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 Draft - Sept 3, 2002 - Richard Collins

The gravitational energy density at the earth's surface is approximately 5.73x10^10 Joules/m^3 or 57.34 gigajoules/m^3.  The gravitational acceleration at the earth's surface is about g=9.806 m/s^2 and the energy density is g^2/(8*pi*G).  (reference Robert Forward's dissertation)

The magnetic field that would be required to produce a magnetic energy density equal to the earth's field is 379.62 Tesla.  The magnetic energy density is U=B^2/(2*mu0), where mu0 is 4*pi*10^-7.  At present this magnetic field can only be reached by pulsed fields, and by intense multibeam lasers in the presence of a magnetic field. (Jackson, Landau & Lifshitz, others.)

The electric field that would be needed to create an energy density equal to the earth's gravitational energy density is 113.81 GeV/m.  E = c*B. (Jackson, L&L, etc)

A blackbody radiation cavity would need to be heated to 4.17 million Kelvin to have the same energy density as the earths gravitational field.  The radiation "temperature" at the peak of the curve is 1263 eV per photon. (Allen)

A laser (counter-propagating lasers) would need to have an intensity of 1.72x10^15 watts/ cm^2 to have the same energy density as the gravitational field at the earth's surface.  I = U*c. (induced transparency, 1000T, electromagnetic crystals, desktop accelerators and fission reactors)

Expressed as a pressure, the gravitational energy density is 565 thousand atmospheres, or 57.34 gigapascals.  The superconducting gravimeter reading are correlated with atmospheric pressure.  Pressure is in some circumstances equivalent to gravity in that it can slow atomic clocks.  The response is dependent on the nuclear structure of the matter and the manner of application of pressure.  The response of electron-capture radioisotopes can be related to the change of time of clocks with a gravitational field, or gravimeter readings with atmospheric pressure. (Gravimeter Network, Segre, 

The gravitational field can be readily measured by a range of gravimeters, including superconducting gravimeters.  The nanogal, picogal, and femtogal are convenient units.  Atomic fountain and atomic interferometry should allow several orders of magnitude improvement.  There are gravity gradiometers, and soon to be gravimeters in orbit, imaging the oceans and crust.  The network of superconducting gravimeters can be calibrated with the ephemerides of the sun, moon and planets, and can then be used to provide routine positions.  These gravimeter readings complement the data anticipated for the gravitational wave detectors.  Complementing these is the data from the GPS and global network of timekeepers and deep space time keepers, all who keep track of slow variations in gravity and absolute velocity to make appropriate general relativistic corrections - now the largest component to the "errors" in the atomic and other clocks.  Gravimeters are currently single axis, but can be built to provide 3-axis readings, then individual gravimeters can be calibrated against the moon.  The network can be calibrated by using the gravity data on the moon to improve precision.  The gravimeter array can see changes in the earth-sun distance, and might be made sensitive to the helioseismic oscillations of the sun and their corresponding mass and gravitational changes.  The precise measurement of the time of arrival of the peak of a gravimeter can determine a bound on the speed of the gravitational interaction.  Since the gravitational field changes during a solar eclipse, then more precise constraints on timing and shape of the field can be made.  This is probably the fastest way to check.

It is hard to get used to the idea of being in an intense radiation field, but once one realizes that the field is nearly isotropic in the horizontal plane and the gradient along the vertical is very gradual, it begins to make more sense.  Also the laser trapping experiments are showing the delicacy with which atoms can be manipulated by intense fields.  Pressures above the gravitational energy density are routine these days.  Lasers and particle accelerators can reach well beyond the earth's gravitational field.  But the fusion reactors are not accounting for gravitational field changes, especially if there is a critical field transition when the electromagnetic energy density matches that of the earth's gravitational field.  An interesting experiment would be to use a spherical or cylindrical cavity excited by electromagnetic energy to do a type of sonoluminescence experiment in a vacuum.  Matter seems to be a catalyst.  Magnetic fields seem to help.  Lasers must be counter-propagating.  Local seismic, gravity, atmosphere, electromagnetic and other sources must be tracked.

A 10 telsa field will readily support a frog by diamagnetic levitation.  If we could dissect the frequencies of the electromagnetic field whose properties were equivalent to a "static" magnetic field, we would have much better constraints on the gravitational field and vacuum fluctuations.

I wonder if we use lasers to boil the vacuum?  What is the heat capacity of the vacuum?  It takes approximately 10^22 joules/m^3 to boil out an electron-positron pair.  This is about 1.66 million tesla or a laser intensity of 3.65x10^17 watts/cm^2.  Probably has to be in the vicinity of a nucleus?  No wonder it looks like a wave and particle.

