I am a retired engineer. I worked on the manufacturing and development of weapon electronic systems during my entire career. I had the rare opportunity to work with and learn from some gifted members of the scientific community.
I have a special interest in electron, positron pair production and the use of Planck units to specify the electron mass and Compton wavelength.
I also have a special interest in the Brian Greene suggestion that subatomic particles may be micro black holes. This is described in his book "The Elegant Universe" chapter 13 (page 320). He said (page 332) "--we see that black holes and elementary particles, like water and ice, are two sides of the same coin. We see that black holes snugly fit within the framework of string theory". In his other book "The Fabric Of The Cosmos" (page358) he explains that the electron mass is about 10 exp -23 times the Planck mass. To a first approximation this is 0 times the Planck mass. He states "Our goal is to better this approximation and show that string theory explains the tiny deviations from 0 times the Planck mass characteristic of the particles in Tabels 12.1 and 12.2".
Electron properties have been found to match the theoretical properties of a Kerr-Newman black hole with charge, spin and a ring singularity at the circumference, 2 pi times (3G m/ c squared). Electrons are in the class called "extremal" black holes. These black holes have charge and have the minimal possible mass consistant with the charge they carry. They do not evaporate or emit Hawking radiation.
I added the article "Is the electron a small black hole?" under Talk:Electron. I also added the article "determining Newtonian gravitational constant G" under Talk: Time dilation. I want to define a specific relationship between the Planck mass and the electron mass. An energy equation I have evaluated will accomplish this but there is presently no way to be sure if it is precisely correct or only approximately correct. If it is correct the true value for the gravitational constant must be very close to 6.6717456x10 exp -11. This is slightly less than the current published value.
The energy equation uses two energy values labeled E1 and E2 that are specifically defined and a third value labeled E3 that is derived. The E1 value is (2/3) exp 1/2, times the Planck mass energy. Using the G value noted above, the E1 energy is 1.5974395x10 exp 9 joule. The E2 value is two times the electron mass energy or 2m c squared. The E2 energy is 1.6374209x10 exp -13 joule. The energy values are related as shown.
The E3 value will then be equal to E2 multiplied by the dimensionless ratio (E2/E1). The E3 value found is 1.6784029x10 exp -35 joule. This can have no other units than energy because it is the product of energy and a dimensionless ratio.
When the E3 energy value is analyzed it is found to be equal to the tiny amount of energy that a photon would have if its wavelength is (2 pi) squared times light velocity times one second. This energy, Planck's constant times frequency, is defined below.
E3=hc divided by (2 pi) squared,times c
The constant value h (the energy of a photon with the wavelength c times one second) becomes a derived constant when divided by the constant (2 pi) squared. With the E3 energy defined as h/(2 pi)squared joules, the E2 energy can then be defined using basic constants.
E1=(hc/3 pi G)exp 1/2,times c squared
E2=2m c squared
2m c squared=(E1xE3)exp 1/2
2m c squared=c(hc/3pi G)exp 1/4,times [h/(2 pi)squared]exp 1/2
This equation is then solved for the electron mass to obtain the value shown.
m=(h/4 pi c)times(c/3 pi hG)exp 1/4
When the energy value (2/3) exp 1/2 times the Planck mass energy, is reduced by the time dilation factor [(1/2 pi) times (3/2) exp 1/2, times (Planck time)] divided by one second, the remaining energy is exactly equal to h divided by (2 pi) squared. In the multiplication, the G value cancels so the remaining energy is correctly determined without knowing the precise value for G.
The ratio E3/E1 is 1.0506832x10 exp-44 to one. This is equal to the time dilation ratio [(1/2 pi) times (3/2) exp 1/2, times (Planck time)]divided by one second. This ratio is stated as seconds per second. Any time units that are selected may be used but the ratio is fixed and is dimensionless. This is proposed to be a limit gravitational time dilation ratio. This ratio when inverted, is referred to as the gamma factor. The gamma factor is equal to E1/E3 or 9.5176171x10 exp 43.
In the book "Three Roads To Quantum Gravity" c 2001, Lee Smolin writes, page 95, "With matter there is a limit to how small we can divide something---. Is the same true of space? --- There are good reasons to believe that the continuous appearance of space is as much an illusion as the smooth appearance of matter. When we look on a small enough scale (Planck scale) we see that space is made of things (units) that we can count."
The amount of energy, 1/2 times the E3 energy, is probably the remaining energy that one unit of space will have, due to intrinsic random motion, when all extractable energy has been removed.
