This study identified the content of the neural representations in the minds of physicists considering some of the classical and post-classical physics concepts that characterize their understanding of the universe. In this discussion, we focus on the representations of post-classical concepts, which are the most recent and most abstract and have not been previously studied psychologically. The neural representations of both the post-classical and classical concepts were underpinned by four underlying neurosemantic dimensions, such that these two types of concepts were located at opposite ends of the dimensions. The neural representations of classical concepts tended to be underpinned by underlying dimensions of measurability of magnitude, association with a mathematical formulation, having a concrete, non-speculative basis, and in some cases, periodicity. By contrast, the post-classical concepts were located at the other ends of these dimensions, stated initially here in terms of what they are not (e.g. they are not periodic and not concrete). Below we discuss what they are.

The main new finding is the underlying neural dimension of representation pertaining to the concepts presence (in the case of the classical concepts) or absence (in the case of the post-classical concepts) of a concrete, non-speculative basis. The semantic characterization of this new dimension is supported by two sources of converging evidence. First, the brain imaging measurement of each concepts location on this underlying dimension (i.e. the concepts factor scores) converged with the behavioral ratings of the concepts degree of association with this dimension (as we have interpreted it) by an independent group of physicists. (This type of convergence occurred for the other three dimensions as well.) Second, the two types of concepts have very distinguishable neural signatures: a classifier can very accurately distinguish the mean of the post-classical concepts signatures from the mean of the classical concepts within each participant, with a grand mean accuracy of 0.93, p<0.001.

As physicists ventured into conceptually new territory in the 20th century and developed new post-classical concepts, their brains organized the new concepts with respect to a new dimension that had not played a role in the representation of classical concepts.

To describe what mental processes might characterize the post-classical end of this new dimension, it is useful to consider what attributes of the post-classical concepts could have led to their being neurally organized as they are and what cognitive and neural processes might operate on these attributes. Previously mentioned was that post-classical concepts often involve their immeasurability and their lower likelihood of being strongly associated with a mathematical formulation and periodicity, both of which are attributes that are often absent from post-classical concepts.

More informative than the absent attributes are four types of cognitive processes evoked by the post-classical concepts: (1) Reasoning about intangibles, taking into account their separation from direct experience and their lack of direct observability; (2) Assessing consilience with other, firmer knowledge; (3) Causal reasoning about relations that are not apparent or observable; and (4) Knowledge management of a large knowledge organization consisting of a multi-level structure of other concepts.

In addition to enabling the decoding of the content of the participants thoughts, whether they were thinking of dark matter or tachyon for example, the brain activation patterns are also informative about the concomitant psychological processes that operate on the concepts, in particular, the four processes listed above are postulated to co-occur specifically with the post-classical concepts. The occurrence of these processes was inferred from those locations of the voxel clusters associated with (having high loadings on) the classical/post-classical factor, specifically the factor locations where the activation levels increased for the post-classical concepts. (These voxel clusters are shown in Fig. 4, and their centroids are included in Table 2). Inferring a psychological process based on previous studies that observed activation in that location is called reverse inference. This can be an uncertain inferential method because many different processes or tasks can evoke activation at the same location. What distinguishes the current study are several sources of independent converging evidence, in conjunction with the brain locations associated with a factor (and not simply observed activation), indicating a particular process.

The factor clusters are encircled and numbered for ease of reference in the text and their centroids are included in Table 2. These locations correspond to the four classes of processes evoked by the post-classical concepts.

First, a statistically reliable decoding model predicted the activation levels for each concept in the factor locations, based on independent ratings of the concepts with respect to the postulated dimension/factor. The activation levels of the voxels in the factor locations were systematically modulated by the stimulus set, with the post-classical concepts, a specific subset of the stimuli eliciting the highest activation levels in these locations, resulting in the highest factor scores for this factor. Thus these brain locations were associated with an activation-modulating factor, not with a stimulus or a task. Second, the processes are consistent with the properties participants reported to have associated with the post-classical concepts. These properties provide converging evidence for these four types of processes occurring. For example, the concept of multiverse evoked properties related to assessing consilience, such as a hypothetical way to explain away constants. Another example is that tachyons and quasars were attributed with properties related to reasoning about intangibles, such as quasi-stellar objects. Third, the processes attributed to the factor locations were based not simply on an occasional previous finding, but on the large-scale meta-analysis (the Neurosynth database, Yarkoni et al.10) using the association based test feature. The association between the location and the process was based on the cluster centroid locations; particularly relevant citations are included in the factor descriptions. Each of the four processes is described in more detail below.

