We used functional MRI (fMRI) to assess neural representations of physics concepts (momentum, energy, etc.) in juniors, seniors, and graduate students majoring in physics or engineering. Our goal was to identify the underlying neural dimensions of these representations. Using factor analysis to reduce the number of dimensions of activation, we obtained four physics-related factors that were mapped to sets of voxels. The four factors were interpretable as causal motion visualization, periodicity, algebraic form, and energy flow. The individual concepts were identifiable from their fMRI signatures with a mean rank accuracy of .75 using a machine-learning (multivoxel) classifier. Furthermore, there was commonality in participants' neural representation of physics; a classifier trained on data from all but one participant identified the concepts in the left-out participant (mean accuracy = .71 across all nine participant samples). The findings indicate that abstract scientific concepts acquired in an educational setting evoke activation patterns that are identifiable and common, indicating that science education builds abstract knowledge using inherent, repurposed brain systems.