The Pierre Auger Observatory detects extensive air showers that are initiated by protons or nuclei reaching Earth's atmosphere with energies exceeding 10**18 eV (ultra-high energy cosmic rays (UHECR)). The center-of-mass energy of the initial interaction of the CRs in the atmosphere exceeds the energies reached at the LHC by more than an order of magnitude. One of the key results of Auger is the discovery that these interactions of UHECRs do not behave as expected. Compared to simulations the measured air showers contain many more muons. This discrepancy could be simply due to the uncertainty inherent in the extrapolation from the energy scale of the LHC, where we can measure interactions in detail, to UHECR energies. Or it could be new physics! This project proposes to distinguish the two scenarios by the detailed measurement of the shower-to-shower distribution of the muon content as the shape of the distribution is driven by the quantum fluctuations in the first UHE interaction which are sensitive to new physics and the details of hadronic interactions. The measurement will for the first time use hybrid data from the surface and radio detectors of the Pierre Auger Observatory.