Is Electromagnetic Theory Incomplete Without Magnetic Monopoles?

[Antonio Lao]

What's EM's Modus Operandi ?

Since Maxwell formulation of the electromagnetic force, its cause remains a mystery. What is an electric field and what is a magnetic field? What is the origin of electric charge? The failure to detect the magnetic monopole is an indication that the present theory is incomplete.

 

[zefram_c]

The failure to detect the magnetic monopole is an indication that the present theory is incomplete.

The failure to *detect* something experimentally cannot be construed to say that the *theory* is incomplete. For example, the top quark and the weak force mediators were not detected until decades after their prediction, but that did not make the theory any less complete in the sense that it could answer all pertaining physically meaningful question we chose to ask.
Regarding magnetic monopoles, they do not occur naturally in the quantum theory of EM although they can be introduced 'by hand'. In classical EM theory, one is always free to locally transform magnetic fields into electric fields, though not the other way around. This indicates that it is electric charge that is fundamental to the interaction and there is no a priori reason to presuppose that magnetic monopoles exists.

 

[Antonio Lao]

This indicates that it is electric charge that is fundamental to the interaction...

But what is electric charge? My hypothesis is that it is the quantized structure of 1D spacetime (1D space and 1D time). When spacetime is quantized, there are two distinct topological structures to which I call them as $H^{+}_n$ and $H^{-}_n$, where $n$ is the level of existence (LOE) for these structures.

The interaction between these structures by matrix addition quantify the values for electric charge.

$$H^{-}_n \oplus H^{+}_n = 0$$
$$H^{-}_n \oplus H^{-}_n = aH^{-}_n$$
$$H^{+}_n \oplus H^{+}_n = bH^{+}_n$$

 

[zefram_c]

You might want to approach things differently, as electric charge is currently regarded as a combination of electroweak quantum numbers (weak isospin and weak hypercharge). This combination happens to correspond to an unbroken symmetry in the EW model and so it gets its own mediator, the massless photon field.

 

[Antonio Lao]

electric charge is currently regarded as a combination of electroweak quantum numbers

Thanks for this information. Since I am not familiar with the electroweak theory, I am now looking into them for any possible relationship with H+ and H-.
The massless photon is made of 4H+ and 4H-. The W boson is made of 8H+ 2H- or 2H+ 8H- and the Z boson is made of 8H+ 8H-. I am not sure about their respective LOEs. The mass of W and Z could have come from higher LOE's interactions.

 

[Antonio Lao]

zefram c,

I think I found the charge relationship to weak isospin and hypercharge by the Weinberg-Salam model, $Q = T^3 + \frac{Y}{2}$.

Note: page 336 of Michio Kaku's book entitled Quantum Field Theory: A Modern introduction.

 

[reilly]

Mr. Lau --Why is your space-time quantized? Seems to me you are replacing one mystery with another.
Regards,
Reilly Atkinson

 

[zefram_c]

Yes that is the formula. Interesting, can you use your model to derive the couplings of the photon and/or other mediators, or at least the mediators to each other (even at tree level)? Note that in GWS, the Z is simply the neutral field orthogonal to the photon - can you suggest why it would be made up of 8H+ /H- instead of 4?

 

[Antonio Lao]

Mr. Lau --Why is your space-time quantized?

The full implication is that spacetime is continuous. It is the 'direction' of local spacetime motion that is quantized. This motion is related to the number of degree of freedom (dof) of each spactime point. The time dimension always has 2 dof's. The 1D space also has 2 dof's. The 2D space has 4 dof's. The 3D space has 6 dof's. The number of dof is the same as the number of closest neighbor that each point can have.

 

[Antonio Lao]

zefram c,

I am now working on a reply to your last post. It seems to be a tall order because of my lack of knowledge in these other theories you mentioned. I seem to be going against the current of three Nobel Prize winners: Glashow, Weinberg and Salam. But I hope I can make their model works to my benefit.

 

[Antonio Lao]

zefram c,

The following partial reply is based on Weak Interactions from chapter 7 of Donald H. Perkins' Introduction to High Energy Physics, 4th edition, starting at page 194.

I begin this reply by first giving some introduction to the concepts of H+ and H-.
From H+/H- theory: all fermions are made of odd number of H+/H-. All bosons are made of even number H+/H-. The number of H+/H- are not necessarily equal. If they are equal, the results are neutrally charged particles. Regardless of their LOE, each H+ or H- has an absolute value for charge as 1/6.

The electron is made of 7H- and 1H+. The muon and tau leptons are made of higher LOE of H+/H-.

The neutrino is made of 1H+ and 1H-. Likewise, Higher LOEs for muon-neutrino and tau-neutrino.
The up quark is made of 5H+ and 1H-. Likewise, Higher LOEs for charm and top)
The down quark is made of 1H+ and 3H-. Likewise, Higher LOEs for strange and bottom.

The vacuum is made of even and odd H+/H- of different LOEs of which energy can be borrowed for a short time in a given interaction.

The tree diagram for vacuum fluctuation is (positron, 7H+1H-) + (electron, 1H+7H-)-->(2 photons or 1 Z0, 8H+8H-). Other tree diagrams are the following:

(7H+1H-) + (W-, 2H+8H-) --> (9H+9H-), a higher LOE of neutrino. But (9H+9H-) is an excited state of neutrino, so (8H+8H-) can be returned to the vacuum, to get a stable neutrino (1H+1H-). Higher LOE means more mass or more energy.

