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Re: [Phys-L] GR and Gravitons



Oops! I realized I said something silly in my previous post. In the part where I wrote:

One big difference between GR & EM is that the physical fields
in GR are the 2nd derivatives of the potential fields, rather
than the first derivatives, as they are in EM. In EM the
A-potential components don't have a physical meaning themselves,
rather the E & B fields, which are the derivatives of the
A-potential components, are the physical force fields acting on
the charged sources and whose values are constrained by the
requirements of Maxwell's equations.

Actually the last part of the last sentence above is not correct. To be correct I ought to have said that Maxwell's equations constrain the values of the *derivatives* of the force fields rather than the field values themselves. Of course after solving for the fields for a given distribution of sources the field values are determined. But, nevertheless, Maxwell's equations themselves only locally relate the sources to the derivatives of the force fields and not the field values themselves.

In *both* GR and EM the sources are related to the derivatives of the force fields via the dynamical equations of motion for the fields. In the EM case the relevant sources are the locally conserved charge 4-current, i.e. charge density, rho & current density j. In the GR case the relevant sources are the various components of the stress-energy-momentum 4-tensor of the matter and radiation present, i.e. mass/energy density, energy current density/momentum density, and momentum current density/stress 3-tensor--being composed of the spatially diagonal axial compression/tensions and the off-diagonal shear stresses.

In spite of this problem I think I would still claim the physical fields of GR are the spacetime curvature components (involving derivatives of the Levi-Civita connection on spacetime), and the physical fields of the EM are the force-fields themselves, rather than their derivatives. This is mostly because in a freely falling frame all the Levi-Civita connection components vanish locally in a spacetime neighborhood coincident with the free-fall condition. It is hard for me to believe that an object which can completely vanish (albeit locally) in some subjectively chosen reference frames has an objective physical existence. The E & B fields (being components the field strength true 4-tensor) of EM do not have such a complete vanishing property. For them if all their components values completely vanish in any reference frame then they must all vanish in all reference frames. And if any such component is non-zero in any frame then in no frame do all of the components of these things vanish.

Dave Bowman