The nature of many of the post-classical concepts entails the consideration of alternative possible worlds. The post-classical factor location in the right temporal area (shown in cluster 5 in Fig. 4) has been associated with hypothetical or speculative reasoning in previous studies. In a hypothetical reasoning task, the left supramarginal factor location (shown in cluster 8) was activated during the generation of novel labels for abstract objects11. Additionally, the right temporal factor location (shown in cluster 5) was activated during the assessment of confidence in probabilistic judgments12.

Another facet of post-classical concepts is that they require the unknown or non-observable to be brought into consilience with what is already known. The right middle frontal cluster (shown in cluster 2) has been shown to be part of a network for integrating evidence that disconfirms a belief13. This consilience process resembles the comprehension of an unfolding narrative, where a new segment of the narrative must be brought into coherence with the parts that preceded it. When readers of a narrative judge the coherence of a new segment of text, the dorsomedial prefrontal cortex location (shown in cluster 6) is activated14. This location is associated with a post-classical factor location, as shown in Fig. 4. Thus understanding the coherence of an unfolding narrative text might involve some of the same psychological and neural consilience-seeking processes as thinking about concepts like multiverse.

Thinking about many of the post-classical concepts requires the generation of novel types of causal inferences to link two events. In particular, the inherent role of the temporal relations in specifying causality between events is especially complex with respect to post-classical concepts. The temporal ordering itself of events is frame-dependent in some situations, despite causality being absolutely preserved, leading to counter-intuitive (though not counter-factual) conclusions. For example, in relativity theory the concept of simultaneity entails two spatially separated events that may occur at the same time for a particular observer but which may not be simultaneous for a second observer, and even the temporal ordering of the events may not be fixed for the second observer. Because the temporal order of events is not absolute, causal reasoning in post-classical terms must eschew inferencing on this basis, but must instead rely on new rules (laws) that lead to consilience with observations that indeed can be directly perceived.

Another example, this one from quantum physics, concerns a particle such as an electron that may be conceived to pass through a small aperture at some speed. Its subsequent momentum becomes indeterminate in such a way that the arrival location of the particle at a distant detector can only be described in probabilistic terms, according to new rules (laws) that are very definite but not intuitive. The perfectly calculable non-local wave function of the particle-like object is said to collapse upon arrival in the standard Copenhagen interpretation of quantum physics. Increasingly elaborate probing of physical systems with one or several particles, interacting alone or in groups with their environment, has for decades elucidated and validated the non-intuitive new rules about limits and alternatives to classical causality in the quantum world. The fact that new rules regarding causal reasoning are needed in such situations was described as the heart of quantum mechanics and as containing the only mystery by Richard Feynman15.

Generating causal inferences to interconnect a sequence of events in a narrative text evokes activation in a right temporal and right frontal location (shown in clusters 3 and 4) which are post-classical factor locations16,17,18 as shown in Fig. 4. Causal reasoning accompanying perceptual events also activates a right middle frontal location (shown in cluster 3) and a right superior parietal location (shown in cluster 1)19. Notably, the right parietal activation is the homolog of a left parietal cluster associated with causal visualization1 found in undergraduates physics conceptualizations, suggesting that post-classical concepts may recruit right hemisphere homologs of regions evoked by classical concepts. Additionally, a factor location in the left supramarginal gyrus (shown in cluster 8) is activated in causal assessment tasks such as determining whether the causality of a social event was person-based (being a hard worker) or situation based (danger)20.

Although we have treated post-classical concepts such as multiverse as a single concept, it is far more complex than velocity. Multiverse entails the consideration of the uncertainty of its existence, the consilience of its probability of existence with measurements of matter in the universe, and the consideration of scientific evidence relevant to a multiverse. Thinking about large, multi-concept units of knowledge, such as the schema for executing a complex multi-step procedure evokes activation in medial frontal regions (shown in cluster 6)21,22. Reading and comprehending the description of such procedures (read, think about, answer questions, listen to, etc.) requires the reader to cognitively organize diverse types of information in a common knowledge structure. Readers who were trained to self-explain expository biological texts activated an anterior prefrontal cortex region (shown in cluster 7 in Fig. 4) during the construction of text models and strategic processing of internal representations23.

This underlying cognitive function of knowledge management associated with the post-classical dimension may generate and utilize a structure to manage a complex array of varied information that is essential to the concept. This type of function has been referred to as a Managerial Knowledge Unit22. As applied to a post-classical concept such as a tachyon, this knowledge management function would contain links to information to evaluate the possibility of the existence of tachyons, hypothetical particles that would travel faster than light-speed in vacuum. The concept invokes a structured network of simpler concepts (mass, velocity, light, etc.) that compose it. This constitutes a knowledge unit larger than a single concept.

