A PF poster recently asked about the Background Independence feature that distiguishes classical 1915 General Relativity from Stringy theories. She suggested that the explanation be at the "basic Xray tech" level. That probably means starting with a short exerpt from Smolin article in January 2004 SciAm, "Atoms of Space and Time". I am a little unsure about what Xray technologists know. Maybe a bunch of physics already. Still let's start with Smolin. -------quote page 68---- ...In the mid-1980s a few of us...Ashtekar...Jacobson...Rovelli...decided to reexamine the question of whether quantum mechanics could be combined consistently with general relativity using the standard techniques. We knew that the negative results from the 1970s had an important loophole. Those calculations assumed that the geometry of space is continuous and smooth, no matter how minutely we examine it, just as people had expected matter to be before the discovery of atoms. Some of our teachers and mentors had pointed out that if this assumption was wrong, the old calculation would not be reliable. So we began searching for a way to do calculations without assuming that space is smooth and continuous. We insisted on not making any assumptions beyond the experimentally well tested principles of general relativity and quantum theory. In particular we kept two key principles of general relativity at the heart of our calculations. The first is known as background independence. This principle says that the geometry of spacetime is not fixed. Instead the geometry is an evolving, dynamical quantity. To find the geometry, one has to solve certain equations that include all the effects of matter and energy. Incidentally, string theory, as currently formulated, is not background independent; the equations describing the strings are set up in a predetermined classical (that is, nonquantum) spacetime. The second principle, known by the imposing name of diffeomorphism invariance, is closely related to background independence. This principle implies that, unlike theories prior to general relativity, one is free to choose any set of coordinates to map spacetime and express the equations. A point in spacetime is defined only by what physically happens at it, not by its location according to some special set of coordinates... ...By carefully combining these two principles with the standard techniques of quantum mechanics, we developed....[the means]...to do a calculation... That calculation revealed, to our delight, that space is quantized. We had laid the foundations of...loop quantum gravity... ------end of exerpt----- The principle is Background Independence because that is the feature that takes work to arrange for, when building a theory. The automatic thing to do when you construct a theory or any kind of mathematical description of nature is to start with some kind of set geometry---some type of graph paper in effect. Then when you have constructed the theory it will be apt to depend on the geometry you started with. Background dependency is not a feature so much as something that happens to a theory if you aren't careful. A favorite background geometry in "Quantum Field Theory" is called "Minkowski space". It is basically a kind of 4D graph paper with a certain distance&angle function (a "Minkowski metric") that AE made prominent in 1905. The hard thing, which AE achieved in 1915, is to construct a theory, where you dont start with any preliminary geometry, no "metric" at all, in other words----you just have an amorphous continuum to begin with and you say how geometry (distances and angles) emerges and evolves in relation to the matter and energy flowing around in it. In Relativity (meaning General, from this perspective the 1905 "special" business doesnt really count) the continuum ends up merely being a mathematical convenience used in defining the geometry. Things that happen, material occurrences like A meeting B, are what define the places and times. Individual points in a continuum dont have physical meaning since any point would do as well as any other for some event to happen at. So what's a good link? Well, you could try some of Rovelli's "Quantum Gravity" (a draft is online) skipping any mathematical formulas and obscure terminology. In other words, read for the downtoearth examples and whatever is in plain language. Page 7 of Rovelli's book (1.1.3 "the physical meaning of general relativity", 1.1.4 "background independent quantum field theory") Page 47 of Rovelli's book (2.2.5 "general covariance") Page 53 (2.3.2 and surrounding pages) Diffeomorphism invariance is discussed in the "general covariance" section---they mean about the same thing. Other people here may have ideas of good entry-level discussion of BI and DI. Maybe the source of any mystery is this: if you have some experience with mathematical models of nature then it seems like a miracle that AE's 1915 could be BI and DI----you can scootch around the space and the stuff in it any old way and the equation keeps on working! You can build the theory on wet kleenex (look ma no graph paper!) and it creates beautiful structures growing from the amorphous blob by the magic of differential equations. Etc Etc Etc. But if you have NOT played around previously with differential equation models of nature then BI and DI probably dont seem miraculous or remarkable or very noticeable, even. This is why its hard to explain them. They are pretty simple but as soon as I tell you what they are you probably wonder "is that all?" Oh yes, consequences. Nondescript as they may seem BI and DI have profound consequences (besides making GR, the prevailing theory of gravity, fundamentally incompatible with conventional Quantum Mechanics and the like) I mean desirable consequences--getting rid of unwanted infinities (eliminating divergences & singularities), getting discrete planck-scale area and volume spectrums. But discussing such consequences makes it seem as if there is a choice about whether to have those features in ones fundamental picture of nature. well maybe someone else will supply some better links for the basic Xray technologist. anyway that's all for now.