To close the present series on the integration of quantum mechanics with the forces of nature, today we discuss efforts to develop quantum theories of gravity (i.e., bringing together quantum mechanics and the gravitational force). According to a Wikipedia document on the subject:
At present, one of the deepest problems in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, planets, galaxies), with quantum mechanics, which describes the other three fundamental forces acting on the microscopic scale.
In his book The Fabric of the Cosmos, Brian Greene notes that:
Even though we don't have a successful theory combining the strong nuclear force and the electroweak force, all three of these forces (electromagnetic, weak, strong) have been described by a single uniform language based on quantum mechanics. But general relativity, our most refined theory of the fourth force, stands outside this framework (p. 329).
He further describes the situation mathematically:
If you use the combined equations of general relativity and quantum mechanics, they almost always yield one answer: infinity. And that's a problem. It's nonsense (p. 335).
More specifically, according to the Wikipedia:
Much of the difficulty in merging these theories comes from the radically different assumptions that these theories make on how the universe works. Quantum field theory depends on particle fields embedded in the flat space-time of special relativity. General relativity models gravity as a curvature within space-time that changes as mass moves. The most obvious ways of combining the two (such as treating gravity as simply another particle field) run quickly into what is known as the renormalization problem. Gravity particles would attract each other and adding together all of the interactions results in many infinite values which cannot easily be cancelled out mathematically to yield sensible, finite results.
The Wikipedia document goes on to list 13 candidate theories that could possibly provide the long-sought-after integration of quantum mechanics and the gravitational force.
In preparation for writing today's entry, over the holidays I read the book Three Roads to Quantum Gravity, by Lee Smolin. This review of Three Roads... from the Guardian provides an excellent overview of the book, to which I will just add a few thoughts.
As noted in the Guardian's review, the three "roads" that Smolin discusses are string theory, loop quantum gravity (LQG), and black hole thermodynamics. String theory has been written about extensively, including by the aforementioned Greene. I did not know much about LQG prior to reading Three Roads... and LQG is indeed a theory associated with author Smolin, so that is where I thought I would learn the most. I found Smolin's writing to be very conceptual, discussing ideas such as relational theories, the universe being "made of processes, not things," and "background independence." LQG struck me as being very geometrically oriented, with less discussion of how matter and other physical processes would fit in.
I will do full postings in the future on string theory, LQG, and black hole thermodynamics. The ideas involving black holes were the hardest for me to grasp, so I'll have to do a lot more reading on them; the following web document helps a bit.
Coincidentally, within days after I finished reading Three Roads..., I noticed a new special issue of Scientific American on "The Frontiers of Physics." The contents include an article on LQG by Smolin and an interview with Greene on string theory. I have enjoyed reading the articles thus far.
To conclude this series on the integration of quantum mechanics with the forces, here's a link to a University of Oregon page that concisely summarizes Quantum Electrodynamics, Quantum Chromodynamics, and Quantum Gravity, all within a single document.