For the standard view of quantum mechanics (QM), the wave function describes an ensemble of possible events. However, there is no agreement about its ontological meaning. Some authors claim that wave functions are real, while others deny their objective reality. “Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds directly to reality. However, there is a long history of suggestions that a quantum state (even a pure state) represents only knowledge or information about some aspect of reality” (Pusey, Barrett, and Rudolph , 475).

While technological applications of QM are abundant and extremely effective, theoretical interpretation is a great challenge. Measurement is, in general, the experimental determination of the value of an observable quantity, but in a quantum context, measurement may yield a variety of possible outcomes. The core quantum measurement problem is to understand why a specific result is obtained on a specific occasion.

It is widely agreed that the measurement problem is the theory's main interpretative concern. It played a central role in debates between Albert Einstein and Niels Bohr, setting the scene for the various paradoxes of the theory (e.g., Schrödinger's cat paradox and the Einstein‐Podolsky‐Rosen paradox) (Wheeler and Zureck ). The measurement problem also raises broader issues (Born ; Krips ), such as the philosophical debate between realism (objects exist independently of our observations) and antirealism (the acts of measurement are constitutive of phenomena), which impact the dialogue between science and religion. Furthermore, as we shall see, different interpretations of quantum theory have various theological consequences as well.

This paper offers a review of several questions QM poses to theological discussion. The first section presents some of the most relevant interpretations of QM, providing a brief description of the key points discussed in further sections, but also suggesting additional bibliography for a fuller understanding of each specific interpretation. In the second section, I approach the question of quantum indeterminism to show that QM does not provide a unanimous answer. For some interpretations indeterminism is real, whereas for others it is only apparent. This brings us to the question about the kind of knowledge that science can obtain. As this issue should be framed within the scientific realism–antirealism debate, the most relevant viewpoints of this discussion are also mentioned. The third section considers the potential theological implications of quantum indeterminism. Given the plurality of interpretations and ontologies arising from QM, the fourth section discusses whether it makes sense to inquire into the theological implications of the quantum world. I suggest that an ontological‐pluralist view is characteristic of how science objectifies reality, but is not necessarily present in other kinds of knowledge, such as metaphysics or theology.

Some Interpretations of Quantum Mechanics

Is It Possible to be a Realist about Quantum Mechanics?

It is widely accepted that there are radical differences between the macroscopic world of Newtonian physics and the microscopic world of QM. Although this is not entirely accurate (Lombardi ), it is usually considered that the macroscopic world is deterministic, because in Newtonian physics inexorable laws govern the movement of the whole cosmos. So if the previous state is known, we can predict the future. Instead, QM introduced randomness in the prediction of the events that occur in the atomic and subatomic levels. However, is it possible to be realist about quantum indeterminacy? As we have seen, the answer depends strongly on the interpretation of QM adopted. To some interpretations (e.g., the Copenhagen interpretation and modal ones), quantum indeterminism is an intrinsic property of the natural world. Other interpretations, however, consider that quantum indeterminism is a mere manifestation of our ignorance or a consequence of the limitations of the current theories (e.g., Bohmian interpretation and the evolution of the whole universe in the Everettian ones). A third group argues that scientific theories—including QM—can neither affirm nor deny the determinism or the indeterminism of the natural world (e.g., some statistical interpretations).

Nevertheless, is quantum indeterminism real or only apparent? Some authors tried to classify not only QM, but also diverse other physical‐mathematical theories into deterministic or indeterministic. It is usually considered that dynamic equations of motion are deterministic when a given value of independent variables univocally fixes the dynamic evolution of a physical system in any given state. In this way, the deterministic character of a certain scientific theory, or the lack of it, will usually be associated with the possibility of finding unique solutions for dynamic equations: if the possible solutions are not unique, there will be no determinism (Earman ). However, the above‐mentioned classification is not easy to accomplish because each of the different theories includes notions—such as “system” or “state”—which are not defined with the necessary precision. We saw, as an example, the difficulty in defining the quantum state. Hence, even within each theory there will be an open space to formulate legitimately a notion of determinism in different ways, thus requiring an interpretative discernment to choose the best formulation in each case (Bishop ). Therefore, in order to affirm the determinism or indeterminism of a given scientific theory, it is necessary to move forward to an in‐depth study of the kind of reasoning behind scientific theories and this requires adopting a meta‐theoretical epistemological perspective.