For the weak charged current interaction: (1H+1H-) + (neutron, 7H+7H-) -->(intermediate, (W+, 8H+2H-) + (6H-)) + (borrow from vacuum, 4H+4H-) --> (intermediate, 12H+12H-) --> (proton, 11H+5H-) + (electron, 1H+7H-)

For the weak neutral current interaction: (1H+1H-) + (7H+7H-) --> (Z0, 8H+8H-) --> (1H+1H-) + (7H+7H-).

 

[zefram_c]

I seem to be going against the current of three Nobel Prize winners: Glashow, Weinberg and Salam

I hope you do not intend that in the sense of "I will replace their theory since theirs is wrong", as GWS is highly successful when confronted by experiments. But there's nothing wrong with trying to find a deeper cause that can generate the GWS model from more basic principles. Anyway the mediators are known to exist and act as predicted so their theory is pretty much confirmed...
Anyway, let me make sure I understand something correctly; I had an idea today on the bus but first I need to know: do your structures H actually carry electric charge?

 

[Antonio Lao]

do your structures H actually carry electric charge?

The electric charge is related to a principle of directional invariance. This principle is associated with 8 directional properties (please see the other thread on this principle). These 8 directional properties mapped into the 8 degrees of freedom for 4D spacetime.
The charge associated with 4 or more degrees of freedom is electric charge. Charge associated with less than 4 degrees of freedom, in the case of gluons, is color charge. In the case of H+ and H- (which each has 2 degrees of freedom but has 4 directional properties), it is called space charge. Each unit of space charge, regardless of LOE, has an absolute value of 1/6. Electric charge is the sum of space charges for each particle. For example, an electron is made of 7H- and 1H+, each H- has a space charge of (-1/6) and each H+ has a space charge of (+1/6), the sum is -1 for the electric charge of the electron. The up quark is made of 5H+ and 1H-, the sum of 5(+1/6) and 1(-1/6) is 4(+1/6) or +2/3 electric charge for the up quark.

 

[Antonio Lao]

zefram c,

The subtle point that came out of the weak charged current interaction using (H+/H-) is that energy can be borrowed permanently from the vacuum. I don't know what the GWS model have to say about this?

 

[Antonio Lao]

The best fusion reaction is given by $H^2_1 + H^3_1 \rightarrow He^4_2 + n^1_0$ and using (H+/H-), this reaction is the fusion of a fermionic state and a bosonic state. But would it be more effective if the fusion is done by just bosonic states or fermionic states? The products seem to be bosonic and fermionic states distinctly separated.

 

[Antonio Lao]

Using (H+/H-), an example of pure bosonic states reaction is given by

$$H^1_1 + H^3_1 \rightarrow He^4_2$$

and a pure fermionic states reaction is given by

$$H^2_1 + H^2_1 \rightarrow He^4_2$$

 

[zefram_c]

Hi again, been away on vacation for the last few days. Will get back to you once I catch up with work. I do not know offhand whether particles' spin plays any significant role in fusion reactions.

 

[Antonio Lao]

I do not know offhand whether particles' spin plays any significant role in fusion reactions.

This is a very interesting question. I don't know the answer either. In another thread, I was discussing with sol2 (a member of this forum) and his question about genus of a topological structure led me to think that spin is somehow related to it. Personally, I don't think the theory of thermonuclear fusion is completely understood. Yet, because of desperate need for a new future energy source, ITER, the international organization on fusion, is going ahead in building this big fusion machine. I have been reading their publications. In other respect, I won't mind to work for ITER as a physics researcher. But their minimum qualification must be at least a PhD. I couldn't be qualified since I only got a Bachelor degree in physics since 1973.

 

[zefram_c]

The full implication is that spacetime is continuous ...
The number of dof is the same as the number of closest neighbor that each point can have.

I am somewhat confused as to how this may come about. If you assume spacetime is continuous, then it follows that we may use the real number system (or pairs thereof in higher dimensions) to assign coordonates to points (for simplicity we will consider flat Minkowski space). Two problems arise. In the real number system, there is no such thing as "closest" neighbor - it is the same as asking "what is the smallest number strictly greater than zero", which cannot be defined. Also, since there is no "closest number" in a given direction, there would be infinitely many DOF even in a 2D spacetime as you can pick arbitrarily small displacements in non-orthogonal directions. (ie you can build a circle of "closest neighbors"). Both of these problems would go away if your spacetime was quantized.

 

[zefram_c]

I cannot be sure without consulting specialized texts, but my knowledge is that spin in scattering processes (of which fusion is a type) simply leads to the introduction of angular dependence factors in the scattering amplitude. For weak interactions this is particularly important due to their peculiar handed natures, but otherwise spin does not fundamentally contribute to the underlying process.

 

[Antonio Lao]

(ie you can build a circle of "closest neighbors").

If we introduce infinitesimal orthogonal forces, one circle in 1D (not 2D or 3D) alone is disjointed into a hyperbolic geometry. So, to quantized spacetime, two of these hyperbolic geometries are needed to form two 1D cirlces linked together into a Hopf ring. There should be two distinct nonequivalent topologies whose matrices have no inverse making all their determinants zero. The closest topological name is that of a fully twisted Moebius strip cut through the middle and shrunk its 2D to 1D.