Thanks for his link. Looking only at the slide you pictured, this approaches mathematical dynamics and ergodic theory which I have seen used mostly by mathematicians, engineers and Russian physicists.

Note that if the diagonal pictured is transformed from a plane surface to a cylindical surface that said diagonal becomes a helix.

This may then correspond to a vortex vector of Valey Kozlov, Russian Academy of Science.

Thanks for that sample slide from the 't Hooft talk! It's looks similar to what Ryder is doing on pages 299-300 of "Quantum Field Theory (2nd ed.)", equations 8.59, 8.62, and 8.65.

The matrix is the "isospinor". The Dirac equation Lagrangian has a spinor or matrix of parameters corresponding to terms in the Dirac equation. The "isospinor" symmetry is different because the symmetries are between say electron neutrinos and left handed electrons, not between electrons and positrons as in the Dirac spinor.

I was really amazed to learn that the weak mixing angle as an ad hoc fix literally mixes up the U(1) gauge boson with the neutral SU(2) gauge boson to produce something that fits the description of the gauge boson of electromagnetism.

It's simply not true that U(1) represents electromagnetism and SU(2) the weak interaction: instead the Standard Model weak mixing angle blends the neutral gauge boson properties of U(1) and of SU(2) (where the massiveness of the SU(2) neutral gauge boson isn't inherently natural, but has to be explained by an external agency, the Higgs field; i.e. the intrinsic mass of the SU(2) gauge bosons is zero and they acquire virtual mass from Higgs bosons).

The gauge boson of U(1) is B, which isn't observed in nature, and the neutral gauge boson of SU(2) is W_0, which again isn't observed in nature. The ad hoc "epicycle" of mixing the B from U(1) with the W_0 from SU(2) yields two mixed up combinations, the observed electromagnetic gauge boson and the massless version of the observed Z_0 weak gauge boson.

So even the electroweak sector of the Standard Model is a messy ad hoc theory. I look forward to reading 't Hooft's paper and seeing if it sheds light on the kind of mathematics which I'm interested in at the moment...

Wow! I've just started to read the 't Hooft paper and was struck by his slide which states:

"Every elementary particle may be viewed as a microscopic black hole:

* it is surrounded by a gravitational field described by the same equations, hence it has a horizon

* just because its mass is small, its radius may look negligibly small

* it obeys exactly the same equations

Every black hole may be viewed as an elementary particle:

* black holes are characterized by distinct quantum states, just as particles are, and they obey the same kinds of Schroedinger equations."

I agree with 't Hooft here. It's important from my perspective as an amateur physicist (which to me means "not a money making professional") to note that the cross-section of a fundamental particle for quantum gravity interactions at low energy is exactly the cross-sectional area of the event horizon of a black hole with similar mass. This isn't an input assumption into the quantum gravity theory I'm working on. You get that size as an output because you can come up with two different equations using different fact-based derivations, and by eliminating common terms between them you arrive at a formula for the gravitational cross-section. Elementary particles are black hole size for graviton interactions.

The radius of the event horizon of a black hole electron is on the 1.4*10^-57 m, the equation being simply r = 2GM/c^2 where M is electron mass.

Compare this to Planck's length 1.6 * 10^−35 metres which is a dimensional analysis based (non physical) length far larger in size, yet historically claimed to be the smallest physically significant size!

The black hole length equation is different from the Planck length equation principally in that Planck's equation includes Planck's constant h, and doesn't include electron mass. Both equations contain c and G. The choice of which is the more fundamental equation should be based on physical criteria, not groupthink or the vagaries of historical precedence.

The Planck length is complete rubbish, it's not based on physics, it's unchecked physically, it's not even wrong uncheckable speculation.

The smaller black hole size is checkable because it causes physical effects. According to the Wikipedia page

http://en.wikipedia.org/wiki/Black_hole_electron

"A paper titled "Is the electron a photon with toroidal topology?" by J. G. Williamson and M. B. van der Mark, describes an electron model consisting of a photon confined in a closed loop. In this paper, the confinement method is not explained. The Wheeler suggestion of gravitational collapse with conserved angular momentum and charge would explain the required confinement. With confinement explained, this model is consistent with many electron properties. This paper argues (page 20) "--that there exists a confined single-wavelength photon state, (that) leads to a model with non-trivial topology which allows a surprising number of the fundamental properties of the electron to be described within a single framework." "

My papers in Electronics World, August 2002 and April 2003, similarly showed that an electron is physically identical to a confined charged photon trapped into a small loop by gravitation(i.e., a massless SU(2) charged gauge boson which has not been supplied by mass from the Higgs field; the detailed way that the magnetic field curls cancel when such energy goes round in a loop or alternatively is exchanged in both directions between charges, prevent the usual infinite-magnetic-self-inductance objection to the motion of charged massless radiations).