Another generally accepted claim by scientists is that Newtonian physics is realistic, since it assumes that scientific theories describe the world regardless of the observer. In various interpretations of QM, however, the observer plays an important role in the measurement process. Until the late nineteenth century, it was commonly assumed that scientific models provide knowledge of different aspects of the world, including unobservable aspects, and helped to understand the structure of the universe. Nevertheless, many experiments showed that the quantum world defies common sense interpretation (Shimony ), fostering philosophers to rethink the nature of scientific knowledge and reality.

Scientific realism is an epistemic positive attitude towards the content of our best theories and models, which yield knowledge of aspects of the world, including unobservable aspects (Chakravartty ). The multiple scientific realisms fall into three basic varieties (Merrill ). Metaphysical realism is a position regarding how our theories are related to the world: the entities postulated by a scientific theory have a mind‐independent existence. Semantic realism is a view concerning how theories are to be interpreted: scientific claims should be construed literally as having truth‐values, whether true or false. Epistemic realism is a position concerning what the acceptance of the theory means: our best scientific theories give true (or approximately true) descriptions of a mind‐independent world.

By contrast, throughout the twentieth century, a variety of rival epistemologies of science, known collectively as forms of scientific antirealism, began to emerge as well (Niiniluoto , 9–13). Scientific antirealists do not seek a correspondence between scientific theories and reality. Among them, instrumentalists deny that theoretical statements have a true value (Carnap ). They consider that they are merely instruments for predicting observable phenomena or systematizing observation reports. Scientific theories would only be suitable human constructions, mere practical tools to achieve a predictive or technical control of reality. Scientific models are imaginative fictions, used in the construction of theories and usually then discarded (Vaihinger ). Skeptics deny the possibility of true knowledge or progress toward it (Feyerabend ). Kantians maintain that although a mind‐independent reality exists, it is “veiled” from our eyes (d'Espagnat ). Pragmatists replace the realist concept of truth as correspondence with some epistemic substitute (i.e., coherence (Rescher ), consensus (Rorty ), among others). Methodological nonrealists regard the truth of the theories as inaccessible, and replace it with an epistemic surrogate, such us successful prediction (Laudan ) or simplicity (Goodman ). Historicists consider that empirical reality is structured by scientific paradigms (Kuhn ). For constructive empiricists, theories should have to save the appearances. Theories have a true value but it is irrelevant for the aims of science (van Fraassen ). All these proposals, among others, deny metaphysical, semantic and/or epistemic realism, although some of them may accept semantic and/or epistemic ones.

An intermediate position between classical realism and instrumentalism is critical realism, which considers that the primary aim of science is to explain the world, and that scientific theories are limited representations of the world. Critical realism assumes “ontological realism (that there is a reality, which is differentiated, structured, and layered, and independent of mind), epistemological relativism (that all beliefs are socially produced and hence potentially fallible), and judgmental rationalism (that despite epistemological relativism, it is still possible, in principle, to provide justifiable grounds for preferring one theory over another)” (Patomaki and Wight , 224). For critical realism “truth is not easily accessible or recognizable, and even our best theories can fail to be true. Nevertheless, it is possible to approach the truth, and to make rational assessments of such cognitive progress. The best explanation for the practical success of science is the assumption that scientific theories in fact are approximately true or sufficiently close to truth in the relevant aspects. Hence, it is rational to believe that the use of the self‐corrective methods of science in the long run has been, and will be, progressive in the cognitive sense” (Niiniluoto , 10).

