I flipped through "the case for background independence" by Lee Smolin. Here is the link.

This article has very few mathematical formulas, if any; Lee Smolin explained everything in words. It was not easy to understand it. Probably, I should buy his book for laymen, "Three Roads to Quanum Gravity" to really understand what loop quantum gravity is. Or at least, I should read his review article on Loop Quantum Gravity.

My understanding of background independence is that a theory which is not background independent (i.e background dependent) has a fixed space-time as the background. That's as far as I could understand. I can't really imagine how one formulated Loop Quantum Gravity based on this principle. Also, in LQG, the spacetime is not continous but discrete. The author wrote that by this principle, the usual energy and momentum relation is modified to "E^2=p^2+m^2+lp E^3+...." which has a possibility of being verified by experiments such as AUGER and GLAST that probes planck sclae physics. (Wow, this is going to be exciting, if LQG is to be verified soon. And, I have never expected that I would see an experiment that probes planck-scale physics in my lifetime.)

Also, what makes LQG more worthwile to study is what Edward Witten said about background independence. According to the LQG entry on wikipedia, Edward Witten is quoted as writing in his article "Finding the right framework for an intrinsic, background independent formulation of string theory is one of the main problems in the subject, and so far has remained out of reach." ... "This problem is fundamental because it is here that one really has to address the question of what kind of geometrical object the string represents." (

http://arxiv.org/abs/hep-th/9306122

My understanding of background independence is that a theory which is not background independent (i.e background dependent) has a fixed space-time as the background. That's as far as I could understand. I can't really imagine how one formulated Loop Quantum Gravity based on this principle. Also, in LQG, the spacetime is not continous but discrete. The author wrote that by this principle, the usual energy and momentum relation is modified to "E^2=p^2+m^2+lp E^3+...." which has a possibility of being verified by experiments such as AUGER and GLAST that probes planck sclae physics. (Wow, this is going to be exciting, if LQG is to be verified soon. And, I have never expected that I would see an experiment that probes planck-scale physics in my lifetime.)

Also, what makes LQG more worthwile to study is what Edward Witten said about background independence. According to the LQG entry on wikipedia, Edward Witten is quoted as writing in his article "Finding the right framework for an intrinsic, background independent formulation of string theory is one of the main problems in the subject, and so far has remained out of reach." ... "This problem is fundamental because it is here that one really has to address the question of what kind of geometrical object the string represents." (

http://arxiv.org/abs/hep-th/9306122

)

Moreover, Lee Smolin claims that the relational approach (As far as I understand, "background independent" approach is a "relational approach.") can give a better alternative to string landscape problem and has a falsifiable prediction which is "there can be no neutron stars with masses larger than 1.6 times the mass of the sun." He noted that "all neutron stars observed have masses less than 1.45 solar masses." I should read his article on his alternative idea to string landscape problem.

Moreover, Lee Smolin claims that the relational approach (As far as I understand, "background independent" approach is a "relational approach.") can give a better alternative to string landscape problem and has a falsifiable prediction which is "there can be no neutron stars with masses larger than 1.6 times the mass of the sun." He noted that "all neutron stars observed have masses less than 1.45 solar masses." I should read his article on his alternative idea to string landscape problem.