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Hydrodynamic and continuum traffic flow models usually require that traffic states are stationary for the model assumptions to hold. The reproducibility of a concave fundamental diagram, FD, is typically assumed to also demonstrate that the underlying states are sufficiently near stationary. This paper uses loop detector data from five locations to empirically demonstrate that the microscopic traffic dynamics giving rise to a concave FD can also invalidate the stationarity assumptions required by the traffic flow models. Specifically, this work develops the exclusionary vehicle aggregation, EVA, method to evaluate conditions underlying conventional fixed time average state measurements. The shape of the FD is shown to be highly correlated with the standard deviation of headways, stdev(h), within the underlying samples: low stdev(h) corresponding to triangular FD and high stdev(h) to concave FD. Furthermore, high stdev(h) is shown to correspond to the presence of large voids within the given sample. These voids are inherently non-stationary because different regions of the sample are perceptively distinct. With these new insights in mind, a review of the earliest FD literature reveals evidence supporting the loop detector-based findings. Collectively, the loop detector and historical FD results span over 75 years of empirical traffic data. Meanwhile, a driver behind a large void can act independent of their leader. From the kinematic wave, KW, perspective, a void creates an ill posed problem: if a driver acts independent of their leader there are no KW from the boundaries that reach the driver during their independence, and thus, there is no way to predict how the driver should act. Generally, this type of ill posed problem is avoided in theoretical developments by requiring stationary conditions for the given model, but as this paper shows, real traffic does not necessarily provide stationary conditions. Although the voids are large enough to disrupt stationarity, their duration remains far below the resolution of fixed time averaging to be perceived. As a result, whenever a traffic flow model depends on stationarity and the shape of the FD, it is imperative to check the data to make sure they support the assumptions placed on the FD, e.g., via the EVA method developed herein. Finally, the empirical results in this paper should facilitate the development of macroscopic models that better capture the dynamics of real traffic.