Coronal mass ejections (CMEs) are episodic eruptions of solar plasma and magnetic flux that travel out through the solar system, driving extreme space weather. Interpretation of CME observations and their interaction with the solar wind typically assumes CMEs are coherent, almost solid-like objects. We show that supersonic radial propagation of CMEs away from the Sun results in geometric expansion of CME plasma parcels at a speed faster than the local wave speed. Thus information cannot propagate across the CME. Comparing our results with observed properties of over 400 CMEs, we show that CMEs cease to be coherent magnetohydrodynamic structures within 0.3 AU of the Sun. This suggests Earth-directed CMEs are less like billiard balls and more like dust clouds, with apparent coherence only due to similar initial conditions and quasi homogeneity of the medium through which they travel. The incoherence of CMEs suggests interpretation of CME observations requires accurate reconstruction of the ambient solar wind with which they interact, and that simple assumptions about the shape of the CMEs are likely to be invalid when significant spatial/temporal gradients in ambient solar wind conditions are present.