Newtonian gravity is an extremely precise approximation for weak gravitational fields. In quantum field theory we study scattering between particles whose mass is very small. Their gravity is very weak. Consequently, newtonian gravity should be an excellent approximation for scattering processes of particles.
A graviton is not completely analogous to a photon. A real graviton carries a mass-energy, that is, a gravity charge. A photon is electrically neutral.
The polarization of the graviton in general relativity is a 4 × 4 matrix and its spin is assumed to be 2. In newtonian gravity, the spin of the graviton probably is 1 because it is analogous to a photon.
Let us study interactions between photons and gravitons in newtonian gravity.
photon ~~~~~~~~~~~~~~
|
| graviton
|
photon ~~~~~~~~~~~~~~
Tree-level "Coulomb scattering" in newtonian gravity is a very simple process, just like in QED.
Vacuum polarization
What happens in vacuum polarization?
photon ~~~~~~~~~~~~~
| graviton q
__|__
/ \ virtual photon
k \______/ q - k
|
| graviton q
photon ~~~~~~~~~~~~~
In QED, the virtual pair pulls both charges together. In the diagram above, one of the virtual photons might have negative mass-energy. Is this allowed? There exist no "positrons" for gravity. No known particle has a negative charge in gravity.
If a virtual photon has zero mass-energy, then its interaction is zero and it cannot participate in the diagram.
Let us assume that negative mass-energy is allowed. If the virtual pair is located between the photons, it pulls one photon and pushes the other. That does not work.
● photon
+ positive energy virtual
photon
● photon
The configuration where the positive energy photon is between the real photons, increases the pull of gravity. But where do we put the negative energy virtual photon? It is hard to find a place where momenta and angular momenta gained by the virtual pair would cancel.
The effect of vacuum polarization in QED is quite small relative to Coulomb attraction. It might be that the effect in newtonian gravity is negligible.
What happens at a black hole horizon?
In general relativity, close to the event horizon, the pull of gravity is immense for a static observer. This has made some people to think that there might be powerful quantum effects there.
In newtonian gravity, for an external observer, all non-gravity forces have grown extremely weak there, while the inertia is larger than in faraway space.
In astronomical black holes we observe huge radiation from the accretion disk, but there is no evidence of similar radiation from the event horizon. If we hold the view that the frame of the external observer is the "true physics" of the events, then the horizon seems to be quiet.
In practice, observers close to the horizon are in a free fall. General relativity says that they will not see anything special. In the frame of the external observer, the falling matter slows down and never reaches the horizon. This all suggests that there are no powerful quantum phenomena at the horizon.
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