# Three Laws of Classical Electromagnetism

1. Mar 6, 2009

### Phrak

I believe classical electrodynamics can be reduced to:

1) Lorentz force
2) Existance of a Lorentz invariant vector field of real entries, $V=V^\mu \hat{e}_\mu$
3) Charge is always associated with mass

Maxwell's equations are obtained by associatating elements of the vector field with measurable quantities.

Last edited: Mar 6, 2009
2. Mar 6, 2009

### confinement

Actually, classical electromagnetism can be deduced from the lagrangian for a free particle along with local U(1) gauge symmetry.

3. Mar 6, 2009

### xepma

You don't need local gauge symmetry or mass to come up with a theory of electromagnetism... All you need is the 2-form, field strength tensor, F, and a Yang-Mills action, F^2. You can introduce matter and couple the fields through a so-called minimal substitution. But classical electrodynamics permits non-trivial solutions in the absence of matter (propagating light).

4. Mar 6, 2009

### Phrak

How does that work, confinement?

5. Mar 6, 2009

### confinement

A readable treatment can be found in the last chapter of Grifith's introduction to elementary particles, or somewhere in Kaku's book on QFT. In the classical case I should not have said "from the Lagrangian", since actually one needs the Hamilton-Jacobi formulation of mechanics, in which Jacobi's function S parallels the wave function Psi in the quantum mechanical case.

6. Mar 6, 2009

### Phrak

This is a classical gauge, right, so that the lagrangian is to act on point particles?
Umm, and is F an exact form?

Classically,

$$G_{\mu \nu} = \frac{1}{2} \epsilon_{\mu \nu}{}^{\sigma \rho} F_{\sigma \rho}$$

$$J_{\pi} = \epsilon_{\pi}{}^{\sigma \mu \nu} \partial_{[\sigma} G_{\mu \nu ]}$$

give or take a negative sign, where

$$J_{\pi} = (-\rho, \vec{J})\ .$$

Hidden away within the differential equation is that the divergence of the electric field is equal to charge density. Within the Yang-Mills action, is there any particular equivalence, or would it be an uninteresting artifact of the field F, unassociated with charge?

Last edited: Mar 6, 2009
7. Mar 6, 2009

### confinement

In electromagnetism the field tensor F is an exact form since we have F = dA, where A is the vector potential.

In a non-abelian Yang-Mills field theory we have F = dA + A /\A and the classical equation of motion is:

d(*F) + F /\ A = *j

Therefore we can think of F /\ A as being the dual of a nonlinear current density.

8. Mar 8, 2009

### Phrak

I haven't seen F = dA + A/\A before. It looks like it would change measurable values in classical electrodynamics where F = dA. Does it?

I'll have to take you word that this gives you d(*F) + F /\ A = *j. It looks like a lot of work to get to, or I'm attempting it the hard way. Somehow d*F + F /\ A = d*(dA + A/\A) , right?

Last edited: Mar 8, 2009
9. Mar 10, 2009

### Geofizz

This is all powerfull stuff but why are our children taught James Clerk Maxwell's Theory of Terresital Magneti'ks at school. There has been no update of this nintenth century theory which is basically flawed and redundant through Schumann and Balser and Wagners work. If we can't apply basic laws of electromagnetics in practical and important situations whats the point putting the cart before the horse.

10. Mar 10, 2009

### Phrak

Because we can apply basic laws of electromagnetism in practial situations.

11. Mar 10, 2009

### Geofizz

Ok good answer but if someone actually appled basic laws or common sense to Maxwell's Tm theory, would it stand up, or be proved science fiction. If its science fiction it has profound implications in medicine and to every "ology" taught today at universities. Proving lightning creates Tm not a hot "metal" core of the earth, changes what we know about history and science forever.

Example. The earth is largly a DC current so a big battery, Question, are we plugging buildings into this battery and whats the effect? If the earths hot metal core produces only radiation, what happens to radiation meeting direct current that must have liner form that travels by its path of least risistance along the earths surface. If the answer is ionising radiation which causes benign tumors 39 forms of cancer gastointestinal disorders bacterial infection electrolite imbalance cateracts and DNA damage in low dose exposure over twenty years thats ok then. We can change dc current in the earth to make it alternating and prevent the problem. Electromagnetic law allows us to do that, if we think it might be important.

Best regards
geofizz

12. Mar 10, 2009

### xepma

What the hell are you talking about? Are you even trying to make a point?

Maxwell's theory has been around for over a hundred year, and its implications cannot be underestimated. Just look around you: transmission cables, radios, fiber optics, the screen you're looking at while reading this, ...

If anything, I suggest you would apply some common sense to your own writings.

13. Mar 10, 2009

### Phrak

"Example. The earth is largly a DC current so a big battery..."

Well. Learn first. Pontificate later. In this way, one reduces the probability of being wrong with every word.

14. Mar 11, 2009

### Geofizz

Learn First, pontifiacat later, good advice so lets be very clear here there's seems little known anywhere about Maxwells Theory of Terrestial Magneticks. It has nothing to do with computers Cables etc and if you dont know all school children are taught the earths a big battery, you should read on Tm before making a judgment that affects peoples lives. Wikpedia has many articles. Alexander Bain produced the first electric clock by using DC currents from the earth, the Earth battery principle powered early teligraph's and while Pylons or Transmision towers carry Ac current. There legs are firmly planted in DC current. An observance thats to obvious to notice for most scientists.

All articles or papers on Tm back and state Maxwells theory like parrots. but if its 19th century science fiction it needs to be questioned, thats how we learn. In 1952 Otto Schumann had a theroy of Resonance involving lighning in the cavity between the earths surface and ionisphere. The theory was proven by Balser and Wagner in 1963. We know today from this work (though not seen locally) over six million lighning strikes a day discharge trillions of volts of electricity into the earth's surface if there were only a hundred it changes everything about Tm. Maxwell never knew that, when was the last time you saw lighning and questioned its effect on Tm. If we don't question we don't learn.
I must admitt here my passion for this subject as its taken over 15 years of my life researching it deeply. I appreciate bieng challenged by logical argument and i know i don't write well but this is heavey stuff that others should question not just me. I havent all the answers, i havent all the questions but what i have says science and medicine are affected by a suspect theory. Using the scientific method all evidence must be gathered and examined, this in not the case with Tm. The earths hot "metal" core has never been proven and Currie Point applies to everything magnetic or electromagnetic but apparantly not the Earth.

Many articles papers and theories relate Schumann's resonance theory to health etc, but the fact is Shumann's resonance is only measured when unimpeded in atmosphere. between fixed points the earth is a DC current not an alternating current resonance suggests. This is very basic electromagnetics, if we can't get the basics right whats left thats safe.

Best regards
geofizz

15. Mar 12, 2009

### Phrak

I'm sure this would all be very facinating in the Earth Sciences Folder. Or if you wish you should start a thread on it. It has nothing to do with the topic at hand other than a name.