Gravity has been considered "non-renormalizable".
Optical gravity shows that the singularities in gravity are actually very tame. For an outside observer, anything which happens close to the horizon will have an almost infinite redshift. This is in contrast to the violent behavior which a Landau pole of QED would involve.
Maybe there is no need for any renormalization of gravity.
Suppose that we have a modest energy density in space, but some quirk makes it all to concentrate into a small spot. Then a black hole horizon will form and time will almost freeze in the spot. Can the mini black hole survive for ever, according to the principles of quantum mechanics? If not, then there is some kind of Hawking radiation.
An eternal black hole would be like a soliton wave in timespace. It would extend to infinity in the time dimension, though it would be finite in the space dimensions. Does such a wave make sense in quantum mechanics?
If any fermion can be scattered back in time by a boson, can that make any collection of fermions to evaporate eventually?
If every fermion is actually a huge vacuum atom loop, then eventually all collections of fermions will be broken. The fermion will return back in time as the antiparticle. A layman observer will think that an antiparticle arrived and annihilated the fermion, releasing bosons.
If there is a nonzero probability for a fermion to be scattered back in time, then eventually that should happen. Note that in this argument we assume that "causality" sometimes can flow backwards in time. The equation and the border conditions which govern waves in timespace may be such that we have to calculate or "create" the solution sometimes backwards in time.
For example, it might be that the only possible solution for a fermion is a loop in time. Then there would be a 100 % probability that some time in the future, every fermion will meet its antiparticle.
Laws of nature are symmetric in time, except for the law of increasing entropy. Entropy is the reason why we calculate solutions to physical systems starting from the past and building the solution towards the future on the time axis.
But there may exist principles that force us to calculate some solutions backward in time, too. A vacuum atom is a stationary state of spacetime. It might be that when we calculate the fate of an electron, we have to turn backwards in time at some point. That is needed if there is a non-zero probability of the electron to scatter back in time.
Some GUT theories speculate about proton decay, though in them the proton would decay without meeting an antiproton. But the decay could happen also by scattering back in time.
If every fermion forms a loop in time, then black holes will probably evaporate eventually, but the evaporation is much slower than Hawking claimed. Every fermion in the black hole will be annihilated by an incoming antifermion at some time. Only bosons will remain. Optical gravity predicts that all bosons will be reflected back from the forming horizon.
There would be no bound states in physics. Eventually every hydrogen atom, proton, electron, any fermion would get annihilated. Bosons cannot form bound states, not even in a black hole.
We have to study if there is some principle which causes a nonzero probability for a fermion to be reflected back in time.
Our speculative world model brings to mind the conformal model of Roger Penrose. He suggested that only bosons will remain eventually.
Conjecture 1. Every electron and positron will eventually be reflected back in time. That is, it will meet its antiparticle.
Sketch of proof. For a wave to propagate without any reflection, the wave equation has to be perfectly linear. But QED is not perfectly linear - because of the possibility of pair production.
Thus the wave equation of QED requires a slight flux which is reflected. Eventually, all particles are reflected.
Suppose that we have a plane wave which describes a flux of electrons in space going to the x direction. Since QED is seriously nonlinear, 2X that plane wave is not a solution.
Because of symmetry in space, the flux cannot be deflected in the z or y directions. It cannot be reflected in the x direction because momentum would not be conserved. The flux has to be reflected in the time direction.
When an electron meets a positron coming from the opposite direction of space, they can annihilate and produce photons. Momentum and energy are conserved. QED.
A photon can be reflected back in time. It meets its antiphoton, annihilates, and produces photons or pairs which will fly to opposite spatial directions.
Conjecture 1 defies our conception of causality. We are used to thinking that events cannot affect their past. But if we have a nonlinear wave equation in timespace, then necessarily present events have to affect the past, or the probability interpretation of quantum mechanics is broken.
Feynman in his 1949 papers noted the breach of causality, but he did not elaborate on it.
Corollary 2. An antiparticle has to exist for the electron and the photon. QED.
Feynman in some lecture said that the existence of a positron is a consequence of special relativity. Actually, the existence is dictated by the fact that the wave equation of the electron is not linear in timespace.
What about gravity? Gravity coupled to any particles is nonlinear. It can make a fermion reflect back in time. What about bosons? Gravity couples all particles together. A boson can be reflected back in time, and the annihilation may produce any particles, as long as energy and momentum conservation are respected?
We do not observe photons annihilating each other because the probability is infinitesimal.
The considerations in this blog post may bear on dark matter, dark energy, inflation, the Big Bang, matter-antimatter imbalance, magnetic monopoles, and so on. We need to think about them.