The ratio E2/E1 is equal to the square root of E3/E1 or 1.0250284x10 exp-22 to one. This is [(1/2 pi) exp 1/2, times (3/2) exp 1/4, times (Planck time) exp 1/2] to one. This is proposed to be the gravitational time dilation ratio at the photon capture radius of a stable K-N black hole with a unit charge. The gamma factor at this radius is 9.7558275x10 exp 21. If this is a specific natural requirement then the gravitational constant will have the value noted earlier, 6.6717456x10 exp -11 and the electron mass will be (h/4 pi c) times (c/3 pi hG) exp 1/4.
The wavelength (2 pi) squared times light velocity times one second is L3 in the length equation that follows. The L1 wavelength value is 2 pi times (Planck length) times (3/2) exponent 1/2.
L1=(3pi hG/c cubed) exp 1/2
L2=(L1xL3) exp 1/2
The L2 wavelength in this equation is found to be 2 pi times (3pi hG/c) exponent 1/4. This is the square root of the product of two segments of length so the L2 value is clearly a length also. The L2 value is 1.2131551x10 exp -12 meters using the gravitational constant value 6.6717456x10 exp -11. The electron Compton wavelength is 2(L2) or 2.4263102x10 exp -12 meters.
In October 1954, J.A.Wheeler presented his geon concept to Einstein;(see page 238 in book "Geons, Black Holes & Quantum Foam" by Wheeler 1998). Einstein was not impressed because he did not like the probabilistic nature of quantum theory, though he himself had considered geon-like compressed energy. On page 236, Wheeler describes a geon (physics), "This hypothetical entity, a gravitating body made entirely of electromagnetic fields, I called a geon ----.---Perhaps geons had a transitory existance early in the history of the universe. Perhaps they are formed and quickly dissipate in today's universe. Perhaps (as some students and I speculated much more recently), they provide an intermediate stage in the creation of black holes". On page 237, he writes "How could I not be lured by the prospect of a miniature quantum geon as small as a single elementary particle?" and on page 238, "But it (the paper sent to Einstein) did contain a few remarks about quantum physics--for instance, how quantum phenomena might change the nature of a geon if it is small, and how a geon might radiate away some of its energy in electron-positron pairs". The speculation that a geon (or a hybrid geon with a preexistent particle near its center) would provide an intermediate stage in the creation of (extremal) black holes, is probably correct. The time dilation associated with the gravitational field of a preexistent particle is expected to be required to achieve photon blue shift, high energy density and subsequent materialization of a pair of electron particles. A geon made of a single photon in a one wavelength loop would be a quantum mechanical entity. It would have one unit of angular momentum (h/2 pi) and would consist of two quantized energy concentrations with opposite electric fields. Each energy concentration would have the 1/2 unit of angular momentum needed to materialize two mass particles with opposite unit charge.
Some quotes from the book "Gravitation" by Misner, Thorne and Wheeler, c 1970, 1971, 1973, (page 1215) show how subatomic particle ideas have evolved: "What else can a particle be but a fossil from the most violent event of all, gravitational collapse?---That an electron here has the same mass as an electron there is also a triviality or a miracle. It is a triviality in quantum electrodynamics because it is assumed rather than derived.---No acceptable explanation for the miraculous identity of particles of the same type has ever been put forward. That identity must be regarded, not as a triviality, but as a central mystery of physics".
Physicists currently explain particles in terms of fields but the theory of fields is full of infinite quantities. This is because the strength of the electric field near a charged particle increases as one gets closer to the particle. The field approaches infinity as one approaches ever closer to a "point" particle. In the book "Three Roads To Quantum Gravity" Lee Smolin writes, page 114, "There are two ways to solve this problem, and we shall see that both play a role in quantum gravity. One way is to deny that space is continuous, which then makes it impossible to get arbitrarily close to a particle. The other way is through the hypothesis of duality. What one can do is replace the particles by strings. This may work because from a distance one cannot really tell if something is a point or a little loop. But if the hypothesis of duality is true, then the strings and the fields may be different ways of looking at the same thing. In this way, by embracing the hypothesis of duality, several of the problems that have clouded our understanding of physics for almost two centuries may be resolved. I personally believe in this hypothesis". A Kerr-Newman quantum black hole with a ring singularity would provide the "little loop" configuration, making the particle (from a distance) look like a point.
In the Geon, Black Hole book, page 236, Wheeler writes; "All of physics, both classical and quantum, faces a conceptual problem in dealing with point particles. We think of electrons and neutrinos and quarks as existing at mathematical points. We think of photons being created and being absorbed at mathematical points. Yet we cannot really deal with the infinite density of mass or the infinite density of charge implied by point particles and point interactions. These points are annoying pinpricks in the body of physics. We endure them because we have to, while hoping that someday we will identify and understand an inner structure in what today seem to be points". A Kerr-Newman black hole has an inner structure that looks and acts like a point source of gravity.
