum. At any rate
in a wire they are kept together, and there is a magnetic field.
If the initial beam speed is high, they hold together for a longer time, enough time and distance for practicle purposes. (ie. tv tube)
Dear Antoine and Juan,
thanks for your kind and persuasive advice!
I propose to come back to the subject of the question, whether a magnetic field vanishes if a neutral, non-charged observer would follow a beam of electrons at a certain speed. This is namely claimed by relativists.
Let now a test be projected perpendicularly, away from the cathode ray (or a moving charged rod). Due to the Lorentz force, that electron is experiencing a small sideways force, parallel to the cathode ray.
When the electron was first approaching the electron beam, it received a Lorentz force in the opposite direction.
Hence, when an electron crosses the ray perpendicularly, it will experience a zig-zag.
The description of this effect by a relativistic approach is impossible for an observer that follows the ray (or rod). Even when one extends SRT to Minkowsky's metric.
What does that mean for the validity of Einstein's relativity?
The magnetic field of the Earth is generated by internal circulation so there is no inertial frame in which the material is not moving. That makes it a difficult example for your question.
TDM: What does that mean for the validity of Einstein's relativity?
The effect of SR is only to introduce the gamma function in some equations, the effect of relative motion at low speeds is unaltered compared to the pre-SR equations.
TDM: I propose to come back to the subject of the question, whether a magnetic field vanishes if a neutral, non-charged observer would follow a beam of electrons at a certain speed. This is namely claimed by relativists.
No, this is a consequence of Ampere's Law, it is nothing to do with SR. How many times does this obvious fact need to be pointed out Thierry?
Dear George,
TDM: "whether a magnetic field vanishes if a neutral, non-charged observer would follow a beam of electrons at a certain speed."
GD: "No, this is a consequence of Ampere's Law, it is nothing to do with SR."
You are historically wrong.
The concept of the observer has always been based upon observations on Earth, of which either all the charged parts were static wrt the Earth, or a part of the experiment had moving charges and a part was static. Some experiments were about rotating charges and fields.
Never have been measured the effects on electromagnetism of which a charge-neutral observer was moving inertially. There was simply no need for it.
Hence, it was utmost difficult for the scientists of the 19th century to disconnect the observer from the sole possible one: an observer standing still on Earth, coinciding with one of the EM-parts of the experiment.
Now, Einstein thought to bring a addendum at that, by looking for solutions when the observer is moving.
Example: Part 1) let a magnetic rod be inserted at a speed v in a cupper solenoid that isn connected to an Ampère meter. Let the observer stand stil. A current will be noticed.
Part 2) Let now the solenoid move at a speed v and the magnetic rod stand still. The observer stand still. A current will be noticed.
Part 3) Let in either of the experiments above, the observer follow either of the parts, the magnetic rod or the solenoid. A current will be noticed.
There is a great difference between the parts 1) en 2) on the one hand, and the part 3) on the other.
However, Einstein stated that it was all the same.
While the first two parts consider in reality EM observers, Einstein now considers a charge-neutral observer!
That is the origin of the "problem of the observer".
However, if an observer will move his head with the magnetic rod or with the solenoid, it is not thàt action that will change anything to the measurements of the involved fields.
That is why there is a huge difference between the 19th Maxwell interpretation and Einstein's interpretation.
Dear Thierry,
TDM: "whether a magnetic field vanishes if a neutral, non-charged observer would follow a beam of electrons at a certain speed."
GD: "No, this is a consequence of Ampere's Law, it is nothing to do with SR."
TDM: You are historically wrong.
No, Ampere wrote a simple equation based on the work of Oersted, it says that if no current flows, there is no magnetic field produced. That is a historical fact.
TDM: The concept of the observer has always been based upon observations on Earth,
The concept of an observer is fairly modern terminology, that maths of Ampere was based on a closed line integral. The current that goes into the equation is the rate of flow of charge through the surface bounded by the line integral. If you move round that path, it must return to the starting point or the path isn't closed. What we would now call "the observer" in that maths must be therefore the coordinate system in which that line integral is at rest, nothing more. If you want to know what a magnetic field sensor will read, you define that frame to be the one in which the sensor is at rest. If the flow of charge through that surface is zero, the line integral of the magnetic field is zero and the sensor will read zero. In that sense, the sensor becomes "the observer".
