Musings

I made a blog post a few years ago that discussed the inability of physicists to discover of magnetic monopoles—the equivalent of particles with positive and negative charges that give rise to electrical currents. The motion of these particles produce an electromagnetic field, and theory suggests that similar particles of magnetism in the form of independent ‘North’ and ‘South’ poles as found in common magnets should exist.

When James Clerk Maxwell derived his famous equations of electromagnetism (based on empirical observations), they lacked these essential elements and thus were asymmetrical. This lack of symmetry disfigured these otherwise beautiful equations.

Well, as of September 3, 2009, this is no longer an issue. The mysterious monopole has finally been observed. You can find the article that discusses these observations at: Magnetic Monopoles Discovered

This partially validates my speculation that magnetism might be an inter-dimensional phenomenon, and also validates certain aspects of string theory.

With this new information in hand, we can now complete Maxwell’s equations and provide the symmetry that was sorely lacking for a century. The equations in their original form and the new form appear below (my thanks to the Dyslectic Mathematician for the discussion) Note that the equations are not in the conventional form:

These are slightly differently than the standard form to emphasize the fact that electric charges create electric and magnetic fields. So the information about the fields is on the left-hand side, and the information about the charges is on the right-hand side. What these fields tell us is the nature of the magnetic and electric fields produced by charges. At least in theory, the strength and direction of the fields at any given point in space can be determined from any arbitrary set of charges or charged objects.

Look at the first two of Maxwell’s equations. The E represents the electric field and the B represents the magnetic field. On the right-hand side of the first equation, the Greek letter rho represents the electric charge distribution, while the epsilon with the zero subscript is a constant number that always stays the same, like pi. The right-hand side of the first equation is written in a generalized way so that the equation applies to any distribution of charge. The information on that side of the equation represents a single point charge, such as a proton or electron. The triangle, called “del”, followed by a dot represents the way the electric field is spreading out from a charge. In the second equation, we have del dot B — so the spreading out of the magnetic field — and this is equal to zero. There is no magnetic charge from which a magnetic field radiates.

In the third equation, del followed by an X and an E, (spoken out loud as “del cross E”), represents the way the electric field is curling around the charge distribution. The d and dt coupled with the B represent how the magnetic field changes in strength and direction as time progresses. On the other side of the equation, we have zero, so there is no charge involved. A changing magnetic field actually induces an electric field. If you had just a static point charge — or even moving charges that are constant in their motion and quantity, and we shall see momentarily from the fourth equation — the magnetic field would not be changing. In fact, with a stationary charge distribution, as we saw from the second equation, no magnetic field at all would be produced. It follows that the electric field of a stationary charge (or unchanging electric current) does not curve. The electric field of a point charge only points straight outward or straight inward; it does not curl around.

In the final equation, del dot B represents the way the magnetic field is curling around. Then there’s the term involving Greek letters (ignore since they are constants), and another set of d’s, this time involving an E. Ignore the constants and what you have left is a term just like the one directly above it except with an E instead of a B. So this term represents the way the electric field is changing over time. On the right-hand side of the equation, we have another Greek letter (constant), and a J. The J represents a distribution of electric current. Electric current is just made up of moving point charges. If the electric field is not changing, then the second term on the left-hand side is zero, and we’re left with the statement that the way the magnetic field of a charge distribution curls is dependent on the way those charges are flowing in a current. If you have a current running through a straight wire, the magnetic field will curl around it in a circle.

This is what Maxwell’s equations will have to be updated to look like now that magnetic monopoles have been discovered:

Here, subscripts have been added to the rho’s and J’s to distinguish electric charges and currents from magnetic charges and currents A magnetic charge will do exactly what an electric charge does in Maxwell’s equations as we know them. A magnetic field would radiate straight out from a magnetic point charge, but no magnetic field would curl around it. An electric field would curl around a moving magnetic charge or current, but would not radiate outward from the magnetic charge.

If you ignore the constants and the plus and minus signs, which just represent direction, in the revised version of Maxwell’s equations, the first equation is exactly the same as the second equation, except with the E and B (and little e and b subscripts) interchanged. The same is true of the third and fourth equations: they are exactly the same as each other except the places of E and B, and e and b, are switched. This is the symmetry that the original equations lacked.

What this all means is that engineers and scientists can perhaps start solving the problems associated with ‘Zero-Point’ energy devices, ‘Warp’ drives, and the inter-dimensional aspects of gravity & electromotive forces.