Nancey Murphy remarks the importance to block the move to relativism based on the recognition of the plurality of perspectives and the historical and social conditioning of knowledge, and suggested a new definition of “true.” According to her, “a true statement (theory) is one that provides (one of) the best solution(s) to an empirical‐conceptual puzzle” (Murphy 308). In my opinion, a proposal that goes beyond critical realism, besides explaining the scientific knowledge, should also admit the possibility of abandoning the Kantian framework to attain knowledge of metaphysical principles. An attempt in this direction can be found in Leonardo Polo's epistemology (1984–1996). This Spanish philosopher argues that knowledge has two dimensions in perfect agreement: one is the cognitive act (methodic dimension), and the other one is the content known (thematic dimension). So, knowledge “is an act that is unitarily thematic or a theme that is unitarily an act” (Polo , 79). In other words, no theme appears without accounting for the intellectual method that led to its consideration, and there is no intellectual act that does not delimit its theme in a clear way. Polo distinguishes several kinds of cognitive acts, and he points out that no cognitive level can be considered absolute. Polo proposed a methodic‐thematic pluralism, which not only relates the gnoseological (methodic) to the ontological (thematic) realms without confusing them, but also paves the way to establish the cognitive status of different disciplines avoiding reductionism. Consequently, scientific knowledge would require the use of specific cognitive acts, accessing knowledge of reality with the limitations identified by critical realism. However, Polo also proposed an appropriate intellectual method to attain metaphysical knowledge, which differs from scientific objectification (Vanney , 2014).

There are general philosophical reasons for regarding realism as an attractive position, but QM strongly puts the realistic conviction to the test. Therefore, is it possible to be a realist about QM? Again, the answer depends strongly on the interpretation of QM adopted. Many antirealist or ontological‐relativist approaches to philosophy of science were vigorously influenced by the Copenhagen instrumentalist stance, which reject any question of reality beyond QM appearances. However, other interpretations, such as Bohmian or many‐worlds, offer a realistic interpretation of the quantum world consistent with the QM predictive‐observational data (Norris ). In general terms, those who clung tightly to realism argue that the earliest formulation of QM did not provide a complete description of atomic systems. Nevertheless, many physicists refuse to postulate entities that are neither observed nor needed, and prefer the family of Copenhagen‐like interpretations. For them, our knowledge of reality is “weakly objective”; that is, we may obtain some limited knowledge of the underlying quantum reality through their manifestations in interaction with our instruments of observation, because reality exists independently, regardless of our recognition of it, which is partially responsible for what we observe in macrophysical or microphysical levels (Stoeger ).

Theological Implications

The antirealist approaches to philosophy of science tend to accentuate the conceptual limitations of human knowledge. Some scholars have extended the instrumentalist worldview of QM to other disciplines such as theology. “According to the instrumentalist construal of theological discourse, statements of that discourse are not capable of being true or false, so the question of whether or not a conjunction of theological propositions can be true does not arise. Instrumentalism, it seems, thus insulates theistic discourse from contradiction” (Le Poidevin , 276). If this position were assumed, neither science nor theology would be able to provide significant information about the real world, and a meaningful dialogue between them could not be possible. There have been different responses to this proposal. Benjamin Cordry, for example, explained that religious fictionalism must address significant philosophical difficulties, including issues of justification, meaning, and interpretation (Cordry ). Jerome Gelman argued that the initial attractiveness of theological realism can be reestablished by a logical reconstruction of the realist approach to religious language (Gelman ).

However, the stimulating controversies which quantum indeterminism has opened among scientists, philosophers, and theologians do not only apply the epistemology of scientific realism, but also deal with the meaning of causality and divine action in the natural world. Even though these issues were discussed at length during the last century, many of them continue to be unresolved.

Does it Make Sense to Inquire into the Theological Implications of the Quantum World?

Science and theology are different kinds of knowledge, and QM provides a new epistemological approach to justify interdisciplinary perspectives. In 1927, Niels Bohr presented at Como the “principle of complementarity.” According to this principle, QM involves mutually exclusive models of description, each complete in itself and complementary to the other mode (Bohr ). As the atomic world cannot be described using classical notions; it is necessary to choose between a wave model and a corpuscular one, between a causal and a temporal–spatial description, between accurate knowledge of the position of a particle and its velocity. Bohr also suggested extending the idea of complementarity to other phenomena, such as the organic models in biology, dialectic argumentations in sociology, and the behavioral and introspective models in psychology (Bohr , ).

