Bruce, Billy asked a question that clearly crosses the boundary between GR and QM. You continually ignore that and try to respond by saying, GR says....
Please give some hint, at least, as to where I brought in ANYTHING to due with QM into the question. For example let X be either a tiny dust particle OR a photon.
I asked: If two Xs were traveling initially on parallel paths only a micron apart, do they gravitationally (or warp space ) to attract each other?
If X = tiny dust particle, or even just a proton, then clearly the correct answer is: Yes.
If X = photon then answer to whether or not they attract each other is: "Yes" if photons do slightly warp space (make a tiny gravitational field that moves with them); but if they don't, then the answer is "No."
Brucep repeatedly refuses to give a clear Yes/No answer. He wants to explain things, speak of geodesics, or claim the answer is mixing GR with QM.
Just because in one case the two Xs are identical photons does not imply it is a QM question. This question could be asked when Planck quantized light - before the even was any QM theory!
Brucep's post 374 begins with: "The photons energy and momentum contribute to the local spacetime curvature. The local spacetime curvature is the gravity...."
My reply in post 375 begins with: "{that} sounds like: Yes, two identical photons traveling parallel to each other at least initially only 1 micron apart for many years do attract each other, ..."
I. E. He forced me to
guess his start of post 374 was a long winded "yes" answer, but then in post 376 he comment on my 375 with:
"No I didn't say anything like your first paragraph (of post 375}. You're Mixing up domain of applicability. GR is a classical theory of gravity and doesn't make any predictions for quantum phenomena. ..."
So I still have no clear answer from Brucep to a simple classical question about photons as a source of very weak gravity. Likewise, I have no idea what QM phenomena he eludes to (And I am quite well educated in QM.)*
If you agree with brucep that I am discussing or asking about QM, please tell why and is the question with X = tiny dust particles also a QM question?
* As evidence of that education, from post 375:
I know QM rather well - I have done calculations of its effects even in the original matrix formulation as well as with Schroder's equation formulation! ...The first classical QM problem any graduate student does is to compute the permitted energy levels of a particle in a box with infinitely high potential walls, then usually one wall is made finite so you can calculated the "tunneling effect." Next you may derive the uncertainty principle,* probably about at this stage you will mathematically watch a mixed state (sum of two weighted eigenvectors) evolve, etc.
For all of this Feynman diagrams are basically useless. I never used them in my first QM course - they find application mainly in nuclear interactions where "virtual particles" are important and you need to consider all possible sets of them. ...
Also note my Ph.D. was an experiment investigation of spectral lines from the Argon ion** - how they were shifted and broadened when the ion radiator was part of high density plasma. - Not even in doing that was ANY quantum mechanical analysis required, nor was any required when I measured the length of some Sodium D lines as ~30 cm.
BTW, don't say: "Anything very small is a QM question." (The proton is at least 1000 times smaller than any atom and all photons are at least a few cm long 1,000 times typical atomic radii!) So that silly reply means you need both GR & QM to know if two carbon atoms near each other gravitationally attract each other.
** Hans Griem had just worked out the theory for these effects for neutral radiators. He had guessed they would be larger for an ion radiator*** - I was first to confirm that. One of the lines I accurately measured the wave length of (with Fabry Perot interferometer cascaded with common spectra graph to "order separate") was displaced by more than an Angstrom.
*** Because a passing electron would curve some due to the ion's positive charge and thus be "near by" the ion longer than if it was passing a neutral. I guessed that the effect would be largest if I made a relatively cool, but 100% ionized plasma. So I did that.