Background-independence has been a much-debated topic in spacetime theories. One of the main lessons of the general theory of relativity is that spacetime is not fixed, as in Newton’s theory, but is dynamical. Since the shape of a spacetime depends on its matter content, the relation between geometry and matter is dynamic. Thus there is no privileged spacetime background on which physics is to be done; unlike the cases of Newtonian space and time, and special relativity’s Minkowski spacetime.

Much has been made, especially in recent discussions of quantum gravity, of this rough idea of ‘background-independence’. More precisely, a basic conception of background-independence is that a theory is background-independent if and only if it contains no absolute object. According to Anderson ([1967], p. 83), an absolute object is a geometric object that is the same (up to isomorphism) in all of the theory’s models. In special relativity, the metric that defines the Minkowski spacetime is such an absolute object. But in general relativity, the metric is not determined to have any particular form across different models and so it is not an absolute object. In this intuitive sense, general relativity is background-independent.

In quantum gravity, background-independence has sometimes been elevated to the status of a fundamental principle that future theories ought to satisfy. Furthermore, as James Read notes in his book Background Independence in Classical and Quantum Gravity, declarations of background-independence are sometimes made ‘from the hip’ (p. 132), that is, on the basis of intuitions rather than precise definitions, and without a proper analysis of the detail of the examples for which verdicts are being announced.

Read has set out to remedy this situation by adapting from the literature six relevant notions of background-independence that he makes precise and then uses to make verdicts about background-independence on a wide range of examples of spacetime theories.

This short book is, in several ways, a worthy and admirable example of how technical philosophy of physics ought to be done. For it both gives precise definitions of the various notions used and lays them against examples from both classical and quantum gravity. Thus, compared to previous discussions of background-independence, Read’s approach is refreshing. It is also commendable that Read engages with the current physics literature.

A good number of Read’s verdicts agree with sensible views about the theories involved. For example, there is a majority verdict that Newtonian gravity theory and its geometric cousin (the Newton–Cartan theory) are background-dependent. General relativity comes out as being background-independent, as do some of its quantum versions (more on this below). There are also some surprises. For example, there is a background-independent cousin of the Newton–Cartan theory; and Kaluza–Klein theory is not diffeomorphism invariant and yet it is background-independent. When some definitions are imprecise or give clearly incorrect verdicts in some examples, this is sometimes used to further improve the definition at issue. Thus Read builds an overall convincing case that the verdicts that are given by the majority of his definitions of background-independence are correct, and that at least some of the conceptions of background-independence that he discusses are valuable.

Chapters 1 and 2 are brief introductions. Chapter 3 discusses the main players in the rest of the book: general covariance, diffeomorphism invariance, absolute objects, and the six main notions of background-independence for classical spacetime theories. With these tools in hand, chapter 4 goes on to study and give verdicts on background-independence in eight main examples: Newtonian gravitational theory, Newton–Cartan gravity (in two different forms), general relativity, teleparallel gravity, Kaluza–Klein theory, and two Machian relationist theories (scale-invariant particle dynamics and shape dynamics). Read summarizes his findings in a helpful table (p. 93).

Chapter 5 discusses quantum gravity: perturbative string theory, AdS–CFT (anti-de Sitter–conformal field theory) duality, and loop quantum gravity. Here, again, the verdicts are sensible, with some of them going against often-repeated claims in the literature. Thus AdS–CFT duality comes out as background-independent, in a very robust sense that contradicts some of the ‘from the hip’ declarations in the literature. The verdict on perturbative string theory is not unexpected: it comes out as background-dependent, but only on the assumption that the spacetime metric is flat or close to flat. By contrast, a more general perturbative formulation of string theory on a curved spacetime would be background-independent. Finally, loop quantum gravity comes out as background-independent, although Read argues that some of the literature is incorrect in claiming that it is ‘manifestly’ so (p. 129). Chapter 6 contains Read’s conclusions about what the book has achieved and about the value of his analysis.

Overall, Read makes a convincing case that a number of the definitions of background-independence that he has adapted from the literature give correct verdicts; and that this topic can, and should, be addressed with precision. The book sets not only the agenda but also the standard required for discussions of background-independence in the years to come.

But there are two broad areas where I find the book to be less convincing. The first concerns a number of specific technical points; the second concerns some aspects of the overall methodology and stated aims of the book. On the technical points, there are three places where there is room for disagreement. The first concerns a particular claim about general relativity that Read endorses: Pitts’s ([2006]) claim that general relativity has an absolute object, namely, the determinant of the metric. The reason for this claim is that for any model of the theory, and for an adequate choice of coordinates, the value of the determinant of the metric, in the neighbourhood of any point, can be set to −1 (alternatively, in the language of active transformations, this can be done by using an appropriate diffeomorphism of the manifold).