In a Quantum gravity article, Chris Isham writes;"One of the major predictions of Einstein's theory is the phenomenon of gravitational collapse in which under a wide range of initial conditions, matter that is compressed to more than a critical density will inevitably collapse under its self-gravitational attraction until it becomes a --- gravitational singularity". The critical (collapse) density is clearly achieved before a particle radius is reduced to zero meters (a point). He later writes; "Indeed, from the viewpoint of quantum theory, the idea of a spacetime point seems singularly inappropriate: by virtue of the Heisenberg uncertainty principle, an infinite amount of energy would be required to localize a particle at a true point; and it is therefore more than a little odd that modern quantum field theory still employs fields that are functions of such points.--- Be this as it may, it is clear that quantum gravity, with its natural Planck length, raises the possibility that the continuum nature of spacetime may not hold below this length, and that a quite different model is needed".
The basic equations relating to photon gravitational collapse reveal a relationship with the L1 wavelength, 2 pi times (Planck length) times (3/2) exponent 1/2. This is a maximum energy photon wavelength that has energy equal to the mass energy of two black holes, each with a photon capture radius (3G m/c squared) equal to the photon wavelength divided by two pi. The energy of a photon with this wavelength is determined either by the Planck constant or the gravitational constant. Energy is (hc/wavelength) or (c) exponent 4, times (wavelength) divided by (3pi G).
(wavelength/2pi)=3G m/c squared
(wavelength/2pi)x(c squared/3G)= m
2(wavelength/2pi)x(c exp 4/3G)=2mc squared
(wavelength)x(c exp 4/3pi G)=hc/wavelength
wavelength=(3pi hG/c cubed) exp 1/2
This is the wavelength previously labeled L1. The L1 wavelength photon has the critical energy density so that the self-gravitational attraction force is equal to the electric force. The L1 wavelength photon is the master model for all photons. All longer wavelength photons are stretched copies of this photon. This photon energy is determined by the gravitational constant and light velocity. Since photon energy is inversely proportional to wavelength, the energy of any wavelength photon can be determined from the gravitational constant and light velocity.
The next length to be considered is labeled L4. This length is the circumference 2 pi (3G m/c squared) where m is the electron mass. The ratio of L4 to L1 is 1.0250284x10 exp -22 to one, the same as the energy ratio E2/E1. All of the dimensionless ratios listed below will then be equal.
L4/L1, E2/E1, E3/E2, L1/L2, L2/L3
The product of the gravitational time dilation factor and the gravitational space contraction factor at the electron gravitational light orbit circumference will be (L1/L2) squared or (L2/L3) squared. Distance will shrink to match gravitational time slowing. The ratio (L1/L2) has a specific (fixed) value because the gravitational potential at the light orbit circumference of any size K-N black hole has a specific value. The gravitational potential determines the time dilation factor.
Time dilation factor=(L4/L2) exp 1/2
Time dilation factor=1.0250284x10 exp -22
The electron mass is then equal to (L2) exponent 3, times (1/2 pi) exponent 5, times (1/3G). Since 2(L2) is the electron Compton wavelength, the electron mass to Compton wavelength equation may be defined as shown.
m = (L2) exp 3, times (1/2 pi) exp 5, times (1/3 G)
Compton wavelength = 2(3G m) exp 1/3, times (2 pi) exp 5/3
In his Quantum Gravity book Lee Smolin writes, page 70; "In a sense, black holes are microscopes of infinite power which make it possible for us to see the physics that operates on the Planck scale". On page 75 he writes; "It (a black hole) is not an ordinary microscope, as it does not act by enlarging images of objects. Rather, it acts by stretching wavelengths of light". When the electron is analyzed as a black hole, the effective microscope power or wavelength stretch factor is found to be very large but not infinite. The wavelength stretch factor is equal to the ratio L2/L1 while space is also stretched by the same factor L2/L1.
The electron Compton wavelength is determined from the L4 circumference when L4 is multiplied by the wavelength stretch factor squared and the factor 2. The factor 2 is needed because a 720 degree rotation completes a spin cycle. The spin cycle probably consists of 360 degrees of expansion followed by 360 degrees of contraction.
Compton wavelength = L4(2)(L2/L1) squared
This Compton wavelength equation is exactly correct because the G value cancels when L4 is divided by (L1) squared. The (L1) squared value is 3pi hG/c cubed.
