### [hep-ph/9708394] A Model of Magnetic Monopoles

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**February 09 2011**This paper (arXiv: hep-ph/9708394) presents a generalization of quantum electrodynamics, called quantum electromagnetodynamics. It includes both electric and magnetic charges. It includes the conventional photon (electric photon) and a second kind of photon, called magnetic photon. The quantum numbers of the magnetic photon are predicted to be the same as those of the electric photon, i. e. spin one, negative parity, zero rest mass, zero electric charge, zero magnetic charge. The difference is that the electric photon couples via vector coupling with electric charges, whereas the magnetic photon is predicted to couple via tensor coupling with electric charges.

Based upon this theory, I suggested a tabletop experiment for the search for the magnetic photon. The basic idea is that light consists of both electric photon and magnetic photon. The experimental setup includes only a light source (laser, lamp), an absorber for the electric photon light (metal layer, metal foil), and an optical detector (photomultiplier, photo diode).

I argued that August Kundt may have observed an effect of the magnetic photon already in 1885 (arXiv: hep-ph/0205229; physics/0403026). My theory has later been tested by Alipasha Vaziri (arXiv: physics/0403026) and by Roderic Lakes (arXiv: physics/0405148). The result of these two experiments was negative.

It is the aim of this note to point out the mistake I made in the interpretation of the equations of my theory. In the following, I will correct the mistake and make a new prediction which is testable by the tabletop experiments mentioned above.

During the preceding years I searched again and again for possible mistakes in my theory and a possible conventional explanation for the result of the August Kundt experiment.

My result is that August Kundt's observation of red solar light which penetrated iron layers of thickness larger than 200 nm cannot be explained by standard theory (classical electrodynamics, one kind of photon).

I think that Alipasha Vaziri's observation (arXiv: physics/0403026) of a 6 standard deviation above background of red laser light which "penetrated" an aluminium foil (of thickness 10 micrometers) can be explained conventionally. Laser light warms the illuminated aluminium foil which then emits infrared light. The high-frequency tail of the infrared light may have been detectable with the avalanche diode Vaziri used and explain the 6 sigma excess.

By contrast, Kundt's observation cannot be explained in this way, because he measured the Faraday rotation of the polarized light.

I agree with Roderic Lakes that he has so far not observed magnetic photon light and that his dark count rate is a heat effect.

I think that I found a mistake in the interpretation of my theory which led me to a wrong prediction.

Previously, I thought that light which penetrates metal has a particle-like nature. So I assumed that the interaction cross-section of a magnetic photon is 10^-6 times the cross-section of an electric photon of the same frequency (10^-6 = square of the absolute speed of the laboratory in units of the speed of light). This assumption, however, is completely wrong. Light in metal behaves wave-like (polariton, more or less a combination of light wave and sound wave).

The new interpretation of the basic equations of my theory (which remain unchanged) is the following. Electric charges can couple to both the four-potential of the electric photon (via vector coupling) and the four-potential of the magnetic photon (via tensor coupling). So an electric charge generates both an electric four-current density (vector part of eq. 11 of my paper arXiv: hep-ph/9708394) and a magnetic four-current density (tensor part of eq. 12). According to the Lagrangian, eq. 9, the four-potential of the electric photon can couple only to the electric four-current density, and the four-potential of the magnetic photon can couple only to the magnetic four-current density. The main difference between the vector part and the tensor part of the four-current density is the appearance of the four-velocity. For emission and absorption processes I interpret this velocity as the absolute velocity of the laboratory (10^-3 in units of the speed of light). So the magnetic current density is 10^-3 times the electric current density. According to Ohm's law, current density is equal to conductivity times the electromagnetic field. By intuition I think that the magnetic conductivity is 10^-3 times the electric conductivity of a given conductor in a terrestrial laboratory.

The penetration depth of light of a given frequency is proportional to the square root of the reciprocal value of the conductivity (eq. 34 of my paper arXiv: hep-ph/0205229). So I predict that the penetration depth of magnetic photon light is 30 times (square root of 10^3) that of electric photon light of the same frequency.

The result would be that in iron (August Kundt experiment) the penetration depth for red light is 7 nm for electric photon light and 210 nm for magnetic photon light. In aluminium (Alipasha Vaziri and Roderic Lakes experiments) the penetration depth for green/red light is 3 resp. 3.5 nm for electric photon light and 90 resp. 100 nm for magnetic photon light.

Lakes' experiment (Phys. Lett. A 329 (2004) 298-300 = arXiv: physics/0405148) with the YAG-laser and the photomultiplier tube would then detect no electric photon light if the aluminium foil (or layer) is thicker than 150 nm, but it could detect penetrating magnetic photon light if the aluminium foil (or layer) is not thicker than 1000 nm.