The Big Bang involves a singularity. Our philosophy is that singularities cannot exist. Also, nonlinearity requires that waves are reflected back. If the waves cannot go to a singularity, then there must exist a universe before the apparent Big Bang. The Big Bounce is the correct model then.
A vacuum atom is like a mini Big Bang where the pair is created, and then the Big Crunch where the pair annihilates.
An eternal black hole would be like a soliton wave in timespace. It would extend to infinity in the time dimension, though it would be finite in the space dimensions. Does such a wave make sense in quantum mechanics?
If any fermion can be scattered back in time by a boson, can that make any collection of fermions to evaporate eventually?
If every fermion is actually a huge vacuum atom loop, then eventually all collections of fermions will be broken. The fermion will return back in time as the antiparticle. A layman observer will think that an antiparticle arrived and annihilated the fermion, releasing bosons.
If there is a nonzero probability for a fermion to be scattered back in time, then eventually that should happen. Note that in this argument we assume that "causality" sometimes can flow backwards in time. The equation and the border conditions which govern waves in timespace may be such that we have to calculate or "create" the solution sometimes backwards in time.
For example, it might be that the only possible solution for a fermion is a loop in time. Then there would be a 100 % probability that some time in the future, every fermion will meet its antiparticle.
Laws of nature are symmetric in time, except for the law of increasing entropy. Entropy is the reason why we calculate solutions to physical systems starting from the past and building the solution towards the future on the time axis.
But there may exist principles that force us to calculate some solutions backward in time, too. A vacuum atom is a stationary state of spacetime. It might be that when we calculate the fate of an electron, we have to turn backwards in time at some point. That is needed if there is a non-zero probability of the electron to scatter back in time.
Some GUT theories speculate about proton decay, though in them the proton would decay without meeting an antiproton. But the decay could happen also by scattering back in time.
If every fermion forms a loop in time, then black holes will probably evaporate eventually, but the evaporation is much slower than Hawking claimed. Every fermion in the black hole will be annihilated by an incoming antifermion at some time. Only bosons will remain. Optical gravity predicts that all bosons will be reflected back from the forming horizon.
There would be no bound states in physics. Eventually every hydrogen atom, proton, electron, any fermion would get annihilated. Bosons cannot form bound states, not even in a black hole.
We have to study if there is some principle which causes a nonzero probability for a fermion to be reflected back in time.
Our speculative world model brings to mind the conformal model of Roger Penrose. He suggested that only bosons will remain eventually.
Conjecture 1. Every electron and positron will eventually be reflected back in time. That is, it will meet its antiparticle.
Sketch of proof. For a wave to propagate without any reflection, the wave equation has to be perfectly linear. But QED is not perfectly linear - because of the possibility of pair production.
Thus the wave equation of QED requires a slight flux which is reflected. Eventually, all particles are reflected.
Suppose that we have a plane wave which describes a flux of electrons in space going to the x direction. Since QED is seriously nonlinear, 2X that plane wave is not a solution.
Because of symmetry in space, the flux cannot be deflected in the z or y directions. It cannot be reflected in the x direction because momentum would not be conserved. The flux has to be reflected in the time direction.
When an electron meets a positron coming from the opposite direction of space, they can annihilate and produce photons. Momentum and energy are conserved. QED.
A photon can be reflected back in time. It meets its antiphoton, annihilates, and produces photons or pairs which will fly to opposite spatial directions.
Conjecture 1 defies our conception of causality. We are used to thinking that events cannot affect their past. But if we have a nonlinear wave equation in timespace, then necessarily present events have to affect the past, or the probability interpretation of quantum mechanics is broken.
Feynman in his 1949 papers noted the breach of causality, but he did not elaborate on it.
Corollary 2. An antiparticle has to exist for the electron and the photon. QED.
Feynman in some lecture said that the existence of a positron is a consequence of special relativity. Actually, the existence is dictated by the fact that the wave equation of the electron is not linear in timespace.
What about gravity? Gravity coupled to any particles is nonlinear. It can make a fermion reflect back in time. What about bosons? Gravity couples all particles together. A boson can be reflected back in time, and the annihilation may produce any particles, as long as energy and momentum conservation are respected?
We do not observe photons annihilating each other because the probability is infinitesimal.
The considerations in this blog post may bear on dark matter, dark energy, inflation, the Big Bang, matter-antimatter imbalance, magnetic monopoles, and so on. We need to think about them.
The Big Bang involves a singularity. Our philosophy is that singularities cannot exist. Also, nonlinearity requires that waves are reflected back. If the waves cannot go to a singularity, then there must exist a universe before the apparent Big Bang. The Big Bounce is the correct model then.
A vacuum atom is like a mini Big Bang where the pair is created, and then the Big Crunch where the pair annihilates.
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