Cognitive neuroscience methods can identify the fMRI-measured neural representation of familiar individual concepts, such as apple, and decompose them into meaningful neural and semantic components. This approach was applied here to determine the neural representations and underlying dimensions of representation of far more abstract physics concepts related to matter and energy, such as fermion and dark matter, in the brains of 10 Carnegie Mellon physics faculty members who thought about the main properties of each of the concepts. One novel dimension coded the measurability vs. immeasurability of a concept. Another novel dimension of representation evoked particularly by post-classical concepts was associated with four types of cognitive processes, each linked to particular brain regions: (1) Reasoning about intangibles, taking into account their separation from direct experience and 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. Two other underlying dimensions, previously found in physics students, periodicity, and mathematical formulation, were also present in this faculty sample. The data were analyzed using factor analysis of stably responding voxels, a Gaussian-naïve Bayes machine-learning classification of the activation patterns associated with each concept, and a regression model that predicted activation patterns associated with each concept based on independent ratings of the dimensions of the concepts. The findings indicate that the human brain systematically organizes novel scientific concepts in terms of new dimensions of neural representation.