Although the discussion has so far focused on the most novel dimension (the classical vs. post-classical), all four dimensions together compose the neural representation of each concept, which indicates where on each dimension a given concept is located (assessed by the concepts factor scores). The bar graphs of Fig. 5 show how the concepts at the extremes of the dimensions can appear at either extreme on several dimensions. These four dimensions are:

the classical vs. post-classical dimension, as described above, which is characterized by contrasting the intangible but consilient nature of post-classical concepts versus the quantifiable, visualizable, otherwise observable nature of classical concepts.

the measurability of a magnitude associated with a concept, that is, the degree to which it has some well-defined extent in space, time, or material properties versus the absence of this property.

the periodicity or oscillation which describes how many systems behave over time versus the absence of periodicity as an important element.

the degree to which a concept is associated with a mathematical formulation that formalizes the rules and principles of the behavior of matter and energy versus being less specified by such formalizations.

A concept may have a high factor score for more than one factor; for example, potential energy appears as measurable, mathematical, and on the classical end of the post-classical dimension. In contrast, multiverse appears as non-measurable, non-periodic, and post-classical.

The locations of the clusters of voxels with high loadings on each of the factors are shown in Fig. 6.

Colors differentiate the factors and greater color transparency indicates greater depth. Sample concepts from the two ends of the dimensions are listed. The post-classical factor locations include those whose activations were high for post-classical concepts (their locations are shown in Fig. 4) as well as those locations whose activations were high for classical concepts.

Classical concepts with high factor scores on the measurability factor, such as frequency, wavelength, acceleration, and torque, are all concepts that are often measured, using devices such as oscilloscopes and torque wrenches, whereas post-classical concepts such as duality and dark matter have an uncertainty of boundedness and no defined magnitude resulting in factor scores at the other end of the dimension. This factor is associated with parietal and precuneus clusters that are often found to be activated when people have to assess or compare magnitudes of various types of objects or numbers24,25,26, a superior frontal cluster that exhibits higher activation when people are comparing the magnitudes of fractions as opposed to decimals27, and an occipital-parietal cluster (dorsolateral extrastriate V3A) that activates when estimating the arrival time of a moving object28. Additional brain locations associated with this factor include left supramarginal and inferior parietal regions that are activated during the processing of numerical magnitudes;26 and left intraparietal sulcus and superior parietal regions activated during the processing of spatial information29. This factor was not observed in a previous study that included only classical concepts and hence the factor would not have differentiated among the concepts1.

The mathematical formulation factor is salient for concepts that are clearly associated with a mathematical formalization. The three concepts that are most strongly associated with this factor, commutator, Lagrangian, and Hamiltonian, are mathematical functions or operators. Cluster locations that are associated with this factor include: parietal regions that tend to activate in tasks involving mathematical representations30,31 and right frontal regions related to difficult mental calculations32,33. The parietal regions associated with the factor, which extend into the precuneus, activate in arithmetic tasks34. While most if not all physics concepts entail some degree of mathematical formulation, post-classical concepts such as quasar, while being measurable, are typically not associated with an algebraic formulation.

The periodicity factor is salient for many of the classical concepts, particularly those related to waves: wave function, light, radio waves, and gamma rays. This factor is associated with right hemisphere clusters and a left inferior frontal cluster, locations that resemble those of a similarly described factor in a neurosemantic analysis of physics concepts in college students1. This factor was also associated with a right hemisphere cluster in the inferior frontal gyrus and bilateral precuneus.

For all four underlying semantic dimensions, the brain activation-based orderings of the physics concepts with respect to their dimensions were correlated with the ratings of those concepts along those dimensions by independent physics faculty. This correlation makes it possible for a linear regression model to predict the activation pattern that will be evoked by future concepts in physicists brains. When a new physics concept becomes commonplace, (such as a new particle category, say, magnetic monopoliae), it should be possible to predict the brain activation that will be the neural signature of the magnetic monopole concept, based on how that concept is rated along the four underlying dimensions.

The neurosemantic conceptual space defined by the four underlying dimensions includes regions that are currently sparsely populated by existing concepts, but these regions may well be the site of some yet-to-be theorized concepts. It is also possible that as future concepts are developed, additional dimensions of neural representation may emerge, expanding the conceptual space that underpins the concepts in the current study.

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