Are there gravitational winds?  When the earth rotates in the field of the moon and sun, is the gravitational field flowing like a fine fluid?

What is the meaning of the vacuum resistance?  During beta decay does the electron entrain the gravitational field?  The special relativity relation between velocity and energy, and the synchrotron radiation remind me a lot of shock waves and viscous (non-linear) effects.  How much energy is going out as gravitational radiation?  How fast is the gravitational interaction propagating?  It looks a lot like the "gravitational interaction" obeys a plasmahydrodynamic equation supporting a range of wave solutions.  

The gravimeters and accelerometers use macroscopic masses to track the earths gravity.  Can atoms be used instead?  The gravity field probably supports frequencies across the board.  There should be gravitational energy from frequencies of 10^-20 hertz to 10^20 hertz, but the most important probably are captured in the tidal modes already tabulated.  The frequencies corresponding to radio, laser, microwave, infrared, and so forth still have to be investigated and will require tracking a small mass, or a large number of small masses.  Lots of options. 

The acceleration of any ordinary mass cannot be separated from the electromagnetic waves it creates.  A neutral hydrogen atom that is accelerated gives off radiation from each of the electrons and protons in the molecule.  The effect is small at large distances, but it is always there.

The neutron is a close proton-electron pair held together by magnetic (primarily dipole) forces.  The electron is relativistic and the charge is primarily magnetic.  The orbital magnetic moment of the electron and that of the proton are aligned.  There are several spin states that might be stable, especially in nuclei.  This model of the neutron allows for mixing of protons and electrons.  The "outer electrons" are somewhat interchangeable with inner or core electrons.  Just do the numbers. My point is that even the neutron is basically a proton-electron pair.  Its acceleration should generate a pair of waves.  The gradient of the velocity should often exceed the average energy density of the gravitational field, then gravitational waves will be excited.  But the gravitons, if the photons of the field can be called that, are moving at about c^2 most of the time, so it is very difficult to excite a large coherent signal of any strength.  The experiments with large pulsed fields are probably doing something, but I am not sure what.

The energy density inside nuclei is comparable to the energy density at their creation.  There is a useful gravitational radius that can be defined for particles on the earth's surface where the energy density of the nucleus is equal to the average gravitational energy density.  Inside that radius, the nuclear properties dominate.  Outside, it is gravity, magnetism and electromagnetism primarily.  As gamma ray lasers get more powerful, then it won't matter.  Mostly the earth's gravity cuts off at about 1.26 keV.  One should see the changes in the earth's gravity in the rate of radioactive decays, in diurnal changes in the fluctuations of fission reactors, in the changes in the rate of atomic clocks.

It still remains to bring together the exact form of the relation between the effect of velocity and of gravitational field on radioactive decay.

The charge parity experiment has an asymmetry because the electron is diamagnetic.  It is not more complicated than that.

It would be a good idea to make a gravitational potential, energy density map of the solar system.

The neutrino detectors, the QCD vacuum, zitterbewegung, neutron beta decay, Casimir and other experiments can be combined with gravimeter, clock and gravitational radiation data to put limits on the spectrum of gravitational fluctuations at the earth's surface.

The gravity field of the earth, the positions of the moon, sun, planets and nearby bodies are fairly well monitored and reported.  From these the superconducting network and other networks can be calibrated for gravitational astronomy.  Once calibrated, the whole network can image the sun, moon, and planets to tune further.  The gravitational network should be able to image the center of the galaxy.

 

Terms: The physical vacuum (725), the QCD vacuum (538), excited vacuum (34), nuclear matter at finite temperatures (14), hyperfragment formation (16), nuclear theory (13,718), true physical vacuum (2), the vacuum structure (198), vacuum structure (842), photon-photon scattering (171), QED properties of the vacuum (1), vacuum condensate field (1), the quark vacuum (10), quantum vacuum (9,039), vacuum polarization (1,404), pair production instability of the vacuum (1), critical QED field strength (1), quantum chromodynamics (17,121), 

Terms: quarks (232,245), quark spectrum (),

The general theory of relativity describes changes in the background metric. But real gravitational fields are not static, so on the scale of the earth the field changes from location to location, from moment to moment, and seems to have variability comparable to electromagnetism. That is, there are ultralow frequency changes which occur on the scale of millions of years, thousands, hundreds, tens, years, months, days, hours, minutes, seconds, milliseconds, microseconds, nanoseconds, picoseconds, femtoseconds, attoseconds and smaller.  The gravitational field at the earth's surface is extremely dense, very fine grained, but noisy.  Intermixed with the gravitational field changes are magnetic, aerodynamic, electromagnetic, electric, acoustic, seismic, thermal, and high energy noise sources. To sort them out, it is helpful to pay close attention to the frequency, size, and types of energy. 

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