The next equation summarizes those previously described and points out the need for a more complete electron theory that includes gravity. Both sides of this equation are dimensionless ratios. They are either equal or very nearly equal. They could be like the Bohr magneton and the electron magnetic moment. These magnetic moment values are almost but not quite equal. The two sides will be precisely equal when the electron Compton wavelength is (4pi)times(3pi hG/c)exponent1/4 meters. Any correction factor that could apply to this wavelength definition is clearly very small. The electron mass is then equal to (h/c) divided by the electron Compton wavelength. This is the mass value (h/4pi c) times (c/3pi hG) exp 1/4,(previously noted). The Planck time is [(hG)/2pi(c)exp5]exp1/2 seconds. The m value is electron mass.
electron Compton wavelength divided by [4pi(3Gm/c squared)] =
2pi seconds divided by [(3/2)exponent 1/2,times (Planck time)]
When this equation is solved for the gravitational constant, it provides a value that is extremely close to laboratory measured values.
This precise value for G is proposed to be more nearly correct than any value that can be consistantly obtained with measuring equipment. Further work is needed to verify that this is true. The average of three gravitational constant values measured in 1942, 1972 and 1982 is 6.672x10exp-11. All measured values have significant uncertainty. Both sides of this equation are expected to be equal to the energy ratio E1/E3 and also equal to the gamma factor 9.5176171x10 exp 43 to one (proposed earlier to be a limit condition).
With the precise G value and electron mass known, the electron Compton wavelength is correctly defined by the following equation (previously described).
The Planck constant may then be defined as a function of the electron mass and the (precise) gravitational constant.
When Planck developed his radiation rule and his constant, during the time 1895 to 1900, his radiation quantum was unexpected and unexplained. A partial explanation was found later by Millikan (experiments performed 1909 through 1912) when the minimum fundamental charge (e) was defined. If an alternating current capable of radiating photon energy cannot be less than one charge per 1/2 cycle, then a space coupling resistance (R) can be determined that will provide the known photon frequency (f) to minimum energy ratio. The coupling resistance is 6453.2016 ohm. This resistance is much greater than 376.73032 ohms due to a relativistic impedance increase consistant with charge acceleration (c squared/r).
volts = 2e(f)x(R)
2e(volts)= (2e)squared, times (f)x(R)
h(f)= (2e)squared, times (f)x(R)
h/(2e)squared = R
h/(2e)squared = 6453.2016 ohm
2e(volts) = h(f)
The last equation also defines the Josephson junction, frequency to voltage ratio.
The product of the ratio (376.73032 ohm divided by 6453.2016 ohm) and the factor 1/8 is equal to the fine structure constant which is another dimensionless ratio. The attractive or repulsive force between two charges is determined from the space impedance value 376.73032 ohm while (at low non-relativistic velocity) the electron energy of motion (1/2 m v squared), the de Broglie wavelength and electron momentum are determined by the 6453.2016 ohm coupling impedance. The electron inductance to capacitance ratio is consistant with the 6453.2016 ohm value.
The electron mass (or energy) to Compton wavelength equation defines the known photon frequency to energy ratio.
From the evaluations described, a pattern of relationships is recognized that should be the basis for an improved electron theory. This new theory must take into account the electron gravitational field and explain why the electron mass is quantized. The pattern indicates that there is a specific time dilation limit, equal to the ratio (L1/L2)squared. The pattern also indicates that a stable K-N black hole will have equal time dilation factors that apply within and outside of the orbit circumference 2pi(3Gm/c squared). A detailed evaluation of K-N black hole properties is expected to confirm this.
Electron spin is a property that is related to the concept of rotation but has no exact counterpart in the classical world. The spin of a K-N black hole includes significant inertial frame dragging and time dilation so there is no classical equivalent. Electron spin explains the gravitational acceleration of an electron toward an external mass. The gravitational lens effect (from the external mass) bends the path of the spinning electron field ever closer to the external mass with each rotation, provided the electron is not restrained by another force. The fact that electron spin is twice as effective in producing magnetic moment as it is in producing angular momentum is evidence linking the electron to the K-N black hole. Small black holes are generally believed to be unstable however, black hole theory predicts that a rotating black hole with maximal spin will not lose mass by Hawking radiation. Maximal spin is a requirement for stability.
The light velocity inertial frame dragging by a K-N black hole can make a confined electromagnetic wave appear to stand still. This is the condition needed to exhibit the quantized high charge voltage that we observe as an electron property.
