Ultracold alkali atoms [1,2,3,4] provide experimentally accessible model systems for probing quantum states that manifest themselves at the macroscopic scale. Recent experimental realizations of superfluidity in dilute gases of ultracold fermionic (half-integer spin) atoms [5,6,7] offer exciting opportunities to directly test theoretical models of related many-body fermion systems that are inaccessible to experimental manipulation, such as neutron stars [8] and quark-gluon plasmas [9]. However, the microscopic interactions between fermions are potentially quite complex, and experiments in ultracold gases to date cannot clearly distinguish between the qualitatively different microscopic models that have been proposed [10,11,12,13]. Here, we theoretically demonstrate that optical measurements of electron spin noise [14,15] -the intrinsic, random fluctuations of spin -can probe the entangled quantum states of ultracold fermionic atomic gases and unambiguously reveal the detailed nature of the interatomic interactions. We show that different models predict different sets of resonances in the noise spectrum, and once the correct effective interatomic interaction model is identified, the line-shapes of the spin noise can be used to constrain this model. Further, experimental measurements of spin noise in classical (Boltzmann) alkali vapors are used to estimate the expected signal magnitudes for spin noise measurements in ultracold atom systems and to show that these measurements are feasible. Owing to their perceived simplicity, the properties of dilute degenerate fermionic systems are sometimes attributed universal character [16], an assertion that must be called into question if the interaction between degenerate alkali atoms turns out to be complex. It is thus unfortunate that the nature of the effective interatomic interactions remains an outstanding fundamental issue. Specifically, the role played by the underlying hyperfine atomic-level structure is not yet understood. To date, experiments on ultracold fermionic atom gases can be interpreted equally well using qualitatively different models for the effective interactions, such as the FermiBose [10,11] or the multi-level models [12,13]. Hence, new experimental observables are needed to distinguish between these competing models, and the principal distinctions between current models will lie in their predicted excitation spectra, which are not yet well studied.The excitation spectra of physical systems are often studied by measuring their response to an external perturbation. Alternatively, measuring the spectrum of intrinsic fluctuations of a physical system can provide the same information, and these "noise spectroscopies" often disturb the physical system less strongly and scale more favorably with system size reduction. At very low temperature, noise from quantum fluctuations of an observable that does not commute with the Hamiltonian of the system can be used as a probe of the system properties. Electron spin is not a good quantum number in alkali gases, and ...