But, as I explain below, I do not think that this implies that there is an absolute object in general relativity. Think, for example, of the Minkowski metric, which has the same value in every model of special relativity. The case of the determinant of the metric in general relativity is different. Here, the correct statement is that, for a particular choice of coordinates, the value of the determinant can locally (that is, in the neighbourhood of a point) be set to −1. There are problems with this, because, as I argue below, being able to reach a particular value by a specific diffeomorphism is not a sufficient condition for a quantity to be an absolute object.

Let me spell out this critique in more detail. It is by no means meant as definitive. I consider these three important points to be not settled; nor have they, to the best of my knowledge, been discussed in any detail in the literature. But having said this, it seems that the three points combined do make a strong case that the determinant of the metric is not an absolute object.

First, the determinant of the metric can be set to −1 only in the neighbourhood of a point (Pitts [2006], p. 366). For, in general, there is no choice of coordinates that can make it have the value −1 everywhere. Thus the putative absolute object is not globally defined; its existence depends on a particular choice of coordinates on a particular region of spacetime. Furthermore, these regions differ between models. And so it can hardly be called an ‘absolute object’.

Second, there is nothing special about the value −1 of the determinant: by a choice of coordinates, it can be set to any negative value −x, where x is any positive number. Thus there is no meaningful sense in which having this value makes the determinant into an absolute object, since it can have whatever negative value one pleases. And there is no a priori reason that says that one should choose coordinates such that the determinant has the value −1. There is nothing absolute about the choice, and nothing absolute about having that particular value, or any other value.

Third, the value −1 has significance only insofar as it reflects the value of the determinant of the metric in the tangent space defined at each point, that the metric of general relativity approaches locally in Riemann normal coordinates. But it is obscure why the tangent space should set the special value.

Anderson’s ([1967], p. 83) absolute objects are defined globally and his definition does not characterize the determinant of the metric as an absolute object; hence my first point. An alternative definition by Friedman ([1983], p. 60) is local and implies that the determinant is an absolute object (Pitts [2006], p. 366; Sus [2008], p. 72). But if so, then two conclusions follow. First, this issue about the determinant is not a good reason to view Anderson’s definition as deficient, since the determinant is not an absolute object à la Anderson, which undercuts an important motivation to search for alternative definitions. Thus it would seem that correcting this verdict, and distinguishing clearly between Anderson’s and Friedman’s definitions, leads to different verdicts for definition 5 in Read’s table on p. 93. Second, Friedman’s local definition of an absolute object is too weak, since it qualifies virtually every theory as background-dependent. Thus I argue that if Pitts’s interpretation of Friedman’s definition is correct, then Friedman’s definition is an error. This leaves us with Anderson’s definition, and with the truth of the first point.

I have mostly used passive language, talking about choices of coordinates and only gesturing at the active interpretation in terms of diffeomorphisms. But so far as I can tell, interpreting the diffeomorphisms required to set the determinant to −x as active diffeomorphisms (one diffeomorphism for each region, and also very specific sets of diffeomorphisms for different models) does not change these three arguments nor justify the claim that the determinant of the metric is an absolute object.

The second technical source of disagreement concerns theoretical equivalence, a topic whose discussion in the book is, in my view, under-developed. First, the book’s definition 6 of background-independence relies on a conception of theoretical equivalence (given in definition 7): a theory is background-independent if and only if it has no formulation that features fixed fields. This then implies that in assessing whether a theory is background-independent one needs to verify that it is so for each and every one of its formulations. And this does not seem feasible in practice. Thus a related methodological consideration (namely, that one wishes to assess the background-independence of a theory formulation on its own terms, irrespective of other theory formulations) prompts Read to drop this dependence on the equivalent reformulations in his later definitions of background-independence. But it being a property of a particular theory formulation seems to go against the spirit of background-independence as a property of theories.  And so, it seems like a weak reason for dropping the relevance of equivalent formulations in the conception of background-independence.

