There are certain coincidences which, we you first hear about them, you sit up all night thinking wild and crazy thoughts. I think my favorite example of this comes from the Kerr-Newman black hole. The Kerr-Newman solution to the Einstein-Maxwell equations describes black holes with charge and angular momentum. What is strange about the Kerr-Newman black holes? Suppose we examine the gyromagnetic ratio for these objects. The gyromagnetic ratio is 2Mm/QJ where M is the mass of the black hole, m is the magnetic moment of the black hole, Q is the charge of the black hole and J is the angular momentum of the black hole. For a Kerr-Newman black hole (and for many other charged solutions in general relativity) the gyromagnetic ratio is exactly 2. Sound familiar? Well it should, because this is the value of the gyromagnetic ratio for a Dirac electron (there are some claims that this value of 2 is a triumph of relativistic quantum field theory, but it must be said that there are nonrelativistic arguments for a value of 2 as well.) Talk about a strange and wonderful coincidence. Or more than a coincidence? So now you can spend the rest of the day worrying about whether the electron is nothing more(!) than a charge spinning black hole!
O brave new quantum world!
Also fun:
A new twist on the theory of black holes ( like here ) is to consider the quadropole rotational moments of the solutions. It seems that while mathematically more involved, it does lead to some new physics.
Is it possible to measure the “quadropole spin” of the electron with the current technology? If it exists, what will it couple to in terms of the EM fields?
Back to marking…
Indeed the triumph of QED is that is not exactly 2. But in the early days following the discovery of the Dirac equation, there were claims that this was one of the triumphs of Dirac’s equation. I think there may be a discussion of why the g=2 result (to first approximation) is not that strange by Feynman somewhere. I’ll have to look it up.
For a Kerr-Newman black hole (and for many other charged solutions in general relativity) the gyromagnetic ratio is exactly 2. Sound familiar? Well it should, because this is the value of the gyromagnetic ratio for a Dirac electron (there are some claims that this value of 2 is a triumph of relativistic quantum field theory, but it must be said that there are nonrelativistic arguments for a value of 2 as well.)
I’ve never heard the value of 2 being called a triumph of relativistic quantum field theory– the impressive thing is that it isn’t exactly 2, and QED lets you calculate the difference from 2 to something like ten decmial places, confirmed by experiment.
Plugging the electron’s charge, spin, and mass values into the charged Kerr solution doesn’t actually produce a black hole, but rather a naked ring singularity, the region near which gives rise to closed timelike curves through every point in spacetime. Maybe that’s why the flux capacitor needs 1.21 Jigawatts of (electric) power to do its thing.
I remember hearing that in the early 20s it was hoped that the Reissner-Nordstrom solution would be a useful model of the electron. I tried to find a little about the history of the idea, but I couldn’t find anything among the papers from the arxiv that had phrases along the lines of, “in order to get the right self-energy behaviour, we reverse engineer the Reissner-Nordstrom solution a little…”
When the electron is analyzed as a black hole we find that its mass is quantized. Its mass is required to be (h/4pi c) times (c/3pi hG) exponent 1/4 kilograms. The electron Compton wavelength is found to be 4pi (3pi hG/c) exponent 1/4 meters. The electron mass is a function of the Planck mass. See “Black hole electron” and “Talk:Black hole electron”- Wikipedia. It is hard to believe that this is just another coincidence.
The idea that the electron has much in common with black holes is supported by the writings of John Wheeler, Brian Greene, Malcolm MacGregor and the Russian theorist Alexander Burinskii. Wheeler evaluated the possibility that self-gravitational attraction could confine electromagnetic wave energy with his study of geons. He has written “What else can a particle (electron) be but a fossil from the most violent event of all, gravitational collapse?” This is his way of saying electrons and black holes have many similar properties.
Greene is the first theorist that I am aware of, who has said clearly, electrons are black holes. He said “–we see that black holes and elementary particles, like water and ice are two sides of the same coin”.
MacGregor has written, electron negative charge elements repel one another so that a force is required to hold the electron together. No combination of electric and magnetic forces has been proposed that can produce a stable state. He said that gravitational forces could solve the stability problem if the electron is extremely small and dense.
Burinskii has written the paper “The Dirac-Kerr electron”. He writes “–angular momentum J = h bar/2 for parameters of electron is so high that the black hole horizons disappear and the source of the spinning particle represents a naked singular ring.” This would violate the “cosmic censorship hypothesis” however some theorists (including Stephen Hawking and Kip Thorne) have recently concluded that the laws of nature do permit the formation of a naked singularity during gravitational collapse.
The derived electron mass formula, like the black hole entropy formula, contains the Planck constant as well as the gravitational constant, indicating that the electron mass value is the result of a quantum-gravitational effect.
Here is another strange and wonderful coincidence (or more than a coincidence). L1/L2 = L2/L3 = L4/L1 = (L4/L2)^1/2
L1 = 2pi(Planck length)(3/2)^1/2
L2 = 1/2 (electron Compton wavelength)
L3 = (2pi)^2 (c times one second)
L4 = 2pi(3Gm/c^2), where m is electron mass
The value L1 is equal to (L2)^2 (1/L3), so the L1 value (and Planck length value) may then be precisely determined. These relationships support the concept that the electron is a ring singularity without an event horizon as proposed by Alexander Burinskii. This electron model has some, but not all of the predicted properties of a black hole.
The electron Compton wavelength is 2(L2).
2(L2) = 2[(L1)(L3)]^1/2
2(L2) = 4pi(3pi h G/c)^1/4
The problems with electrons as black holes always come down to electromagnetism and quantum effects.
Perhaps the answer lies in letting both quantum phenomena and electromagnetism emerge as a result of gravitation.
There are ways to create forces much more powerful than simple gravity: Some forces can scale with frequency, just wind up a wave effect to 10e50 Hz and large forces can result.
Reply to Tom Anderson,
Quantized photon energy is a result of gravitation. The photon wavelength that is linked to electron mass energy is 2pi(Planck length)(3/2)^1/2 meters. This photon energy is equal to hc/wavelength and also equal to:
E = (wavelength)(c^4)(1/3pi G)
This photon, with this wavelength, is an effective model for all photons because photon energy is inversely proportional to wavelength. See “Quantum-gravitational effect” under “Talk:Black hole electron” Wikipedia.
Tom Andersen,
Here are some words by Leonard Susskind.
“In recent years we have been accumulating evidence that the machinery in the interior of particles (electrons) is not much bigger, nor is it much smaller, than the Planck length.”– “What this means is that down at the bottom of the world – distances so small that even electrons are complicated structures – gravity may be the most important force holding those particles together. So you see, gravity and Quantum Mechanics may well come together at the Planck scale and explain the properties of electrons, quarks, photons and all their friends”. (From pages 214 and 215 of his book, The Black Hole War, 2008)
I have advised three theorists including Susskind (4/20/2009) that nature’s electron mass code is broken. The electron radius is (3/2)^1/2 times the Planck length. The electron is gravitationally confined as Susskind, Burinskii and some other theorists anticipated.
Don Stevens
The Wikipedia article “Black hole electron” has recently been altered so that much of the information has been stripped out (deleted due to interpretation that it contained original research). Useful information is still present in “Talk:Black hole electron”.
Item #8, “Balanced pattern” (in Talk:Black hole electron) is significant because it shows that general relativity and quantum mechanics can merge without conflict. I will do all that I can to encourage further evaluation of this concept.
See book “The Elegant Universe” by Brian Greene, pages 320-322 subject, “Black Holes and Elementary Particles”.
Don Stevens