Literature says that quantum gravity is non-renormalizable. What that exactly means is somewhat vague. QED is certainly not renormalizable at a Landau pole, where the vacuum may collapse. In gravity, a black hole horizon might involve similar problems.
One may ask if physicists are interested in scattering experiments with gravity at all. In particle accelerators, gravity can be ignored.
The interesting things in quantum gravity happen with black holes. A black hole is a bound state. Feynman diagrams do not handle bound states. Non-perturbative physics is what interests physicists in quantum gravity.
Thus, renormalizability is not that central in quantum gravity. Anyway, we are interested in learning what kind of behavior will happen in hypothetical scattering experiments with 10^28 eV particles, at the Planck energy.
We have powerful tools available in optical gravity and in our analysis of QED classical models and regularization. We believe that we will be able to solve some mysteries of quantum gravity in this blog.
Classical model of scattering
Just as in QED, we need to understand the role of virtual particles in scattering. We need a classical model to figure out what is going on.
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v neutrino
We let an electron and a neutrino collide. The electron has an enormous kinetic energy in the Planck energy 10^28 eV range. We assume that the rest mass of the neutrino is negligible compared to the electron. Let the neutrino be initially at rest in the laboratory frame.
If we have an inertial frame which moves with the electron, the electron has just its rest mass in that frame. It is not a black hole.
The behavior of two colliding point masses is probably an open problem in general relativity. Let us study it more. The electron travels essentially at the speed of light.
The neutrino may come within the calculated Schwarzschild radius of the electron kinetic energy. But in the electron rest frame, the neutrino passes the electron much further away than the calculated Schwartzschild radius of the neutrino kinetic energy.
Our conclusion is that the neutrino cannot get captured by the electron gravitational field. Is the effect on the neutrino actually negligible? In the electron rest frame, the neutrino is like a photon which is slightly deflected in the field of the electron. Suppose that the neutrino passes the electron at the distance of one Planck length. How big is the deflection?
https://en.m.wikipedia.org/wiki/Gravitational_lens
The angle is
4GM / (r c^2) = 2 * 10^-22.
In the rest frame of the electron, the neutrino attains a vertical speed of 6 * 10^-14 m/s.
We assumed that the kinetic energy of the electron is the Planck energy 10^28 eV. Let us divide it by the rest mass of the electron. We get 2 * 10^22. That is the Lorentz factor. If we multiply this by 6 * 10^-14 m/s, we get 12 * 10^8 m/s, which is four times the speed of light. Why? We assumed that the speed of the neutrino in it its original rest frame in the x direction stays zero. In fact, the neutrino will fly at almost the light speed to the direction of the positive x-axis.
The collision with the electron does not suck the neutrino in a black hole, but the neutrino will speed up to almost the speed of light.
What about a collision of two equal mass particles? Can they form a black hole? If the kinetic energy of the particles is turned into other particles, and those other particles remain in the collision area, then a black hole might form.
What if we only assume general relativity? Maybe enough energy is converted into gravitational waves, and that energy lingers in the collision area long enough, so that a black hole forms? The Vaidya model of escaping photons speaks against this possibility.
https://en.m.wikipedia.org/wiki/Vaidya_metric
The particles themselves are so light that their rest mass cannot form a black hole. If the particles start to orbit each other, retaining their huge kinetic energy, that is another way to concentrate enough energy in a small area. Then a black hole might form.
We see that open problems in general relativity are an obstacle to our classical analysis of the collision.
If we have an inertial frame which moves with the electron, the electron has just its rest mass in that frame. It is not a black hole.
The behavior of two colliding point masses is probably an open problem in general relativity. Let us study it more. The electron travels essentially at the speed of light.
The neutrino may come within the calculated Schwarzschild radius of the electron kinetic energy. But in the electron rest frame, the neutrino passes the electron much further away than the calculated Schwartzschild radius of the neutrino kinetic energy.
Our conclusion is that the neutrino cannot get captured by the electron gravitational field. Is the effect on the neutrino actually negligible? In the electron rest frame, the neutrino is like a photon which is slightly deflected in the field of the electron. Suppose that the neutrino passes the electron at the distance of one Planck length. How big is the deflection?
https://en.m.wikipedia.org/wiki/Gravitational_lens
The angle is
4GM / (r c^2) = 2 * 10^-22.
In the rest frame of the electron, the neutrino attains a vertical speed of 6 * 10^-14 m/s.
We assumed that the kinetic energy of the electron is the Planck energy 10^28 eV. Let us divide it by the rest mass of the electron. We get 2 * 10^22. That is the Lorentz factor. If we multiply this by 6 * 10^-14 m/s, we get 12 * 10^8 m/s, which is four times the speed of light. Why? We assumed that the speed of the neutrino in it its original rest frame in the x direction stays zero. In fact, the neutrino will fly at almost the light speed to the direction of the positive x-axis.
The collision with the electron does not suck the neutrino in a black hole, but the neutrino will speed up to almost the speed of light.
What about a collision of two equal mass particles? Can they form a black hole? If the kinetic energy of the particles is turned into other particles, and those other particles remain in the collision area, then a black hole might form.
What if we only assume general relativity? Maybe enough energy is converted into gravitational waves, and that energy lingers in the collision area long enough, so that a black hole forms? The Vaidya model of escaping photons speaks against this possibility.
https://en.m.wikipedia.org/wiki/Vaidya_metric
The particles themselves are so light that their rest mass cannot form a black hole. If the particles start to orbit each other, retaining their huge kinetic energy, that is another way to concentrate enough energy in a small area. Then a black hole might form.
We see that open problems in general relativity are an obstacle to our classical analysis of the collision.
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