What is background independent physics?
I don't know what that means. Perhaps you're asking about a background independent formalism/theory. Through the 19th century, physics consisted entirely of background independent theories as far as I know. In fact, the only theory that I know to be background dependent is GR. From what I have gathered, "background independent" simply means that the framework in which you express/define your physical objects gives you a reliable frame of reference against which to compare. GR is not like this because the metric is also a physical object that is influenced dynamically. Therefore, if you erect a system of intersecting parallel and perpendicular planes (a coordinate system that you intend to be Cartesian), then they will eventually evolve into unrecognizable distortion.
the way the words are normally used in theoretical physics, you have it backwards.
GR is a background independent theory
does not depend on a prior choice of geometry or a prior choice of metric (by which lengths, areas, angles etc are measured). The metric is dynamic and emerges as a solution of the equations.
In background dependent theories, fields, trajectories etc are mapped out on an arbitrary geometric grid chosen ahead of time
from a GR standpoint this is unrealistic----the gravitational field (which determines the geometry of spacetime) is not a fixed thing
Somewhere in his extensive website, John Baez gives an example of a background-dependent theory. A bead sliding along a ring, under the idealization that the bead is affected by the ring but the ring is not affected by the bead, is background-dependent.
examples of backgr. dependent theories are easy to find
most physical models---string theory, newtonian gravity, QFT, Maxwell's eqns---are formulated on geometric backgrounds fixed in advance. They are background dependent-----not independent
There has been a longstanding effort to formulate string theory in a background independent way, see for example Edward Witten's paper
on quantum background independence
---start of Witten's paper---
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...
Various possibilities have been explored. Examples of attempts to achieve BI in M-theory are
Someone here mentioned that Vafa was currently working on getting BI.
In 2003 background independence was despaired of by the eminent string theorist Tom Banks in
-----Bank's page 6----
The above discussion and  make it clear (to me at least) that the old dream of background independence in string theory is a chimaera...
I think he meant to say a "will-o-the-wisp" or a mirage.
The abstract (for Bank's Critique) reinforces this: "I argue against the possibility of a background independent formulation of the theory,..."
So from Witten's paper to Bank's there is a span of 10 years of trying to achieve background independence without success. Not enough, anyway, to satisfy Banks (one of the inventors of M-theory)
The fact that LQG is a Background Independent theory has, in the past, been offered as an argument for some kind of merger----some kind of hybridization or crossing of the lines of research. It was said that the two approaches (string and loop) had complementary strengths and weaknesses. I forget what the strengths of string theory were supposed to be. The idea was put forward that string theory could use LQG techniques to gain B.I.
I guess the moral is that most physical theories dont have BI, and General Relativity (and quantized versions like LQG) are exceptional. Background Independence sets GR apart, and sets Quantum Gravity theories that are quantized versions of GR apart.
And BI is hard to get, hard to build into a theory. Which is why Banks was despairing of it in 2003
GR teaches that nature is not fixed-background----spacetime geometry (the gravitational field) is dynamic. So any fixed-background theory must be an approximation, maybe a very workable effective one but not fundamentally correct. Since there is no fixed background, theories that depend on such a fiction are unrealistic in that regard.
By dynamic, do you mean that the geometry of spacetime changes? And changes compare to what?
Is quantum physics by itself a background dependent?
The geometry changes compared to what it was previously. For instance, if you start out by choosing a coordinate system that gives you a perpendicular intersection of geodesics as axes, then, the next moment, these axes may no longer be perpendicular.
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