When the electron is analyzed as a thin superconducting ring, angular momentum can be used to define a ring radius and a charge acceleration value. Angular momentum will be mass times velocity times radius. (The ring radius value defined will have a ring circumference equal to 1/2 of the electron Compton wavelength. This circumference matches the electron Compton wavelength because a 720 degree rotation is required to complete a spin cycle.)
h/4 pi = mcr
h/4 pi mc = r
4 pi mc/h = 1/r
c squared/r = acceleration
4 pi m c cubed/h = acceleration
A charge with this acceleration will have elevated temperature as shown. The K value is the Boltzmann constant.
T = (1/K)x(h/2)x(1/2 pi c)x(acceleration)
T = (1/K)x(h/2)x(1/2 pi c)x(4 pi m c cubed/h)
T = (1/K) m c squared
T = 5.9298899x10 exp 9 deg Kelvin
A charge raised to this temperature will have energy equal to 5.1099889x10 exp 5 electron volts. The only way that this angular momentum and associated acceleration can be sustained with stability is by gravitational collapse with the critical energy density for gravitational confinement attained. With this condition, angular momentum is a conserved quantity. The elevated charge temperature due to acceleration, is related to the Unruh effect.
Spin is a requirement for electron stability. This spin is due to inertial frame dragging. In accordance with black hole theory, a black hole electron will not have elevated temperature if it has maximal angular momentum. When an electron and positron merge, their angular momentum values, with opposite sign, will be added. The sum of the two angular momentum values is zero so each particle will immediately become hot and lose all of its mass energy by Hawking radiation. The particles will convert from mass energy to photon energy. The radiation will usually consist of two photons but may, at reduced probability, consist of more than two photons. Electrons with the same charge will not merge because they repel with increasing force as they approach closer together.
Faraday used the principle of symmetry when he asked; if electricity produces magnetism, does magnetism produce electricity? Using this principle we can ask; if an electric charge can produce an electromagnetic wave, can an electromagnetic wave produce a charge? The answer is yes but the wave must produce a pair of opposing charges and each charge will require its own gravitationally confined, or gravitationally collapsed, electromagnetic wave. It follows that each charged particle produced will have a specific minimum mass value that is consistant with the charge it carries.
A quantized mass value based on the L1 photon wavelength provides an explanation for the fact that all electrons have the same mass. Some theorists who believe the Planck units play a fundamental role in subatomic particle physics will find that the gravitational collapse concept supports this belief. Since there is no other explanation for the quantized mass of the electron, gravitational collapse must be evaluated. Also, there is no logical reason why the electron mass is equal to (electron Compton wavelength/2) cubed, times (1/2 pi) exponent 5, times (1/3 G) if the electron is not a gravitationally confined entity. The Dirac description of the electron is not complete because it does not take into account the electron gravitational field.
The reader who has an interest in modeling the electron as a small black hole will want to read the paper "The Dirac-Kerr electron" by Alexander Burinskii, Gravity Research Group, NSI Russian Academy of Sciences, B. Tulskaya 52, 115191 Moscow, Russia. Burinskii writes (page 1) "The Kerr solution has a fundamental meaning, penetrating all the regions of theoretical physics from cosmology to superstring theory. Interest to the Kerr solution in the physics of elementary particles has been raised recently by the conjecture that black holes may be created in the laboratory conditions".
My published material includes the small book: "A Gravitational Collapse Model of the Electron". Copyright 2001,Library of Congress Control Number: 2002103999.
This book provides a new equation defining electron mass and other evidence suggesting that the electron is a gravitationally confined entity. In 2005, Alexander Burinskii published information showing that electron angular momentum is so great that it does not have an event horizon. It is a gravitationally confined ring singularity with no (black hole) event horizon. The electron has some but not all of, the properties predicted for a black hole. Though the book includes some errors, the electron mass equation is believed to be correct as shown.
I advised Alexander Burinskii (3/30/2009) and Leonard Susskind (4/20/2009) that nature's electron mass code is broken. The electron is gravitationally confined as Burinskii, Susskind, Greene and many other theorists anticipated.
electron mass = (h/4pi c) (c/3pi hG)^1/4 kilogram
applicable G value = (Le/4pi)^3 (1/2pi)^2 (1/3m)
The (Le) value is the electron Compton wavelength and (m) is the electron mass. See http://www.absoluteastronomy.com/discussionpost/Electron_as_a_ring_singularity_56595 See, http://www.absoluteastronomy.com/discussionpost/Relationship_of_electron_mass_to_Planck_mass_particle_96506908 Also see http://donjstevensaolcom.blogspot.com/2010/02/gravitationally-collapsed-electron.html