One of the main problems periodically facing the scientific community is how to decide on the direction of future research: evaluate what programs are worth pursuing, what kind of principles should underlie their foundations and what kind of phenomena they need to account for. Ever since its formulation it has become clear that the standard model of particle physics cannot be the final word in high energy physics. The reason of course is that it does not include one of the four fundamental interactions, gravity. Although gravitational effects might not be detectable with the level of technology we currently possess, we expect that any description of nature at its most fundamental level will be complete and will still incorporate them. In fact, this goal seems less quixotic or abstract when evidence from a different domain, that of astrophysics, is taken into account. It has also become increasingly clear that general relativity breaks down and fails to describe phenomena related to black holes – an indication that a theory that will incorporate quantum corrections is needed.
A myriad of ways towards a quantum theory of gravity have been put on the table, but two research programs have arguably emerged dominant: string theory and loop quantum gravity. String theory has traditionally been the preferred approach of most physicists. The key idea behind it is to expand on the field theoretic approach that has dominated particle physics by replacing fields interacting at spacetime points with interactions of strings extended in space. This shift has the advantage of not only dealing with many technical problems plaguing interactions in the standard model, but also the equally important feature of subsuming all possible interactions under a common framework, which, to everyone’s satisfaction, includes gravity. String theory thus presents itself as a (final) theory of everything: a set of principles that governs all physical occurrences at the most fundamental level of reality. Loop quantum gravity, on the other hand, is a less ambitious project. It does not seek to describe all interactions under a common set of principles nor cure any inadequacies of the standard model. The goal is rather to produce a quantum description of the gravitational force by treating geometry itself (represented by metric structure in Einstein’s theory) as a “feral” field that needs to be put through a quantisation procedure. The key difference with (perturbative) string theory is that it does not split gravitational fields into two components one of which corresponds to some fixed structure (the spatiotemporal part) and the other as a perturbation that will be described using quantum field-theoretic methods.
Assuming that both approaches have their respective merits and succeeding in explaining diverse phenomena, the puzzle remains or perhaps is accentuated: how can we decide which one to pursue? Of course, from a certain perspective it might be better to refrain from making a choice. After all, without concrete empirical predictions that will confirm or disconfirm either project, it is perhaps wisest to pursue both while awaiting further (tangible) results. This is always a viable option, but it leaves something to be desired. Following these more pragmatic or practical considerations, we want to be able to make something akin to an educated guess that will at the very list rationalise the community’s investing time and energy on any of the projects. In particular, given the enormous attention that string theory has received in comparison to all its rivals, it would be important to ensure that this wave of enthusiasm was not driven by mere sociological factors having to do with the internal workings of academic research [Woit 2006] but relies on firmer, more physically sound, reasons. On the other hand, if other approaches have been unfairly disfavoured in this process it would most certainly be to the benefit of the community to redirect some of its resources to their investigation. From a broader, more philosophical/methodological point of view, we would like to investigate to what extent heuristics can be reliable guides to the choice of research programs and to offering insights into the essential principles that underlie our theories. Have some of these heuristics worked reliably in the past and if so, can our putting faith in them guarantee future success?
One such heuristic or (depending on one’s attitude towards it) principle promulgated as a reliable guide for theory choice is the demand for background independence. According to proponents of this argument [e.g. Rovelli 2000, Smolin 2005], one key insight we obtained in the course of the development of spacetime theories from the 17thcentury to Einstein’s theory of gravity was that trying to get rid of “surplus” structure leads to more accurate physical theories. Thus, the story goes, Newton’s theory was greatly improved when it was realised that spatiotemporal structure adequate to describe the physics of systems did not rely on a distinction between rest and motion with respect to an absolute spatial background – like the one Newton had postulated. This key move towards a more relational understanding of space and time gave Einstein enough flexibility to suggest a modification to the transformations of mechanics such that they could be compatible with the more recently developed theory of electromagnetism. The last remnants of this absolute structure were completely demolished with the advent of general relativity and the adoption of a dynamic geometry that is influenced by the presence of matter: spacetime itself became a dynamical entity. Supporters of the LQG program seem to suggest that this program is to be favoured as the main candidate for a quantum theory of gravity because it adheres to this same principle. Following onto this tradition of eliminating surplus structure, LQG seems to achieve something truly inconceivable: eliminating spacetime altogether!
