Do coronal loops oscillate in isolation?

Images of the solar corona by extreme-ultraviolet (EUV) telescopes reveal elegant arches of glowing plasma that trace the corona's magnetic field. Typically, these loops are preferentially illuminated segments of an arcade of vaulted field lines and such loops are often observed to sway in response to nearby solar flares. A flurry of observational and theoretical effort has been devoted to the exploitation of these oscillations with the grand hope that seismic techniques might be used as probes of the strength and structure of the corona's magnetic field. The commonly accepted viewpoint is that each visible loop oscillates as an independent entity and acts as a one-dimensional (1D) wave cavity for magnetohydrodynamic (MHD) kink waves. We argue that for many events, this generally accepted model for the wave cavity is fundamentally flawed. In particular, the 3D magnetic arcade in which the bright loop resides participates in the oscillation. Thus, the true wave cavity is larger than the individual loop and inherently multidimensional. We derive the skin depth of the near-field response for an oscillating loop and demonstrate that most loops are too close to other magnetic structures to oscillate in isolation. Further, we present a simple model of a loop embedded within an arcade and explore how the eigenmodes of the arcade and the eigenmodes of the loop become coupled. In particular, we discuss how distinguishing between these two types of modes can be difficult when the motions within the arcade are often invisible.