Some authors have proposed extending QM's principle of complementarity to the relationship between science and theology, arguing that both disciplines study the same reality, but under complementary perspectives. “Physicists have popularized this term to represent the relation between ‘wave’ and ‘particle’ aspects of the behavior of light without fully understanding it. Why should not the theologian ease his conscience by following in such distinguished footsteps and broadly declare his theological statements and those made in other disciplines to be simply ‘complementary’?” (MacKay , 225).

However, the extension of complementarity to the relationship between science and theology presents several problems. Ian Barbour warned that it should be used with caution, since complementarity involves the consideration of alternatives that come from the same logical level, and this does not apply to science and religion (Barbour , 77–78). Therefore, for Barbour, the assumption of an overly broad interpretation of the principle of complementarity runs the risk of admitting uncritically inconsistent dichotomies, which could emerge from nonoverlapping magisteria (Barbour , 77). In response to this objection, K. Helmut Reich suggested distinguishing between “logical or parallel complementarity” and “epistemological complementarity.” For Reich, the second option, that is “to think in terms of complementarity,” could also be applied to hierarchical levels, serving as a fruitful heuristic and cognitive device for gaining a deepened understanding of several problems (Reich ). I agree with Reich´s distinction, but I think that such an “epistemological complementarity” requires a more comprehensive theory of knowledge than critical realism.

If some difficulties appear in the relationship between science and theology in general, the situation is even more intricate when it is applied to QM. While there are no important disagreements among physicists on the use of QM, disputes on the meaning of quantum physics began with its inception and continue today. Given the multiple interpretations of QM, it is feasible for scientists to make only a pragmatic use of mathematical formalism, without assuming (tacitly or explicitly) its ontological implications (Healey ). Undoubtedly QM represents a significant expansion of scientific knowledge, but as physicists’ daily research is mainly directed towards specific ends, it is possible for them to avoid questions about the ontological meaning of quantum formalism (Fuchs and Peres ). However, this position is unacceptable for philosophers of physics, who specifically study the foundations of physical theories.

In general, to tell us something about the world, mathematical formalism needs an interpretation in terms of measurable quantities. Through an ontological interpretation, mathematical formalism becomes a physical formalism such us QM. Many philosophers of physics have been involved in the task of interpreting the quantum formalism in the last century. “Otherwise, the debate over interpretations is likely to become isolated from the data of physics (to its own detriment) and unable to offer heuristic ideas to physics (to the detriment of physics)” (Butterfield , 113).

The move from mathematical formalism to its ontological interpretation has always been problematic in mechanics, and is even more acute in QM, where the empirical data underdetermine the interpretative position. The fact that quantum formalism yields very different ontologies (Copenhagen indeterminism, Bohmian nonlocal hidden‐variable determinism, many‐branched tree in many‐worlds interpretations, among others) makes the problem extremely complex. It is undeniable that contemporary physics proposes an ontological pluralism (Lombardi and Pérez Ranzanz ). However, could this pluralism be related to a limited access to knowledge of reality through physics? According to John Polkinghorne, the choice between different ontologies has to be made on the basis of extra‐scientific criteria, including metaphysical principles. “Science alone will never provide the key to the nature of agency, yet seeks patient clarification of the complex character of physical process as being the best basis for the elaboration of further metaphysical ideas” (Polkinghorne , 190).