It might be worthwhile to examine the roots of this demand for background independence. Skipping a few centuries ahead we turn to Einstein’s agonising and thriving years in the 1910s when he was trying to formulate the general theory of relativity. Among the principles that Einstein considered as essential for the new theory to obey was the so-called principle of general covariance – effectively the progenitor to background independence. This principle dictates that the laws of nature be covariant, i.e. retain the same form in any frame of reference. This means that there should not be new terms emerging in the equations one employs to describe a system just in virtue of the relative motion of their reference frame with respect to that system. The values of the various terms in the equations might of course vary across variant frames but the very form of the equation, the way the terms combine and the kind of mathematical objects involved, would need to be the same under any kind of transformations (which correspond to a change in the frame of reference adopted). However, it was soon pointed out by Kretschmann that the principle of general covariance, to the extent that it said something meaningful at all could be satisfied by any physical theory. Equipped with enough patience and the tools of differential geometry, one can formulate any theory in a fully coordinate-independent way, i.e. such that equations retain the same form irrespective of the frame of reference. In fact the so-called Newton-Cartan theory proved that this is possible even for the case of Newton’s theory of gravitation.
With this apparent trivialisation of general covariance the question becomes: can the demand for background independence be turned into a substantive claim we make of our theories? In particular, if general covariance on its own is not a distinctive characteristic of general relativity but is rather a formal feature (i.e. a way of presenting any physical theory) we need to ask whether there are other features of the theory that underlie this principle. J. Read’s talk offers the conceptual scrutiny we require. By going through multiple criteria meant to adequately capture the meaning of background independence, he shows that the verdict is far from uncontroversial (even) in the case of general relativity. For instance, if we take BI to mean that there are no absolute objects in the theory, i.e. that there are no fields that remain the same in all possible solutions of the theory, then general relativity also fails the test (for at least one such object can be provided). The rest of the criteria considered succeed in characterising general relativity as a background independent theory, but fail to do so uniquely. That is because there are other theories that will also come out as background independent depending on particular choices we make in the way we treat some of the quantities involved. For instance, if we try to assess our theory based on the kind of terms that figure in its Lagrangian [demanding that they are physical fields like the electromagnetic field], we make the verdict dependent on our definition of what fields would count as physical as opposed to pure geometrical or background fields. The rather thorny task now is to present a non-question begging account of this division, i.e. motivate it on independent grounds, not chosen solely in virtue of the fact that general relativity is included in the class of background independent theories whereas the unwanted theory is not.
Perhaps the most fascinating and indeed more relevant, for our discussion, aspect of this analysis is the way it transfers to the context of theories of quantum gravity and in particular, string theory. Recall that one of the purported disadvantages of string theory compared to loop quantum gravity is that it still requires a perturbative treatment of the gravitational field. Despite already muddying the waters in the case of general relativity, Read applies the set of examined criteria to string theory. With the assumption that an analogy holds between classical and quantum field theories as to how their physical content can be spelled out, the criteria examined beforehand can now be straightforwardly applied to the quantum case. In fact, the verdicts themselves follow a similar pattern: again examples of absolute objects can be presented in string theory that render it background dependent while the Lagrangian-based criterion we mentioned above still requires a properly motivated standard on which to decide whether the (operator) fields included in the action are physical or not. Worse still, matters are even more complicated than touched upon here because in string theory there is one further choice to be made at the onset of the analysis. Indeed, one can check background independence with respect to the fields as defined in a target space [i.e. when the strings are mapped to some other manifold like Minkowski 4D spacetime – here we care about the excited states of the string] or the worldsheet fields [the 2D trails (surface) that strings leave behind as they transverse space]. The results obtained are rather ambivalent: depending on choices we make in characterising the featured fields string theory can come out as both background dependent and independent even when applying the same criterion!
In conclusion, it is far from obvious how one might try to characterise the alleged background dependence of string theory. It is thus far from obvious whether this demand can play a decisive role in favouring the LQG to the string theoretic approach. When it comes to BI as a more general principle underlying theory development, we saw that the conceptual ancestor to background independence also suffered from the same inadequacy – indeed bordering with trivialisation. Its heuristic value is perhaps noteworthy especially in the way it motivated physicists to take a certain approach to theory construction but it is dubious whether it could be elevated to the status of principle meant to guide theory selection. Of course, it is possible that future formulations will be proposed that will lead to the anticipated verdicts in familiar cases so that they can be reliably extended to a constraining principle for research in theories of quantum gravity.