Furthermore, it is not clear that Read’s negative formulation of background-independence in definition 6 (‘a theory is background-independent iff it has no formulation which features fixed fields’) was correct to begin with. For if background-independence is a property of a whole theory, rather than of an individual theory formulation, then it should suffice to find one formulation where the theory is background-independent for the whole theory to be background-independent. In other words, being manifestly background-independent in one formulation should secure that a theory is background-independent in all other theoretically equivalent formulations, even if this is not immediately apparent for each individual one. After all, theoretically equivalent formulations of a theory are mere reformulations—they are ‘the same theory, written in different words’—and a substantive physical notion like background-independence should not depend on the words used to formulate a theory. Think of the analogy with the gauge-invariance or coordinate-invariance of a given property in a gauge-invariant or coordinate-invariant theory: to demonstrate that some quantity has a gauge-invariant or a coordinate-invariant property, one does not need to demonstrate this property for every possible gauge or coordinate system in which the quantity can be expressed. Rather, it suffices to find, among all those equivalent formulations, one formulation in which the property is instantiated.

Thus, on any account, background-independence must be compatible with theoretical equivalence. But this is not to claim that I have a worked-out view of the compatibility between background-independence and theoretical equivalence (hence my earlier use of the word ‘should’). Rather, I am saying that Read’s dismissal of the question of theoretical equivalence without further discussion, based only on the methodological principle stated above, seems too quick.

The third point of technical disagreement concerns Read’s critique of other authors. In a section titled ‘Coda’, Read correctly criticizes a footnote in a paper I wrote a decade ago (mea culpa!) for conflating the uses of the phrases ‘general covariance’ and ‘diffeomorphism invariance’ (p. 123; see De Haro [2017], p. 115). And on several central points, Read makes an effort to correctly represent work by other authors. But on various other points, his reading of my work seems a bit off and unrecognizable. For example, in his discussion of my minimalist criterion of background independence, he misconstrues the reason for one of the conditions for such independence, which he then drops (p. 188). And he claims that I am committed to a notion of a theory where the boundary conditions are arbitrary (p. 120). I mention these corrections not just in ‘self-defence’, but also because, since the book criticizes other authors, the above leaves me wondering about the degree to which its critical engagement with other authors’ work is also accurate.

Turning to more general concerns, I have two methodological issues and some further comments about the stated aims of the book. The first methodological issue is that the treatment of background-independence is mostly formal and engages little with interpretation. This is surprising, especially given that in his other work, Read stresses the importance of the interpretative aspects of physical theories, in addition to the formal ones (see, for example, Read [2016]; Read and Møller-Nielsen [2020]; Pooley and Read [2025]). I here give two instances of this methodological issue.

One of the book’s main conceptions of background-independence requires that the solution space is determined by a generally covariant action, all of whose dependent variables are subject to Hamilton’s principle (definition 10, p. 24). Since, up to this point, definitions of background-independence had made no reference to Hamilton’s principle, one would expect some motivating discussion as to why a variational principle is required here (the more so because Read correctly insists on the fact that not all theories in physics have an associated action from which the field equations can be derived). While one can think of reasons of convenience for introducing the variational principle (for example, allowing an extension of a classical theory into a quantum field theory by using Feynman’s path integral over trajectories), there is no clear principle that requires a treatment in terms of an action and its variation. Agreed, Read was following Pooley’s lead for the sake of being comprehensive, while acknowledging the limits on the scope of any definition in terms of variational principles. But a discussion of the physical motivation for focusing on a variational principle would have been desirable.

A more central point is that Read does not say whether we should take background-independence to be a formal (non-interpretative) notion or whether it is also interpretative. (Think of the analogy with symmetry: various formal methods can give us an account of the notion of a symmetry, but only an interpretative analysis can tell us whether a given symmetry is ‘gauge’.) Read declares in the introduction: ‘I am concerned with the formal features’ of background-independence (p. 2). But since (as he also stresses) some of his definitions include an interpretative aspect, this seems to be a methodological choice rather than the expression of a firm conviction that background-independence must be formal. Thus I find his silence about this central question disconcerting. A book on background-independence merited a more substantial discussion of this crucial point.

My own view is that background-independence does have an interpretative aspect. And Read’s analysis of the examples suggests that a two-step procedure can be successful. Here, I mean ‘two-step procedure’ by analogy to other notions in philosophy of science—for example, theoretical equivalence. The first step in giving a conception of theoretical equivalence is a suitable formal notion of equivalence of theories (for example, duality or categorical equivalence) with only minimal constraints on interpretation. The second step is an interpretative criterion of equivalence (for example, that in terms of a referential semantics the two theories have the same domains of application, with formally equivalent terms referring to the same items in the domain of application). While there is debate about both types of criteria, distinguishing these two steps facilitates the analysis, since it allows focusing on the relevant discussions at each step.