Note that electric conductivity and magnetic conductivity determine the reflection of electric and magnetic photon light, respectively (cf. eqs. 37 - 39 of hep-ph/0205229). The electric conductivity of a metal is predicted to be 10^3 times larger than the magnetic conductivity. This results in a stronger reflection of electric photon light than magnetic photon light. To give an example: I predict that silver reflects 94% of the electric photon light, but only 13% of the magnetic photon light, if green light of the wavelength 532 nm is used. Therefore the use of mirrors (for reflection) should be avoided for the search for the magnetic photon light.

Based upon this theory, I suggested a tabletop experiment for the search for the magnetic photon. The basic idea is that light consists of both electric photon and magnetic photon. The experimental setup includes only a light source (laser, lamp), an absorber for the electric photon light (metal layer, metal foil), and an optical detector (photomultiplier, photo diode).

I argued that August Kundt may have observed an effect of the magnetic photon already in 1885 (arXiv: hep-ph/0205229; physics/0403026). My theory has later been tested by Alipasha Vaziri (arXiv: physics/0403026) and by Roderic Lakes (arXiv: physics/0405148). The result of these two experiments was negative.

It is the aim of this note to point out the mistake I made in the interpretation of the equations of my theory. In the following, I will correct the mistake and make a new prediction which is testable by the tabletop experiments mentioned above.

During the preceding years I searched again and again for possible mistakes in my theory and a possible conventional explanation for the result of the August Kundt experiment.

My result is that August Kundt's observation of red solar light which penetrated iron layers of thickness larger than 200 nm cannot be explained by standard theory (classical electrodynamics, one kind of photon).

I think that Alipasha Vaziri's observation (arXiv: physics/0403026) of a 6 standard deviation above background of red laser light which "penetrated" an aluminium foil (of thickness 10 micrometers) can be explained conventionally. Laser light warms the illuminated aluminium foil which then emits infrared light. The high-frequency tail of the infrared light may have been detectable with the avalanche diode Vaziri used and explain the 6 sigma excess.

By contrast, Kundt's observation cannot be explained in this way, because he measured the Faraday rotation of the polarized light.

I agree with Roderic Lakes that he has so far not observed magnetic photon light and that his dark count rate is a heat effect.

I think that I found a mistake in the interpretation of my theory which led me to a wrong prediction.

Previously, I thought that light which penetrates metal has a particle-like nature. So I assumed that the interaction cross-section of a magnetic photon is 10^-6 times the cross-section of an electric photon of the same frequency (10^-6 = square of the absolute speed of the laboratory in units of the speed of light). This assumption, however, is completely wrong. Light in metal behaves wave-like (polariton, more or less a combination of light wave and sound wave).

The new interpretation of the basic equations of my theory (which remain unchanged) is the following. Electric charges can couple to both the four-potential of the electric photon (via vector coupling) and the four-potential of the magnetic photon (via tensor coupling). So an electric charge generates both an electric four-current density (vector part of eq. 11 of my paper arXiv: hep-ph/9708394) and a magnetic four-current density (tensor part of eq. 12). According to the Lagrangian, eq. 9, the four-potential of the electric photon can couple only to the electric four-current density, and the four-potential of the magnetic photon can couple only to the magnetic four-current density. The main difference between the vector part and the tensor part of the four-current density is the appearance of the four-velocity. For emission and absorption processes I interpret this velocity as the absolute velocity of the laboratory (10^-3 in units of the speed of light). So the magnetic current density is 10^-3 times the electric current density. According to Ohm's law, current density is equal to conductivity times the electromagnetic field. By intuition I think that the magnetic conductivity is 10^-3 times the electric conductivity of a given conductor in a terrestrial laboratory.

The penetration depth of light of a given frequency is proportional to the square root of the reciprocal value of the conductivity (eq. 34 of my paper arXiv: hep-ph/0205229). So I predict that the penetration depth of magnetic photon light is 30 times (square root of 10^3) that of electric photon light of the same frequency.

The result would be that in iron (August Kundt experiment) the penetration depth for red light is 7 nm for electric photon light and 210 nm for magnetic photon light. In aluminium (Alipasha Vaziri and Roderic Lakes experiments) the penetration depth for green/red light is 3 resp. 3.5 nm for electric photon light and 90 resp. 100 nm for magnetic photon light.

Lakes' experiment (Phys. Lett. A 329 (2004) 298-300 = arXiv: physics/0405148) with the YAG-laser and the photomultiplier tube would then detect no electric photon light if the aluminium foil (or layer) is thicker than 150 nm, but it could detect penetrating magnetic photon light if the aluminium foil (or layer) is not thicker than 1000 nm.

Note that electric conductivity and magnetic conductivity determine the reflection of electric and magnetic photon light, respectively (cf. eqs. 37 - 39 of hep-ph/0205229). The electric conductivity of a metal is predicted to be 10^3 times larger than the magnetic conductivity. This results in a stronger reflection of electric photon light than magnetic photon light. To give an example: I predict that silver reflects 94% of the electric photon light, but only 13% of the magnetic photon light, if green light of the wavelength 532 nm is used. Therefore the use of mirrors (for reflection) should be avoided for the search for the magnetic photon light.