The Wiki page on black hole electrons then claims wrongly that:

"... the black hole electron theory is incomplete. The first problem is that black holes tend to merge when they meet. Therefore, a collection of black-hole electrons would be expected to become one big black hole. Also, an electron-positron collision would be expected to produce a larger neutral black hole instead of two photons as is observed. These problems reflect the non-quantum nature of general relativity theory.

A more serious issue is Hawking radiation. According to Hawking's theory, a black hole the size and mass of an electron should vanish in a shower of photons (not just two photons of a given energy) within a small fraction of a second. Again, the current incompatibility of general relativity and quantum mechanics at electron scales prevents us from understanding why this never occurs. ..."

All of these "objections" are based on flawed versions Hawking's black hole radiation theory which neglects a lot of vital physics which make the correct theory more subtle.

See the Schwinger equation for pair production field strength requirements: equation 359 of the mainstream work http://arxiv.org/abs/quant-ph/0608140 or equation 8.20 of the mainstream work http://arxiv.org/abs/hep-th/0510040.

First of all, Schwinger showed that you can't get spontaneous pair-production in the vacuum if the electromagnetic field strength is below the critical threshold of 1.3*10^18 volts/metre.

Hawking's radiation theory requires this, because his explanation is that pair production must occur near the event horizon of the black hole.

One virtual fermion falls into the black hole, and the other escapes from the black hole and thus becomes a "real" particle (i.e., one that doesn't get drawn to its antiparticle and annihilated into bosonic radiation after the brief Heisenberg uncertainty time).

In Hawking's argument, the black hole is electrically uncharged, so this mechanism of randomly escaping fermions allows them to annihilate into real gamma rays outside the event horizon, and Hawking's theory describes the emission spectrum of these gamma rays (they are described by a black body type radiation spectrum with a specific equivalent radiating temperature).

The problem is that, if the black hole does need pair production at the event horizon in order to produce gamma rays, this won't happen the way Hawking suggests.

The electrical charge needed to produce Schwinger's 1.3*10^18 v/m electric field which is the minimum needed to cause pair-production /annihilation loops in the vacuum, will modify Hawking's mechanism.

Instead of virtual positrons and virtual electrons both having an equal chance of falling into the real core of the black hole electron, what will happen is that the pair will be on average polarized, with the virtual positron moving further towards the real electron core, and therefore being more likely to fall into it.

So, statistically you will get an excess of virtual positrons falling into an electron core and an excess of virtual electrons escaping from the black hole event horizon of the real electron core.

From a long distance, the sum of the charge distribution will make the electron appear to have the same charge as before, but the net negative charge will then come from the excess electrons around the event horizon.

Those electrons (produced by pair production) can't annihilate into gamma rays, because not enough virtual positrons are escaping from the event horizon to enable them to annihilate.

This really changes Hawking's theory when applied to fundamental particles as radiating black holes.

Black hole electrons radiate negatively charged massless radiation: gauge bosons. These are the Hawking radiation from black hole electrons. The electrons don't evaporate to nothing, because they're all evaporating and therefore all receiving radiation in equilibrium with emission.

This is part of the reason why SU(2) rather than U(1)xSU(2), looks to me like the best way to deal with electromagnetism as well as the weak and gravitational interaction! By simply getting rid of the Higgs mechanism and replacing it with something that provides mass to only a proportion of the SU(2) gauge bosons, we end up with massless charged SU(2) gauge bosons which mimic the charged, force-causing, Hawking radiation from black hole fermions. The massless neutral SU(2) gauge boson is then a spin-1 graviton, which fits in nicely with a quantum gravity mechanism that makes checkable predictions and is compatible with observed approximations such as checked parts of general relativity and quantum field theory.