I think you are making the classic layman error of thinking of "the observer" in anthropomorphic terms. If you picked up a textbook and started learning the basics of the subject, all of this would become obvious.
Dear George,
The conclusion is: *only* physical fields can be used to define reference frames, not Einsteinians.
No Thierry, you cannot define a coordinate system relative to a field, see your other thread for the details:
https://www.researchgate.net/post/Can_a_theory_be_falsified_by_another_theory
No George, the thread shows that you are wrong.
The electric field is independent from the magnetic field, which is velocity dependent.
The curvature of an orbiting charge defines the velocity and so, the magnetic field.
Hence, the non-moving, electric field of the orbiting charge, is the reference frame, of which the orbit's center is the origin.
So, the electric field of the orbiting charge defines the reference frame.
No Thierry, I'm not wrong on this point, nor was Einstein, nor Maxwell or any other physicist in the last 200 years. You don't seem to understand that you are arguing against all of them.
TDM: Hence, the non-moving, electric field of the orbiting charge,
If the charge is moving, the field it creates cannot be "non-moving". Think before posting Thierry.
You can of course measure relative to a charged body, but not relative to a generic field.
Go back and think again about what it means to say "velocity relative to green" in the illustration of a temperature field. How would you go about measuring a precise value for velocity relative to nothing more than the definition of the colour? You could do it if only one pixel had that colour to give a unique origin, but not when whole areas have the the same value hence are indistinguishable. That is inherent in the nature of a field.
Dear George,
“If the charge is moving, the field it creates cannot be "non-moving".”
What defines “moving”, George? Think about that first before posting! Like LeVerrier's calculus for the Newtonian perihelion advance, where he smeared the planets' masses over the orbits, as if they were rings, the same way, the global gravity field of an orbiting set of masses can be seen as a set of rings with a steady gravity field, which is the reference field.
“You can of course measure relative to a charged body, but not relative to a generic field.” Of course you can! The field propagates with the speed of light. Hence, with a moving charge, at a distance, the local field has to be taken into account, which differ!
TDM: What defines “moving”, George?
Non-zero derivative of the displacement vector in a given coordinate system. Come on Thierry, this is primary school stuff, can't you raise the level of discussion a bit.
GD: “You can of course measure relative to a charged body, but not relative to a generic field.”
TDM: Of course you can!
No Thierry, you can't.
TDM: Hence, with a moving charge, at a distance, the local field has to be taken into account, which differ!
At a distance from a charge, the field has some unique potential (relative to a reference value of course), but that potential does NOT define a unique point, a potential only defines a surface because multiple points can have the same potential. To define the origin of a coordinate system, you need find a point that can be tracked unambiguously over time, and the potential of a field doesn't allow you to do that.
Again Thierry, this is a very basic fact, schoolboy stuff that you should know instinctively. Look back at the example I gave of a temperature field or coloured regions if you still don't get it.
Dear George,
Think a little bit about the fact that the divergence of gravity is the mass density. Hence, the origin is defined. The zero angle of the polar coordinates is conventional.
TDM: Hence, the origin is defined.
Only if the field emanates from a point source in which case you are using the source as the origin, not the field. The field itself is distributed, it exists everywhere so cannot be used that way. Learn the basics Thierry, this applies to every type of field.
Dear George,
A field that exists everywhere and has a gradient because of divergence is well defined at every point of space.
That is the case of the (modernized) Newtonian field and the Coulomb field.
The single fact of a presence of a magnetic field (or a gyrotation field, for gravity) translates the fact that there is a velocity involved for the considered object (charge or mass).
That velocity (and the consequent magnetic or gyrotation field) can only exist in relation to the local divergent field (Newton or Coulomb) at the place where the magnetic field has been measured.
TDM: A field that exists everywhere and has a gradient because of divergence is well defined at every point of space.
Exactly, that is the problem, it doesn't distinguish locations that can be used as the unique origin of a coordinate system.
A smooth surface doesn't identify a point Thierry. Please learn the basics.
Since gravity is diverging, the gravity field defines the point. Do you know any Newtonian basics, George ?