Nevertheless, the problem of multiplicity of ontologies still appears to be more critical when we seek to address the theological implications of QM. Ernan McMullin claims that there are important challenges to the relations between QM and theology (McMullin , 55–56). Theology, as well as theoretical physics, often relies on the underlying structure of the world. Because “to serve theological ends, theory has to declare (or at least strongly suggest) how the world is” (McMullin , 55), and the theological implications of the diverse interpretations of QM are considerably different. The warning by McMullin is relevant, but does not necessarily imply the lack of QM's theological consequences. Thomas Tracy comments:

This interpretative pluralism creates both an opportunity and a hazard for theologians. On the one hand, it is perfectly legitimate under these circumstances for a thinker grappling with the theology of nature to prefer one interpretation to another on theological grounds. Indeed, there can be no theological appropriation of quantum mechanics that does not make use of one or another of the currently viable interpretations. On the other hand, in casting our theological lot with a particular interpretation, we take the risk that new developments in physics or in the philosophy of physics will significantly undercut our theological constructions. (Tracy , 253–54)

Just as philosophers of physics defend the importance of having a consistent interpretation of the mathematical formalism, and metaphysicians the aim to unify the multiplicity of ontologies that follow from the various interpretations of QM, some theologians emphasize the importance of considering the theological implications of the theory. Philip Clayton remarks:

The conceptual space defined by the quantum mathematical formalism and the associated empirical observations neither proves nor disproves the existence of any divine being. Nor will it, by itself, establish—or rule out—any claim about divine action. But it may tell us something about how a being (human or divine) must act if it acts in the physical world and in conformity with physical laws. That is, the conceptual space of quantum physics may constrain the ways such a being could be manifested and the sorts of actions a human observer could in principle detect. (Clayton , 212)

Moreover, if the constraints imposed by the physical order tell us something interesting about nature, the constraints of physics could represent the context within which God chooses to act. Serious theological positions can be defended in light of science, even with highly speculative conjectures, but we should be aware of the hypothetical and contingent nature of all such theological reflections, as well as of the differences between theology and the sciences (Clayton , 214–15).

Concluding Remarks

A few statements can summarize the results of this investigation. The domain of applications of QM is enormously wide and successful. Therefore, we must indeed take QM as a description of the world. However, as diverse ontologies emerge from different interpretations of QM, it is difficult to find a satisfactory interpretation of the theory. The dissimilar interpretations of QM save the phenomena, but is it sufficient to use an interpretation that only saves the phenomena? Since in QM there is no valid inference from the empirical success of the theory to its ontological truth, the multiplicity of coexisting interpretations highlights the need for a meta‐scientific perspective to evaluate the different interpretations of the theory.

As we have seen, QM has renewed the interest in fundamental questions about the natural world, human knowledge and God, topics that concern not only physics, but also philosophy and theology. Although disciplinary views are inevitable in research, fundamental questions require a special approach and a solution that overcomes partial descriptions. Therefore, only an interdisciplinary effort can pave the way for an adequate understanding of the actual complex relationship between sciences.

Natural sciences, philosophy, and theology have distinct cognitive methods, which correspond to different ways in which the mind grasps truth. As every discipline works within the framework of a theoretical doctrine, and with their own methodology and procedures, it is extremely necessary for interdisciplinary work to have a wide and powerful epistemological framework, one that is able to recognize the dissimilar levels of discourse and domains, and to determine the cognitive scope of various contributions. Probably, critical realism is the best proposal available to explain the knowledge of physics, but it is not enough to account without the knowledge of metaphysics and theology.

The contemporary scenario faces us with the following dilemma: should we adopt an ontological pluralism or a cognitive pluralism? If we assume a priori a “cognitive monism”—the only valid or possible knowledge is the scientific one—we may embrace, in the best of cases, different ontological descriptions. On the other hand, if we assume a “cognitive pluralism,” we can also admit a metaphysical knowledge of reality, which would lack the constraints of scientific objectification and would be more suitable for theological reflection. But to assume a cognitive pluralism—including not only scientific knowledge but also metaphysical knowledge—demands the development of an appropriate theory of knowledge, a more comprehensive one than critical realism.

In spite of more than a century of discussions, we are still at the very beginning. The understanding of quantum physics is still an open issue and has too many subtleties, making it impossible to accept a trivial solution. Furthermore, QM is only the first step in a series of more general quantum theories, such as quantum field theories (i.e., string theory, loop quantum gravity, etc.), which are the mathematical and conceptual frameworks for contemporary elementary particle physics.