## 3 Comments:

Hi Kea,

Thanks for his link.

Looking only at the slide you pictured, this approaches mathematical dynamics and ergodic theory which I have seen used mostly by mathematicians, engineers and Russian physicists.

Note that if the diagonal pictured is transformed from a plane surface to a cylindical surface that said diagonal becomes a helix.

This may then correspond to a vortex vector of Valey Kozlov, Russian Academy of Science.

Thanks for that sample slide from the 't Hooft talk! It's looks similar to what Ryder is doing on pages 299-300 of "Quantum Field Theory (2nd ed.)", equations 8.59, 8.62, and 8.65.

The matrix is the "isospinor". The Dirac equation Lagrangian has a spinor or matrix of parameters corresponding to terms in the Dirac equation. The "isospinor" symmetry is different because the symmetries are between say electron neutrinos and left handed electrons, not between electrons and positrons as in the Dirac spinor.

I was really amazed to learn that the weak mixing angle as an ad hoc fix literally mixes up the U(1) gauge boson with the neutral SU(2) gauge boson to produce something that fits the description of the gauge boson of electromagnetism.

It's simply not true that U(1) represents electromagnetism and SU(2) the weak interaction: instead the Standard Model weak mixing angle blends the neutral gauge boson properties of U(1) and of SU(2) (where the massiveness of the SU(2) neutral gauge boson isn't inherently natural, but has to be explained by an external agency, the Higgs field; i.e. the intrinsic mass of the SU(2) gauge bosons is zero and they acquire virtual mass from Higgs bosons).

The gauge boson of U(1) is B, which isn't observed in nature, and the neutral gauge boson of SU(2) is W_0, which again isn't observed in nature. The ad hoc "epicycle" of mixing the B from U(1) with the W_0 from SU(2) yields two mixed up combinations, the observed electromagnetic gauge boson and the massless version of the observed Z_0 weak gauge boson.

So even the electroweak sector of the Standard Model is a messy ad hoc theory. I look forward to reading 't Hooft's paper and seeing if it sheds light on the kind of mathematics which I'm interested in at the moment...

Wow! I've just started to read the 't Hooft paper and was struck by his slide which states:

"Every elementary particle may be viewed as a microscopic black hole:

* it is surrounded by a gravitational field described by the same equations, hence it has a

horizon* just because its mass is small, its radius may look negligibly small

* it obeys exactly the same equations

Every black hole may be viewed as an elementary particle:

* black holes are characterized by distinct quantum states, just as particles are, and they obey the same kinds of Schroedinger equations."

I agree with 't Hooft here. It's important from my perspective as an amateur physicist (which to me means "not a money making professional") to note that the cross-section of a fundamental particle for quantum gravity interactions at low energy is exactly the cross-sectional area of the event horizon of a black hole with similar mass. This isn't an input assumption into the quantum gravity theory I'm working on. You get that size as an output because you can come up with two different equations using different fact-based derivations, and by eliminating common terms between them you arrive at a formula for the gravitational cross-section. Elementary particles are black hole size for graviton interactions.

The radius of the event horizon of a black hole electron is on the 1.4*10^-57 m, the equation being simply r = 2GM/c^2 where M is electron mass.

Compare this to Planck's length 1.6 * 10^−35 metres which is a dimensional analysis based (non physical) length far larger in size, yet historically claimed to be the smallest physically significant size!

The black hole length equation is different from the Planck length equation principally in that Planck's equation includes Planck's constant h, and doesn't include electron mass. Both equations contain c and G. The choice of which is the more fundamental equation should be based on physical criteria, not groupthink or the vagaries of historical precedence.

The Planck length is complete rubbish, it's not based on physics, it's unchecked physically, it's not even wrong uncheckable speculation.

