Monica Dance proposes to replace the metric tensor with one scalar field E(x) that is not really a scalar field and that gives points a nonzero probability to exist or not exist. ;-) Not sure why she thinks that this will mimick the metric tensor and Einstein's equations.
Nothing against her original ideas: they are exactly the type of alternative thinking about quantum gravity that Peter Woit and Lee Smolin, among others, have been calling for in the last many years, and they are still doing so.
One of them suddenly blames arXiv.org for accepting this kind of papers. It is hard to find a more obvious example of hypocricy because this paper is exactly the type of research that they want everyone else to do.
The state-of-the-art situation is clear: string theory is the only framework that is at least in qualitative agreement with the real world but that goes beyond quantum field theory - and the difficult task is to extract new information from it that we don't yet know.
We know that we won't be able to answer any of these questions beyond QFT scientifically unless we carefully analyze all insights that we have accumulated - including the insights of string theory that is the only framework that can offer rational arguments for questions such as "do we need the anthropic principle". Without using the mathematical tools of physics, our guesses would be just a random war between different preconceptions - will Bert Schroer or Juan R. from the Center for Canonical Science scream louder?
This would not be science. Only string theory is a scientific framework to answer questions that can't be answered by effective field theories. This much we know.
Every single paper that has been written in the last 20 years about theoretical physics beyond the Standard Model that avoided the tools of both conventional quantum field theory as well as string theory has been nonsensical just like Monica Dance's paper about the scalar-field-non-scalar-field is, and the only reason why some of their authors have not been called crackpots is that they acquired a certain political influence.
According to everything we know, it probably can't be otherwise: string theory is the only predictive theory that reduces to quantum field theory in the appropriate limit but that is more accurate and far-reaching. Decades of failures with all hypothetical "alternatives" indicate this fact sociologically, but more importantly, we have rather concrete arguments showing what goes wrong if one avoids string theory or some of its general features.
I am pretty sure that Peter Woit could not explain why Monica Dance's idea can't work - why it's impossible for all of physics to arise from an unusual type of a scalar field, E(x). He just relies on the expectation that his readers will automatically assume that a female unaffiliated author can only submit nonsensical papers. Of course that the people on his blog would tell you that the idea of particles as different octopi is smarter, without having any rational reasons.
I am not sure which of these ideas is more promising.
The reaction to Monica Dance's paper is an example of a community that likes to discriminate against women and against people according to their profession, even in 2006. But it's an example that no one cares about. I want to assure Monica Dance that even though I think that her idea, at least in its current form, can't have anything to do with real physics, hers is at least an average alternative paper about quantum gravity.