Maxwell–Faraday equation symmetry violation

[LostConjugate]

I still wonder about this.

A simple results of this equation is:

If a charge has a velocity in the positive y direction [v = (0,1,0)] and it accelerates in the positive x direction (it curls) then there will be a magnetic field in the positive z direction. There will be no magnetic field in the negative z direction.

The problem here is that negative and positive z are symmetrical, there is no physical difference, and the xy plane is orthogonal so there is no interaction with the z plane to choose one direction or another. Yet nature always chooses the same direction to put the field based on the motion of an electric charge in an orthogonal plane.

Because of this I do not see how the magnetic field is a field at all. It only appears to be a mathematical object used for simplification in describing the physical interactions of electric charges.

 

[Creator]

And your question is?

 

[LostConjugate]

How can one direction be chosen over the other for the magnetic field unless the magnetic field is not a field at all but rather a mere vector that is the consolidated collection of electric fields permeating from the accelerated charge in the z direction.

 

[my_wan]

Couldn't the same argument be used to claim a velocity can't be a velocity, since any two people with different velocities can both call their own velocity zero? Just because a velocity changes how you measure it doesn't mean that what is measured is not what it is. In fact, it's an electromagnetic field, and what you see as electric or magnetic is dependent on your perspective of the field.

Another example would be clocks. Go fast enough and it looks like everybody's clock back home is going slow. They say it appears your clocks are slow. If they come to you, you are right. If you go to them, they are right. Does this mean clocks aren't real, or time is not real?

 

[LostConjugate]

Couldn't the same argument be used to claim a velocity can't be a velocity, since any two people with different velocities can both call their own velocity zero? Just because a velocity changes how you measure it doesn't mean that what is measured is not what it is. In fact, it's an electromagnetic field, and what you see as electric or magnetic is dependent on your perspective of the field.

Another example would be clocks. Go fast enough and it looks like everybody's clock back home is going slow. They say it appears your clocks are slow. If they come to you, you are right. If you go to them, they are right. Does this mean clocks aren't real, or time is not real?

However if the magnetic field is only a notation for simplifying the ability to work with electric fields in three dimensions then there would be no reason to continue the search and work related to magnetic monopoles.

 

[my_wan]

I always found the monopole search exceedingly speculative anyway. I'm still happy that such things are looked for. We should always be looking for things contrary to our presumptions, not just those that supports them.

 

[LostConjugate]

It is because there is proof of the possibility of a magnetic monopole, however this proof is based on the magnetic field being something of a different field (though coupled) than the electric field. So what I am saying is that the symmetry violation disproves the magnetic field as being anything more than the electric field itself which would disprove the possibility of the magnetic monopole.

 

[cabraham]

However if the magnetic field is only a notation for simplifying the ability to work with electric fields in three dimensions then there would be no reason to continue the search and work related to magnetic monopoles.

The magnetic field is as important as the electric field. Just as the H field can be viewed as an E in another frame of reference, it is also true that an E field can be viewed as H in another frame. Neither one "comes first".

Regarding monopoles, it's hard to prove that something does not exist somply because it has not yet been observed. Maybe magnetic monopoles do or don't exist. But magnetic fields are real, they just happen to be di-polar, not mono-polar.

Also, E fields come in 2 types, Ec (due to discrete charge particles, or "monopoles"), & Ei (due to induction). The "Ei" type of electric field is di-polar, no monopoles have yet been found. When induction takes place, the induced E field is the "Ei" type, having a solenoidal closed loop type of behavior just like a magnetic field. Yet di-polar E fields, Ei, carry energy just as H fields do.

The lack of a monopole does not negate the fact that a dipolar field carries energy. Both types of E, as well as H field, are important. Does this help?

Claude

 

[Antiphon]

The manetic field is a pseudovector. It's sign depends on the coordinate system so you are right. The key is that the forces are in the right direction regardless of which convention you adopt.

 

[LostConjugate]

So the Magnetic Field is or is not just components of the electric field?

For example:

You have two conductive coils in an inductor. According to the M equations if a current is run through one, a magnetic field will be generated and this field will generate a current through the next. However there are also accelerated electric fields that when summed over will generate a current in the second coil (the particles follow the acceleration). Add this to the magnetic field current and you would get a current that is twice that of which the M equations propose.

So the Magnetic field is just the sum of the accelerated electric fields and this is why those fields are dropped in the equation of an inductor.

 

[Creator]

For example:

You have two conductive coils in an inductor. According to the M equations if a current is run through one, a magnetic field will be generated and this field will generate a current through the next.

Not. It must be an ALTERNATING current. A direct current generates a static magnetic field, B, and it doesn't generate a current in the neighboring coil. Induction of current only takes place by a time rate of change in the magnetic field according to Maxwell's eqns. (Faraday's law of induction)...
.....curl E = - dB/dt

It is the induced E field that generate the current in the neighboring coil.

What is an "M" equation? Please use standard physics terminology.

