mentioning further (online) reading
tenzin said:
Quantum theory of gravity
Does anyone know if the same field theory approach that was applied to the electromagnetic force (resulting in QED) has been attempted with gravity. This would entail ignoring GR and trying to develop a quantum field theory of gravity from scratch. Any insights?
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lethe said:
yes, this was tried. the theory is nonrenormalizable.
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tenzin continued:
Could you mention any further reading on this.
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tenzin's initial question was historical in nature
"does anyone know if a QED-style QFT has been tried with gravity?"
the history of attempts to quantize gravity goes back before 1960 and it is kind of interesting to see what people have tried. Appendix B of Rovelli's textbook "Quantum Gravity" is all about
the history
and a draft of it is online at Rovelli's homepage
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html
It is well worth the 10 minutes or so it takes to download and
convert the PDF file
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something like the idea tenzin suggests was tried at least as early as 1952
(see Rovelli page 292) and sometimes called the "flat space quantization"
as tenzin indicates it involves throwing out the basic GR idea of a dynamic changeable geometry and working with a fixed (in this case flat) background space.
after all, QED and other quantum field theories are built on a fixed background geometry, chosen at the outset, which makes them incompatible with General Relativity at a fundamental level. GR is background-independent.
tenzin, I would say that your question points up something very fundamental about approaches to quantum gravity---for 50 years or so there has been this split: some approaches are background-independent (like GR itself and like Loop Gravity) and some are not (like string/brane approaches, and that earlier QFT 1952 approach)
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In 1971, 't Hooft and Veltman start studying the renormalizability of GR and "almost as a warm-up exercise" (Rovelli page 295) they tackle Yang-Mills first---and this wins them the Nobel prize.
But by 1973 they have found evidence that gravity is not renormalizable----that is in this "flat space" or so-called "covariant", fixed-background field theoretical approach.
Calling this approach "covariant" is customary and I believe goes back to the fact that the usual flat space is Minkowski space, the space of special relativity---covariant here refers to the symmetries of special relativity.
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By 1975, Rovelli says, it is generally accepted that the flat space approach is not renormalizable. After that the history of quantum gravity divides into two streams
keeping GR and its basic ideas of background-independence and (smooth) invariance intact leads to several background-independent approaches such as Loop
trying to save the "flat space" approach of field theory and high-energy-physics, by replacing GR with something else (that reproduces GR at low energy limit) leads to Stringy theories.
Rovelli tracks the history of these two lines of research up to near the present.
A good description of the "Divide" is on page 302. It has quotes from representative people----a field theorist/particle theorist on one hand, a relativist (GR specialist) on the other. (Note that when Rovelli says "relativity" he means General R, not Special R.
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amazing how true that old proverb is about
those who don't pay attention to history
being doomed to repeat it
the 70 year history of quantum gravity is fascinating, I find,
and I kind of wish more people would look at Rovelli's
condensed outline of it. Pages 287-303.