The potential around a point is spherically symmetric Thierry, all points on the surface are indistinguishable so you cannot use that potential locally to define the origin of a coordinate system. You can use the shape if you know it globally to infer the location of the point source, but then to are not using the field per se, you are using the inferred point are your origin. You are still failing to understand the basic problem, a field can have the same value in many places (for example over a surface) hence the value of the field does not uniquely identify any one point. It doesn't matter if you are talking about gravitational potential or electrical potential or a field of temperature readings or colour or whatever, the same fact applies.
Let me add another example, altitude above the geoid is a scalar field, and I assume you understand the concept of a contour line on a map. If I then ask "Point X is 100m above mean sea level, how far is it from Big Ben?", there is no way you can answer because there are many such location, and in particular a contour line showing surface altitude of 100m is a continuous function.
Dear George,
My point was: "The conclusion is: *only* physical fields can be used to define reference frames, not Einsteinians."
You pretend now that it is a problem to define an unique point based upon the field since a field has an equipotential surface. So what? That was not the point!
The point was that the Einsteinian approach got nothing at all as a reference and that deBroglie (and Einstein) have confirmed in 1937 that SRT is only about the alteration of measuring signals between the inertial reference frames! The reason is that in the nowadays wrong interpretation, each reference frame can pretend that it is standing still and that the other is moving, resulting in a mutual claim of increasing time and mass, and decreasing length!
In reality, electric fields or gravity fields that are divergent/convergent, have the perfect capacity to refer to each of the masses involved or to their superposition.
Nature will create a magnetic field or a gyrotation (= magnetic-like for gravity) field if there is a motion between the local electric or gravity field and the considered charge or mass.
Never I have spoken of an unique point that has to be defined, and that is not relevant of course! It is defined wrt the considered charge or mass in that field.
TDM: My point was: "The conclusion is: *only* physical fields can be used to define reference frames, not Einsteinians."
TDM: You pretend now that it is a problem to define an unique point based upon the field since a field has an equipotential surface. So what?
My point has always been that you cannot define a frame based on any field, regardless of type (whatever you mean by that), because defining a frame requires a way to identify the origin of the coordinate system and track that unique point through time.
Dear George,
Can you give a realistic example where it would not be possible to define that?
I have done so several times Thierry but I'll try again.
Suppose you wanted to specify the location of a house in Paris. You could give its location as so many km east and north of the centre of the Eiffel Tower. That would work.
On the other hand, temperature is a field, every point in Paris has a temperature that you can measure with a thermometer. You could measure the temperature at the centre of the Eiffel Tower, let's say it is 12C today, and then say the house is located so many km east and north of the point where the temperature is 12C. That wouldn't work because there would be many places in Paris where the value of the temperature field is 12C, knowing only the temperature does not identify a location that is unique.
A reference frame is a definition for a set of coordinates that allow you to locate events relative to a unique specific origin, the temperature field alone doesn't identify a unique origin.
Do you follow the problem yet Thierry?
Dear George,
"Do you follow the problem yet Thierry?"
No, I don't. It is not a matter of just measuring the temperature. It is a matter of knowing the gradient, so you can find the source. And if there many sources, one finds the gradient of the equivalent global source.
Hence you find the source and you can define the given particle, of which you know the coordinates, wrt the field.
Dear all,
An example: it is possible to make a charge A (on a tiny mass) orbit another charge B (on a heavy mass) in a lab environment.
If the charge B is linearily moving wrt the lab, there should be a precession of the charge B's orbit.
This means that, necessarily, velocity has to be defined in absolute terms wrt the lab. Now, we know that there are many spontaneous ions in the air and free electrons at the surface of metals.
I come to the following conclusion: the magnetic field of a moving charge will be settled with respect to the same physical electric reference field as the one that defined the velocity of that charge.
It means that one cannot assign an arbitrary velocity to a charge at wish, because the electric reference field is physical.
Hence, the magnetic field is to be considered as absolute as well.
The conclusion is also valid for gravity, since the Gravity Probe B has proven that 3-vector gravitomagnetism perfectly reflects this gravity's experiment. Since gravitomagnetism entirely explains Mercury's anomalous precession out of the induction of the moving Sun upon Mercury's orbit, also the (gravito)magnetic effect has to be seen as (locally) absolute.
Best regards,
Thierry De Mees
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