However there are also accelerated electric fields that when summed over will generate a current in the second coil.
.

What are you referring to as an "accelerated electric field"?? Again you are using non-standard terms. Do you means 'time varying' E fields?
It would be better if you write the equations you are referring to.
...

 

[Born2bwire]

Perhaps you should look at the scalar and vector potentials. The electric and magnetic fields result from different manipulations of these potentials. The manipulation of the potentials means that there are physical effects that can only be contained in the magnetic fields and some only contained in the electric fields. While we can use Lorentz transformations to show that the electric and magnetic fields can be transformed into each other by judicious choice of your frame of reference, this suggests the equivalency of the force of the fields, not the equivalency of the fields themselves. When we get down to it, we are expressing the electromagnetic force as the result of two sets of properties. We can use the electric and magnetic fields to express this or we could use the scalar and vector potentials. However, there hasn't been a theory that I have seen that can reduce this to a single field or potential.

 

[LostConjugate]

By M equations I meant Maxwell equations.

By accelerated field I meant that the E field between the electrons in the coil was changing position in an accelerated way. Since the electrons in the coil are accelerating the magnetic field would be changing, same as an alternating electric current, which works fine for the point I was trying to get across as well.

So when you have an electron accelerating around in a coil, the electric field between that electron and an electron in the other coil would be changing, which would cause the electron in the second coil to move (or follow it). What I am saying is that the summation of these movements due to an acceleration in the position of the E field is what we call the effects of a magnetic field.

But the E field is a real field, it attracts/repels charged particles, if the magnetic field is just the change in position of an E field it should not be classified as a fundamental field.

 

[Dale]

But the E field is a real field, it attracts/repels charged particles

A magnetic field also exerts force on charged particles. It is every bit as "real" as an E field (although defining "real" is notoriously tricky).
Did yoy read Antiphon's post. The answer to your OP is that the magnetic field is a pseudovector field, not a vector field. Your same symmetry violation would hold for any pseudovector like angular momentum.

 

[LostConjugate]

A magnetic field also exerts force on charged particles. It is every bit as "real" as an E field (although defining "real" is notoriously tricky).
Did yoy read Antiphon's post. The answer to your OP is that the magnetic field is a pseudovector field, not a vector field. Your same symmetry violation would hold for any pseudovector like angular momentum.

But why call it a fundamental field if it is just a pseudovector?

And why call it the electro-magnetic field? This explains why there is a supposed magnetic field in a light wave, there isnt! It can all be explained as components of perturbation in the electric field.

 

[Born2bwire]

But why call it a fundamental field if it is just a pseudovector?

And why call it the electro-magnetic field? This explains why there is a supposed magnetic field in a light wave, there isnt! It can all be explained as components of perturbation in the electric field.

But there is no frame where light is only composed of electric fields.

 

[Dale]

But why call it a fundamental field if it is just a pseudovector?

What's wrong with pseudovectors?

And why call it the electro-magnetic field? This explains why there is a supposed magnetic field in a light wave, there isnt! It can all be explained as components of perturbation in the electric field.

I have certainly never seen any theory that could describe EM in terms of the E field only. AFAIK, the best that you can do is reduce it to a four-potential. I don't know of any way to reduce it to a single scalar potential.

 

[LostConjugate]

But there is no frame where light is only composed of electric fields.

I am not sure what this has to do with frames but if you sum over all the electric components you don't even have to use a magnetic field. Its far more complicated mathematics I am sure, but it is a better explanation of how charges are effected by other charges in motion since it only requires one field. That is what I have been trying to say.

 

[Dale]

I am not sure what this has to do with frames but if you sum over all the electric components you don't even have to use a magnetic field. Its far more complicated mathematics I am sure, but it is a better explanation of how charges are effected by other charges in motion since it only requires one field. That is what I have been trying to say.

I don't know of any possible way that this could be correct. It is not just a matter of more complicated mathematics, it is an under-determined problem without the B field. In other words, you can have two problems with the exact same E field but different B fields and the motion of particles will be vastly different. You cannot just mathematically massage the E field to get the information out.

 

[LostConjugate]

Ok then back to my original question, if the Magnetic field is a real field, why is it directionally bias? Why does it always go in the same perpendicular direction.

 

[Dale]

Ok then back to my original question, if the Magnetic field is a real field, why is it directionally bias? Why does it always go in the same perpendicular direction.

I don't understand what the two have to do with each other. Why should a "real field" (whatever that means) not be "directionally biased" (whatever that means)?

I think somehow your question has to do with the symmetry of a pseudovector, but I don't understand what makes you believe that a pseudovector field cannot be a "real field".

 

[LostConjugate]

I just think that when a charge curls the change in the electric field causes other charges to curl as well, and therefor the magnetic field is just this curl in the electric force and nothing more. This does away with the problem of why the magnetic field always points in one direction based on the movement of a charge in an orthogonal plane.

 

[Dale]

This does away with the problem of why the magnetic field always points in one direction based on the movement of a charge in an orthogonal plane.