The smaller black hole size is checkable because it causes physical effects. According to the Wikipedia page

http://en.wikipedia.org/wiki/Black_hole_electron

"A paper titled "Is the electron a photon with toroidal topology?" by J. G. Williamson and M. B. van der Mark, describes an electron model consisting of a photon confined in a closed loop. In this paper, the confinement method is not explained. The Wheeler suggestion of gravitational collapse with conserved angular momentum and charge would explain the required confinement. With confinement explained, this model is consistent with many electron properties. This paper argues (page 20) "--that there exists a confined single-wavelength photon state, (that) leads to a model with non-trivial topology which allows a surprising number of the fundamental properties of the electron to be described within a single framework." "My papers in Electronics World, August 2002 and April 2003, similarly showed that an electron is physically identical to a confined charged photon trapped into a small loop by gravitation(i.e., a massless SU(2) charged gauge boson which has not been supplied by mass from the Higgs field; the detailed way that the magnetic field curls cancel when such energy goes round in a loop or alternatively is exchanged in both directions between charges, prevent the usual infinite-magnetic-self-inductance objection to the motion of charged massless radiations).

The Wiki page on black hole electrons then claims wrongly that:

"... the black hole electron theory is incomplete. The first problem is that black holes tend to merge when they meet. Therefore, a collection of black-hole electrons would be expected to become one big black hole. Also, an electron-positron collision would be expected to produce a larger neutral black hole instead of two photons as is observed. These problems reflect the non-quantum nature of general relativity theory.

A more serious issue is Hawking radiation. According to Hawking's theory, a black hole the size and mass of an electron should vanish in a shower of photons (not just two photons of a given energy) within a small fraction of a second. Again, the current incompatibility of general relativity and quantum mechanics at electron scales prevents us from understanding why this never occurs. ..."

All of these "objections" are based on flawed versions Hawking's black hole radiation theory which neglects a lot of vital physics which make the correct theory more subtle.

See the Schwinger equation for pair production field strength requirements: equation 359 of the mainstream work http://arxiv.org/abs/quant-ph/0608140 or equation 8.20 of the mainstream work http://arxiv.org/abs/hep-th/0510040.

First of all, Schwinger showed that you can't get spontaneous pair-production in the vacuum if the electromagnetic field strength is below the critical threshold of 1.3*10^18 volts/metre.

Hawking's radiation theory requires this, because his explanation is that pair production must occur near the event horizon of the black hole.

One virtual fermion falls into the black hole, and the other escapes from the black hole and thus becomes a "real" particle (i.e., one that doesn't get drawn to its antiparticle and annihilated into bosonic radiation after the brief Heisenberg uncertainty time).

In Hawking's argument, the black hole is electrically uncharged, so this mechanism of randomly escaping fermions allows them to annihilate into real gamma rays outside the event horizon, and Hawking's theory describes the emission spectrum of these gamma rays (they are described by a black body type radiation spectrum with a specific equivalent radiating temperature).

The problem is that, if the black hole does need pair production at the event horizon in order to produce gamma rays, this won't happen the way Hawking suggests.

The electrical charge needed to produce Schwinger's 1.3*10^18 v/m electric field which is the minimum needed to cause pair-production /annihilation loops in the vacuum, will modify Hawking's mechanism.

Instead of virtual positrons and virtual electrons both having an equal chance of falling into the real core of the black hole electron, what will happen is that the pair will be on average polarized, with the virtual positron moving further towards the real electron core, and therefore being more likely to fall into it.

So, statistically you will get an excess of virtual positrons falling into an electron core and an excess of virtual electrons escaping from the black hole event horizon of the real electron core.

From a long distance, the sum of the charge distribution will make the electron appear to have the same charge as before, but the net negative charge will then come from the excess electrons around the event horizon.

Those electrons (produced by pair production) can't annihilate into gamma rays, because not enough virtual positrons are escaping from the event horizon to enable them to annihilate.

This really changes Hawking's theory when applied to fundamental particles as radiating black holes.

Black hole electrons radiate negatively charged massless radiation: gauge bosons. These are the Hawking radiation from black hole electrons. The electrons don't evaporate to nothing, because they're all evaporating and therefore all receiving radiation in equilibrium with emission.

This is part of the reason why SU(2) rather than U(1)xSU(2), looks to me like the best way to deal with electromagnetism as well as the weak and gravitational interaction! By simply getting rid of the Higgs mechanism and replacing it with something that provides mass to only a proportion of the SU(2) gauge bosons, we end up with massless charged SU(2) gauge bosons which mimic the charged, force-causing, Hawking radiation from black hole fermions. The massless neutral SU(2) gauge boson is then a spin-1 graviton, which fits in nicely with a quantum gravity mechanism that makes checkable predictions and is compatible with observed approximations such as checked parts of general relativity and quantum field theory.

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