Hi Steven,
My turn to apologize. As you know, I've been preoccupied. You write:
"My remark about 'blustery' wasn't directed toward Petkov's essay at all; it was directed at those who contend that the non-renormalizability of the perturbation expansion of quantized gravity theory implies that gravity and quantization are 'mutually incompatible', and therefore that the REPLACEMENT of quantum theory, gravity theory, or both is REQUIRED -- a contention dear to the hearts of, inter alia, adherents of string theory (who after almost four decades of riding high are at very long last now entering their richly merited twilight era)."
Sorry I misunderstood. I'm not as critical of string theory -- as an extension of quantum field theory, it has after all shown us new rigorous paths toward reconciling a continuous field theory with discrete measurement functions that may not be possible to realize without extra dimensions.
"It in fact turns out that the non-renormalizability of the perturbation expansion of quantized gravity theory is due to NOTHING MORE than the gross misapplication to quantized gravity of perturbation expansion in straight powers of G: a little reflection quickly reveals that quantized-gravity transition amplitudes are non-analytic in G at the point G = 0, just as ANY quantum transition amplitude is non-analytic in hbar at the 'classical limit point' hbar = 0 (which is the reason why semi-classical approximations are NOT straight power-series expansions in powers of hbar, to do a straight power-series expansion about a non-analytic point is a transparent recipe for disaster, of course, which obviously has NOTHING to do with PHYSICAL CONTENT."
I agree. We've always known that if hbar is zero, the world is classical without boundary between quantum and classical events.
"For more detail see my paper,
http://arxiv.org/abs/0908.3024
Although Petkov calmly makes a point which SOUNDS not implausible at first reading, I HAVE TO BE SKEPTICAL because so many other competent physicists over a period of so many decades have theoretically argued for radiation from the Einstein equation. Certainly the LINEARIZED form of the Einstein equation is so VERY HIGHLY ANALOGOUS to the Maxwell equation that a universal ABSENCE of radiation would appear to be impossible."
However, is it necessary for gravity to be quantized in order to be gravitational? -- that's Petkov's question. Because in classical gravity particles do not resist their motion, do we really have warrant to believe that quantum particles resist their motion? If not, we should stop worrying about discontinuous energy jumps. I think Lucien Hardy is on to something, too, in that radiation without annihilation leads to a continuous (field) description of attractive phenomena -- "I anticipate that quantum gravity will be a theory having indefinite causal structure whereas quantum theory has definite causal structure." Which plays into your next comment, and I am going to leave off at this point because it is as far as I'm willing to go at the moment:
"Now Steven Weinberg lays great emphasis on the fact that the idealized local 'freely-falling frame' is a matter of SCALE. EVEN in electromagnetism there is a 'near zone' where a field is NOT RADIATIVE -- electromagnetic radiation can ONLY actually be ASCERTAINED sufficiently FAR AWAY from its source. Recall that gravitational TIDAL forces can COEXIST with the idealized local freely-falling frame concept PRECISELY BECAUSE of that hierarchy of SCALES which Weinberg so strongly emphasizes. Thus I am highly inclined to think that gravitational radiation, which, LIKE electromagnetic radiation, could only be ASCERTAINED over a SUFFICIENTLY large SCALE, can ALSO peacefully COEXIST with a local freely-falling frame conception that is 'hemmed in' to a much SMALLER SCALE than the WAVELENGTH SCALE of that gravitational radiation."
All best,
Tom
"So I guess my answer to Petkov is that gravitational radiation is NOT prima-facie any more antithetical to the idealized local freely-falling frame concept than are tidal gravitational forces: BOTH tidal gravitational forces AND gravitational radiation can be reduced as much as one wishes by CONFINING OBSERVATION to SUFFICIENTLY SMALL local freely-falling frames. In other words, I suggest that Petkov reread and take very seriously the Weinberg HIERARCHY OF SCALES idea in CONJUNCTION with the strong Principle of Equivalence -- see Weinberg's celebrated 1972 textbook on General Relativity and Cosmology. I must say that Weinberg seems to be an amazingly perceptive physicist.
I think you can now see that when I concluded that QUANTIZATION of gravity is largely IRRELEVANT to the functioning of the universe, I did so for reasons that are QUITE DIFFERENT from those of Petkov. In particular, although the GREAT BULK of gravity is INDEED non-dynamical, I see no theoretical (or observational) reason to DOUBT that gravity AS WELL has a (relatively much less important) dynamical RADIATIVE part that indeed IS, in principle, subject to quantization. For me the key controlling fact in this regard is that the very SMALL actual physical value of G DRIVES this quantized gravitational field theory very strongly toward its classical limit, which of course makes its quantization largely irrelevant. In other words, the NATURE of quantized gravity is such that it is driven toward its classical limit by EITHER taking the familiar hbar -> 0 limit OR by taking G -> 0. That is because the PRODUCT of G TIMES hbar SUPPLANTS the GENERIC occurrence of hbar on its own in key expressions of quantized gravity theory. Once again, for the details see my,
http://arxiv.org/abs/0908.3024
All the best, Steven