Why is that a problem?

 

[nonequilibrium]

As I see it, the OP has a problem with the situation at hand because he sees perfect symmetry in the scenario described until the magnetic fields manifests itself and destroys the symmetry, correct?

Well I'd say the symmetry was broken the moment acceleration was brought in, because from then on out, it was possible to distinguish the negative z-axis from the positive one (--imagine yourself as an observer on either). As a result, the B-field never broke any symmetry.

Or am I way out on interpreting your question?

 

[Dale]

Well I'd say the symmetry was broken the moment acceleration was brought in, because from then on out, it was possible to distinguish the negative z-axis from the positive one (--imagine yourself as an observer on either). As a result, the B-field never broke any symmetry.

That is a good point. As soon as the charge has a velocity there is a direction and therefore you have an axisymmetric source, not a spherically symmetric source. The B-field is also axisymmetric but not spherically symmetric.

LostConjugate, do you see how the B field is axisymmetric which is the same symmetry as the source?

 

[Born2bwire]

I am not sure what this has to do with frames but if you sum over all the electric components you don't even have to use a magnetic field. Its far more complicated mathematics I am sure, but it is a better explanation of how charges are effected by other charges in motion since it only requires one field. That is what I have been trying to say.

This is important because, as DaleSpam and I have stated previously, there are situations where you cannot describe a problem based solely on the electric fields. There is a relationship between them that we can see from the fact that application of Lorentz transformations can give rise to electric fields from a magnetic field and vice-versa. However, not every situation can be resolved from a mixed-field problem to a purely electric field problem via Lorentz transformations. For example, what if you had three static magneti fields at normal angles to each other? You would then always have a magnetic field component in the direction of the frame's relative velocity. Rather then, it is better to think of them as the electromagnetic field. The two fields are intertwined but they are not completely equivalent. Another way to look at it is in terms of the scalar and vector potenials, which happen to be the primitives of the electromagnetic field in QED. This completely removes the idea of the fields but you can still see that we cannot rely on one or the other to fully describe the behavior of the electromagnetic force.

 

[LostConjugate]

That is a good point. As soon as the charge has a velocity there is a direction and therefore you have an axisymmetric source, not a spherically symmetric source. The B-field is also axisymmetric but not spherically symmetric.

LostConjugate, do you see how the B field is axisymmetric which is the same symmetry as the source?

Thats why I think it is just the electric field, from the point of view of another charged object on the z axis it will follow the moving charged particle as the electric field changes position. Now you could also say that instead a magnetic field is generated, then work out the action this field has on the second charged particle and get the same result, but then you have to drop the effect of the changing electric field, since you encompassed this into your magnetic field. But then the magnetic field is just a simplification of the fluctuation in the electric field.

Perhaps it is just not possible for me to understand this.

 

[Dale]

Thats why I think it is just the electric field, from the point of view of another charged object on the z axis it will follow the moving charged particle as the electric field changes position. Now you could also say that instead a magnetic field is generated, then work out the action this field has on the second charged particle and get the same result, but then you have to drop the effect of the changing electric field, since you encompassed this into your magnetic field. But then the magnetic field is just a simplification of the fluctuation in the electric field.

For the simple case of a single charged particle you are absolutely correct, you can always transform it to a reference frame where there is a pure electric field with no magnetic field. However, as soon as you have two or more charged particles it is no longer generally possible to transform it into a pure electric field.

 

[LostConjugate]

For the simple case of a single charged particle you are absolutely correct, you can always transform it to a reference frame where there is a pure electric field with no magnetic field. However, as soon as you have two or more charged particles it is no longer generally possible to transform it into a pure electric field.

You can't or it is just very complicated? Seems like you could just take the summation of multiple fields to see how it acts on other charges.

Like a current in a loop, its real simple to calculate the magnetic field and it's effect on another loop or charge. But you can see that the magnetic field's effect on another charge or loop could just be the summation of all the electric fields coming from the current loop.

 

[Vanadium 50]

You can't. With one particle, I can always find a frame where it is at rest. With two particles, I can't in general find a frame where they are both at rest.

If I wanted to, I could define a "nagmetic" field, which is just like the magnetic field but points in the opposite direction. I could then redefine the Maxwell and Lorentz equations to use this nagmentic field and I would have a perfectly consistent system. Note, though, the physical observables would be exactly the same. That's because every sign is flipped twice - once at the origination of the field, and once when the particle responds to the field.

 

[Antiphon]

I'm feeling devious.

How would you feel about the electric field if you had moving magnetic charges? Now it's the electric field that is the pseudovector.

Finally, you have a wave in free space. E and H both relate to one another via identical looking curl equations. So now which field is real and which is the pseudovector?

The answer is that just as there is space-time where space and time are mixed for different inertial frames, the same is true for E and H. As has been mentioned already, neither field alone is the complete picture. Both together (EM field tensor) is an object you can hang your hat on.