Since Read’s formal definitions of background-independence are successful in terms of scope and reasonableness of his verdicts (especially definitions 9 and 10), I take this as an indication that the two-step approach to background-independence is the preferred one.

The second methodological issue concerns the number of alternative definitions of the same concept, especially ‘background-independence’, that the reader is asked to keep track of. We are offered little guidance as to whether a new definition is better than the previous one. (As I discussed above, this is the case with the introduction of definition 10, which incorporates the unmotivated idea of a variational principle.) In his conclusion, Read celebrates this ‘pluralism’: ‘there is a plurality of definitions, each of which is helpful in enriching our understanding of the workings of our physical theories: and it is this enrichment, rather than identifying any “true” notion of background-independence, which is the goal’ (p. 133).

This type of pluralism is fine, so far as it goes. But not searching for the one true notion of background-independence in one thing; carrying along six classical notions (plus four quantum ones) without providing guidance about their relative merits and their acting as motivations for introducing new principles is another. For example, although the various verdicts are illustrated for different theories, some of the definitions give incorrect verdicts; definition 5 classifies virtually any spacetime theory as background-dependent. Read continues to carry definition 5 along, rather than dropping it as inadequate. And despite the ‘majority verdicts’ that Read emphasizes, the various notions have minority disagreements about several central examples that were worth trying to explain. More guidance and judgement about which notions to keep and how these different notions rank relative to each other (perhaps for different types of theories) would have been desirable.

This leads me to the stated aims of the book. The introduction advertises that background-independence is a heuristic for theory construction, rather than a norm to be fulfilled (p. 2). And the conclusion reassures us that background-independence is a guiding principle for the construction of new physical theories and that ‘the more nebulous ‘spirit’ of background-independence, loosely construed, can also be used as such a guiding principle’ (p. 134). But notwithstanding this assurance, one is left wondering whether background-independence thus construed can realistically be considered a guiding principle for theory construction, especially given the number of different classical conceptions of background-independence, the lack of principles for when to use each of them, and the very limited attention to physical interpretation. ‘[G]iven the flexibility and potential lack of univocity’ (p. 131) of the notion of background-independence, which Read himself admits, how useful a guide to theory construction by physicists can this notion be?

As a self-declared empiricist, Read denies that background-independence should be understood as a rationalist principle or necessary condition for good theory construction (p. 134). But an empiricist can analyse and discuss a given conception of background-independence without being thereby committed to a priori knowledge of how an ideal theory should be constructed. This is what the debates about the best conceptions of many notions used by philosophers of physics are about: symmetries, manifolds, gauge, entropy, and so on. Thus I think that such work is yet to be done for background-independence, though Read’s book gives a good formal basis on which to build.

To sum up: Read has given us a wonderful analysis of the formal aspects of various conceptions of background-independence, with minimal discussion of their interpretation. Thus the enterprise of discussing with comparable precision the adequacy of each of these notions (perhaps in various contexts), and the interpretative and epistemic principles according to which we choose one notion over another, is yet to begin.

Acknowledgements

I thank James Read and Adan Sus for discussion of some of the points raised here, and Jeremy Butterfield and Enrico Cinti for comments on the review.

Sebastian De Haro
University of Amsterdam
s.deharo@uva.nl

References

Anderson, J. L. [1967]: Principles of Relativity Physics, New York: Academic Press.

De Haro, S. [2017]: ‘Dualities and Emergent Gravity: Gauge/Gravity Duality’, Studies in History and Philosophy of Modern Physics, 59, pp. 109–25.

Friedman, M. [1983]: Foundations of Space-Time Theories, Princeton, NJ: Princeton University Press.

Pitts, J. B. [2006]: ‘Absolute Objects and Counterexamples: Jones–Geroch Dust, Torretti Constant Curvature, Tetrad-Spinor, and Scalar Density’, Studies in History and Philosophy of Modern Physics, 37, pp. 347–71.

Pooley, O. and Read, J. A. M. [2025]: ‘On the Mathematics and Metaphysics of the Hole Argument’, British Journal for the Philosophy of Science, 76, available at <doi.org/10.1086/718274>.

Read, J. [2016]: ‘The Interpretation of String-Theoretic Dualities’, Foundations of Physics, 46, pp. 209–35.

Read, J. and Møller-Nielsen, T. [2020]: ‘Motivating Dualities’, Synthese, 197, pp. 263–91.

Sus, A. [2008]: ‘General Relativity and the Physical Content of General Covariance’, Ph.D. Thesis, Universitat Autònoma de Barcelona.