The classical gravitational radiation of Atoms:
Over the course of the lifetime of the universe, the Hydrogen atom releases 8 eV of energy as gravitational waves. So if its in a bath of these waves, then the loss would be much less – virtually zero.
For large atoms one would think that this energy exchange would be bigger. Of course ‘the actual path’ of the electron matters. The base energy level of an electron
Einstein in 1916 when wrote:
“Nevertheless, due to the inner-atomic movement of electrons, atoms would have to radiate not only electro-magnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.”
Why did Einstein worry about something that would effect the lifetime of an atom on time scales of the universe vs the tiny amount of time that a classical hydrogen at radiates EM energy?
Possibility of measuring something here.
- Get a lot of heavy atoms in ‘sync’ (NMR?)
- Radiating some amount of GR away, perhaps measure that on another bunch of similarly prepared atoms?
- ??? likely nothing…?
Also related — ? http://arxiv.org/abs/0708.3343 Thermal gravitational waves. 80 MW from the Sun, from atoms sliding near each other.
Its also easy to see that the resulting model is fully compatible with relativity and GR. Its after all made entirely out of gravity.
Calculation – watts emitted from one mole of uranium atoms (~200 grams of
uranium
)
- Use formula for watts emitted by a rod of mass m rotating at a frequency.
- http://www.twinkletoesengineering.info/atoms.htm
- So the uranium inner orbit has a velocity of 0.5c and a radius 1/8 that of hydrogen
- http://www.wolframalpha.com/input/?i=(0.5*c)%2F(2*pi*(hydrogen+atom+radius)%2F8)
- So we have 7.3e18 Hz and a radiative power of 10^-23 watts
Take this radiated power, and assume that uranium is thus in a bath of GR waves at 10^19 hz, so that it emits on average the same amount that it absorbs, (like SEDs only a lot easier to imagine).
Experiment: Now take a semi-sphere of uranium and put a test mass in the middle. If its uranium (i.e. tuned to the neighbouring shell) it will feel some force, but if its something with a different material and hence different frequency pattern of gravitational waves, it will not feel the force from the shell. Better experiment: Two massive plates, one uranium or lead, the other with a different material of same mass but different inner orbital frequencies. Then hook up one of those torsion threads to two balls on an arm, one of each material, and look for a rotational force. (Using some with force materials).
Classical Nucleus – nucleus GW interaction.
Iron nucleus – speed of nucleons is (20 MeV kinetic energy) and say one pair is radiating Gravitational waves: r = 1 fm, so
I get about 1e-25 watts or so. (using this) . Model is that nucleons are moving about in the nucleus, and at times have a quadrupole motion, which is on the order of a bar of mass 2 nucleons, spinning about a fm apart at the 10^23 hz of the nucleon rotational period in a fermi gas model nucleus. (Note that the Sivaram and Arun paper about thermal gravitational radiation from neutron stars shows about a billion times less than this.
Taking 1e-25 watts – which is 10e-7 eV/second I can calculate the pressure between two 10kg masses 0.1 metres apart, I get 10^-10 newtons. This is about the right amount of effect to mess up all the newtonian gravitational constant experiments.
Using Pressure = E/c , where E is in Watts/metres^2 and 1e-25 watts per nucleon emitted, assume complete absorption. (not cross section is assumed about the physical size of the nucleon, which is also the gravitational wavelength). Then we get the 10^-10 newtons.
Gravity force between 2 10kg masses at 0.1 apart is 6.7e-7 Newtons.
This force is not the nuclear strong force or the electromagnetic force, (which are stronger) but simply assuming that the nucleus can be treated classically for gravitational waves. The nucleons generate GWs which are can be absorbed by another nucleon of the same kind.
Andersen, T. C. on ORCID
General Relativity 